WEBVTT

NOTE
Matthieu Leroy | www.silemio.com
AI-assisted English translation of the original French course.

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Let's get started. Today's course
is called Never without my subs.

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The subject of this
course is the coupling and

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directivity control of
low-frequency loudspeakers.

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We'll look at how to combine
these loudspeakers. We won't cover

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aligning them with the main
loudspeakers or anything like that.

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System alignment is a
subject we may cover another

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time. If we do, I'd prefer
to teach it in person.

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Today we'll focus on coupling.
The mechanical aspects of this

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equipment could fill a whole
course, covering crossovers,

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how subs work, how they're built,
bass-reflex designs and so on. I

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won't have time for that today.
We'll really concentrate on coupling.

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For reference, the video of this
course will be posted online.

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All the slides are already
online, so you can use them if

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needed. There will be lots of
parameters and a few equations.

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I've removed as many equations as
possible. Don't worry if you don't

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remember everything: you can look it
up later, like a reference catalogue.

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You might think, 'Mathieu mentioned
this; I'd like to see how it

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worked.' You can go back and
refer to it. There will also be

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several simulations, illustrated
with images during the course.

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For all these simulations,
I've included the images

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and the simulation files in
the shared folder as well.

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With a small piece of software
installed, you can reproduce

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them at home, run them again
and change things if needed.

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It really doesn't matter if
you don't remember everything.

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I've already put the outline
in the shared folder and

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sent some of it on WhatsApp.
There have been a few changes.

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Today's course is divided
into eight main sections.

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We'll concentrate on the first
four. Sections five, six,

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seven and eight are
additional material that isn't

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necessarily essential. The first
four are the main sections.

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By the time we reach section
four, we'll be well over halfway

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through. The first section
covers the fundamentals. If you

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took the line-array course,
some of this will be familiar,

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so I'll move through it fairly
quickly where appropriate.

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The second section covers what
we call the steering effect.

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Steering means controlling directivity,
essentially. Literally, the

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English word 'steering' refers
to guiding or driving something.

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Then we'll focus on a particular type
of steering: forward and vertical

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steering. That's where we'll really
get into cardioid subwoofers.

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How do they work? How are they
arranged? What are the main

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configurations? Then we'll
look at special configurations:

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a few unusual subwoofer
arrangements that have been used.

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These are just a few examples
among many. That section is fairly

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short. The material up to section
three is the substantial part.

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Then there's a brief page on
classification. I'll put the

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configurations into a table
to show how we can classify

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them according to their
advantages and disadvantages.

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Then we'll touch on simulation:
what types of software we

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can use, and the advantages
and disadvantages of each.

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You'll see a little of how I produce
the results shown here. After

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that, if we have time, there's
some material I haven't written

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up. I just have files on my
computer that I can open if needed.

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I'll show you additional
configuration examples. There's

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also an appendix section,
which we may not even get to.

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You can simply look at those
slides if you're interested. They

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contain a few formulas and
additional concepts we could discuss.

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Let's begin with the fundamentals.
Don't worry: you know

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this material by heart, so
we'll move through it quickly.

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Throughout the course, we'll talk a lot
about frequency, wavelength and period.

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Let me briefly remind you what these
mean, starting in the time domain.

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For an oscillating wave,
a sinusoidal signal, we

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look at the time between
two identical states,

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two identical states of oscillation.
This is called the period,

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denoted T. You'll see T throughout
the course. It is the time

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interval between two successive
identical states of an oscillation.

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You know this by heart. Frequency is
the number of cycles per unit of time.

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When the unit is the second, we express
it in hertz. The formula is f = 1/T.

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Again, that's first-year physics;
you know it well. If we change

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our frame of reference and look
at distance instead of time,

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because we're talking about audio
signals, these waves propagate

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through space and therefore
travel a certain distance,

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we get the wavelength. We translate
that time into a wavelength: the

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distance travelled during one period.
Wavelength is denoted by lambda, λ,

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and is calculated as c/f, where c
is the speed of sound. Those are

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the basic concepts. To keep things
simple throughout the course,

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whenever we refer to the
speed of sound, I'll use 340

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metres per second, the value
you're all familiar with.

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I'm using 340 metres per second, but
please bear in mind that this speed

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varies. That's covered in the
appendix, so I won't go into it here.

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The speed isn't always the
same: it depends on altitude,

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temperature and many other
parameters. When you start working

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with systems, especially subs,
you need to account for it.

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It changes, and all our calculations
change with it. But today we'll

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use 340 metres per second to
simplify things. That settles that.

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Today we're discussing subs: the
large, often black loudspeakers

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we see in our installations.
Let's look at the frequencies

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and waves they're intended to reproduce.
Taking a fairly broad range, they

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reproduce frequencies between 20 and 75
Hz. At 20 Hz, one wavelength is 17 metres.

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At 125 Hz, it's 2.72 metres.
These are waves on a large scale,

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very large waves. That's
different from the line-array

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course, where at times we dealt
with very small dimensions.

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Here we're dealing with
much larger dimensions.

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To represent those values in space,
let's compare them with a Paris metro

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train. Here's a lovely Paris metro
train: you can admire my drawing skills.

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You may not know this, but a Paris
metro train is 75 metres long, on almost

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every line except lines 1 and 14. So
each carriage is roughly 15 metres long.

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If we draw a wave along this
train, with one cycle per

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carriage, that would give
us a frequency of 23 Hz,

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with a wavelength of about 15
metres. These are physically tangible

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dimensions. The waves we'll be working
with are really on a large scale.

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If we increase the frequency
to fit three cycles per

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carriage, we're at about 70
Hz, roughly 69 Hz, with a

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wavelength of 5 metres,
assuming 340 metres per second.

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As you can see, the waves
we'll be working with always

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have tangible dimensions.
Try to picture them in space.

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When working with low frequencies,
you need to visualise them: here's one

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oscillation, here's a peak, and here
the wave has completed a full cycle.

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It's useful to have that sense of scale
and physical size. Is everyone following

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so far? Yes? Good. Could everyone
except Mathieu mute their microphone?

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Sorry, yes. Your sound cuts out
a little when you speak, Mathieu.

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No problem. Feel free to react,
though. All right, it seems fine.

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We're still covering the basics here:
phase and frequency. Phase is often

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denoted by phi, the Greek symbol you
see at the top, and frequency by f.

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For everyone who took the line-array
course, this is a recap, so I'll move

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on. Take a circle and mark the
different angles in degrees around it.

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Those angles around the circle
can also be expressed in radians,

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as multiples of pi. Remember that
a circle's circumference is 2πr.

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If we represent our wave on this
circle, you can see the point going

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around. I made this animation recently;
I haven't quite perfected it yet.

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If I lay out those different angles and
multiples of pi along a straight line,

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we can see how to represent the wave using a

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circle that changes over
time. The phase changes

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according to where we are on
the circle. It's actually going

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backwards here, but the principle
is the same. We have 90°,

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180° at half a wavelength, 270°
and 360°, running from 0 to 2π.

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Let's take several frequencies:
20, 40 and 80 Hz. We'll stay in the

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low-frequency range that concerns
us, doubling the frequency each time.

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You also saw this in the line-array
course, so apologies for repeating it.

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These frequencies evolve over time, each
at twice the rate of the previous one.

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If we look at phase, using
the angles I mentioned

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earlier, and go to a quarter
of a wavelength at 20 Hz,

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that occurs after 12.5 milliseconds,
still at 350 metres per second.

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It corresponds to 90°. After 12.5
milliseconds, the phase is at 90°.

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At 40 Hz, we're at 180°:
half a cycle. At 80 Hz, we've

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already completed a full cycle,
reaching 360°. It's important

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to see that the relative
phases of these frequencies

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are different at a given time. If we move
further along to 50 milliseconds, we've

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completed one full cycle at 20 Hz, two
at 40 Hz, and four at 80 Hz, or 1,440°.

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It's fairly straightforward:
we're doubling each time. We move

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between a logarithmic scale and
a linear scale. Remember that

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wavelength is always calculated
using the speed of sound.

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What interests us in today's
course is coupling. We'll add these

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frequencies together at different
points in their phase cycles.

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This is exactly the same slide
as in the line-array course.

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We're going to discuss phase
difference. I've now added

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the symbol that wasn't there
last time: delta phi, Δϕ.

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This means phase difference.
Let's go through it again. What

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happens when two signals have
a phase difference of 0°?

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You should remember this from last time:
we get a nice 6 dB summation. That's

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in a perfect world; in acoustics it
won't be exactly 6 dB, but approximately.

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If we start shifting these waves,
putting them 20° apart, the summation

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is slightly less than 6 dB. We
still gain level, but a little less.

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At 90°, still with two otherwise
identical waves, we get about

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3 dB of summation. Move on to
120°, and there's no change.

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We neither gain nor lose
level. At 150°, we start losing

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level, by roughly 3 dB.
Push it all the way to 180°,

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and we get complete cancellation.
We can represent all of this

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on our famous magic circle.
Unlike in the line-array course,

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today we'll use the whole circle.
Last time we mainly used the top,

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with 3 dB and 6 dB gains, because
we were interested in summation.

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Today we'll still use summation
in this green area, but we'll

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also work with subtraction. We'll
start looking at cancellation.

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The figures here indicate phase
difference: the difference in phase

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between two waves, rather than
the phase of an individual wave.

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When two identical waves have a
90° phase difference, we get 3 dB.

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We can calculate that phase difference
as well. Here's the formula.

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In a physical arrangement,
for example, we can calculate

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phase difference from the
path-length difference. Take the

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distance difference, Δd, multiply
it by frequency and by 360,

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the 360 degrees of the circle,
and divide by the speed of sound.

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You don't need to memorise it, but
if you ever want to work it out

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with pencil and paper, you can
calculate the phase difference

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between the same signal
arriving from two sources simply

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by measuring their path lengths
and knowing the frequency.

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That tells you the phase difference
and where you are on the magic

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circle. You can keep that for
reference; I'll explain the

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calculation in more detail in the
appendix for anyone interested.

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Now let's discuss different kinds of
difference. Forgive the wording, but it's

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important to understand the distinction.
We'll start with spatial difference,

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which I denote Δd. Here's a first
source: a loudspeaker. The letter A

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simply identifies it, and the plus
sign means its polarity is normal.

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Let's add a second source, another
loudspeaker. Here are our two sources.

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Now add a listener: that's you,
listening to those lovely curved arrays

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in last week's line-array course.

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If we draw a circle through
the listener's head,

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centred between the two
sources, we can measure

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the distance from the
listener to A, which is

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d1, and from the listener to B, which is d2.

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In this case, if we calculate
Δd, d1 − d2 is less than zero.

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Simply put, the listener is closer
to A, so d1 is shorter than d2.

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Now move only the listener.
At the very top of the

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circle, we can see that
d1 = d2, so d1 − d2 = 0.

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The path-length difference is
zero. In the earlier formula,

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which I haven't repeated here,
that difference is a multiplying

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factor. Zero times anything
gives a phase difference of 0°.

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We can put our listener somewhere else.
Using the same calculation, d1 − d2, this

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time the result is greater than zero.
Obviously, we're closer to B than to A.

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That's straightforward. We were
discussing spatial difference:

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we simply changed the listener's
position. Depending on that

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position, source A arrives
earlier or later than source B.

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Sound travels at a given speed, so that
distance can be expressed as a time

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difference between A and B. Another
type of difference is a time difference.

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If we now think only in terms of
time, I've converted that distance

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to time, since sound travels at
a given speed. Now let's apply

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a delay to source B. Just a delay:
we haven't physically moved it.

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It's as though we've created a
phantom source a little further away,

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with an arrival time equal to
t2, the original time, plus our

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Δt. If we now move the listener,
we see that the phantom source

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moves as well. Before it was fixed;
now it moves. We still have the

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new t2, which is a little shorter
than before, plus that same Δt.

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If we did this around all
360° of the circle, we could

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trace the region through which
our phantom source B moves.

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00:16:18.190 --> 00:16:23.392
It moves along this ellipse-like shape.
I've only drawn part of it, but the

214
00:16:23.392 --> 00:16:29.010
phantom source always lies on this ellipse,
depending on the listener's position.

215
00:16:29.110 --> 00:16:32.766
Now we've changed another variable.
Simply by introducing a Δt, it's

216
00:16:32.766 --> 00:16:36.690
almost as though we've created a new
source that wasn't there originally.

217
00:16:37.090 --> 00:16:41.411
That's the distinction between
spatial and temporal differences:

218
00:16:41.411 --> 00:16:45.530
we now have a parameter that
makes the source appear to move.

219
00:16:48.560 --> 00:16:52.283
Remember the calculation I showed
you earlier. We can still use it,

220
00:16:52.283 --> 00:16:55.840
because this time plus Δt can
also be converted into a distance.

221
00:16:55.960 --> 00:17:00.835
We can perform the reverse calculation
and work out the phase difference

222
00:17:00.835 --> 00:17:05.440
between sources B and A, assuming
they emit exactly the same signal.

223
00:17:08.740 --> 00:17:13.160
Another important point about subs
is what I've called the suction myth.

224
00:17:15.060 --> 00:17:20.869
Take another source with normal
polarity, source A. Here it's a sub. It

225
00:17:20.869 --> 00:17:26.760
could also be a whole array of subs,
a large group all coupled together.

226
00:17:26.840 --> 00:17:27.680
For our purposes, it's the same thing.

227
00:17:29.960 --> 00:17:36.055
If this source emits a
signal, positive at this point

228
00:17:36.055 --> 00:17:41.920
and negative here, what
does it emit behind itself?

229
00:17:41.920 --> 00:17:46.870
You've probably noticed that subs often
radiate strongly in every direction.

230
00:17:46.870 --> 00:17:51.820
What do you think the wave looks like
behind it? Does anyone have an answer?

231
00:17:51.980 --> 00:17:57.906
Your microphones are muted anyway.
All right. Remember that a sub

232
00:17:57.906 --> 00:18:03.740
is rather like the point source
we saw in the line-array course:

233
00:18:03.740 --> 00:18:09.674
a point radiating in every
direction in space. The wave behind

234
00:18:09.674 --> 00:18:15.320
that source is almost at the
same phase at the same moment.

235
00:18:15.980 --> 00:18:18.725
In other words, if there's a
positive pressure in front, there's

236
00:18:18.725 --> 00:18:21.469
almost the same positive pressure
behind. People often think the

237
00:18:21.469 --> 00:18:24.300
front of the loudspeaker is in
phase and the back is out of phase.

238
00:18:24.400 --> 00:18:28.317
That isn't true. The wave
travels around the cabinet and

239
00:18:28.317 --> 00:18:32.373
radiates backwards, remaining
almost in phase at the rear.

240
00:18:32.373 --> 00:18:36.220
If we measure at exactly
equal distances here and here,

241
00:18:36.420 --> 00:18:40.092
the difference is almost 0°. Not
quite, because the mechanical

242
00:18:40.092 --> 00:18:43.587
and physical characteristics
of the cabinet affect the wave

243
00:18:43.587 --> 00:18:47.200
slightly. The travel time is
also slightly longer, of course.

244
00:18:48.140 --> 00:18:51.704
But the wave is almost in
phase, with almost 0° of offset.

245
00:18:51.704 --> 00:18:54.961
It's important to understand
that our wave travels in

246
00:18:54.961 --> 00:18:58.280
all directions with the same
phase at the same moment.

247
00:18:59.640 --> 00:19:02.737
There is a qualification:
this applies to conventional

248
00:19:02.737 --> 00:19:05.835
subs. With bass-reflex
systems, reversed loudspeakers,

249
00:19:05.835 --> 00:19:08.760
cardioid designs and so
on, it's not entirely true.

250
00:19:08.900 --> 00:19:13.300
But with a conventional sub, this
is more or less what you'll find.

251
00:19:15.940 --> 00:19:21.231
You may also have been taught that a
sub radiates in every direction and is

252
00:19:21.231 --> 00:19:26.380
completely omnidirectional: here's
our sub, radiating equally all around.

253
00:19:26.500 --> 00:19:30.647
There is, however, the small
phase difference we saw. Although

254
00:19:30.647 --> 00:19:34.660
it's close to 0°, that difference
still has a slight effect.

255
00:19:34.960 --> 00:19:39.017
And mechanically, the loudspeaker
faces one way rather than the

256
00:19:39.017 --> 00:19:43.460
other. Various factors mean the sub
isn't completely omnidirectional.

257
00:19:43.900 --> 00:19:49.049
It tends to favour the front slightly; I've
exaggerated it here. We often calculate

258
00:19:49.049 --> 00:19:53.640
using perfect omnidirectional sources,
but in reality they're not perfect.

259
00:19:53.640 --> 00:19:58.661
There's always a small difference
between simulation and reality.

260
00:19:58.661 --> 00:20:03.760
To show you what that looks like,
let's run our first simulations.

261
00:20:05.220 --> 00:20:08.570
I'll show you a single sub. You'll see these

262
00:20:08.570 --> 00:20:11.920
plots a lot, so I'll explain this first one.

263
00:20:12.340 --> 00:20:16.758
Our source is here. Blue means
a lower level; red means a

264
00:20:16.758 --> 00:20:21.020
high level. This shows the
level distribution in space.

265
00:20:21.260 --> 00:20:26.451
It's a view from above. When I
label it 31 Hz here and show an

266
00:20:26.451 --> 00:20:32.060
octave band, we've combined the
frequencies up to one octave above,

267
00:20:32.200 --> 00:20:37.857
about 60 Hz, and one octave below,
about 15 Hz. This shows how the sub

268
00:20:37.857 --> 00:20:44.080
radiates around 31 Hz. The shape is
almost a perfect circle, but only almost.

269
00:20:44.400 --> 00:20:49.829
It's slightly larger here
than here. Go up an octave

270
00:20:49.829 --> 00:20:54.840
to 63 Hz, and it starts
to flatten out a little.

271
00:20:56.340 --> 00:21:01.133
At 120 Hz, it starts to flatten
out noticeably. My sub is becoming

272
00:21:01.133 --> 00:21:06.580
directional. As you can see, a single
sub isn't completely omnidirectional.

273
00:21:06.640 --> 00:21:08.989
I've used a Meyer 500-HP
for this example, but

274
00:21:08.989 --> 00:21:11.440
you'd get something similar
with almost any sub.

275
00:21:13.420 --> 00:21:19.174
One way to make it perfect is
to add a second sub. It has the

276
00:21:19.174 --> 00:21:24.740
same slightly potato-shaped
pattern, and we turn it around.

277
00:21:25.800 --> 00:21:29.101
I haven't changed its polarity,
just rotated the pattern.

278
00:21:29.101 --> 00:21:31.997
Then I virtually place it
on top of the other sub,

279
00:21:31.997 --> 00:21:35.240
imagining that both radiate
from exactly the same point.

280
00:21:35.860 --> 00:21:41.125
This is a virtual arrangement, because it
isn't physically possible. In software,

281
00:21:41.125 --> 00:21:46.000
I can put them in the same place, and
that gives me a much rounder pattern.

282
00:21:46.080 --> 00:21:51.356
It's difficult to compare because I
haven't put the earlier plots alongside

283
00:21:51.356 --> 00:21:56.140
these. But at 31 Hz, 63 Hz and even
125 Hz, this simulation gives us

284
00:21:56.140 --> 00:22:00.180
a much more omnidirectional pattern.
We're much closer to a perfect omni.

285
00:22:02.580 --> 00:22:06.112
It's useful to understand
that, in software, if we want

286
00:22:06.112 --> 00:22:09.965
perfect omnis for our calculations,
we may create artificial

287
00:22:09.965 --> 00:22:13.240
arrangements like this that
don't physically exist.

288
00:22:13.800 --> 00:22:19.367
That's very convenient in software.
Another way to get closer to perfect

289
00:22:19.367 --> 00:22:25.320
omnis is a real arrangement, where I
can't merge my subs into a single point.

290
00:22:26.520 --> 00:22:30.497
I place two subs face to
face, like this, looking at

291
00:22:30.497 --> 00:22:34.780
each other. Generally, the
gap won't be more than 30 cm.

292
00:22:34.960 --> 00:22:40.626
Sometimes we put them even closer, but
they really must be close. We'll see why

293
00:22:40.626 --> 00:22:46.220
I've placed them 30 cm apart. When we
measure this, our sub looks pretty good.

294
00:22:46.360 --> 00:22:49.746
Across these three plots, it's
almost omnidirectional. It

295
00:22:49.746 --> 00:22:53.133
still flattens slightly at
120 Hz. It isn't as perfect as

296
00:22:53.133 --> 00:22:56.400
the virtual method, but it's
much more omnidirectional.

297
00:22:58.280 --> 00:23:02.151
Why this digression about perfect and
imperfect omnis? Because many of the

298
00:23:02.151 --> 00:23:06.440
configurations you're about to see assume
the subs are completely omnidirectional.

299
00:23:07.520 --> 00:23:11.849
That isn't the case in reality, but
you can improve your configurations

300
00:23:11.849 --> 00:23:16.300
with this kind of arrangement,
calculating from the new acoustic centres.

301
00:23:16.820 --> 00:23:21.124
You can model something like this
in software: a fully omnidirectional

302
00:23:21.124 --> 00:23:24.690
sub that also gains some output
because it consists of two

303
00:23:24.690 --> 00:23:28.440
loudspeakers sharing an acoustic
centre. All the arrangements

304
00:23:28.440 --> 00:23:33.999
you're about to see can use this kind of
sub. In the next diagrams, you'll see a

305
00:23:33.999 --> 00:23:39.420
single sub symbol, but each could actually
represent an arrangement like this,

306
00:23:40.120 --> 00:23:43.096
perfectly omnidirectional,
improving the simulation results

307
00:23:43.096 --> 00:23:46.224
further. At a concert, if we're
lucky enough to have plenty of

308
00:23:46.224 --> 00:23:49.200
subs, we can build arrays from
these omnidirectional units.

309
00:23:49.320 --> 00:23:53.371
It creates a large virtual
enclosure like this, with this small

310
00:23:53.371 --> 00:23:57.101
point as its reference. We get
a fully omnidirectional sub

311
00:23:57.101 --> 00:24:00.960
with a gain in dB, so more
output, and we can achieve better

312
00:24:00.960 --> 00:24:04.858
summation because we have something
ideal. Once we've achieved

313
00:24:04.858 --> 00:24:09.008
that ideal behaviour, we can really
call it a point source. Unlike

314
00:24:09.008 --> 00:24:12.780
in the line-array course, here
we like having point sources.

315
00:24:13.280 --> 00:24:17.614
We aren't necessarily trying to
create line sources to begin with.

316
00:24:17.614 --> 00:24:21.620
Is everyone following? Give me
a nod, those of you I can see.

317
00:24:22.660 --> 00:24:28.688
So what's the theoretical distance
between the two subs to make

318
00:24:28.688 --> 00:24:34.620
a perfect point source? I've
placed them here. The distance...

319
00:24:34.720 --> 00:24:38.560
Let me go back. The distance
between A and B generally

320
00:24:38.560 --> 00:24:42.471
doesn't exceed 30 cm. That's
already quite small. If we

321
00:24:42.471 --> 00:24:46.240
place them too far apart,
we'll see later that beyond

322
00:24:46.240 --> 00:24:51.242
a certain distance, problems
start to appear. What determines

323
00:24:51.242 --> 00:24:56.080
that distance? What calculation
do you use to establish it?

324
00:24:56.080 --> 00:24:59.199
Is it related to what we've
already seen? It's related to

325
00:24:59.199 --> 00:25:02.537
wavelength, which we'll look at
later, along with the spacing

326
00:25:02.537 --> 00:25:05.820
to use. Is it connected to the
spacing you showed us before?

327
00:25:05.820 --> 00:25:10.514
Yes, exactly, it's related to that
spacing. We'll revisit it. Essentially,

328
00:25:10.514 --> 00:25:14.700
the spacing between two subs will
rarely exceed half a wavelength.

329
00:25:14.780 --> 00:25:19.663
We'll see why. In any case,
at 30 cm we're dealing with a

330
00:25:19.663 --> 00:25:24.460
short wavelength, perhaps
corresponding to about 500 Hz.

331
00:25:25.420 --> 00:25:31.136
My sub doesn't reproduce 500 Hz. With
30 cm spacing, all the frequencies

332
00:25:31.136 --> 00:25:35.900
below 500 Hz will sum well.
We'll come back to that, Nadège.

333
00:25:37.180 --> 00:25:42.860
I hope that was clear. All right?
I chose to put them 30 cm apart.

334
00:25:45.580 --> 00:25:50.867
Now let's start adding things together.
That was just a brief aside about

335
00:25:50.867 --> 00:25:56.660
omnidirectional subs. Let's combine subs,
starting with two placed side by side.

336
00:25:56.720 --> 00:26:02.103
They'll be right next to each
other. Let me remind you of a

337
00:26:02.103 --> 00:26:07.760
few values: at 31 Hz, the period
is 32 milliseconds. At 63 Hz,

338
00:26:07.940 --> 00:26:13.916
we halve it, and at 125 Hz we halve
it again. I've also shown half

339
00:26:13.916 --> 00:26:19.440
and quarter wavelengths—periods,
sorry. I often mix those up.

340
00:26:20.280 --> 00:26:25.244
Feel free to correct me. Let's put these
two subs together and see what happens.

341
00:26:25.244 --> 00:26:29.960
They're identical, with the same polarity,
and the result looks fairly good.

342
00:26:30.160 --> 00:26:32.240
At 31 Hz, they seem to sum quite well.

343
00:26:35.290 --> 00:26:39.103
At 63 Hz, the pattern starts
to flatten slightly. We

344
00:26:39.103 --> 00:26:43.210
begin to see some directionality,
a beam forming. At 125

345
00:26:43.210 --> 00:26:47.170
Hz, remember that we're still
looking one octave above

346
00:26:47.210 --> 00:26:49.825
and one octave below, the
pattern becomes noticeably

347
00:26:49.825 --> 00:26:52.390
more forward-facing. We
get a nice elongated shape.

348
00:26:54.330 --> 00:27:00.288
The two subs have the same
polarity and are right next to each

349
00:27:00.288 --> 00:27:06.150
other. I've added the coverage
angles. At 31 Hz, we're almost

350
00:27:06.150 --> 00:27:11.557
over 270°. It's difficult to measure,
but the coverage is still very wide.

351
00:27:11.557 --> 00:27:17.110
At 63 Hz, it narrows a little; the main
beam is in this region, around 270°.

352
00:27:17.210 --> 00:27:22.080
At 125 Hz, the beam starts to narrow,
to 120°. Essentially, the higher

353
00:27:22.080 --> 00:27:26.950
the frequency we reproduce, the
narrower the coverage tends to become.

354
00:27:29.150 --> 00:27:34.475
Keep the same subs, but this time reverse
the polarity of sub B. Let's look.

355
00:27:34.475 --> 00:27:39.590
Sorry to interrupt, Mathieu, but how
are you defining the coverage angle?

356
00:27:39.590 --> 00:27:45.316
Is it at −6 dB? The usual
convention is −6 dB, more

357
00:27:45.316 --> 00:27:50.930
or less. Some people use
−3, others −6, others −9.

358
00:27:51.470 --> 00:27:53.710
I'm using −6 dB. Thank you.

359
00:27:55.610 --> 00:27:58.657
Here are the same two subs, with
one polarity inverted. Let's

360
00:27:58.657 --> 00:28:01.254
look at those three
frequencies. It's fairly easy to

361
00:28:01.254 --> 00:28:04.350
understand: we see clear blue
areas, with strong cancellation.

362
00:28:05.530 --> 00:28:09.257
We're using a lot of energy
for little result. We've

363
00:28:09.257 --> 00:28:13.128
created an almost figure-of-eight
pattern, with a lobe

364
00:28:13.128 --> 00:28:17.070
on each side, at every
frequency. The frequencies start

365
00:28:17.070 --> 00:28:21.132
cancelling here, roughly at the
front and rear, with a slight forward

366
00:28:21.132 --> 00:28:25.430
bias. We see the small effect from
earlier, with some areas of summation.

367
00:28:26.550 --> 00:28:28.205
That's what happens with
two subs when we invert one

368
00:28:28.205 --> 00:28:30.050
polarity. The two subs are
still right next to each other.

369
00:28:32.800 --> 00:28:37.637
Now restore normal polarity on
sub B and add a small delay of 0.8

370
00:28:37.637 --> 00:28:42.400
milliseconds. I've made a mistake:
it's 8 milliseconds, not 0.8.

371
00:28:42.680 --> 00:28:47.826
It's 8 milliseconds, here. Sorry,
I'll correct that. We now have an

372
00:28:47.826 --> 00:28:53.740
8-millisecond delay between the two
subs. Let's look at the same plots again.

373
00:28:54.440 --> 00:29:00.002
At 31 Hz, we see the pattern
beginning to lean slightly

374
00:29:00.002 --> 00:29:05.260
to one side. At 63 Hz, it
looks as though we're back

375
00:29:05.960 --> 00:29:11.522
to almost exactly the same pattern as
the inverted-polarity case here. At 125

376
00:29:11.522 --> 00:29:16.940
Hz, something else happens: the pattern
looks rather like the original one.

377
00:29:17.500 --> 00:29:21.932
What has changed? Before, we had
two identical subs. Now we have an

378
00:29:21.932 --> 00:29:26.760
8-millisecond delay between them. We
can see the beam changing direction.

379
00:29:27.120 --> 00:29:32.779
At 63 Hz, inverted polarity and
an 8-millisecond delay give us the

380
00:29:32.779 --> 00:29:38.780
same result. At 125 Hz, we get the
original result again. Essentially,

381
00:29:39.140 --> 00:29:45.183
if we look at the diagram,
those 8 milliseconds

382
00:29:45.183 --> 00:29:50.840
correspond to a quarter of a cycle at 31 Hz.

383
00:29:52.380 --> 00:29:56.366
That quarter-cycle difference
has steered the beam slightly,

384
00:29:56.366 --> 00:30:00.020
as though summation were
occurring on the delayed side.

385
00:30:00.440 --> 00:30:06.097
We have more sound towards the
bottom than the top. At 63 Hz,

386
00:30:06.097 --> 00:30:11.940
the delay is exactly half a cycle,
which has the same effect as

387
00:30:11.940 --> 00:30:18.398
inverting polarity at 63 Hz. At 125
Hz, however, those 8 milliseconds

388
00:30:18.398 --> 00:30:23.920
make up one complete period.
We've completed a whole cycle,

389
00:30:23.920 --> 00:30:28.726
which is 360°. After 360°, we're
back to something completely

390
00:30:28.726 --> 00:30:33.060
equivalent to the starting
point: one full cycle later.

391
00:30:33.540 --> 00:30:39.560
Does that make sense? Everyone
following? Any comments? No?

392
00:30:43.270 --> 00:30:49.296
Those were our first examples of summation.
We can see that reversing polarity,

393
00:30:49.296 --> 00:30:55.170
shifting timing and similar changes
produce results that vary with frequency,

394
00:30:55.170 --> 00:31:01.099
and those differences are clearly
related to the period shown

395
00:31:01.099 --> 00:31:06.930
here. Now we'll move on to what
we call the steering effect.

396
00:31:08.550 --> 00:31:12.410
What is the steering effect?
We've already begun exploring

397
00:31:12.410 --> 00:31:16.003
it by placing two subs side
by side. We'll look at how

398
00:31:16.003 --> 00:31:19.530
the number and position of
subs influence the signal.

399
00:31:20.710 --> 00:31:25.120
Let's return to our single-sub example. The

400
00:31:25.120 --> 00:31:29.530
pattern looks like a nice round grapefruit.

401
00:31:31.210 --> 00:31:36.181
Now take two subs spaced 12 metres
apart. Something rather strange

402
00:31:36.181 --> 00:31:40.550
happens: we get a butterfly
pattern, as it's often called.

403
00:31:40.890 --> 00:31:43.400
If the front is here, the
listener directly in front

404
00:31:43.400 --> 00:31:45.959
still has sound, but those
to the left and right lose

405
00:31:45.959 --> 00:31:48.710
level, and so on. I call this
the Ground Control warning.

406
00:31:49.530 --> 00:31:55.150
That's the phenomenon shown there.
If we instead distribute eight subs

407
00:31:55.150 --> 00:32:00.530
across 12 metres, the pattern
becomes strongly forward-facing. What

408
00:32:00.530 --> 00:32:06.469
has happened? We've made a
nice laser beam. This brings us

409
00:32:06.469 --> 00:32:12.510
back to Nadège's question. This
is the same diagram you saw

410
00:32:12.510 --> 00:32:16.275
in the line-array course. We'll
discuss the maximum spacing

411
00:32:16.275 --> 00:32:19.912
between two sources that still
produces useful summation.

412
00:32:19.912 --> 00:32:23.230
To avoid that butterfly
pattern and get this result,

413
00:32:23.570 --> 00:32:28.969
what is the maximum spacing
we can use? Start with a

414
00:32:28.969 --> 00:32:34.990
distance B between two sources
and consider the dimensions

415
00:32:34.990 --> 00:32:38.969
of the wavelengths at the
frequencies we want to

416
00:32:38.969 --> 00:32:43.030
reproduce. Here we're
below 120 Hz. There's a law

417
00:32:44.980 --> 00:32:48.914
called Olson's law, dating from
around 1950. It's been around

418
00:32:48.914 --> 00:32:52.848
a long time and hasn't changed:
if that distance is less than

419
00:32:52.848 --> 00:32:56.460
half a wavelength, we get a
nice forward beam like this.

420
00:32:57.280 --> 00:33:00.856
If the distance is greater than
half a wavelength, we get those

421
00:33:00.856 --> 00:33:04.660
butterfly patterns, alternating
between summation and cancellation.

422
00:33:06.340 --> 00:33:12.340
For subs reproducing frequencies
up to 125 Hz, once our sources

423
00:33:12.340 --> 00:33:18.340
are more than 1.36 metres apart,
we start getting cancellation,

424
00:33:18.340 --> 00:33:22.404
at least around those frequencies. If
we only need to reproduce frequencies

425
00:33:22.404 --> 00:33:26.360
up to 80 Hz, the allowable spacing
increases to 2.12 metres between subs.

426
00:33:26.960 --> 00:33:30.698
Once we exceed that spacing,
there's no way around it: we'll

427
00:33:30.698 --> 00:33:34.560
get this pattern at frequencies
above the corresponding limit.

428
00:33:36.560 --> 00:33:38.919
That's exactly what we saw with
line arrays. Much of line-array

429
00:33:38.919 --> 00:33:40.941
design involved bringing the
sources as close together

430
00:33:40.941 --> 00:33:43.000
as possible, because the
wavelengths were much shorter.

431
00:33:43.100 --> 00:33:48.933
With subs, we have more room to
work with: roughly 1.36 metres. So,

432
00:33:48.933 --> 00:33:54.940
Nadège, my 30 cm spacing was
comfortably within that limit, giving me

433
00:33:54.940 --> 00:33:58.717
a truly omnidirectional sub.
In theory I could have spaced

434
00:33:58.717 --> 00:34:02.233
them up to 1.36 metres, but
I might as well bring them

435
00:34:02.233 --> 00:34:05.880
closer. That's Olson's law.
There's also a demonstration

436
00:34:05.880 --> 00:34:07.520
that I hadn't shown you.

437
00:34:09.720 --> 00:34:14.468
Now we've established that our
subs should be spaced less than

438
00:34:14.468 --> 00:34:19.140
half a wavelength apart, let's
continue adding them together.

439
00:34:19.760 --> 00:34:25.558
Take four subs, all with
the same polarity, and

440
00:34:25.558 --> 00:34:31.480
see what happens with 80
cm spacing. Those 80 cm

441
00:34:31.820 --> 00:34:37.555
are half a wavelength at
212 Hz, for reference, well

442
00:34:37.555 --> 00:34:43.180
above 125 Hz. With four
subs, looking around 31 Hz,

443
00:34:43.420 --> 00:34:48.285
one octave above and below, the pattern
becomes slightly directional but

444
00:34:48.285 --> 00:34:52.880
remains almost round. At 63 Hz,
it's more elongated and directional.

445
00:34:53.140 --> 00:34:58.706
At 126 Hz, we start getting something
like a laser beam. That's just four subs

446
00:34:58.706 --> 00:35:04.200
at 0.8-metre spacing. I want to investigate
quantity, so let's add more subs.

447
00:35:05.600 --> 00:35:09.380
I've put these labels back;
sorry, I'd forgotten them.

448
00:35:09.380 --> 00:35:13.020
Coverage narrows as frequency
increases: as we go up

449
00:35:13.020 --> 00:35:16.520
in frequency, the beam
becomes more forward-facing

450
00:35:17.140 --> 00:35:23.161
and narrower. Now let's add more subs,
still spaced 80 cm apart. We haven't

451
00:35:23.161 --> 00:35:28.780
changed the spacing, only the number.
There's an obvious gain in level

452
00:35:28.780 --> 00:35:33.368
because we have more sources.
What interests me is the

453
00:35:33.368 --> 00:35:38.380
coverage: the almost 360° we
had before is suddenly halved.

454
00:35:38.420 --> 00:35:41.067
We've gone down to 180°:
180° on one side and 180° on

455
00:35:41.067 --> 00:35:43.913
the other. I should have moved
a little further away. You

456
00:35:43.913 --> 00:35:46.560
can see blue here, where
there's cancellation behind.

457
00:35:47.940 --> 00:35:53.854
Compare four subs with eight at 63
Hz, and the coverage is still halved.

458
00:35:53.854 --> 00:35:59.440
At 120 Hz, it's halved again. So,
as we increase the number of subs,

459
00:36:01.100 --> 00:36:04.496
the coverage narrows. Let's
increase it again: now we have

460
00:36:04.496 --> 00:36:07.541
sixteen instead of eight.
Place sixteen subs side by

461
00:36:07.541 --> 00:36:10.820
side at 80 cm spacing, and
the coverage keeps narrowing.

462
00:36:11.760 --> 00:36:16.740
The more subs we add, the
longer our line becomes,

463
00:36:18.940 --> 00:36:24.132
and the coverage narrows with
frequency. Looking in the other

464
00:36:24.132 --> 00:36:29.580
direction, as frequency increases
across the plots, this is true

465
00:36:29.580 --> 00:36:35.505
for every line length: coverage
narrows. And in the other direction, the

466
00:36:35.505 --> 00:36:41.100
more subs we add, the longer the
line and the narrower the coverage.

467
00:36:41.680 --> 00:36:47.463
There's a clear relationship between the
number of subs, and therefore the line

468
00:36:47.463 --> 00:36:52.880
length, and the coverage and beam we
create. Is the quantity effect clear?

469
00:36:57.030 --> 00:37:02.821
The second effect is position. Let's
return to our four subs, but this time

470
00:37:02.821 --> 00:37:08.690
space them 3.2 metres apart. That's
fairly wide: half a wavelength at 53 Hz.

471
00:37:09.030 --> 00:37:14.339
According to Olson's law, which
we saw earlier, below 53 Hz things

472
00:37:14.339 --> 00:37:20.130
should become a little complicated.
We can already see it slightly here.

473
00:37:20.210 --> 00:37:24.276
At 31 Hz, the combined
effect is still acceptable,

474
00:37:24.276 --> 00:37:28.830
because we're below the limit,
and we obtain a 60° beam.

475
00:37:30.070 --> 00:37:34.406
As frequency increases, the
beam narrows: first to 30°, then

476
00:37:34.406 --> 00:37:38.670
to 17°, with these additional
beams going off to the sides.

477
00:37:38.890 --> 00:37:42.466
Here we've clearly exceeded the
limit set by Olson's law. At 63 Hz,

478
00:37:42.466 --> 00:37:46.094
since we're using an octave range,
we're measuring from around 30 to

479
00:37:46.094 --> 00:37:49.670
120 Hz. That's why we see these
small streaks, but it's acceptable.

480
00:37:50.290 --> 00:37:53.703
At 125 Hz, we're measuring from
around 60 to 250 Hz, and the

481
00:37:53.703 --> 00:37:56.490
pattern becomes quite a
mess. We've exceeded that

482
00:37:56.490 --> 00:38:00.130
half-wavelength spacing, so it
isn't a particularly good system.

483
00:38:00.570 --> 00:38:05.923
What interests me here is that coverage
narrows with frequency. Now we'll

484
00:38:05.923 --> 00:38:11.350
add more subs across the same overall
span, bringing them closer together.

485
00:38:11.510 --> 00:38:17.103
They'll be 1.5 metres apart, corresponding
to half a wavelength at 106 Hz.

486
00:38:17.103 --> 00:38:22.470
We've raised the frequency limit set
by Olson's law. We still see that,

487
00:38:24.530 --> 00:38:29.534
looking from top to bottom, as
frequency increases the coverage angle

488
00:38:29.534 --> 00:38:34.610
narrows. But across the rows, that
angle doesn't seem to have changed.

489
00:38:34.750 --> 00:38:40.002
When we go from four subs at 3.2-metre
spacing to eight at 1.5 metres,

490
00:38:40.002 --> 00:38:45.330
the combined effect on coverage is
almost identical. We obtain the same

491
00:38:45.950 --> 00:38:48.950
coverage angles. Now increase
the number to sixteen subs.

492
00:38:51.110 --> 00:38:55.282
We still see the same effect: as
frequency rises, the angle narrows.

493
00:38:55.282 --> 00:38:58.962
But the number of subs changes
while the overall line length

494
00:38:58.962 --> 00:39:02.950
stays the same. Previously we had
four subs at 3.2-metre spacing;

495
00:39:03.070 --> 00:39:07.754
now we have sixteen at 0.8-metre spacing.
The overall line length has stayed

496
00:39:07.754 --> 00:39:12.130
the same throughout. We've simply
changed the spacing between the subs.

497
00:39:14.250 --> 00:39:19.990
The angle always narrows as frequency
increases, but it stays the same

498
00:39:19.990 --> 00:39:25.730
for a given line length. What we've
gained, again through Olson's law,

499
00:39:26.390 --> 00:39:28.887
is control over those
artefacts we saw initially. The

500
00:39:28.887 --> 00:39:31.431
frequency limit was very low
there, and the result was

501
00:39:31.431 --> 00:39:34.070
really poor. Here, we can
control the pattern at 125 Hz.

502
00:39:34.750 --> 00:39:37.806
That makes sense, because the
half-wavelength frequency for our

503
00:39:37.806 --> 00:39:40.765
spacing is well above that.
Olson's law is respected: 212 Hz.

504
00:39:40.765 --> 00:39:43.870
Here too, it's more or less
respected; we're close to the limit.

505
00:39:44.490 --> 00:39:49.540
So this is acceptable. To recap: as
frequency increases, coverage narrows.

506
00:39:49.540 --> 00:39:54.590
But when we increase the number of
subs here, the coverage doesn't change.

507
00:39:54.790 --> 00:39:57.890
The line length hasn't changed,
so the coverage doesn't change.

508
00:39:59.830 --> 00:40:03.872
When you say spacing, do you
mean between the cabinets'

509
00:40:03.872 --> 00:40:07.842
acoustic centres? Exactly:
between the centres. Let me

510
00:40:07.842 --> 00:40:11.590
go back. It's between the
centres of E and D, here.

511
00:40:12.150 --> 00:40:14.835
I'm using a virtual point that
doesn't physically exist, but

512
00:40:14.835 --> 00:40:17.565
I always take the acoustic
centres of the units. It's not the

513
00:40:17.565 --> 00:40:20.250
empty gap between the cabinets:
it's their acoustic centres.

514
00:40:25.210 --> 00:40:30.351
Here's another effect, the second
to last, don't worry: lateral

515
00:40:30.351 --> 00:40:35.410
steering. I'll use just eight
subs and stick with those eight.

516
00:40:35.610 --> 00:40:40.372
This time, I arrange them in a straight
line. The exact spacing doesn't matter

517
00:40:40.372 --> 00:40:44.950
here; let's assume it's close enough
to comply with Olson's law. Let's look

518
00:40:46.130 --> 00:40:52.257
at the beam at different frequencies.
There's absolutely no delay between my eight

519
00:40:52.257 --> 00:40:58.010
subs: zero milliseconds. They're all in
time. The beam points straight ahead.

520
00:40:58.370 --> 00:41:03.813
That's its direction. Now I'll
add a small delay to some of the

521
00:41:03.813 --> 00:41:09.170
subs. You can see the delays
increase from 0 to 4 milliseconds

522
00:41:09.170 --> 00:41:13.874
in regular steps. The first sub has
no delay, and the bottom one has 4

523
00:41:13.874 --> 00:41:19.250
milliseconds. We can see the beam beginning
to turn slightly towards the bottom.

524
00:41:21.920 --> 00:41:27.495
That's true at almost every frequency:
the angle changes in the same way across

525
00:41:27.495 --> 00:41:33.140
the frequencies. Let's increase the delays
to 8 milliseconds. I've doubled them.

526
00:41:33.720 --> 00:41:39.232
The beam turns even further. That's
what we call lateral steering:

527
00:41:39.232 --> 00:41:45.580
increasing the delays between subs
steers the beam towards the delayed side.

528
00:41:45.760 --> 00:41:49.530
The beam points towards the sub
with the greatest delay. Here it

529
00:41:49.530 --> 00:41:53.300
points downwards, because the
most delayed sub is at the bottom.

530
00:41:55.120 --> 00:42:00.598
That's lateral steering. The
final effect is the subwoofer

531
00:42:00.598 --> 00:42:06.360
arc. You've probably heard of
this. Let's take our eight subs

532
00:42:06.460 --> 00:42:11.126
and arrange them in an
arc, working out from the

533
00:42:11.126 --> 00:42:15.500
centre. Let's see what
the measurements show.

534
00:42:16.820 --> 00:42:22.970
If I angle each of the eight subs by 5°
relative to its neighbour, that gives

535
00:42:22.970 --> 00:42:28.800
a total of 40°. Again, as frequency
increases, the beam narrows slightly.

536
00:42:29.480 --> 00:42:35.250
Now I'll change only those
angles. The coverage still narrows

537
00:42:35.250 --> 00:42:41.020
with frequency, just as before.
Let's introduce a little more

538
00:42:41.020 --> 00:42:46.947
angle between the subs, increasing
the arc. Instead of 5° between them,

539
00:42:46.947 --> 00:42:52.540
I'll use 7.5°. At the lowest
frequencies there's little change, but

540
00:42:52.980 --> 00:42:58.194
at 63 and 125 Hz, the beam tends to
widen slightly. It's clear at the

541
00:42:58.194 --> 00:43:03.560
higher frequencies: coverage is wider
than in the previous arrangement,

542
00:43:04.460 --> 00:43:09.622
which had less angle. If
I increase the curvature

543
00:43:09.622 --> 00:43:15.100
again, to 10° between subs,
we increase the coverage

544
00:43:16.040 --> 00:43:20.889
of the original line. We've
gone from 50° with the shallower

545
00:43:20.889 --> 00:43:25.980
arc to 72°. The geometry of the
arc therefore affects coverage.

546
00:43:26.620 --> 00:43:29.835
Increasing the curvature
of the arc widens coverage.

547
00:43:29.835 --> 00:43:33.296
Everything you've just seen
is what we call the steering

548
00:43:33.296 --> 00:43:36.820
effect. You may have heard of
beam-steering loudspeakers.

549
00:43:36.920 --> 00:43:40.625
Beam steering is exactly
this. We're applying it to low

550
00:43:40.625 --> 00:43:44.600
frequencies, but it also works
at mid and high frequencies.

551
00:43:44.600 --> 00:43:48.440
By adjusting delays, arc
geometry, spacing and curvature,

552
00:43:48.660 --> 00:43:52.888
we can point a beam in the desired
direction. We're doing it with

553
00:43:52.888 --> 00:43:56.920
subs, whose advantage is that
it's physically very easy to do.

554
00:43:57.460 --> 00:44:01.442
They're large boxes working
with long wavelengths. Look at

555
00:44:01.442 --> 00:44:05.493
this arc: we've physically
arranged the subs along a curve.

556
00:44:05.493 --> 00:44:09.200
Technically, that can be
difficult because it takes up

557
00:44:09.200 --> 00:44:09.920
a huge amount of space.

558
00:44:11.740 --> 00:44:17.537
Remember Δd and Δt, the spatial
and temporal differences we

559
00:44:17.537 --> 00:44:23.040
discussed. We can reproduce
this arc without introducing

560
00:44:23.740 --> 00:44:29.521
a Δd, using Δt instead. We
shift the two centre subs

561
00:44:29.521 --> 00:44:35.080
back in time by Δt, the
next pair outwards by Δt2,

562
00:44:35.940 --> 00:44:42.006
then t3 and t4. You can see
that I shift them progressively

563
00:44:42.006 --> 00:44:47.660
further back. The phantom
sources appear here, creating

564
00:44:47.660 --> 00:44:52.196
a virtual subwoofer arc that's easier to

565
00:44:52.196 --> 00:44:57.640
implement. Let's see what
the measurements show.

566
00:44:58.700 --> 00:45:03.579
First, with zero milliseconds
of delay, there is no arc:

567
00:45:03.579 --> 00:45:08.720
it's a straight line. Our subs
are spaced 1.4 metres apart.

568
00:45:09.260 --> 00:45:12.220
Remember, the spacing here is 1.4
metres, at the half-wavelength limit.

569
00:45:14.640 --> 00:45:19.797
Here are our eight subs at 1.4-metre
spacing. Now increase the delays

570
00:45:19.797 --> 00:45:24.880
from 0 to 2.6 milliseconds. The
coverage starts to open up slightly.

571
00:45:25.820 --> 00:45:31.765
We're increasing the virtual arc,
which widens the coverage. These

572
00:45:31.765 --> 00:45:37.800
delays let us adjust the coverage,
the opening angle of the system,

573
00:45:37.920 --> 00:45:41.578
of the line we've created,
simply by adding delays to form

574
00:45:41.578 --> 00:45:45.174
a virtual arc. Increasing the
arc delays widens coverage,

575
00:45:45.174 --> 00:45:48.580
just as increasing the
physical curvature did earlier.

576
00:45:50.140 --> 00:45:52.540
Any questions? This is a good
moment for a short pause.

577
00:45:54.800 --> 00:46:00.489
Not too difficult? It gets
harder later! All good? Great,

578
00:46:00.489 --> 00:46:05.580
we're making progress. Hold
on, we're taking notes.

579
00:46:08.740 --> 00:46:13.154
Now let's move on. We've seen
what a subwoofer arc is. I gave

580
00:46:13.154 --> 00:46:17.640
you example values, but you
haven't learned to calculate them.

581
00:46:17.900 --> 00:46:20.632
At the end, I'll show you
ways to calculate them and

582
00:46:20.632 --> 00:46:23.626
achieve the coverage you want
for the distances involved.

583
00:46:23.626 --> 00:46:26.620
Now we'll move to another
effect, still part of steering.

584
00:46:26.720 --> 00:46:30.522
It's called forward steering.
This is where we really

585
00:46:30.522 --> 00:46:34.540
get into cardioid configurations,
which we'll use a lot.

586
00:46:35.340 --> 00:46:39.414
We'll see how to create cardioid
configurations. We like these in live sound

587
00:46:39.414 --> 00:46:43.380
because they let us put more sound on
one side and reduce it on the other.

588
00:46:43.600 --> 00:46:45.240
That's why we'll spend some time on them.

589
00:46:47.800 --> 00:46:49.060
To create cardioid subwoofer arrays,

590
00:46:51.860 --> 00:46:55.093
there are two main methods.
There are many variations,

591
00:46:55.093 --> 00:46:58.267
but two principal methods
for making subwoofer arrays

592
00:46:58.267 --> 00:47:01.800
directional. These arrays are
often simply called cardioid.

593
00:47:02.200 --> 00:47:05.113
They aren't necessarily cardioid,
though: they're directional.

594
00:47:05.113 --> 00:47:07.743
We'll see subcardioid,
hypercardioid and figure-of-eight

595
00:47:07.743 --> 00:47:10.280
patterns, all the same shapes
we get with microphones.

596
00:47:10.720 --> 00:47:14.280
We often say cardioid, so I
may use that term even when the

597
00:47:14.280 --> 00:47:18.020
pattern is actually subcardioid.
Please forgive the shorthand.

598
00:47:18.020 --> 00:47:21.580
In any case, we'll look at the
two main methods one by one.

599
00:47:22.700 --> 00:47:28.755
First, we have a method known as a
'native' configuration: two subs spaced

600
00:47:28.755 --> 00:47:34.400
a certain distance apart, with a
delay, Δt, applied to the front sub.

601
00:47:35.860 --> 00:47:39.367
The other type is the
pressure-gradient configuration. We

602
00:47:39.367 --> 00:47:42.873
still have two subs, but here
the delay is applied to the

603
00:47:42.873 --> 00:47:46.380
rear one, and a phase adjustment
is involved at the rear.

604
00:47:46.640 --> 00:47:51.202
We will examine each
configuration in detail. The two

605
00:47:51.202 --> 00:47:55.420
main methods are 'native'
mode and gradient mode.

606
00:47:55.760 --> 00:47:59.767
Sometimes I will just say 'native'
or 'gradient', without always saying

607
00:47:59.767 --> 00:48:04.000
'pressure gradient'. First, let's look
at how 'native' configurations work.

608
00:48:04.220 --> 00:48:06.993
I will spend some time on
the 'native' configuration so

609
00:48:06.993 --> 00:48:09.715
you understand how we produce
this summation. Then the

610
00:48:09.715 --> 00:48:12.740
pressure-gradient explanation
will follow much more quickly.

611
00:48:15.610 --> 00:48:20.685
Let's take two subs. The arrow points
in the direction we want the signal

612
00:48:20.685 --> 00:48:25.830
to travel: normally towards the audience,
where we want to send the sound.

613
00:48:27.210 --> 00:48:32.608
Every configuration you will see depends
on several parameters. We will work

614
00:48:32.608 --> 00:48:38.290
through them and give them numerical
values later. For now, we will use symbols.

615
00:48:39.130 --> 00:48:42.518
The first parameter is a frequency
I call the centre frequency:

616
00:48:42.518 --> 00:48:45.423
the frequency at which I am
working. You will see why,

617
00:48:45.423 --> 00:48:48.650
because the behaviour differs
from one frequency to another.

618
00:48:48.770 --> 00:48:53.512
This centre frequency is the
starting point from which everything

619
00:48:53.512 --> 00:48:57.670
else follows. It necessarily
corresponds to a wavelength.

620
00:48:58.050 --> 00:49:03.782
That is λ at the centre
frequency. It also has

621
00:49:03.782 --> 00:49:09.390
a period: the period of
the centre frequency.

622
00:49:09.390 --> 00:49:13.682
We will frequently use fc, λfc and
Tfc, which is why I am introducing

623
00:49:13.682 --> 00:49:17.290
them now. For the moment, our
parameters are just letters.

624
00:49:19.550 --> 00:49:23.092
Imagine placing these two
subs a distance apart equal to

625
00:49:23.092 --> 00:49:26.570
one quarter of the wavelength
at this centre frequency.

626
00:49:30.080 --> 00:49:34.304
I apply no delay to the first
sub: Δt = 0. I delay the second

627
00:49:34.304 --> 00:49:38.320
sub by one quarter of the
period at this centre frequency.

628
00:49:38.940 --> 00:49:43.860
So we have one quarter here, and another
quarter there. Let's see what happens.

629
00:49:46.740 --> 00:49:49.935
Here are our two subs again. I will
show you two ways of visualising this,

630
00:49:49.935 --> 00:49:53.260
because different people find different
representations easier to understand.

631
00:49:53.720 --> 00:49:57.886
We will look at two
representations, then use just one.

632
00:49:57.886 --> 00:50:02.280
First, the wave representation:
what happens to the waves?

633
00:50:04.260 --> 00:50:07.772
Here is our listener. For
now, we are only looking from

634
00:50:07.772 --> 00:50:11.220
the front and ignoring what
happens behind the system.

635
00:50:12.620 --> 00:50:17.676
Our first sub, B, emits a wave at the centre

636
00:50:17.676 --> 00:50:23.880
frequency. We draw it to the
same scale, then apply...

637
00:50:24.260 --> 00:50:27.355
...a time offset equivalent to
one quarter of a wavelength.

638
00:50:27.355 --> 00:50:30.765
Remember that the spacing corresponds
to one quarter of a period:

639
00:50:30.765 --> 00:50:33.860
this quarter wavelength
corresponds to that quarter period.

640
00:50:34.080 --> 00:50:39.861
It is the same distance. Sub B therefore
appears to move virtually onto A.

641
00:50:39.861 --> 00:50:45.720
For our listener in front, the wave
has effectively moved from this area...

642
00:50:46.500 --> 00:50:52.201
...to this area. It has
been delayed in time and

643
00:50:52.201 --> 00:50:58.140
space. If sub A emits a
wave, shown here in red...

644
00:50:59.200 --> 00:51:04.744
...we see that the waves overlap
exactly, because this sub has no

645
00:51:04.744 --> 00:51:10.800
delay. With the two waves perfectly
aligned, the phase difference is...

646
00:51:10.800 --> 00:51:16.720
...0° at this centre frequency. This
applies to the frequency whose quarter

647
00:51:16.720 --> 00:51:22.640
wavelength equals this distance and
whose quarter period equals this delay.

648
00:51:23.300 --> 00:51:26.982
It applies to that frequency.
We have summation at 0°.

649
00:51:26.982 --> 00:51:30.937
Remember the magic circle: 0°
gives approximately +6 dB. I

650
00:51:30.937 --> 00:51:34.960
say approximately because real
acoustic constraints also...

651
00:51:35.460 --> 00:51:38.320
...affect the result, and their
influence can be substantial.

652
00:51:40.570 --> 00:51:46.080
Now let's move behind the
system. Our listener is at the

653
00:51:46.080 --> 00:51:51.590
rear. Sub B is still delayed
by one quarter of a period.

654
00:51:52.070 --> 00:51:55.972
The source now appears virtually
at this position, farther

655
00:51:55.972 --> 00:52:00.075
away. Remember, there is one
quarter here and another quarter

656
00:52:00.075 --> 00:52:03.910
here, although the diagram
does not show it very clearly.

657
00:52:05.170 --> 00:52:10.370
Sub A still emits its normal wave
towards the rear, originally in

658
00:52:10.370 --> 00:52:15.650
phase with the first one. We can
see that the two waves are now...

659
00:52:15.650 --> 00:52:19.138
...exactly 180° apart. What
does 180° give us? Strong

660
00:52:19.138 --> 00:52:23.153
cancellation: theoretically
minus infinity. In reality, it is

661
00:52:23.153 --> 00:52:26.970
not minus infinity, but it
provides very good attenuation.

662
00:52:28.010 --> 00:52:33.893
The front and rear views are different:
on one side the waves sum, and on the

663
00:52:33.893 --> 00:52:39.470
other they cancel. If that was not
clear, there is another way to see it.

664
00:52:39.610 --> 00:52:45.292
This is the circular representation.
Draw a circle with a diameter of twice

665
00:52:45.292 --> 00:52:50.670
the wavelength at the centre frequency.
Whether the listener is here...

666
00:52:50.670 --> 00:52:56.088
...or here, here or here, they
are always the same distance away.

667
00:52:56.088 --> 00:53:01.590
Do the same for sub B. This shows
what would happen with no delay.

668
00:53:02.470 --> 00:53:07.504
The distance between the two is
one quarter of a wavelength: this

669
00:53:07.504 --> 00:53:12.770
spacing is the same as that spacing.
If we apply a delay to sub B...

670
00:53:13.130 --> 00:53:18.431
...the whole circle appears to move
backwards, at least when viewed from the

671
00:53:18.431 --> 00:53:24.010
front. The behaviour varies slightly at
the sides. The two circles now coincide.

672
00:53:24.090 --> 00:53:29.894
Viewed from the front, the waves
arrive at exactly the same time.

673
00:53:29.894 --> 00:53:35.430
The phase difference is 0°,
giving us +6 dB. If I return to...

674
00:53:35.430 --> 00:53:41.020
...the two original waves, with
the same spacing, and look from the

675
00:53:41.020 --> 00:53:46.610
rear, what happens? As the sub
moves backwards in this rear view...

676
00:53:47.050 --> 00:53:52.510
...we obtain half a period, or a 180°
difference. We have the physical quarter

677
00:53:52.510 --> 00:53:57.970
wavelength plus another quarter: one
quarter plus one quarter equals one half.

678
00:54:00.210 --> 00:54:03.749
One quarter plus one quarter
equals one half. We therefore

679
00:54:03.749 --> 00:54:07.348
have a half-wavelength difference
and opposite phase at the

680
00:54:07.348 --> 00:54:11.070
rear. We can now represent the
front and rear views together.

681
00:54:11.170 --> 00:54:16.927
You may remember the little ellipse
I drew at the beginning. We can now

682
00:54:16.927 --> 00:54:23.090
picture the entire pattern: something
like this ellipse for the delayed sub.

683
00:54:24.170 --> 00:54:28.546
From there, by measuring these
distances, we could calculate

684
00:54:28.546 --> 00:54:32.850
the phase difference geometrically
at every point in space.

685
00:54:34.550 --> 00:54:38.122
Those were two ways of viewing
it. If I combine the two and

686
00:54:38.122 --> 00:54:41.876
place them on top of each other,
we see the wave at the front.

687
00:54:41.876 --> 00:54:45.630
I drew it poorly here: it should
be a little larger and wider.

688
00:54:46.130 --> 00:54:49.711
At the front, the waves add together;
at the rear, cancellation at

689
00:54:49.711 --> 00:54:53.130
180° is almost complete. This is
what I call the combined view.

690
00:54:56.030 --> 00:55:01.351
All of that was at the centre
frequency: its period and the distance

691
00:55:01.351 --> 00:55:06.750
derived from it. It applied only to
the frequency we initially chose.

692
00:55:06.890 --> 00:55:12.330
If I chose 80 Hz, it applied only
to 80 Hz, not 90 Hz or perhaps

693
00:55:12.330 --> 00:55:17.090
60 Hz. This shows how important
the centre frequency is.

694
00:55:18.370 --> 00:55:22.594
The settings are now fixed:
a delay of one quarter of the

695
00:55:22.594 --> 00:55:27.930
centre-frequency period, and a spacing
of one quarter of its wavelength.

696
00:55:29.030 --> 00:55:33.154
Here is a reminder of a little
formula we will see often, so

697
00:55:33.154 --> 00:55:37.003
do not focus too much on it
yet. Watch what happens if I

698
00:55:37.003 --> 00:55:40.990
raise the frequency and listen
above the centre frequency.

699
00:55:40.990 --> 00:55:45.532
As I increase the frequency,
the wavelengths become

700
00:55:45.532 --> 00:55:50.430
shorter and shorter, and we
see the behaviour changing.

701
00:55:51.010 --> 00:55:56.475
Let me show that again, starting
from where we were. Notice

702
00:55:56.475 --> 00:56:01.570
that the phase difference at
the front does not change.

703
00:56:02.810 --> 00:56:06.546
The phase difference at the
rear does change. At the front

704
00:56:06.546 --> 00:56:10.411
it stays at 0° as the frequency
rises. At the rear, although

705
00:56:10.411 --> 00:56:13.890
I have not calculated the
value, it is no longer 180°.

706
00:56:14.410 --> 00:56:17.278
We no longer have the phase
relationship for perfect cancellation.

707
00:56:17.278 --> 00:56:20.450
Depending on the frequency, we may
instead get summation or cancellation.

708
00:56:20.970 --> 00:56:25.232
If I lower the frequency
instead, we again see that the

709
00:56:25.232 --> 00:56:29.650
phase difference behind the
system varies with frequency.

710
00:56:32.120 --> 00:56:38.074
As I lower this frequency, the phase
difference changes again at the rear, while

711
00:56:38.074 --> 00:56:43.880
it still does not change at the front.
In other words, the phase difference...

712
00:56:43.880 --> 00:56:47.291
...at the front does not
vary with frequency. Above

713
00:56:47.291 --> 00:56:50.970
and below the centre frequency,
different things happen

714
00:56:50.970 --> 00:56:54.180
around the system, at the
front and at the rear.

715
00:56:55.360 --> 00:56:57.920
Does that make sense? This is
the trickiest part to understand.

716
00:57:00.090 --> 00:57:02.710
Are we all right? It seems
so. OK. You look exhausted!

717
00:57:07.060 --> 00:57:10.875
Now let's put some numbers on
this. So far, it has all been

718
00:57:10.875 --> 00:57:14.820
abstract, and we have not even
looked at the measured result.

719
00:57:14.920 --> 00:57:18.512
I have prepared examples using different
values. They are commonly used values,

720
00:57:18.512 --> 00:57:21.740
which is why I chose them, but you
can choose whatever values you need.

721
00:57:22.280 --> 00:57:26.601
These can go into your reference
collection in the slides. Let's choose

722
00:57:26.601 --> 00:57:30.800
a centre frequency of 100 Hz, because
it makes the calculations easy.

723
00:57:30.920 --> 00:57:33.140
The numbers come out almost
exactly. At 100 Hz...

724
00:57:36.120 --> 00:57:41.676
...the period is 10 milliseconds.
We space the subs one quarter of

725
00:57:41.676 --> 00:57:46.980
a wavelength apart: 0.85 metres,
or 85 cm between the two subs.

726
00:57:47.600 --> 00:57:52.981
We delay the front sub by 2.5
milliseconds, one quarter of 10. Let's

727
00:57:52.981 --> 00:57:58.520
look at the measured result for our
chosen centre frequency of 100 Hz.

728
00:57:58.760 --> 00:58:04.771
At 31 Hz, the effect is not very impressive.
The pattern is almost a blob, nearly

729
00:58:04.771 --> 00:58:10.560
the original omnidirectional pattern.
At 63 Hz, it starts pointing slightly...

730
00:58:10.560 --> 00:58:16.166
...towards the front. At 125 Hz we are
much closer to 100 Hz, and the result

731
00:58:16.166 --> 00:58:21.920
is not quite cardioid, more like a
subcardioid, but it is clearly directional.

732
00:58:22.120 --> 00:58:24.982
There is considerably less
sound here. We have created

733
00:58:24.982 --> 00:58:28.003
our first cardioid in 'native'
mode. Its design frequency

734
00:58:28.003 --> 00:58:30.600
is fairly high, admittedly,
but it is a cardioid.

735
00:58:31.280 --> 00:58:37.214
If we focus on the front, we
see that it stays almost the

736
00:58:37.214 --> 00:58:42.940
same at every frequency.
Remember how, as we changed...

737
00:58:42.940 --> 00:58:47.267
...the frequency up or down, little
seemed to change at the front, whereas the

738
00:58:47.267 --> 00:58:51.760
phase difference clearly changed at the
rear? This simulation shows exactly that.

739
00:58:52.740 --> 00:58:57.421
The changing phase difference at the
rear changes the radiation pattern and

740
00:58:57.421 --> 00:59:02.040
coverage depending on the frequency
we listen to. Let's try another value.

741
00:59:03.320 --> 00:59:06.127
Here I used 85 Hz. This is useful
because the numbers work out

742
00:59:06.127 --> 00:59:09.160
neatly. It is a very common example
because it is easy to remember.

743
00:59:10.640 --> 00:59:15.454
With a centre frequency of 85
Hz, the spacing is exactly 1 m,

744
00:59:15.454 --> 00:59:20.820
because the wavelength is 4 m. One
quarter is 1 m: easy to remember.

745
00:59:21.680 --> 00:59:25.387
The period is 11.66 milliseconds,
with a quarter-period

746
00:59:25.387 --> 00:59:28.758
delay of 2.94 milliseconds.
Many people know those

747
00:59:28.758 --> 00:59:32.600
numbers by heart. So, with a
centre frequency of 85 Hz...

748
00:59:33.200 --> 00:59:39.264
...the measurement shows a slightly
forward-facing pattern here. At 63 Hz,

749
00:59:39.264 --> 00:59:45.000
it develops a subcardioid shape, and
at 125 Hz it has almost become...

750
00:59:45.000 --> 00:59:50.701
...hypercardioid. At 85 Hz, somewhere
in between, on the plot that is

751
00:59:50.701 --> 00:59:56.320
not shown here, the pattern would
be closest to cardioid. This is...

752
00:59:56.320 --> 01:00:01.147
...the 85 Hz configuration. Again,
we get the same result at the

753
01:00:01.147 --> 01:00:06.200
front, while the rear varies with
frequency. Let's change it again.

754
01:00:06.840 --> 01:00:09.900
Personally, this is the
configuration I use most often.

755
01:00:11.910 --> 01:00:15.799
Let's take a centre frequency
of 60 Hz. Why do I often use

756
01:00:15.799 --> 01:00:19.354
it? That is often where the
kick drum sits. I like to

757
01:00:19.354 --> 01:00:23.310
target the low end of the kick
to maximise isolation there.

758
01:00:24.330 --> 01:00:28.294
If I know the music well and the kick
is at 58 Hz, I will adapt all the

759
01:00:28.294 --> 01:00:32.090
values accordingly. But as a starting
point, I often use this value.

760
01:00:32.930 --> 01:00:38.320
At 60 Hz, one quarter of a wavelength
is 1.42 m, which takes up quite a lot of

761
01:00:38.320 --> 01:00:43.710
space. One quarter of the period is 4.17
milliseconds. Let's see what happens.

762
01:00:43.770 --> 01:00:49.049
At 31 Hz, the pattern is already
slightly blob-shaped. At 63 Hz, it

763
01:00:49.049 --> 01:00:54.170
looks quite good, and at 125 Hz
it starts becoming hypercardioid.

764
01:00:54.550 --> 01:00:57.693
That may not look ideal, but
it depends on the music being

765
01:00:57.693 --> 01:01:01.053
reproduced. Many subs are
low-passed at 80 Hz, for example, in

766
01:01:01.053 --> 01:01:04.250
which case this higher-frequency
behaviour does not matter.

767
01:01:05.370 --> 01:01:07.883
I therefore concentrate
on this region, targeting

768
01:01:07.883 --> 01:01:10.190
the frequencies I actually
want to reproduce.

769
01:01:13.330 --> 01:01:19.230
Let's compare the three numerical
examples: 0.85 m, 1 m and

770
01:01:19.230 --> 01:01:25.230
1.42 m, corresponding to 100
Hz, 85 Hz and 60 Hz. Here is...

771
01:01:25.230 --> 01:01:30.085
...what they produce at low, middle
and 'high' frequencies, if we

772
01:01:30.085 --> 01:01:35.090
can call 125 Hz high. These are
some of the patterns we can obtain.

773
01:01:35.230 --> 01:01:39.013
This gives you a comparison
table based on the spacing you

774
01:01:39.013 --> 01:01:42.797
choose and, consequently, the
delays you choose. 'When you

775
01:01:42.797 --> 01:01:46.450
do this, where do you place
them relative to the stage?'

776
01:01:46.450 --> 01:01:48.110
'You need a fair amount of space to make...'

777
01:01:50.090 --> 01:01:54.756
'...a 'native' cardioid at 60 Hz.' Yes,
that is the problem: it is a compromise.

778
01:01:54.756 --> 01:01:59.130
A spacing of 1.42 m is substantial, so
it will be difficult in some venues.

779
01:02:00.670 --> 01:02:03.719
The aim is to avoid rearward
sound on stage, so it depends.

780
01:02:03.719 --> 01:02:06.614
'Does it work under the stage?'
Under the stage, you are

781
01:02:06.614 --> 01:02:09.870
effectively on stage, and the
sound travels in every direction.

782
01:02:10.510 --> 01:02:14.640
It will be audible. But it depends
on the sub's position. I might try

783
01:02:14.640 --> 01:02:18.530
a hypercardioid configuration like
this; that can also work well.

784
01:02:20.110 --> 01:02:25.621
If you are here, for example... 'Yes, it
does not send much sound to the sides.'

785
01:02:25.621 --> 01:02:30.650
I am showing you several systems, but
broadly, the spacing of the subs...

786
01:02:31.310 --> 01:02:34.962
...and the frequency at which
you aim for cancellation

787
01:02:34.962 --> 01:02:38.682
change many things. For each
configuration, you need to

788
01:02:38.682 --> 01:02:42.470
choose the centre frequency
that produces the pattern...

789
01:02:42.470 --> 01:02:45.990
...best suited to the physical
area you want to isolate.

790
01:02:47.990 --> 01:02:51.290
The centre frequency determines
the spacing, but the spacing

791
01:02:51.290 --> 01:02:54.425
also determines the centre
frequency. We work through the

792
01:02:54.425 --> 01:02:57.670
calculation in whichever
direction the constraints require.

793
01:02:57.790 --> 01:03:01.625
If I have only 1 m of space,
I may choose one configuration

794
01:03:01.625 --> 01:03:04.680
over another for that
reason. But with only 1 m

795
01:03:04.680 --> 01:03:08.190
available, I know I will not
be able to control 60 Hz.

796
01:03:09.250 --> 01:03:12.874
Does that make sense? 'I
imagine you can combine the sub

797
01:03:12.874 --> 01:03:16.757
lines you showed us earlier
with rear cancellation?' We will

798
01:03:16.757 --> 01:03:20.510
look at that later. Nadège,
you are always one step ahead.

799
01:03:21.350 --> 01:03:27.090
'So, the lower you make the design
frequency, the more nearly bidirectional

800
01:03:27.090 --> 01:03:32.370
the pattern becomes at higher
frequencies? It becomes supercardioid.'

801
01:03:32.770 --> 01:03:37.028
Yes, exactly. A rear lobe
develops. Why does it develop?

802
01:03:37.028 --> 01:03:41.590
Because we start making a full
turn around the circle again.

803
01:03:42.390 --> 01:03:46.650
A phase difference of 360° is equivalent
to 0°, and the same applies to 720° and

804
01:03:46.650 --> 01:03:50.750
so on. Broadly speaking, the waves start
summing again at higher frequencies.

805
01:03:51.390 --> 01:03:56.334
I hope that makes sense. We will see this
later: we will combine the line-array

806
01:03:56.334 --> 01:04:00.590
effect and beam steering we saw
earlier with these cardioid effects.

807
01:04:01.530 --> 01:04:04.559
We will get there. From these
principles, we can derive whatever

808
01:04:04.559 --> 01:04:07.210
we want. We could practically
write our names with subs.

809
01:04:11.200 --> 01:04:16.410
Returning to the earlier 'native'
configuration, we still have

810
01:04:16.410 --> 01:04:21.620
two subs, A and B, spaced one
quarter of a wavelength apart...

811
01:04:22.560 --> 01:04:26.022
...with a delay of one quarter
of a period. This is exactly

812
01:04:26.022 --> 01:04:29.660
what we have just seen, regardless
of the numerical values. To

813
01:04:29.660 --> 01:04:33.180
take it a little further, there
is a system called end-fire.

814
01:04:33.360 --> 01:04:39.110
You have probably heard of end-fire.
We take the idea further by

815
01:04:39.110 --> 01:04:45.220
adding another sub, again spaced
one quarter of a wavelength away...

816
01:04:46.400 --> 01:04:51.753
...and adding another quarter-period
delay to the existing delay. That

817
01:04:51.753 --> 01:04:56.800
makes half a period: one quarter
plus one quarter equals one half.

818
01:04:58.140 --> 01:05:03.820
Let's go further and add a fourth
sub, with the same quarter-wavelength

819
01:05:03.820 --> 01:05:09.340
spacing and another quarter-period
delay. That gives us two thirds...

820
01:05:12.300 --> 01:05:16.634
...of a period. We have used four subs,
but we could use 10, 15, 20 or 30. At

821
01:05:16.634 --> 01:05:21.080
some point, installation becomes rather
complicated. He is watching his series.

822
01:05:25.470 --> 01:05:29.733
What is happening in that
series? I do not know, but

823
01:05:29.733 --> 01:05:33.750
he looks exhausted.
Returning to our four subs...

824
01:05:36.320 --> 01:05:41.540
...in the combined circular view, we can
see an effect emerging. I will not go

825
01:05:41.540 --> 01:05:46.760
through the wave representation again,
because that would be too much at once.

826
01:05:47.920 --> 01:05:52.235
At the front of the system, at the
first sub, the phase difference

827
01:05:52.235 --> 01:05:56.093
between all four subs is exactly
0°. At the rear, depending

828
01:05:56.093 --> 01:05:59.820
on the position, we get
cancellation, some subtraction...

829
01:05:59.920 --> 01:06:03.417
...or some addition. It is
difficult to visualise, but the key

830
01:06:03.417 --> 01:06:07.140
point is that we drive the signal
very strongly towards the front.

831
01:06:07.440 --> 01:06:12.415
This is still a 'native' configuration.
All the subs are in phase. 'Sorry,

832
01:06:12.415 --> 01:06:16.920
Mathieu, are they each offset by
one quarter of a period?' Exactly.

833
01:06:17.140 --> 01:06:22.456
Let me go back to the
diagram. They are all spaced

834
01:06:22.456 --> 01:06:27.560
one quarter of a wavelength
apart, and we add...

835
01:06:27.560 --> 01:06:29.740
...one quarter of a period.

836
01:06:32.650 --> 01:06:35.129
Each step is linear: we
advance by one quarter

837
01:06:35.129 --> 01:06:37.230
of the period at this centre frequency.

838
01:06:39.390 --> 01:06:43.638
Let's put numbers on it and
look at the result, using 85 Hz.

839
01:06:43.638 --> 01:06:48.170
Remember, 85 Hz is convenient
because it gives a spacing of 1 m.

840
01:06:49.810 --> 01:06:54.694
Each time, we use another quarter
wavelength and add another quarter

841
01:06:54.694 --> 01:06:59.650
period. The final sub is starting
to reach a delay of 8 milliseconds.

842
01:06:59.910 --> 01:07:03.664
The simulation shows considerably
less output at the rear

843
01:07:03.664 --> 01:07:07.550
and a signal that is pushed
increasingly towards the front.

844
01:07:08.030 --> 01:07:11.197
We still have a cardioid,
as before, but with much

845
01:07:11.197 --> 01:07:14.870
stronger, more forceful output
towards the front. However,

846
01:07:14.870 --> 01:07:18.290
the line is quite long: here
it occupies 4 m in total.

847
01:07:19.510 --> 01:07:22.960
If we change the frequency...
Actually, this example stays at 85 Hz;

848
01:07:22.960 --> 01:07:26.562
sorry. If I lowered the design
frequency, the pattern would become more

849
01:07:26.562 --> 01:07:29.910
stable at lower frequencies, but
it would require more and more...

850
01:07:29.910 --> 01:07:30.270
...space.

851
01:07:32.720 --> 01:07:36.134
Do not try to memorise all
this end-fire detail; it will

852
01:07:36.134 --> 01:07:39.671
give you a headache. We have
just seen a standard end-fire

853
01:07:39.671 --> 01:07:42.780
array with four subs and
a single centre frequency.

854
01:07:43.560 --> 01:07:47.423
We can take it further. Working
at 85 Hz is useful, but I may also

855
01:07:47.423 --> 01:07:51.520
want cancellation at several other
frequencies, both lower and higher.

856
01:07:52.060 --> 01:07:55.676
It is frustrating to have just
one frequency working well.

857
01:07:55.676 --> 01:07:59.480
Some clever people thought:
'What if we made it logarithmic?'

858
01:08:01.520 --> 01:08:05.477
Instead of one frequency, we use
three frequencies offset from

859
01:08:05.477 --> 01:08:08.923
one another. This gets
complicated, so keep it in your

860
01:08:08.923 --> 01:08:12.880
reference collection rather than
learning everything by heart.

861
01:08:13.420 --> 01:08:16.309
For the first spacing, we use
one quarter of the wavelength at

862
01:08:16.309 --> 01:08:19.244
the first frequency. For the
second spacing, one quarter of the

863
01:08:19.244 --> 01:08:22.180
wavelength at the second frequency,
and likewise for the third.

864
01:08:22.860 --> 01:08:28.816
We do the same with the period at each
stage. The result is quite intricate.

865
01:08:28.816 --> 01:08:34.380
For a numerical example, I choose
three frequencies: 100, 85 and 60 Hz.

866
01:08:35.480 --> 01:08:38.834
These give wavelengths of
around 3 m, 4 m and 5.60 m, and

867
01:08:38.834 --> 01:08:42.247
so on. Applying the numerical
values, you can see that the

868
01:08:42.247 --> 01:08:45.660
subs become progressively
farther apart along the array...

869
01:08:46.760 --> 01:08:52.484
...with increasing delays as we move
along it. This is no longer linear at

870
01:08:52.484 --> 01:08:58.440
all. Let's look at the measurements; we
will compare the versions afterwards.

871
01:08:59.140 --> 01:09:01.740
Here the result becomes more
stable across all the frequencies.

872
01:09:04.700 --> 01:09:10.757
Many end-fire arrays use this
approach. The spacing between

873
01:09:10.757 --> 01:09:16.300
the subs is not uniform. In
effect, we have created...

874
01:09:17.900 --> 01:09:21.751
...a 'native' pair here, another here
and another here, all interacting.

875
01:09:21.751 --> 01:09:24.960
There is also another 'native'
relationship between A and C.

876
01:09:26.680 --> 01:09:30.266
A second technique adds a
further 90° phase rotation to

877
01:09:30.266 --> 01:09:33.983
these three frequencies, to
improve the result at 125 Hz.

878
01:09:33.983 --> 01:09:37.700
This is for subs intended to
project over long distances.

879
01:09:38.420 --> 01:09:43.712
I add another phase rotation
based on the wavelength at 125 Hz.

880
01:09:43.712 --> 01:09:49.340
This gets very complicated. We keep
the same distances as before...

881
01:09:50.160 --> 01:09:54.217
...but add a further 90° rotation at 125 Hz

882
01:09:54.217 --> 01:09:58.180
to the delay values. That adds more delay.

883
01:10:00.550 --> 01:10:04.759
Here is the result: something extremely
stable across almost the entire

884
01:10:04.759 --> 01:10:08.730
frequency band. At 125 Hz, notice
the strong diagonal cancellation.

885
01:10:09.130 --> 01:10:14.051
It is almost hypercardioid. Yes? 'When
you say rotation, do you mean physically

886
01:10:14.051 --> 01:10:18.910
turning the subs?' No, the phase rotation
is produced entirely through timing.

887
01:10:19.510 --> 01:10:23.753
A delay puts me at a different
point on the signal's phase circle.

888
01:10:23.753 --> 01:10:27.610
'So you add delay?' Yes, I add
delay. The only difference...

889
01:10:27.610 --> 01:10:32.466
'How much delay here?' Look: these
were the original delays in the

890
01:10:32.466 --> 01:10:37.470
first end-fire array, using my three
frequencies, 100, 85 and 60 Hz.

891
01:10:38.430 --> 01:10:44.490
I added one quarter at 125 Hz, one quarter
of λ at 125 Hz: 0.6 milliseconds; then

892
01:10:44.490 --> 01:10:50.250
one half, one quarter plus one quarter,
and... This should be one third here.

893
01:10:50.330 --> 01:10:56.134
That is an error: it should say
one third here. That makes 2.3. In

894
01:10:56.134 --> 01:11:01.850
effect, I add a phase offset at
125 Hz: another 90° at each step.

895
01:11:02.110 --> 01:11:08.018
I have added those to the
values above, and that is what

896
01:11:08.018 --> 01:11:13.610
produces this directivity.
Let's look at it together.

897
01:11:14.830 --> 01:11:19.850
'Mathieu?' Yes? 'Is this what is
used for ArrayProcessing?' No,

898
01:11:19.850 --> 01:11:24.790
ArrayProcessing is something
else. 'Like at d&b, for example?'

899
01:11:25.130 --> 01:11:28.540
Yes, but ArrayProcessing
is another subject. They

900
01:11:28.540 --> 01:11:31.810
use techniques like these
to increase coverage.

901
01:11:32.250 --> 01:11:34.990
'But is this the kind of thing
done in ArrayProcessing?'

902
01:11:37.990 --> 01:11:39.509
It also involves frequency
correction, which is

903
01:11:39.509 --> 01:11:41.190
another matter. It is better
not to confuse the two.

904
01:11:43.540 --> 01:11:46.643
In any case, this Log 2 end-fire
array is probably the most

905
01:11:46.643 --> 01:11:49.747
complicated. I used it quite
often when I had enough space.

906
01:11:49.747 --> 01:11:52.640
The person who developed it
is called Mauricio Ramirez.

907
01:11:52.820 --> 01:11:53.400
He is Mexican.

908
01:11:55.280 --> 01:11:58.635
He is known as Mago. His ideas are
intricate, and he has developed many

909
01:11:58.635 --> 01:12:02.320
techniques like this. He teaches and has
close links with Meyer, among others.

910
01:12:02.740 --> 01:12:03.965
That is just a little background, so I do

911
01:12:03.965 --> 01:12:05.160
not take credit for someone else's work.

912
01:12:09.360 --> 01:12:12.693
Here are the three end-fire
types, still using four subs:

913
01:12:12.693 --> 01:12:16.144
standard end-fire, Log 1
end-fire, and logarithmic end-fire

914
01:12:16.144 --> 01:12:19.360
with a 90° phase rotation.
You can see the progression.

915
01:12:19.840 --> 01:12:24.410
I would not say one is better than the
others. Depending on the application,

916
01:12:24.410 --> 01:12:29.040
we want different results. Look at 125
Hz, for example, which is fairly high.

917
01:12:29.240 --> 01:12:34.859
Cancellation is quite good in the first
version. However, although it is hard

918
01:12:34.859 --> 01:12:40.260
to see here, the last version has
greater reach. Cancellation is weaker...

919
01:12:40.700 --> 01:12:44.708
...at the rear of the
logarithmic versions, at least at

920
01:12:44.708 --> 01:12:48.498
31 Hz, but they also have
better reach. Every system

921
01:12:48.498 --> 01:12:52.360
has advantages and disadvantages.
I have shown you...

922
01:12:52.360 --> 01:12:56.207
...three examples, but there
are many others. It is up

923
01:12:56.207 --> 01:13:00.267
to you to research and experiment
to find what best suits

924
01:13:00.267 --> 01:13:03.900
the venue. These were all
systems in 'native' mode.

925
01:13:04.360 --> 01:13:07.305
So far, we have only covered
'native' systems. Are there any

926
01:13:07.305 --> 01:13:10.300
questions, or is it reasonably
clear? 'Could you put back...'

927
01:13:12.800 --> 01:13:16.187
'...the Log 2 slide? I just
want to look at the values.'

928
01:13:16.187 --> 01:13:19.272
Yes, Log 2 is complicated.
'So, in Log 2, the phase

929
01:13:19.272 --> 01:13:22.780
rotation must be at 125 Hz
rather than another frequency?'

930
01:13:23.240 --> 01:13:28.540
'Is that fixed?' Let me bring
back the previous slide. I have

931
01:13:28.540 --> 01:13:33.580
just noticed an error on Log
2 as well. This value here...

932
01:13:33.580 --> 01:13:35.300
'It is one third, right?' One third.

933
01:13:37.860 --> 01:13:43.085
With Log 2, let me get the
laser pointer, we still have an

934
01:13:43.085 --> 01:13:48.580
initial phase rotation here for
100 Hz, because we have 85...

935
01:13:48.580 --> 01:13:53.916
...a distance of 85 cm and a
time of 1.8. Here we still have

936
01:13:53.916 --> 01:13:59.340
the phase rotation for 85 Hz,
and here another one for 60 Hz.

937
01:13:59.840 --> 01:14:06.043
Using the appropriate values. But
we add another quarter wavelength

938
01:14:06.043 --> 01:14:11.320
at 125 Hz to that delay. 'Why
125?' Because it is 125 Hz.

939
01:14:13.100 --> 01:14:16.990
'Yes, but why 125 Hz?' Because I
chose it; it could be something

940
01:14:16.990 --> 01:14:20.940
else. 'Ah, so you could choose a
different frequency?' Of course.

941
01:14:20.940 --> 01:14:24.540
'So it is not fixed?' No. It
is just the numerical example I

942
01:14:24.540 --> 01:14:28.200
chose. You can place this phase
rotation wherever you want...

943
01:14:28.320 --> 01:14:31.800
...at whichever frequency you
want. And that does change...

944
01:14:34.100 --> 01:14:39.282
...your coverage and directivity.
'What makes you choose 125 rather than

945
01:14:39.282 --> 01:14:44.680
something else?' Because I felt like
it! 'Well, that was the wrong choice!'

946
01:14:45.200 --> 01:14:49.055
Perhaps, but it is a choice.
This example comes from Mauricio

947
01:14:49.055 --> 01:14:52.720
Ramirez, who used 125 Hz. We
could do it at 110 or 111 Hz.

948
01:14:52.800 --> 01:14:57.266
I would simply take one quarter
of the wavelength at 120 Hz. 'But

949
01:14:57.266 --> 01:15:01.800
why choose such a high frequency?
A sub does not go up to 120 Hz.'

950
01:15:01.900 --> 01:15:06.470
'Why apply this phase rotation at
such a high frequency?' That is

951
01:15:06.470 --> 01:15:11.180
where it gets more complex. We
always say a sub goes up to 80 Hz...

952
01:15:11.800 --> 01:15:15.285
...but actually, the crossover
starts at 80 Hz. At 80 Hz, we

953
01:15:15.285 --> 01:15:18.713
generally have 3 dB of attenuation,
followed by a roll-off.

954
01:15:18.713 --> 01:15:22.140
There is still sound at 125
Hz: quieter, but still present.

955
01:15:22.820 --> 01:15:26.338
We also want to control
that. Sometimes we create

956
01:15:26.338 --> 01:15:30.216
cancellation or subtraction
at 125 Hz, fairly high for

957
01:15:30.216 --> 01:15:34.380
subs, to attenuate or reinforce
those frequencies as well.

958
01:15:35.420 --> 01:15:40.040
That is the general idea.
Many subs still produce

959
01:15:40.040 --> 01:15:44.660
sound at 125 Hz; plenty
of them extend that high.

960
01:15:46.360 --> 01:15:51.580
The responses often overlap. 'The
Fohhn sub even goes up to 300 or

961
01:15:51.580 --> 01:15:56.800
400 Hz.' That is something else.
That is not a sub; it is rubbish.

962
01:15:57.260 --> 01:16:01.415
It is a low-mid speaker. It is
pointless. Anyway, Log 2 end-fire

963
01:16:01.415 --> 01:16:05.375
with its 90° rotation is very
complicated; I would not try to

964
01:16:05.375 --> 01:16:09.140
memorise it. 'But it seems to
be the one that works best.'

965
01:16:09.420 --> 01:16:13.614
It works well, depending on
what you are trying to achieve.

966
01:16:13.614 --> 01:16:17.880
Very often, we stop at a 'native'
configuration. 'At Log 1?'

967
01:16:17.880 --> 01:16:22.926
No, a 'native' configuration with
two loudspeakers. You need quite

968
01:16:22.926 --> 01:16:27.820
a lot of space for four. 'But
does Log 2 take up less than 4 m?'

969
01:16:27.820 --> 01:16:31.092
Yes, it is a little shorter.
With 1.4 m plus 1 m and the

970
01:16:31.092 --> 01:16:34.305
other spacing, we are at
three metres and something. It

971
01:16:34.305 --> 01:16:37.460
is not much less; it still
takes up substantial space.

972
01:16:38.120 --> 01:16:39.360
Yes, it is still fairly large.

973
01:16:42.080 --> 01:16:45.616
Let's move to the second
type: pressure-gradient

974
01:16:45.616 --> 01:16:49.594
configurations. Remember the
'native' configuration: a

975
01:16:49.594 --> 01:16:53.940
quarter-wavelength spacing and
a quarter-period delay on B.

976
01:16:55.760 --> 01:17:01.620
Now we invert the polarity of the
rear sub. A changes from +A to

977
01:17:01.620 --> 01:17:07.480
−A. Instead of producing compression,
it produces rarefaction...

978
01:17:07.480 --> 01:17:11.060
...and vice versa. Sub B continues
operating in the original direction.

979
01:17:13.020 --> 01:17:18.704
We still space them one quarter of a
wavelength apart. The distance and the

980
01:17:18.704 --> 01:17:24.540
space occupied are exactly the same.
This time, however, we apply no delay...

981
01:17:24.540 --> 01:17:29.089
...to sub B. We delay sub A
instead. Earlier we delayed

982
01:17:29.089 --> 01:17:33.720
B; now we delay A, whose
polarity we have also inverted.

983
01:17:34.060 --> 01:17:38.072
That makes all the difference.
Let's visualise what happens.

984
01:17:38.072 --> 01:17:41.950
This time I will only use the
wave representation and skip

985
01:17:41.950 --> 01:17:45.560
the circular view. Our
listener is still at the front.

986
01:17:46.360 --> 01:17:52.280
Here is the wave from sub B. Before
applying any electronic delay, we have

987
01:17:52.280 --> 01:17:58.120
only the spatial offset of one quarter
wavelength. Sub A also radiates...

988
01:17:58.200 --> 01:18:04.322
...but with inverted polarity: when
B produces compression, A produces

989
01:18:04.322 --> 01:18:09.920
rarefaction. We now delay sub A,
and its wave moves backwards...

990
01:18:10.480 --> 01:18:16.260
...by another quarter wavelength.
Summation is again at 0°, at

991
01:18:16.260 --> 01:18:22.320
this centre frequency, since
everything depends on the spacing...

992
01:18:22.320 --> 01:18:27.528
...and the Δt chosen at
the start. Just as before,

993
01:18:27.528 --> 01:18:32.320
we have achieved +6 dB
summation at the front.

994
01:18:33.980 --> 01:18:39.688
Now let's go behind the system.
Sub B produces compression followed

995
01:18:39.688 --> 01:18:45.140
by rarefaction. Sub A does the
same, but with inverted polarity.

996
01:18:45.860 --> 01:18:51.547
It produces rarefaction
followed by compression. As we

997
01:18:51.547 --> 01:18:57.760
delay it, it moves virtually
onto B. We can see its wave...

998
01:18:57.760 --> 01:19:01.485
...move backwards by that
quarter wavelength. What

999
01:19:01.485 --> 01:19:05.211
happens? We again get a
180° difference where they

1000
01:19:05.211 --> 01:19:09.160
overlap, and the result is
once again minus infinity.

1001
01:19:10.160 --> 01:19:14.483
It seems that we have done exactly
the same thing, so why choose one

1002
01:19:14.483 --> 01:19:19.060
method over the other? There is a
very important difference. Here it is.

1003
01:19:20.360 --> 01:19:23.761
In the combined view, we see the
front and rear together. Imagine a

1004
01:19:23.761 --> 01:19:27.060
dividing line between them, because
they are two different views.

1005
01:19:28.500 --> 01:19:33.261
The frequency equals the centre
frequency: the ideal case. At the front

1006
01:19:33.261 --> 01:19:37.820
we have 0°, perfect summation and
+6 dB. At the rear we have 180°...

1007
01:19:37.980 --> 01:19:43.040
...and perfect cancellation, minus
infinity. If I increase the frequency...

1008
01:19:45.650 --> 01:19:49.757
...what happens? The waves start
shifting relative to one another

1009
01:19:49.757 --> 01:19:53.739
at the front, but at the rear
they remain 180° apart. The phase

1010
01:19:53.739 --> 01:19:57.530
difference at the front no
longer stays at 0°; it changes...

1011
01:19:57.530 --> 01:20:03.488
...with frequency. At the rear,
however, it remains extremely stable

1012
01:20:03.488 --> 01:20:09.270
at 180°. The rear phase difference
does not change with frequency.

1013
01:20:10.630 --> 01:20:16.225
What happens if I lower the
frequency? Once again, the

1014
01:20:16.225 --> 01:20:22.130
phase difference at the rear
has not moved. It remains...

1015
01:20:22.130 --> 01:20:26.200
...at 180°, giving strong cancellation.
At the front, we no longer

1016
01:20:26.200 --> 01:20:30.147
have the 0° relationship we had
at the centre frequency. We have

1017
01:20:30.147 --> 01:20:33.970
moved away from that summation
point. In fact, this behaves...

1018
01:20:33.970 --> 01:20:38.027
...in exactly the opposite way to what
we saw earlier. Previously, the front

1019
01:20:38.027 --> 01:20:42.190
was extremely stable, with perfect
summation, while the rear tended to change.

1020
01:20:42.870 --> 01:20:46.705
Now it is the reverse: the
front changes, while the

1021
01:20:46.705 --> 01:20:50.390
rear stays the same. That
is the main difference.

1022
01:20:52.370 --> 01:20:57.400
Let's look at some numbers.
With a centre frequency of

1023
01:20:57.400 --> 01:21:02.150
100 Hz, we again use our
quarter wavelength: 85 cm.

1024
01:21:02.370 --> 01:21:07.760
One quarter of the period at 100
Hz is 2.5 milliseconds. Looking at

1025
01:21:07.760 --> 01:21:13.230
31 Hz, we get output at the front
and virtually nothing at the rear.

1026
01:21:14.670 --> 01:21:17.458
At 63 Hz, there is very little,
practically nothing, behind the

1027
01:21:17.458 --> 01:21:20.422
system, and a very good result at
the front. At 125 Hz, the forward

1028
01:21:20.422 --> 01:21:23.210
output increases slightly, with
still virtually nothing behind.

1029
01:21:23.730 --> 01:21:27.202
Comparing these, the important point
is that the rear remains extremely

1030
01:21:27.202 --> 01:21:30.430
stable with frequency. There is
never any sound behind the system.

1031
01:21:30.970 --> 01:21:36.587
We are always at 180°, at every
frequency. 'That is what we did at

1032
01:21:36.587 --> 01:21:42.290
the Trans.' Yes, exactly. However,
the front behaves differently...

1033
01:21:42.290 --> 01:21:46.576
...at different frequencies. The response
at 125 Hz differs from 63 Hz and 31

1034
01:21:46.576 --> 01:21:51.030
Hz. It is easier to see at 31 Hz: the
circle is slightly smaller than at 125 Hz.

1035
01:21:51.710 --> 01:21:57.371
So the rear is very stable, and the front
less stable. Let's change the design

1036
01:21:57.371 --> 01:22:03.250
frequency to 85 Hz. As we go lower, the
spacing increases, the delay increases...

1037
01:22:03.330 --> 01:22:08.086
...everything increases. Here is the
85 Hz configuration. At 31 Hz, we

1038
01:22:08.086 --> 01:22:12.910
still have very good cancellation,
with a slightly blob-shaped pattern.

1039
01:22:13.070 --> 01:22:16.407
It is also blob-shaped here, and
at 125 Hz it is really cardioid.

1040
01:22:16.407 --> 01:22:19.384
The cardioid design point was
actually between them, at 85

1041
01:22:19.384 --> 01:22:22.310
Hz. Another spacing I like,
which we used at the Trans...

1042
01:22:23.470 --> 01:22:28.823
...is 1.42 m. That targets 60 Hz, again
matching the kick as usual. Julie, earlier

1043
01:22:28.823 --> 01:22:33.850
you said we did not care about 35 Hz.
In this particular case, that was true.

1044
01:22:34.090 --> 01:22:36.983
Look what happens at 35 Hz
with a 1.42 m spacing. A lot

1045
01:22:36.983 --> 01:22:39.824
of sound starts going to the
sides, and we lose output

1046
01:22:39.824 --> 01:22:42.770
behind. This system is not
particularly efficient there.

1047
01:22:43.370 --> 01:22:47.055
In the plot below, however, it works
very well. At 60 Hz, there is nothing

1048
01:22:47.055 --> 01:22:50.790
behind: no sound. If the kick is at 60
Hz, there really is no sound behind.

1049
01:22:51.230 --> 01:22:56.610
In any case, that rear cancellation
remains extremely stable

1050
01:22:56.610 --> 01:23:01.990
throughout the spectrum. Let's
compare these three spacings.

1051
01:23:02.790 --> 01:23:08.460
We have 0.85 m, 1 m and 1.42 m,
corresponding to 100 Hz, 85 Hz and 60

1052
01:23:08.460 --> 01:23:14.130
Hz. Looking behind, we get almost
the same result at any frequency...

1053
01:23:14.130 --> 01:23:18.201
...with any spacing. What are we
trying to achieve with a gradient

1054
01:23:18.201 --> 01:23:22.210
array? We want no sound behind
it, and this works extremely well.

1055
01:23:22.950 --> 01:23:27.985
At the front, however, we should
expect a less optimal result than with

1056
01:23:27.985 --> 01:23:33.090
the 'native' configuration, because
the response changes with frequency.

1057
01:23:34.310 --> 01:23:37.073
Those are two methods,
each with advantages and

1058
01:23:37.073 --> 01:23:40.130
disadvantages, depending
on what we want to achieve.

1059
01:23:42.770 --> 01:23:46.894
An interesting point with this
pressure-gradient array, and we could also

1060
01:23:46.894 --> 01:23:50.792
do it with a 'native' array, is to
return to the 85 Hz example: a 4 m

1061
01:23:50.792 --> 01:23:54.690
wavelength and its corresponding
period. Here is the configuration...

1062
01:23:54.690 --> 01:23:58.671
...we called cardioid,
although it is actually a

1063
01:23:58.671 --> 01:24:03.150
little subcardioid here.
This is the pattern at 63 Hz.

1064
01:24:05.210 --> 01:24:10.632
If we change only Δt, moving A
virtually farther backwards, the

1065
01:24:10.632 --> 01:24:16.570
result tends towards subcardioid.
It is difficult to see here, but...

1066
01:24:16.910 --> 01:24:20.784
...it opens up a little more
at the rear. Reducing the delay

1067
01:24:20.784 --> 01:24:24.465
instead moves us towards
hypercardioid. Starting with our

1068
01:24:24.465 --> 01:24:28.210
centre frequency and the values
we carefully calculated...

1069
01:24:28.250 --> 01:24:33.389
...one quarter of a period and
one quarter of a wavelength, if I

1070
01:24:33.389 --> 01:24:39.010
shorten the time offset, to one
eighth, one sixth or whatever value...

1071
01:24:39.390 --> 01:24:43.093
...I move towards hypercardioid.
Increasing it moves

1072
01:24:43.093 --> 01:24:47.223
towards subcardioid. So, at a
fixed spacing, starting from

1073
01:24:47.223 --> 01:24:51.210
an accurately calculated
delay, I can vary that delay...

1074
01:24:51.270 --> 01:24:56.914
...to change the system's coverage.
Imagine that I have created a perfect

1075
01:24:56.914 --> 01:25:02.790
cardioid with a 1 m spacing and a delay
of 2.94 milliseconds. My audience...

1076
01:25:02.790 --> 01:25:06.544
...is here, my performer is
there, and the performer hears too

1077
01:25:06.544 --> 01:25:10.418
much sub. Without moving or turning
down the subs, I may be able

1078
01:25:10.418 --> 01:25:13.990
to reduce the delay and keep
the sound away from my singer.

1079
01:25:14.830 --> 01:25:20.721
That allows me to shape directivity
using delays alone. A few clicks, and

1080
01:25:20.721 --> 01:25:26.290
there is no more sub on stage. As
Tanguy said, that is what we did...

1081
01:25:26.290 --> 01:25:28.850
...at the Trans. You can
see it here... You rascal!

1082
01:25:31.450 --> 01:25:35.589
You can see the word 'gradient'.
Here are two cabinets at

1083
01:25:35.589 --> 01:25:39.654
the front, with another behind
them, roughly 1.42 metres

1084
01:25:39.654 --> 01:25:43.430
apart. This one has inverted
polarity and a delay...

1085
01:25:43.430 --> 01:25:47.430
...of 4.12 milliseconds,
since we are working at 60 Hz.

1086
01:25:49.650 --> 01:25:52.701
Any questions about these
two modes, gradient and

1087
01:25:52.701 --> 01:25:55.690
'native'? Are we all
right? We have lost Romain.

1088
01:25:58.430 --> 01:26:04.136
It seems clear. 'Sorry, with
pressure gradients, can you also use

1089
01:26:04.136 --> 01:26:09.930
those logarithmic techniques?'
Yes, we can make end-fire arrays...

1090
01:26:09.930 --> 01:26:13.782
...using pressure gradients, but
that is more complicated, so I have

1091
01:26:13.782 --> 01:26:17.351
not included it here. 'But it
exists?' Yes. We can line up four

1092
01:26:17.351 --> 01:26:21.090
subs like this and calculate the
settings for an end-fire array...

1093
01:26:21.090 --> 01:26:23.903
...and also vary it
logarithmically. That gets extremely

1094
01:26:23.903 --> 01:26:26.866
involved, so I would rather
skip it here. Julie, if you are

1095
01:26:26.866 --> 01:26:29.930
interested, I can make some
simulations and send them to you.

1096
01:26:30.070 --> 01:26:36.445
No problem. 'Wait, would it be more
effective than a normal pressure-gradient

1097
01:26:36.445 --> 01:26:41.910
array?' The more subs you add, and
the longer the end-fire line...

1098
01:26:41.910 --> 01:26:45.988
...the more effective it
becomes. A long pressure-gradient

1099
01:26:45.988 --> 01:26:49.573
line means you want even
more rear isolation than a

1100
01:26:49.573 --> 01:26:53.510
single pair, which already
provides very good isolation.

1101
01:26:54.810 --> 01:26:59.044
Pressure gradients are
often used where space

1102
01:26:59.044 --> 01:27:03.090
is limited and we want excellent isolation.

1103
01:27:04.430 --> 01:27:10.242
'Mathieu, in your previous
diagram, does hypercardioid mode

1104
01:27:10.242 --> 01:27:16.250
give better isolation on stage?
I am missing something here.'

1105
01:27:16.350 --> 01:27:22.008
Look: if the stage is behind, then
no, it does not. If it is at the

1106
01:27:22.008 --> 01:27:27.750
side, however... My singer is here,
and is happier in this position.

1107
01:27:28.430 --> 01:27:33.839
'I understand. I thought you meant
behind.' There is a good 20 dB

1108
01:27:33.839 --> 01:27:39.830
between the dark blue and the sky
blue; light blue and dark blue, sorry.

1109
01:27:40.050 --> 01:27:44.910
I am not very good with colours.
'No, it is a song.' Never

1110
01:27:44.910 --> 01:27:50.190
mind. That is my France Bleu side
coming out. 'I can see that.'

1111
01:27:50.470 --> 01:27:53.730
Romain is back. So, that is
our pressure-gradient array.

1112
01:27:55.530 --> 01:27:58.959
Now we will look at other configurations.
This will go much faster; we have

1113
01:27:58.959 --> 01:28:02.570
done the hardest part. I do not know how
long I have been talking. It is 4 p.m.

1114
01:28:04.930 --> 01:28:10.411
We will look at a common arrangement:
horizontal or vertical inverted gradient

1115
01:28:10.411 --> 01:28:15.330
stacks. You have often seen a group
of subs with one facing backwards.

1116
01:28:16.870 --> 01:28:20.467
Besides facing backwards, that sub
usually has inverted polarity. We

1117
01:28:20.467 --> 01:28:24.170
can build this ourselves, although
we often simply load the presets...

1118
01:28:24.430 --> 01:28:30.028
...and the manufacturer has already
done the work. 'What do you mean,

1119
01:28:30.028 --> 01:28:35.950
facing backwards? Did we not say subs
were more or less omnidirectional?'

1120
01:28:35.950 --> 01:28:40.956
Turning it around does change things.
It is a little like placing the subs

1121
01:28:40.956 --> 01:28:46.030
face to face, as I showed earlier when
discussing omnidirectional patterns.

1122
01:28:46.990 --> 01:28:51.862
It makes the system more perfectly
omnidirectional, making the calculations

1123
01:28:51.862 --> 01:28:56.150
and delay settings easier. It makes
the behaviour more consistent.

1124
01:28:56.790 --> 01:28:57.850
That is why the sub faces backwards.

1125
01:29:00.160 --> 01:29:06.236
We could leave it facing forwards, but
turning it around is a way of obtaining

1126
01:29:06.236 --> 01:29:12.000
the desired basic shape. If I apply
no processing to that sub, not even...

1127
01:29:13.180 --> 01:29:15.878
...a polarity inversion,
it produces a completely

1128
01:29:15.878 --> 01:29:18.741
omnidirectional pattern.
Remember what we saw at the

1129
01:29:18.741 --> 01:29:22.100
beginning: individual subs are
not perfectly omnidirectional.

1130
01:29:22.360 --> 01:29:27.322
So it faces backwards to improve the
basic coverage. However, the aim of a

1131
01:29:27.322 --> 01:29:32.620
horizontal inverted gradient stack is
not to create an omnidirectional pattern.

1132
01:29:33.840 --> 01:29:39.993
We want a directional, cardioid
pattern. In gradient mode, we therefore

1133
01:29:39.993 --> 01:29:45.800
invert its polarity, as before.
Here are some approximate values...

1134
01:29:45.800 --> 01:29:51.266
...because the settings are always
approximate when the subs are in a single

1135
01:29:51.266 --> 01:29:56.660
line. To target 85 Hz, here are the
values. We apply no Δt to the A subs...

1136
01:29:56.940 --> 01:30:02.263
...and a Δt of about 3.97 milliseconds
to the other sub. That creates a

1137
01:30:02.263 --> 01:30:07.960
roughly directional system like this.
You may ask where 3.97 milliseconds...

1138
01:30:08.020 --> 01:30:12.914
...came from. Earlier I said that one
quarter wavelength at 85 Hz corresponded

1139
01:30:12.914 --> 01:30:17.620
to 2.94 milliseconds. Yes, but that
was with the subs one behind the other.

1140
01:30:17.840 --> 01:30:20.376
We also had a quarter-wavelength
spacing. Here the aim

1141
01:30:20.376 --> 01:30:23.099
is to bring everything together,
or arrange it vertically,

1142
01:30:23.099 --> 01:30:25.400
to save space. Saving
space is the whole purpose.

1143
01:30:25.700 --> 01:30:30.761
It is about saving space rather than
improving the sound. Broadly, 3.97

1144
01:30:30.761 --> 01:30:35.680
comes from one quarter wavelength,
2.94, plus one third of that 2.94.

1145
01:30:36.100 --> 01:30:39.943
Why one third? Normally, if it were
one quarter farther away, we would add

1146
01:30:39.943 --> 01:30:43.629
another quarter. But because it is
directly above, that would not work.

1147
01:30:43.629 --> 01:30:47.420
Adding one quarter plus one quarter
would put it completely out of phase.

1148
01:30:47.540 --> 01:30:52.746
That would cause problems. So it is an
approximate compromise between a quarter

1149
01:30:52.746 --> 01:30:57.820
and a third, choosing something in
between. The result works reasonably well.

1150
01:30:58.000 --> 01:31:02.282
It is a compromise, not a
perfect solution. We can adjust

1151
01:31:02.282 --> 01:31:06.640
that time, which slightly
changes the pattern shown below.

1152
01:31:07.280 --> 01:31:11.324
When we take unfamiliar subs,
any available model, stack them,

1153
01:31:11.324 --> 01:31:15.107
and try to create a gradient
arrangement in a single line,

1154
01:31:15.107 --> 01:31:19.020
we use approximate parameters
based on a centre frequency...

1155
01:31:19.020 --> 01:31:22.220
...and add a quarter plus a
third. It works reasonably

1156
01:31:22.220 --> 01:31:25.598
well, but is not perfect. This
is the horizontal gradient

1157
01:31:25.598 --> 01:31:28.620
stack; imagine that we are
looking down from above.

1158
01:31:29.020 --> 01:31:32.640
For example, in front of the
stage, we place three subs side

1159
01:31:32.640 --> 01:31:36.260
by side on the floor, in the
middle, in front of the singer.

1160
01:31:38.600 --> 01:31:44.170
'Wait, I thought it was horizontal.
Was it vertical?' No, this one is

1161
01:31:44.170 --> 01:31:49.740
horizontal. The subs sit like this,
and I turn the centre sub around.

1162
01:31:50.580 --> 01:31:55.429
That pushes the sound forwards. If
I put it at the side, as we will

1163
01:31:55.429 --> 01:32:00.060
see shortly, the sound goes
sideways. Imagine the stage is here.

1164
01:32:00.260 --> 01:32:05.226
'We thought they were stacked.' Here
they are next to one another, on

1165
01:32:05.226 --> 01:32:10.120
the floor. With three like this,
they are often placed side by side.

1166
01:32:10.660 --> 01:32:13.529
We could also stack them;
that would work too. You can

1167
01:32:13.529 --> 01:32:16.664
picture either arrangement. We
often see this configuration

1168
01:32:16.664 --> 01:32:19.320
laid out on the floor, but
both arrangements work.

1169
01:32:19.480 --> 01:32:24.280
Stacking them one above another
works, as we will see next. 'Math, is

1170
01:32:24.280 --> 01:32:29.220
the reason for having three that it
makes the arrangement symmetrical?'

1171
01:32:29.980 --> 01:32:34.810
Exactly. 'Otherwise it goes to the
side?' Exactly. If B were moved

1172
01:32:34.810 --> 01:32:39.420
here, the wave would go sideways
like this. That can be useful.

1173
01:32:39.740 --> 01:32:44.007
We sometimes use it, but here I
want the wave to travel straight

1174
01:32:44.007 --> 01:32:48.140
forwards. The sideways arrangement
does exist and can be used.

1175
01:32:50.080 --> 01:32:52.300
Let's imagine that this is the ground.

1176
01:32:54.400 --> 01:32:58.142
We will do the same with four
subs. I call this a vertical

1177
01:32:58.142 --> 01:33:01.820
arrangement. This time, we
turn the bottom sub around and

1178
01:33:01.820 --> 01:33:05.240
invert its polarity. This
is the most common version.

1179
01:33:05.860 --> 01:33:09.820
Many d&b and L-Acoustics
configurations use this arrangement.

1180
01:33:12.280 --> 01:33:15.730
With four subs, I do exactly the same thing

1181
01:33:15.730 --> 01:33:19.020
as with three, using the same parameters.

1182
01:33:19.380 --> 01:33:25.141
A Δt of 3.97 milliseconds should give
approximately this result, but it

1183
01:33:25.141 --> 01:33:30.820
needs testing. It can also depend
on the sub model and its dimensions.

1184
01:33:30.920 --> 01:33:34.578
Now we will see exactly what
you were asking about, Nico.

1185
01:33:34.578 --> 01:33:38.043
Look at the result: it goes
completely to the side. Do

1186
01:33:38.043 --> 01:33:41.700
you see the pattern we have
created? The sound travels...

1187
01:33:42.900 --> 01:33:44.940
...in the opposite direction to the
sub with inverted polarity and delay.

1188
01:33:47.180 --> 01:33:52.565
Remember that this simulation is in
free field. In practice, the whole

1189
01:33:52.565 --> 01:33:58.720
arrangement is generally placed on the
ground. When we place it on the ground...

1190
01:33:58.820 --> 01:34:04.278
...we can imagine reflected subs
beneath it. The wave reaches the

1191
01:34:04.278 --> 01:34:09.820
ground and is reflected back out:
we get coupling with the ground.

1192
01:34:10.420 --> 01:34:15.718
It is as though we had four mirror-image
subs. This is what we call the mirror

1193
01:34:15.718 --> 01:34:21.220
effect. That is why we put them on the
ground. To simulate that ground placement,

1194
01:34:21.480 --> 01:34:25.790
If my software lets me include the ground,
I add another four subs below it. I

1195
01:34:25.790 --> 01:34:30.100
can attenuate them slightly because, in
reality, the summation is not perfect.

1196
01:34:31.200 --> 01:34:34.556
Once I include that ground
plane, the wavefront straightens

1197
01:34:34.556 --> 01:34:37.799
out completely. We create a
signal that travels forwards.

1198
01:34:37.799 --> 01:34:40.700
This configuration is
extremely common at concerts.

1199
01:34:41.560 --> 01:34:43.869
You see stacks of four
like this, with the bottom

1200
01:34:43.869 --> 01:34:46.320
cabinet reversed. Is that
clear? Does it make sense?

1201
01:34:49.580 --> 01:34:53.538
So I imagine you have that on
either side of a stage? Yes,

1202
01:34:53.538 --> 01:34:57.291
often on the sides, but
sometimes in front of the stage

1203
01:34:57.291 --> 01:35:01.180
too. You can make subwoofer
arcs with systems like these.

1204
01:35:01.980 --> 01:35:04.665
For the steering effect, we
saw lots of subs positioned

1205
01:35:04.665 --> 01:35:07.349
side by side. You can also
put a series of these stacks

1206
01:35:07.349 --> 01:35:10.180
side by side. That is what the
photograph behind me shows.

1207
01:35:17.200 --> 01:35:20.316
Here is another type of inverted
gradient stack, like the one you

1208
01:35:20.316 --> 01:35:23.528
have. I have made a mistake: it
should be the other way round. D is

1209
01:35:23.528 --> 01:35:26.740
underneath and C is above. That is
my fault, a significant mistake.

1210
01:35:27.120 --> 01:35:31.017
I will correct it for you.
Imagine D at the bottom and C

1211
01:35:31.017 --> 01:35:34.843
above it. This is what you
have in this type of system.

1212
01:35:34.843 --> 01:35:38.740
You can place them side by
side, or one above the other.

1213
01:35:38.960 --> 01:35:42.130
Both work, but remember that
when they are side by side,

1214
01:35:42.130 --> 01:35:45.186
the radiation tilts slightly
sideways. Here it travels

1215
01:35:45.186 --> 01:35:47.960
much straighter. Two
systems, two configurations.

1216
01:35:48.680 --> 01:35:50.390
This system, imagining D at the bottom and

1217
01:35:50.390 --> 01:35:52.140
C above it, is what you have in Studio 104.

1218
01:35:54.350 --> 01:35:56.850
The MDCs in 104, on the left and
right: that is this arrangement.

1219
01:36:00.850 --> 01:36:03.921
We have made inverted gradient
stacks of two, three or four,

1220
01:36:03.921 --> 01:36:06.941
however we want. You can imagine
all sorts of arrangements.

1221
01:36:06.941 --> 01:36:09.910
The manufacturers do this for
us. They are helpful people.

1222
01:36:10.130 --> 01:36:13.332
Manufacturers know far more about
their loudspeakers than we do. They

1223
01:36:13.332 --> 01:36:16.302
have measured them precisely.
They know the acoustic centre, the

1224
01:36:16.302 --> 01:36:19.550
dimensions, the volume and the phase
shifts introduced by the filters.

1225
01:36:19.550 --> 01:36:23.128
There are many parameters. I have
demonstrated it rather roughly, just

1226
01:36:23.128 --> 01:36:26.348
adding a delay and a polarity
inversion. Essentially, they sell

1227
01:36:26.348 --> 01:36:30.130
configurations and tell you: place
four subs like this, apply this preset,

1228
01:36:30.610 --> 01:36:33.286
and it works very well. We do
not know what delay is applied to

1229
01:36:33.286 --> 01:36:35.749
the bottom cabinet. We do not
know whether its polarity is

1230
01:36:35.749 --> 01:36:38.510
inverted or normal. Usually, when
you measure it, it is inverted.

1231
01:36:39.910 --> 01:36:43.636
They offer all sorts of
configurations. Here is the familiar

1232
01:36:43.636 --> 01:36:47.052
arrangement from 104: A over
minus B, with a delta T of

1233
01:36:47.052 --> 01:36:50.530
X milliseconds, because we
do not know the actual value.

1234
01:36:50.690 --> 01:36:54.445
It is in the preset, but the
presets are not open. We do not know

1235
01:36:54.445 --> 01:36:58.200
what is inside them. The result
is a directional pattern. Various

1236
01:36:58.200 --> 01:37:02.070
manufacturers do this: JBL, Adamson,
d&b, Nexo, L-Acoustics, Meyer.

1237
01:37:02.750 --> 01:37:06.380
They all do it. Every
manufacturer offers presets like

1238
01:37:06.380 --> 01:37:09.875
these. The commercial appeal
is to sell very compact

1239
01:37:09.875 --> 01:37:14.110
arrangements, stacks that give
you directivity, instead of subs

1240
01:37:14.110 --> 01:37:16.700
placed front to back as in
gradient and end-fire arrays. It is

1241
01:37:16.700 --> 01:37:19.164
never quite as good as gradient
or "native" configurations,

1242
01:37:19.164 --> 01:37:21.670
but it is a useful compromise
between space and directivity.

1243
01:37:23.670 --> 01:37:26.850
Each manufacturer uses its own
parameters. Unless you know

1244
01:37:26.850 --> 01:37:30.250
them well, you cannot know what
they are. One development that

1245
01:37:30.250 --> 01:37:33.430
has changed things considerably
is the use of FIR filters.

1246
01:37:33.430 --> 01:37:38.973
FIR filters are a type of filter with
what we call a linear-phase response.

1247
01:37:38.973 --> 01:37:43.850
Essentially, the phase does not
change with the filters we create.

1248
01:37:44.830 --> 01:37:50.279
With these extremely powerful
filters in their processors, they can

1249
01:37:50.279 --> 01:37:55.890
divide the frequency range from 20
to 100 Hz into four or five bands,

1250
01:37:55.890 --> 01:37:59.289
then apply a different delay
to each band. By giving all

1251
01:37:59.289 --> 01:38:02.992
these bands different delays,
they can make a sub directional

1252
01:38:02.992 --> 01:38:06.270
over a much wider frequency
range than we saw earlier.

1253
01:38:06.670 --> 01:38:10.566
Before, we always had one centre
frequency. Here, they can work with three,

1254
01:38:10.566 --> 01:38:14.514
four, five or six centre frequencies.
Since the filters are linear-phase, we

1255
01:38:14.514 --> 01:38:18.670
create perfect filters that do not damage
the sound or introduce phase rotation,

1256
01:38:18.750 --> 01:38:22.448
then apply a different delay
to each one. Four or five

1257
01:38:22.448 --> 01:38:26.215
different delays are involved.
That is what you have in

1258
01:38:26.215 --> 01:38:30.050
104: an inverted gradient
stack of two with FIR filters,

1259
01:38:30.050 --> 01:38:34.910
which makes the rear attenuation of the
two MDC1s very steep, because it operates

1260
01:38:34.910 --> 01:38:39.230
at several frequencies. An inversion
is built in at several frequencies.

1261
01:38:40.610 --> 01:38:43.610
To understand what they do, always read
the manuals: it is explained there.

1262
01:38:43.610 --> 01:38:46.610
They may not give you the actual values,
but they will explain the concept.

1263
01:38:47.010 --> 01:38:50.010
They explain that the two
MDC1s, with this preset applied

1264
01:38:50.010 --> 01:38:52.853
in the processor, produce
this inverted gradient stack

1265
01:38:52.853 --> 01:38:55.590
with a cardioid pattern
over a wide frequency range.

1266
01:38:57.610 --> 01:39:00.789
Here is an example using KS28s.
It looks a little unusual.

1267
01:39:00.789 --> 01:39:04.077
There are plenty of other
examples. This is a stack with one

1268
01:39:04.077 --> 01:39:07.530
facing backwards, two facing
forwards and one facing backwards.

1269
01:39:08.790 --> 01:39:13.654
You can devise, calculate, test or
simulate these arrangements. They are

1270
01:39:13.654 --> 01:39:18.450
also often documented in the manuals:
do this, and you get that result.

1271
01:39:18.550 --> 01:39:20.650
Do this, and you get that. But
you can always simulate it.

1272
01:39:24.170 --> 01:39:29.150
Any questions, or are we still all
right? We are making good progress.

1273
01:39:31.890 --> 01:39:36.864
Here is a configuration I like, which
relates to what Nadège said earlier: the

1274
01:39:36.864 --> 01:39:41.710
cardioid gradient subwoofer arc. We
will start with a gradient system again.

1275
01:39:42.370 --> 01:39:54.370
A gradient system, as a reminder, is...
I have made a mistake. It is here.

1276
01:39:54.770 --> 01:39:59.180
My mistake. There are always
errors to find. Essentially,

1277
01:39:59.180 --> 01:40:03.590
I take my gradient array.
Ignore that value: it is wrong.

1278
01:40:05.730 --> 01:40:09.193
I create a whole series of
gradient arrays. No, actually

1279
01:40:09.193 --> 01:40:12.409
that is right, because I
am in gradient mode. I just

1280
01:40:12.409 --> 01:40:15.810
forgot the phase inversion
shown here. This is minus A.

1281
01:40:19.190 --> 01:40:22.863
Now I put a whole series of
gradient arrays one behind another.

1282
01:40:22.863 --> 01:40:26.770
This is a top view. Imagine that
we are recreating a subwoofer arc.

1283
01:40:26.990 --> 01:40:30.516
We arrange one large group of
subs and another group behind

1284
01:40:30.516 --> 01:40:33.922
it, with a polarity inversion
and a quarter-period delay.

1285
01:40:33.922 --> 01:40:36.970
We separate them in space
by a quarter of a period.

1286
01:40:37.590 --> 01:40:43.296
We space them no more than
a quarter of a period apart,

1287
01:40:43.296 --> 01:40:49.210
so we do not run into Olson's
law. Then we add the delays

1288
01:40:49.210 --> 01:40:52.972
for the dispersion, which can
be calculated. I will show

1289
01:40:52.972 --> 01:40:56.263
you how we recreate a kind
of subwoofer arc. This

1290
01:40:56.263 --> 01:40:59.890
produces a series of virtual
subs, one behind another.

1291
01:41:01.690 --> 01:41:07.869
We have now created a cardioid
subwoofer arc in gradient mode.

1292
01:41:07.869 --> 01:41:13.450
If we measure it and look at
some figures, say at 60 Hz,

1293
01:41:13.450 --> 01:41:19.345
this is the sort of result we get.
You can see how powerful it is. We

1294
01:41:19.345 --> 01:41:25.410
have the steering effect from the
coupling, as well as the directivity:

1295
01:41:25.410 --> 01:41:28.758
extremely strong rear cancellation
and sound that reaches a long way

1296
01:41:28.758 --> 01:41:32.550
forwards. At 120 Hz it starts to fall
apart, because I designed it for 60 Hz.

1297
01:41:33.510 --> 01:41:38.236
But with closer spacing, we could
control higher frequencies, depending on

1298
01:41:38.236 --> 01:41:43.090
our aim. This is a configuration I love.
Mathieu, what is the distance here?

1299
01:41:43.090 --> 01:41:48.293
How wide is one little square, just
to get a sense of the scale? This

1300
01:41:48.293 --> 01:41:53.270
square here? Is that the distance
you mean? Roughly how far is it?

1301
01:41:53.270 --> 01:41:55.545
The distance is, so to speak,
beside the point, because

1302
01:41:55.545 --> 01:41:57.613
it depends on the original
output level. These are

1303
01:41:57.613 --> 01:41:59.970
500-HPs, to give you an idea.
This distance is 60 metres.

1304
01:42:01.190 --> 01:42:04.761
But if I use MDC3s, which are
much more powerful, we will

1305
01:42:04.761 --> 01:42:08.270
reach 80 metres. It depends
on the original output. What

1306
01:42:08.270 --> 01:42:11.590
interests me is the difference
between here and here.

1307
01:42:12.870 --> 01:42:16.677
With more powerful subs, the
sound reaches further. It is

1308
01:42:16.677 --> 01:42:20.484
as simple as that. So the
scale here is not the important

1309
01:42:20.484 --> 01:42:24.090
thing. If these were miniature
subs measuring 10 by 10

1310
01:42:24.090 --> 01:42:28.031
centimetres, you would get the same
graph, but the sound would reach

1311
01:42:28.031 --> 01:42:32.030
much less far. The graph and its
orientation would still be the same.

1312
01:42:33.570 --> 01:42:38.191
That is why I did not include
dimensions. Here, with the Meyer

1313
01:42:38.191 --> 01:42:43.110
500-HPs I simulated, the grid is
60 metres long by 42 metres wide.

1314
01:42:46.770 --> 01:42:50.703
That is all very well. We have
learned to build subwoofer arrays,

1315
01:42:50.703 --> 01:42:54.817
almost learned to make a subwoofer
arc, and learned to make cardioid

1316
01:42:54.817 --> 01:42:58.750
subs from omnidirectional ones:
cardioid gradient configurations.

1317
01:42:59.370 --> 01:43:02.895
The nice thing is that manufacturers
do not just make omnidirectional

1318
01:43:02.895 --> 01:43:06.523
subs. They also make subs that are
more or less cardioid. That can help

1319
01:43:06.523 --> 01:43:10.150
a lot, because the boxes they sell
us already have a cardioid response.

1320
01:43:10.610 --> 01:43:14.218
Each has its own way of doing
it. I will not go into the

1321
01:43:14.218 --> 01:43:18.406
construction details of every
model. Here are some examples. This

1322
01:43:18.406 --> 01:43:22.530
is the GEO CD18 that used to be
suspended in the old Studio 106.

1323
01:43:22.610 --> 01:43:27.925
Those were Nexo subs. They are already
cardioid by design. It is a "native"

1324
01:43:27.925 --> 01:43:33.170
operating mode. They can direct the
signal forwards with a single cabinet.

1325
01:43:34.050 --> 01:43:39.262
d&b does this too, with the J-SUB,
SL-SUB, V-SUB and KSL-SUB. They

1326
01:43:39.262 --> 01:43:44.790
have a whole series of cardioid subs.
Manufacturers often do this now,

1327
01:43:45.270 --> 01:43:48.110
selling cardioid or omnidirectional
subs. But one problem with cardioid

1328
01:43:48.110 --> 01:43:50.910
subs is that you often lose some
definition. Some manufacturers do not

1329
01:43:50.910 --> 01:43:53.790
want to make that compromise, such
as L-Acoustics, which does not do it.

1330
01:43:53.950 --> 01:43:57.557
Adamson does not do it either,
because they see it as an

1331
01:43:57.557 --> 01:44:01.163
inevitable slight loss of
quality. If we compare the two

1332
01:44:01.163 --> 01:44:04.770
main systems we saw at the
start, "native" and gradient,

1333
01:44:06.130 --> 01:44:09.980
we had the "native" system and the
gradient system, with the same spacing

1334
01:44:09.980 --> 01:44:13.618
and the same delay, but applied to
a different sub, together with the

1335
01:44:13.618 --> 01:44:17.310
polarity inversion. Let us compare
their advantages and disadvantages.

1336
01:44:17.430 --> 01:44:21.379
Here they are side by side.
The frequency I used does

1337
01:44:21.379 --> 01:44:25.476
not matter; I used one metre
of spacing. What we see in

1338
01:44:25.476 --> 01:44:29.350
the "native" configuration
is extremely stable phase

1339
01:44:29.350 --> 01:44:34.158
in front of the system. It never changes
at the front. At the rear, however,

1340
01:44:34.158 --> 01:44:39.030
it varies with frequency. We have good
sound quality, but moderate rejection.

1341
01:44:40.610 --> 01:44:45.683
With the gradient configuration, the
opposite happens. The phase varies in

1342
01:44:45.683 --> 01:44:50.550
front of the system and is extremely
stable behind it. Here the quality

1343
01:44:50.550 --> 01:44:54.499
at the front is a little less precise;
I should have written that here too.

1344
01:44:54.499 --> 01:44:58.343
In any case, rear rejection is stronger
with gradient than with "native".

1345
01:44:58.343 --> 01:45:02.450
These are two approaches, two operating
modes we can use depending on our aim.

1346
01:45:04.840 --> 01:45:08.647
It is all very well to
couple our subs and make them

1347
01:45:08.647 --> 01:45:12.600
directional, but there are
consequences. Most subs are

1348
01:45:12.600 --> 01:45:16.700
designed to operate almost
omnidirectionally, apart from

1349
01:45:16.700 --> 01:45:20.417
manufacturers' cardioid models.
When we change directivity

1350
01:45:20.417 --> 01:45:24.263
through coupling, we alter the
impulse response. The impulse

1351
01:45:24.263 --> 01:45:27.980
response is something we measure
with measurement systems;

1352
01:45:28.120 --> 01:45:31.643
we will cover that later.
If we measure the response

1353
01:45:31.643 --> 01:45:35.369
precisely, we will see the
effect. These changes affect

1354
01:45:35.369 --> 01:45:38.960
definition: essentially, we
lose a little definition.

1355
01:45:39.360 --> 01:45:41.969
Often, when we create cardioid
subs, the impact is slightly

1356
01:45:41.969 --> 01:45:44.224
less pronounced. We lose
a little compared with our

1357
01:45:44.224 --> 01:45:46.700
lovely omnidirectional sub
radiating in every direction.

1358
01:45:47.120 --> 01:45:49.590
In practice, we often
need less sound in certain

1359
01:45:49.590 --> 01:45:51.700
places, if only to keep it off the stage.

1360
01:45:53.520 --> 01:45:56.969
However, this slight loss of
impact is often offset by more

1361
01:45:56.969 --> 01:46:00.535
precise coverage. We get fewer
cancellations and subtractions

1362
01:46:00.535 --> 01:46:03.400
within the coverage area,
and can be more precise

1363
01:46:03.400 --> 01:46:06.464
about where we send the sound.
For example, with less sound on

1364
01:46:06.464 --> 01:46:09.527
stage, we can sometimes turn the
subs up a little. In terms of

1365
01:46:09.527 --> 01:46:12.640
sensation, we regain at least
what we lost in impulse response.

1366
01:46:13.300 --> 01:46:19.480
Working with all these types of
systems always has consequences.

1367
01:46:22.980 --> 01:46:25.853
I will show you two or three
special configurations, and

1368
01:46:25.853 --> 01:46:28.623
then we can relax. Some
slightly strange arrangements,

1369
01:46:28.623 --> 01:46:31.240
a bit like mode two earlier.
Get your brains ready.

1370
01:46:31.900 --> 01:46:36.037
The first is straightforward:
subwoofer fills. Sometimes

1371
01:46:36.037 --> 01:46:39.509
we need them. When levels
are measured, the low

1372
01:46:39.509 --> 01:46:43.720
frequencies reproduced by subs
are generally not included

1373
01:46:43.720 --> 01:46:46.549
in official measurements, which are
in dBA. We will not go into weighting

1374
01:46:46.549 --> 01:46:49.340
curves and the reasons for that, but
essentially they are not taken into

1375
01:46:49.340 --> 01:46:52.440
account. You can turn the subs right up
and it will not show in the measurement.

1376
01:46:52.540 --> 01:46:56.339
Even so, battering the front rows
is not very pleasant. Sometimes it

1377
01:46:56.339 --> 01:47:00.081
helps to add fills, so you can have
a reasonable level at the front

1378
01:47:00.081 --> 01:47:03.880
without overwhelming the first rows
just to reach another 60 metres.

1379
01:47:04.100 --> 01:47:09.511
So we add subwoofer fills. This is
fairly common. Here are some examples.

1380
01:47:09.511 --> 01:47:14.180
You can see these lovely subwoofer
lines, with fills over here.

1381
01:47:15.200 --> 01:47:18.204
Looking at these fills, we can
see subs flown in the air. Here

1382
01:47:18.204 --> 01:47:20.868
are our two groups of subs.
This is a pressure-gradient

1383
01:47:20.868 --> 01:47:23.920
configuration. I will show you
what the measurement looks like.

1384
01:47:27.600 --> 01:47:31.760
Let us compare that with a fill made
from omnidirectional subs. I have

1385
01:47:31.760 --> 01:47:35.980
brought back what we saw at the start:
completely omnidirectional subs.

1386
01:47:37.740 --> 01:47:42.500
Very nice: the subs facing each other.
I can hear some noise in the background.

1387
01:47:44.320 --> 01:47:48.407
With these omnidirectional fills,
our first stack is here and

1388
01:47:48.407 --> 01:47:52.361
the second here. Look at what
happens at 31 Hz. This is the

1389
01:47:52.361 --> 01:47:56.180
pattern we would get:
high-pressure areas, cancellations,

1390
01:47:56.360 --> 01:48:00.174
high-pressure areas, cancellations.
It makes quite a mess,

1391
01:48:00.174 --> 01:48:03.660
just to add some sound. Can
you mute your microphone?

1392
01:48:05.680 --> 01:48:08.301
That is what I can hear.
We have been hearing that

1393
01:48:08.301 --> 01:48:11.080
microphone for a while. I
do not think I can mute it.

1394
01:48:13.240 --> 01:48:18.255
I have muted it myself.
Goodbye to that. Here we have

1395
01:48:18.255 --> 01:48:24.500
omnidirectional subwoofer fills,
at 31, 125 and 63 Hz. When we add

1396
01:48:24.500 --> 01:48:27.111
omnidirectional subs some
distance away, we create strong

1397
01:48:27.111 --> 01:48:29.951
cancellation and summation in
different areas. That is what we

1398
01:48:29.951 --> 01:48:32.746
sometimes hear as we walk through
a concert: cancellation and

1399
01:48:32.746 --> 01:48:35.540
subtraction. We get the same
effect with a left-right system.

1400
01:48:35.960 --> 01:48:39.780
A left-right arrangement would produce
the same effect. It is the same

1401
01:48:39.780 --> 01:48:43.600
with fills. But if we make our fills
like this, using gradient arrays,

1402
01:48:45.910 --> 01:48:49.211
we still have the first stack and
the second stack. At 31 Hz, we

1403
01:48:49.211 --> 01:48:52.357
still see cancellation, addition
and subtraction. It is never

1404
01:48:52.357 --> 01:48:55.710
perfect, but it is already quite
different from what we had here.

1405
01:48:56.110 --> 01:48:58.785
The effect looks less
pronounced. There is still one

1406
01:48:58.785 --> 01:49:01.615
area that is not great: sorry
for the people there. But

1407
01:49:01.615 --> 01:49:04.290
at 63 Hz, the result is
much more stable and smooth.

1408
01:49:04.730 --> 01:49:08.614
There are still differences,
but they are gentle. At 125

1409
01:49:08.614 --> 01:49:12.497
Hz it works well too. By
making fills with fairly strong

1410
01:49:12.497 --> 01:49:16.450
directivity, using a gradient
configuration and therefore

1411
01:49:16.450 --> 01:49:20.308
strong rear rejection, we create
much more consistent coverage

1412
01:49:20.308 --> 01:49:23.792
behind the subs. With fills,
what interests me is not so

1413
01:49:23.792 --> 01:49:27.090
much what we gain here, but
what we lose behind them.

1414
01:49:27.090 --> 01:49:30.727
So when adding fills, it is often
better to measure behind them and

1415
01:49:30.727 --> 01:49:34.364
see what happens. People sometimes
measure in front and say: great,

1416
01:49:34.364 --> 01:49:37.730
I have aligned the phase, set
my delay, everything is perfect.

1417
01:49:38.030 --> 01:49:40.941
Mathieu? Behind them, there is
no sound left. Mathieu, that

1418
01:49:40.941 --> 01:49:43.950
first diagram, with two
omnidirectional systems: is that what

1419
01:49:43.950 --> 01:49:46.910
you were talking about and were
worried about at the concert

1420
01:49:48.890 --> 01:49:52.084
at Ground Control? Yes,
I told you it was a pain

1421
01:49:52.084 --> 01:49:55.610
adding more subs. I remember.
So I switched them off,

1422
01:49:57.590 --> 01:50:00.530
because adding sound at the
back was making me lose sound at

1423
01:50:00.530 --> 01:50:03.568
the front. That was rather
awkward. Gradient arrays would have

1424
01:50:03.568 --> 01:50:06.606
worked quite well; "native"
configurations a little less well,

1425
01:50:06.606 --> 01:50:09.350
because gradient arrays give
very strong rear rejection.

1426
01:50:09.850 --> 01:50:14.212
We have much more control. There is still
some loss because the subs are spaced

1427
01:50:14.212 --> 01:50:18.630
far apart. We are beyond that half-period
spacing, so things get a little messy.

1428
01:50:18.910 --> 01:50:22.433
And that is not true at
every position. It is always

1429
01:50:22.433 --> 01:50:26.024
the same issue. Yes, it can
change. It depends on the

1430
01:50:26.024 --> 01:50:29.750
spacing between the two.
Ground Control is quite small,

1431
01:50:29.830 --> 01:50:35.362
isn't it? At 30 Hz, you get patterns
like these. We had added fills,

1432
01:50:35.362 --> 01:50:40.650
Nadège, at that concert where we
opened the curtains at the back.

1433
01:50:41.070 --> 01:50:44.196
We opened the curtains, so
we installed a second system.

1434
01:50:44.196 --> 01:50:47.489
That was precisely what caused
the problem. Right. The subs

1435
01:50:47.489 --> 01:50:50.670
at the back were omnidirectional,
so I switched them off.

1436
01:50:51.170 --> 01:50:51.910
It worked better that way.

1437
01:50:54.480 --> 01:50:57.722
In general, cardioid subs are
recommended for fills. Everyone

1438
01:50:57.722 --> 01:51:01.390
can do as they wish, but using
omnidirectional subs has consequences,

1439
01:51:01.390 --> 01:51:04.420
unless they are very far away.
Perhaps we should have put

1440
01:51:04.420 --> 01:51:10.405
fills in earlier. Here is another
configuration, which I call Flower Fire.

1441
01:51:10.405 --> 01:51:16.390
I will show it quickly, because it is
quite fun. There are many variations

1442
01:51:16.390 --> 01:51:19.751
on this system. We take a sub
with inverted polarity and delay

1443
01:51:19.751 --> 01:51:22.786
it by a quarter of a period.
Here is that quarter-period

1444
01:51:22.786 --> 01:51:25.930
spacing. This really is a
pressure-gradient configuration.

1445
01:51:26.030 --> 01:51:31.693
The front one has no delay. Then
we add subs around this circle,

1446
01:51:31.693 --> 01:51:37.090
with delays relative to one
another. Let us see what happens.

1447
01:51:37.230 --> 01:51:41.750
We choose a value of 4.17
milliseconds, corresponding to 60 Hz.

1448
01:51:43.690 --> 01:51:46.997
Looking at the measurement
for Flower Fire, here we are

1449
01:51:46.997 --> 01:51:50.484
at around 30 Hz. It creates a
sort of forward-facing blob,

1450
01:51:50.484 --> 01:51:53.610
because all the front subs
are at zero milliseconds.

1451
01:51:54.530 --> 01:51:59.185
Now I will play with this delay,
just the delay on D. I will delay

1452
01:51:59.185 --> 01:52:03.910
that sub slightly. At two milliseconds,
the pattern starts to turn.

1453
01:52:04.690 --> 01:52:10.855
At three, it turns further; at four,
further still; then five. I have not shown

1454
01:52:10.855 --> 01:52:16.630
five. By adjusting this delay, we can
steer the wave, a little like we did

1455
01:52:16.630 --> 01:52:20.413
with the stacks earlier. This is just
to demonstrate the principle. We can

1456
01:52:20.413 --> 01:52:24.350
have lots of subs arranged around one
another in all sorts of configurations.

1457
01:52:24.410 --> 01:52:27.964
We can steer the wave towards
the side where we apply the

1458
01:52:27.964 --> 01:52:31.644
delay. For example, if the subs
have fixed positions and we

1459
01:52:31.644 --> 01:52:35.510
really want to redirect the wave,
adjusting that delay lets us

1460
01:52:35.510 --> 01:52:41.750
rotate the sound around like the hands
of a clock. That was one configuration.

1461
01:52:41.750 --> 01:52:47.350
Some other fun configurations were
developed by a man called Dave Rat.

1462
01:52:47.850 --> 01:52:53.155
I do not know whether you know Dave
Rat. This is him. As you can see, he is

1463
01:52:53.155 --> 01:52:58.530
a bit of a character, rather unusual.
This is him too. Dave Rat is American.

1464
01:52:59.370 --> 01:53:01.985
For context, he has been a
sound engineer for the Red Hot

1465
01:53:01.985 --> 01:53:04.738
Chili Peppers, Soundgarden and
many other bands. His company

1466
01:53:04.738 --> 01:53:07.170
is called Rat Sound, and
they do a great many things.

1467
01:53:07.790 --> 01:53:11.019
This gentleman particularly
loves subs. He has developed

1468
01:53:11.019 --> 01:53:14.132
all sorts of configurations.
I have included a link at

1469
01:53:14.132 --> 01:53:17.130
the end to his website,
where he shows many of them.

1470
01:53:17.310 --> 01:53:21.030
I will show you one example. He
comes up with all sorts of unusual

1471
01:53:21.030 --> 01:53:24.355
but generally very clever ideas.
The first configuration is

1472
01:53:24.355 --> 01:53:27.850
called Slot Fire. You can see
those large stacks at the sides.

1473
01:53:27.990 --> 01:53:33.912
There are three stacks of three each
time. The subs face each other: here

1474
01:53:33.912 --> 01:53:39.590
and here. This gap is smaller than
that one, and the same as this one.

1475
01:53:40.790 --> 01:53:45.027
Here is the top view of what we call
Slot Fire. The stage is here, we

1476
01:53:45.027 --> 01:53:49.510
need to radiate this way, and there
is a wall here and another wall here.

1477
01:53:49.930 --> 01:53:54.412
There are a lot of subs, so plenty of
output, but the audience is right beside

1478
01:53:54.412 --> 01:53:58.550
them. The idea is to reduce the sound
coming out to the side of the sub.

1479
01:53:59.490 --> 01:54:03.528
How does Slot Fire achieve
that? He starts with a point

1480
01:54:03.528 --> 01:54:07.199
source: two subs facing
each other. That creates a

1481
01:54:07.199 --> 01:54:11.310
completely omnidirectional
sub, with its acoustic centre

1482
01:54:11.310 --> 01:54:11.870
in the middle.

1483
01:54:14.090 --> 01:54:19.997
He makes two of these point sources.
Each consists of the two stacks

1484
01:54:19.997 --> 01:54:25.990
we saw. Imagine the walls here, the
stage here and the audience here.

1485
01:54:26.110 --> 01:54:32.421
We will steer this whole arrangement,
these two omnidirectional systems,

1486
01:54:32.421 --> 01:54:38.030
towards the audience over here.
One way he does this is to space

1487
01:54:38.030 --> 01:54:40.965
the centres of these two new
point sources one third of a

1488
01:54:40.965 --> 01:54:43.643
wavelength apart. He uses
one third of a wavelength,

1489
01:54:43.643 --> 01:54:46.630
rather than the quarter
wavelength I have used throughout.

1490
01:54:48.070 --> 01:54:54.387
Putting numbers on it, if he takes 45 Hz
as the reference, a fairly low frequency,

1491
01:54:54.387 --> 01:55:00.010
that allows quite long systems. One
third of a wavelength is 2.52 metres,

1492
01:55:00.230 --> 01:55:02.818
so he spaces the two point
sources 2.52 metres apart,

1493
01:55:02.818 --> 01:55:05.210
measured between the
centres of these assemblies.

1494
01:55:07.110 --> 01:55:10.666
Then he adds a delay equivalent
to one sixth of a wavelength, 3.7

1495
01:55:10.666 --> 01:55:14.715
milliseconds, because one third plus
one sixth gives one half. We are back

1496
01:55:14.715 --> 01:55:18.490
to that familiar half wavelength,
giving cancellation at 180 degrees.

1497
01:55:19.490 --> 01:55:22.947
Here is the measurement. I
have drawn the walls rather

1498
01:55:22.947 --> 01:55:26.661
crudely, but it gives you an
idea. This lets him use a lot

1499
01:55:26.661 --> 01:55:30.310
of subs in large stacks and
create very powerful systems.

1500
01:55:30.730 --> 01:55:33.002
They are side by side because
there was no room to put them

1501
01:55:33.002 --> 01:55:35.390
one behind another. He would
have liked to do that: a gradient

1502
01:55:35.390 --> 01:55:37.470
arrangement works just as
well, but there is no space.

1503
01:55:38.030 --> 01:55:41.995
Even with them side by side, we
can steer the sound this way.

1504
01:55:41.995 --> 01:55:46.025
Here we see the result with 3.7
milliseconds, one sixth. If he

1505
01:55:46.025 --> 01:55:49.990
reduces it slightly, the wave
turns a little further inwards.

1506
01:55:50.630 --> 01:55:56.678
Again, by adjusting the timing while
keeping the spacing the same, we

1507
01:55:56.678 --> 01:56:02.550
create a sort of end-fire, or at
least a gradient-type arrangement,

1508
01:56:02.630 --> 01:56:08.453
that points to the side. By lining up
the subs along the side, we can steer the

1509
01:56:08.453 --> 01:56:14.350
wave at right angles within a fairly
compact space. Here is a photograph showing

1510
01:56:14.350 --> 01:56:19.198
his actual Slot Fire system, with
a stack next to it. Generally, he

1511
01:56:19.198 --> 01:56:24.190
adds a little delay to this whole
assembly too, to steer it sideways.

1512
01:56:24.710 --> 01:56:28.637
He has created something very
directional, with the subs positioned

1513
01:56:28.637 --> 01:56:32.270
side by side and the sound
projecting at right angles to them.

1514
01:56:34.590 --> 01:56:37.827
Another system he developed, which
I will just show without explaining,

1515
01:56:37.827 --> 01:56:41.110
is the Vortex. You can see these
groups of four subs facing one another.

1516
01:56:41.890 --> 01:56:44.468
They form a nice diagonal like
this. The stage is here, and

1517
01:56:44.468 --> 01:56:46.872
there are people on it. We
must not send sound onto it.

1518
01:56:46.872 --> 01:56:49.450
Instead, we want plenty of bass
for the audience over here.

1519
01:56:50.710 --> 01:56:54.020
There is not much space. That is why
he cannot put a large subwoofer arc

1520
01:56:54.020 --> 01:56:57.330
in front, line them all up side by
side, or put them one behind another.

1521
01:56:57.410 --> 01:57:02.710
So he puts them in a square. Looking more
closely, we can see our four subs. He

1522
01:57:02.710 --> 01:57:08.010
calls it the Vortex, or Orgasmotron. Very
subtle. That is his face you can see.

1523
01:57:08.890 --> 01:57:12.076
Essentially, these subs face
inwards, as do these and these:

1524
01:57:12.076 --> 01:57:15.103
everything faces inwards. That
creates one enormous point

1525
01:57:15.103 --> 01:57:17.970
source, something initially
extremely omnidirectional.

1526
01:57:18.450 --> 01:57:21.874
By adjusting the delay on
each sub, he steers the wave

1527
01:57:21.874 --> 01:57:25.299
exactly where he wants it.
He delays this one slightly

1528
01:57:25.299 --> 01:57:28.850
relative to that one, and
this one relative to that one.

1529
01:57:28.850 --> 01:57:32.677
The link I have provided
explains it, and it is also in

1530
01:57:32.677 --> 01:57:36.643
the simulations I have supplied.
By adjusting the delays,

1531
01:57:36.643 --> 01:57:40.470
we can project the sound wave
exactly where we want it,

1532
01:57:40.470 --> 01:57:44.130
while keeping it off the stage. This
allows very powerful configurations,

1533
01:57:44.130 --> 01:57:47.590
because we can build a tall stack
of subs here. We could use 25 if we

1534
01:57:47.590 --> 01:57:51.250
wanted, and still keep sound off the
stage while having plenty of output.

1535
01:57:54.650 --> 01:58:00.940
One last configuration, developed by
Thomas Mundorf, is called the TM Array.

1536
01:58:00.940 --> 01:58:06.650
You probably know that little band
Metallica. This is Thomas Mundorf.

1537
01:58:08.570 --> 01:58:12.086
Metallica tours with a 360-degree stage.
They used this arrangement. The idea is

1538
01:58:12.086 --> 01:58:15.470
to put subs all around, so everyone gets
bass while keeping it off the stage.

1539
01:58:15.970 --> 01:58:19.308
You can put subs all around,
but that makes a mess in the

1540
01:58:19.308 --> 01:58:22.821
middle, with cancellations
everywhere. Instead, they created

1541
01:58:22.821 --> 01:58:26.510
one large central array like
this, rather like the Vortex idea.

1542
01:58:26.670 --> 01:58:30.310
We can see four stacks of
subs facing one another.

1543
01:58:32.170 --> 01:58:37.732
That creates an enormous point source,
a completely omnidirectional system.

1544
01:58:37.732 --> 01:58:43.590
Remember the steering effect earlier,
when we lined subs up beside one another:

1545
01:58:43.670 --> 01:58:49.391
the wave became cumulative and formed a
sort of laser beam. Here is the top, here

1546
01:58:49.391 --> 01:58:54.830
the bottom, and here the stage. By
creating this perfect point-source system,

1547
01:58:55.770 --> 01:58:59.560
we create a wave that spreads
out on all sides. Then,

1548
01:58:59.560 --> 01:59:03.420
using the steering effect,
adding delays at the bottom

1549
01:59:03.420 --> 01:59:07.210
or top as required, we can
steer the signal laterally

1550
01:59:07.210 --> 01:59:09.380
and tilt it down without sending sound onto

1551
01:59:09.380 --> 01:59:11.650
the stage. This is what
we call the TM Array.

1552
01:59:16.160 --> 01:59:20.460
We will stop there with the systems.
We have seen quite a few, although

1553
01:59:20.460 --> 01:59:24.820
there are many others. I have made a
small classification table for you.

1554
01:59:26.240 --> 01:59:30.114
We will not go into detail, but
the main families are "native"

1555
01:59:30.114 --> 01:59:33.863
and gradient, with the various
names I have given them. When

1556
01:59:33.863 --> 01:59:37.300
I write "native 2", that
means there are only two subs.

1557
01:59:39.700 --> 01:59:44.950
Here are the usual spacings, always
expressed in terms of wavelength.

1558
01:59:44.950 --> 01:59:50.200
Then rear rejection: the more plus
signs, the stronger the rejection.

1559
01:59:51.140 --> 01:59:54.131
For radiation stability, more
plus signs mean better sound

1560
01:59:54.131 --> 01:59:56.966
quality in front, shall we
say. Then there is the space

1561
01:59:56.966 --> 02:00:00.060
required: lots of plus signs
mean it takes up a lot of room.

1562
02:00:00.200 --> 02:00:03.202
A cardioid subwoofer arc is
something I love, but it takes

1563
02:00:03.202 --> 02:00:06.100
up a lot of space. Nor do we
build a TM Array every day.

1564
02:00:06.700 --> 02:00:10.235
By contrast, "native 2"
and "gradient 2" are fairly

1565
02:00:10.235 --> 02:00:13.840
small, take up little space
and are quite effective.

1566
02:00:15.950 --> 02:00:18.930
Are you still with me,
or have I lost everyone?

1567
02:00:20.820 --> 02:00:26.552
I do not know. Is everyone all right?
Yes, great. We are fine. "Native 2"

1568
02:00:26.552 --> 02:00:32.520
and "gradient 2" mean two subs? Yes,
two. I call them that to make it clear,

1569
02:00:32.580 --> 02:00:38.790
so we remember. The TM Array is what
we saw with Metallica? Yes, the Thomas

1570
02:00:38.790 --> 02:00:44.420
Mundorf Array. Is that all you
remembered? Exactly. I have built one

1571
02:00:45.040 --> 02:00:49.005
on a smaller scale, though
about as tall. Have you made

1572
02:00:49.005 --> 02:00:52.827
one already? Yes, with a
line of eight, arranged like

1573
02:00:52.827 --> 02:00:56.720
this. Was it for a 360-degree
setup? Yes, 360 degrees.

1574
02:00:57.160 --> 02:01:00.987
It works very well. Generally,
we keep the spacing between

1575
02:01:00.987 --> 02:01:04.485
subs here below 1.3 or 1.4
metres. That gives control

1576
02:01:04.485 --> 02:01:08.180
fairly high up in frequency.
With the cumulative effect,

1577
02:01:08.260 --> 02:01:11.245
you get very even 360-degree
coverage without sending

1578
02:01:11.245 --> 02:01:14.117
sound onto the stage. It
is quite powerful. For the

1579
02:01:14.117 --> 02:01:17.440
auditorium? Yes, for the
auditorium, if people agree to it.

1580
02:01:17.440 --> 02:01:18.722
It is fine, we do not need bass in the

1581
02:01:18.722 --> 02:01:20.140
auditorium. No need for bass there either.

1582
02:01:26.170 --> 02:01:30.370
The useful thing is being able to
simulate all these arrangements. How do

1583
02:01:30.370 --> 02:01:34.570
I do that? I have shown you some
examples. I love your car. It is lovely.

1584
02:01:36.550 --> 02:01:41.754
There are several methods
for simulating all these

1585
02:01:41.754 --> 02:01:48.310
arrangements. The first method
I used, and still use, helped me

1586
02:01:48.310 --> 02:01:54.147
understand a great deal: Excel. I
made myself a little Excel file.

1587
02:01:54.147 --> 02:01:59.630
I have a short video of it, which
we will watch. In this file,

1588
02:01:59.730 --> 02:02:05.325
the first sheet shows all the frequencies,
then the periods, wavelength fractions,

1589
02:02:05.325 --> 02:02:10.170
period fractions and so on, with the
corresponding distances and times.

1590
02:02:10.970 --> 02:02:15.569
All of it depends on the speed of
sound, which depends on temperature. As

1591
02:02:15.569 --> 02:02:20.230
you can see, changing the temperature
changes the speed and all my values.

1592
02:02:21.110 --> 02:02:23.729
If I change a frequency, everything
is calculated: wavelength

1593
02:02:23.729 --> 02:02:26.220
fractions, thirds, sixths and
tenths. There are other ways

1594
02:02:26.220 --> 02:02:28.710
of making cardioid arrays using
sixths and three quarters.

1595
02:02:29.370 --> 02:02:32.823
Then I have all the different
configurations in separate tabs: "native",

1596
02:02:32.823 --> 02:02:36.325
end-fire, four-element end-fire,
gradient, and gradient arrangements with

1597
02:02:36.325 --> 02:02:39.730
fixed spacing, where I have no choice
and have to adjust the frequency.

1598
02:02:39.830 --> 02:02:42.550
There are the Slot Fire
arrangements you saw, and lots

1599
02:02:42.550 --> 02:02:45.471
of other things, even the
Vortex, which I did not explain.

1600
02:02:45.471 --> 02:02:48.090
So you have made a simulator
in Excel? Yes, exactly.

1601
02:02:49.190 --> 02:02:52.918
For example, if I choose a
gradient array and enter the

1602
02:02:52.918 --> 02:02:56.444
frequency I want to work
at, my cutoff frequency, it

1603
02:02:56.444 --> 02:03:00.850
automatically calculates the
spacing I need, the polarity to use,

1604
02:03:00.950 --> 02:03:04.401
and the delay to apply. If I position
one at, say, minus ten metres,

1605
02:03:04.401 --> 02:03:07.750
it tells me the other should be
at minus 9.05 metres, for example.

1606
02:03:08.290 --> 02:03:12.165
It lets me calculate everything. My
little magic circle is always there

1607
02:03:12.165 --> 02:03:16.095
in front of me. I can do this for
every system, including a four-element

1608
02:03:16.095 --> 02:03:19.370
end-fire. I choose 65 Hz, and
we see the required dimensions

1609
02:03:19.370 --> 02:03:23.073
and positions. That was the
first method I used. Building

1610
02:03:23.073 --> 02:03:26.842
an Excel spreadsheet helps you
understand many parameters,

1611
02:03:26.842 --> 02:03:30.350
because you have to work out
how everything functions.

1612
02:03:30.810 --> 02:03:34.343
Doing it yourself helps you
understand. That is why I am showing

1613
02:03:34.343 --> 02:03:37.932
you, and why I encourage you to
try if you are interested. If you

1614
02:03:37.932 --> 02:03:41.410
think, I would like to calculate
this in Excel, it can be done.

1615
02:03:42.890 --> 02:03:46.610
Another method, because there
are friendlier tools, is MAPP XT.

1616
02:03:46.610 --> 02:03:50.270
All the little diagrams you have
seen today were made with it.

1617
02:03:51.390 --> 02:03:54.470
MAPP XT is made by Meyer Sound.
It is fairly straightforward

1618
02:03:54.470 --> 02:03:57.499
software, but extremely powerful.
You can do a lot with it,

1619
02:03:57.499 --> 02:04:00.630
and its predictions are quite
accurate, unlike some software.

1620
02:04:01.830 --> 02:04:05.299
This is how MAPP XT works.
We have a plan view. We can

1621
02:04:05.299 --> 02:04:09.090
create projects and adjust the
size of the plan, of course.

1622
02:04:10.370 --> 02:04:13.067
We can add loudspeakers. I will say: let us

1623
02:04:13.067 --> 02:04:15.890
add a loudspeaker, which
in this case will be

1624
02:04:17.930 --> 02:04:20.680
a Meyer sub. Whether we use
a Meyer sub, an L-Acoustics

1625
02:04:20.680 --> 02:04:23.580
sub or something else, broadly
speaking the parameters are

1626
02:04:23.580 --> 02:04:26.330
almost the same, apart from
output and similar details.

1627
02:04:26.570 --> 02:04:31.408
The summation calculations work
whichever sub we choose. Here I

1628
02:04:31.408 --> 02:04:36.170
have positioned a sub in space,
and I can change its settings.

1629
02:04:36.370 --> 02:04:39.861
I can edit information, its
position, and connect it to a

1630
02:04:39.861 --> 02:04:43.658
physical output, a processor
output. I can duplicate this sub.

1631
02:04:43.658 --> 02:04:47.210
This is how all the simulations
I have shown you are made.

1632
02:04:48.090 --> 02:04:53.216
For example, I position another sub
behind it. I have copied it, and we

1633
02:04:53.216 --> 02:04:58.630
will modify it slightly. We will connect
it to channel two and put it at...

1634
02:04:59.070 --> 02:05:01.522
Let us set the parameters
precisely. I will put it at

1635
02:05:01.522 --> 02:05:04.205
the same height, ten metres,
and one metre away. The other

1636
02:05:04.205 --> 02:05:06.610
was at 20 metres; we will
put this one at 19 metres.

1637
02:05:07.950 --> 02:05:11.929
There we are: two subs, one behind
another. Very nice. Now I will

1638
02:05:11.929 --> 02:05:16.030
change the settings. Here are all
my channels: sub one and sub two.

1639
02:05:18.230 --> 02:05:22.360
To create a gradient array, since
they are one metre apart, I invert

1640
02:05:22.360 --> 02:05:26.430
the polarity of the rear sub, number
two. The spacing is one metre.

1641
02:05:26.510 --> 02:05:31.710
I apply 2.94 milliseconds. Good.
Now I will calculate the result.

1642
02:05:33.550 --> 02:05:38.828
Here I can choose the calculation
frequency and bandwidth. I will use one

1643
02:05:38.828 --> 02:05:43.890
octave at 63 Hz and run the prediction.
It produces these nice graphs.

1644
02:05:44.770 --> 02:05:49.840
Then I can experiment very
quickly. For example, I will

1645
02:05:49.840 --> 02:05:54.910
return the polarity to normal.
Let us see what happens.

1646
02:05:55.090 --> 02:05:58.945
Now the pattern points slightly
to the left. I can create

1647
02:05:58.945 --> 02:06:02.733
all sorts of simulations, try
different ways of building

1648
02:06:02.733 --> 02:06:06.250
my configurations and test
them almost in real time.

1649
02:06:06.570 --> 02:06:10.150
Remember that the predictions do not
include the venue's acoustic properties:

1650
02:06:10.150 --> 02:06:13.870
there are no reflections or anything like
that. But they are extremely accurate.

1651
02:06:14.010 --> 02:06:18.310
It is one of the most accurate tools
that also runs quickly. That is MAPP XT.

1652
02:06:20.640 --> 02:06:24.273
Another very useful tool is
ArrayCalc. Made by d&b, it is

1653
02:06:24.273 --> 02:06:28.288
particularly convenient for
subwoofer arcs. As you saw, in MAPP

1654
02:06:28.288 --> 02:06:32.240
XT I can take any sub, move it
around and calculate summation.

1655
02:06:32.640 --> 02:06:36.073
As I keep saying, whether I
simulate Meyer subs in MAPP XT or

1656
02:06:36.073 --> 02:06:39.619
use L-Acoustics, Nexo or anything
else, as long as the subs are

1657
02:06:39.619 --> 02:06:42.940
omnidirectional, my results
will almost always be the same.

1658
02:06:43.620 --> 02:06:47.106
I very often simulate arrangements
in MAPP XT and then apply them to

1659
02:06:47.106 --> 02:06:50.900
L-Acoustics, because I get the same
result. Only the output levels change.

1660
02:06:51.420 --> 02:06:56.646
ArrayCalc lets me do that too. I
can calculate with it. Here I have a

1661
02:06:56.646 --> 02:07:01.720
venue with different sources, and
I add a sub here in the same way.

1662
02:07:02.880 --> 02:07:06.950
I can choose the type of sub and
the number of positions. I will add

1663
02:07:06.950 --> 02:07:10.900
one sub. We immediately see its
directivity: it is a cardioid sub.

1664
02:07:11.300 --> 02:07:14.807
They have given me a cardioid
sub, how nice. Let us choose

1665
02:07:14.807 --> 02:07:18.133
an omnidirectional one instead.
This one, the Q-SUB, is

1666
02:07:18.133 --> 02:07:21.700
omnidirectional. I will take
one. Actually, I will take 16.

1667
02:07:22.920 --> 02:07:28.420
I have 16 subs, all listed
at the bottom. I will spread

1668
02:07:28.420 --> 02:07:34.220
them over a distance of 18
metres, along an 18-metre line.

1669
02:07:35.280 --> 02:07:39.517
I tell it to apply that. Here all my
subs are virtually at the same point; now

1670
02:07:39.517 --> 02:07:43.700
they are spread over 18 metres. It
immediately calculates the resulting beam.

1671
02:07:44.800 --> 02:07:46.980
As you can see, there are no
delays between these subs.

1672
02:07:49.340 --> 02:07:52.218
But I can change that. Over
18 metres, the main frequency

1673
02:07:52.218 --> 02:07:54.794
corresponding to half-wavelength
spacing is 173 Hz,

1674
02:07:54.794 --> 02:07:57.420
which I can control. I will
spread them out further.

1675
02:07:58.220 --> 02:08:01.759
Now it says I can control up to
150 Hz, because they are spaced

1676
02:08:01.759 --> 02:08:04.905
further apart. Over 40 metres,
I can only control 76 Hz,

1677
02:08:04.905 --> 02:08:08.220
because each time we exceed
those half-wavelength spacings.

1678
02:08:08.580 --> 02:08:11.559
It is useful: it calculates
all that for me. I will put

1679
02:08:11.559 --> 02:08:14.593
them back over 18 metres. Now
I want 90-degree coverage,

1680
02:08:14.593 --> 02:08:17.680
a 90-degree subwoofer arc.
You can see there is no delay.

1681
02:08:17.800 --> 02:08:21.313
Well, there is 0.3: the default
preset is 30 degrees. Now I ask

1682
02:08:21.313 --> 02:08:24.827
it to calculate the delays for
90 degrees, and it automatically

1683
02:08:24.827 --> 02:08:28.340
applies the delays to the subs
to produce 90-degree dispersion.

1684
02:08:29.000 --> 02:08:32.654
That is quite handy. If I
now choose 45 degrees, it

1685
02:08:32.654 --> 02:08:36.882
reduces the delays and makes
a less pronounced arc. I could

1686
02:08:36.882 --> 02:08:40.680
show you how to calculate
arcs if you are interested.

1687
02:08:40.800 --> 02:08:45.446
But here the software does it very well
for us automatically. Why make life

1688
02:08:45.446 --> 02:08:50.340
difficult? It works well. I use ArrayCalc
a lot to calculate my subwoofer arcs.

1689
02:08:51.160 --> 02:08:54.453
As I make a lot of subwoofer
arcs, it is very useful.

1690
02:08:54.453 --> 02:08:57.933
And one final free program.
We are only looking at four,

1691
02:08:57.933 --> 02:09:01.040
but there are a good ten
of them. May I interrupt?

1692
02:09:01.720 --> 02:09:07.708
I took the d&b training. They run sessions
every week, on Tuesday, Wednesday,

1693
02:09:07.708 --> 02:09:12.840
Thursday and Friday. They are
excellent and explain this software,

1694
02:09:13.500 --> 02:09:17.313
including how to make
subwoofer arcs. Yes, including

1695
02:09:17.313 --> 02:09:21.200
subwoofer arcs, and the
training is excellent. An arc

1696
02:09:21.200 --> 02:09:25.160
calculated with d&b can also
be used with L-Acoustics.

1697
02:09:25.240 --> 02:09:29.134
For example, you can make subwoofer arcs
in L-Acoustics Soundvision, but it has

1698
02:09:29.134 --> 02:09:32.880
some constraints. The subs are always
touching; you cannot space them apart.

1699
02:09:33.000 --> 02:09:35.538
There are little limitations
like that. When working with

1700
02:09:35.538 --> 02:09:38.344
L-Acoustics, I used to calculate
my subwoofer arcs in d&b, then

1701
02:09:38.344 --> 02:09:41.060
apply those settings to L-Acoustics,
and it worked very well.

1702
02:09:41.920 --> 02:09:46.250
It saves time. One final useful
free program is Focus. It comes

1703
02:09:46.250 --> 02:09:50.580
from EASE. EASE is really the
top level of simulation software.

1704
02:09:50.960 --> 02:09:54.440
The paid version of EASE
is extremely expensive, but

1705
02:09:54.440 --> 02:09:57.986
Focus costs nothing. It has
limitations, but is still

1706
02:09:57.986 --> 02:10:01.600
very powerful. Here, for
example, I have France Inter.

1707
02:10:01.800 --> 02:10:04.727
There are lots of loudspeakers
placed here. They are all

1708
02:10:04.727 --> 02:10:07.445
muted, hence the crosses.
I have created my coverage

1709
02:10:07.445 --> 02:10:10.320
surface, and I can view it
from the side or from above.

1710
02:10:11.780 --> 02:10:16.427
I will add loudspeakers to this
system by adding a source. I have

1711
02:10:16.427 --> 02:10:20.860
a whole catalogue of sources to
choose from. I will add a sub.

1712
02:10:21.080 --> 02:10:25.528
Let us choose any sub, an MLA218.
It is a large omnidirectional

1713
02:10:25.528 --> 02:10:29.199
sub. It appears here, and
I position it on the grid.

1714
02:10:29.199 --> 02:10:32.800
In real time, the software
automatically calculates

1715
02:10:32.800 --> 02:10:38.057
its radiation pattern. You can see a
nice omnidirectional pattern appearing.

1716
02:10:38.057 --> 02:10:42.760
I will put it at exactly 12 metres,
to give it a precise coordinate.

1717
02:10:43.640 --> 02:10:49.564
I will set Y to zero, so I know it is
at 12, zero. Here is my lovely sub. Now

1718
02:10:49.564 --> 02:10:55.180
let us create a cardioid configuration.
How do we do that? I will copy it

1719
02:10:55.180 --> 02:11:01.137
and simply paste it. Now I have two
copies of my sub. Very straightforward.

1720
02:11:01.137 --> 02:11:06.140
The second sub has the same
settings as the first. On this sub,

1721
02:11:06.980 --> 02:11:11.071
we will apply the settings. The
coordinates are on the left.

1722
02:11:11.071 --> 02:11:14.889
I will move it one metre
behind: the other was at 12, so

1723
02:11:14.889 --> 02:11:18.980
this goes at 11. Now I will
apply my 2.94-millisecond delay.

1724
02:11:20.360 --> 02:11:26.209
It calculates the result immediately.
I have not inverted the polarity yet.

1725
02:11:26.209 --> 02:11:31.980
I invert it, and there is my lovely
cardioid pattern. That is quite clear.

1726
02:11:32.240 --> 02:11:36.783
Again, this software is rather basic
in some respects, but its simulations

1727
02:11:36.783 --> 02:11:41.080
are almost perfect. They are extremely
good, so it can be worth using.

1728
02:11:41.780 --> 02:11:46.930
There are also some Fohhn models
included in this software. I have

1729
02:11:46.930 --> 02:11:52.080
shown you four programs, but
simulation software is never perfect.

1730
02:11:52.640 --> 02:11:56.440
Few programs take the venue's
acoustic properties into account. Some

1731
02:11:56.440 --> 02:11:59.960
do, but they are more complex,
such as EASE, which I mentioned.

1732
02:12:00.380 --> 02:12:04.488
Fohhn Designer now does that too,
in the new online-only version.

1733
02:12:04.488 --> 02:12:08.028
It is more complex and takes
much more time, because you

1734
02:12:08.028 --> 02:12:11.820
have to enter the venue's
reflection coefficients and so on.

1735
02:12:11.940 --> 02:12:13.640
So it is a little involved. It is not quick.

1736
02:12:15.580 --> 02:12:18.229
Depending on the configuration,
each tool's strengths and your

1737
02:12:18.229 --> 02:12:20.836
habits, it is useful to move
between programs. That is what I

1738
02:12:20.836 --> 02:12:23.400
showed you with ArrayCalc. I
make my subwoofer arcs in Focus

1739
02:12:23.560 --> 02:12:26.891
to save time. With MAPP, I run all
sorts of simulations and experiments.

1740
02:12:26.891 --> 02:12:29.899
It is useful to know three or four
tools. You do not have to know

1741
02:12:29.899 --> 02:12:32.860
every feature, but being able to
work with them lets you explore

1742
02:12:32.860 --> 02:12:36.869
a lot of things. All these simulations
look beautiful and perfect,

1743
02:12:36.869 --> 02:12:40.817
but they always represent ideal
conditions. When we start working

1744
02:12:40.817 --> 02:12:44.340
with directivity, place one
sub or two, enter the settings

1745
02:12:44.440 --> 02:12:48.187
and set the distances, it is worth
measuring, or at least listening, to check

1746
02:12:48.187 --> 02:12:51.982
whether the prediction matches reality.
For example, at Ground Control, with a

1747
02:12:51.982 --> 02:12:55.680
sub on the left and one on the right,
we would expect lots of cancellations.

1748
02:12:55.860 --> 02:13:00.040
Surprisingly, there are not that many
at Ground Control, because all the

1749
02:13:00.040 --> 02:13:04.220
reflections play a huge part. Those
reflections mean we lose definition.

1750
02:13:04.360 --> 02:13:07.579
The cancellation is not as
deep as expected, because many

1751
02:13:07.579 --> 02:13:10.854
other parameters are not
included in the simulation. So it

1752
02:13:10.854 --> 02:13:13.960
is important always to check
the actual result on site.

1753
02:13:16.260 --> 02:13:19.920
Is everyone all right?
We are nearly at the end.

1754
02:13:22.580 --> 02:13:25.860
Let us conclude. There are still
some sections, but they are optional.

1755
02:13:27.700 --> 02:13:31.196
Understanding and properly controlling
subwoofer behaviour is essential

1756
02:13:31.196 --> 02:13:34.840
for coherent coverage and fewer acoustic
problems. That is fairly obvious.

1757
02:13:37.180 --> 02:13:40.459
Simulation software is a great
help. That is how I learned

1758
02:13:40.459 --> 02:13:43.398
a lot: using programs,
learning at least the basics,

1759
02:13:43.398 --> 02:13:46.960
experimenting and learning, along
with a great deal of reading.

1760
02:13:47.600 --> 02:13:49.457
It really helps. It keeps you from doing

1761
02:13:49.457 --> 02:13:51.500
things at random or simply making things up.

1762
02:13:53.670 --> 02:13:57.273
We have not covered it much in this
course, but managing relative levels

1763
02:13:57.273 --> 02:14:00.777
and the electrical side is essential.
In all the gradient and end-fire

1764
02:14:00.777 --> 02:14:04.230
configurations you saw, each assembly
always produced the same level.

1765
02:14:04.230 --> 02:14:08.059
As soon as we adjust those
levels, other things change

1766
02:14:08.059 --> 02:14:11.745
too. Obviously, in a gradient
array, if the rear sub

1767
02:14:11.745 --> 02:14:16.070
providing cancellation is louder
or quieter, that will change

1768
02:14:16.070 --> 02:14:19.997
the radiation pattern and the
balance again. We can use that too:

1769
02:14:19.997 --> 02:14:24.044
we can control directivity through
acoustic levels. For example, in

1770
02:14:24.044 --> 02:14:27.910
a subwoofer arc, we had the line
and the delays, which we adjust

1771
02:14:27.910 --> 02:14:30.858
for the required coverage. But
simply changing the levels at the

1772
02:14:30.858 --> 02:14:33.760
sides or in the middle also
redirects the beam. We can use that

1773
02:14:33.760 --> 02:14:36.570
parameter too. I have not shown
it here, but it also matters.

1774
02:14:38.590 --> 02:14:41.829
As always in audio, the answer is often: it

1775
02:14:41.829 --> 02:14:45.670
depends. You have seen the
theory, but in practice,

1776
02:14:47.610 --> 02:14:51.439
there is never one certain
conclusion for a given problem. We

1777
02:14:51.439 --> 02:14:55.330
always have to adapt and change
according to the requirements.

1778
02:14:57.290 --> 02:15:03.210
That gives you an idea.
Is everyone happy so far?

1779
02:15:03.210 --> 02:15:09.250
Thank you. Very good.
Great. I had a little series

1780
02:15:09.250 --> 02:15:15.367
of examples. If you like, I could
open the software and show you some

1781
02:15:15.367 --> 02:15:21.130
things I have done and how they
were made, if that interests you.

1782
02:15:22.990 --> 02:15:25.782
We can look at them. Shall
we do that later, Mathieu?

1783
02:15:25.782 --> 02:15:28.731
That is what I was thinking
too. For now, I have not put

1784
02:15:28.731 --> 02:15:31.470
anything in that section.
In any case, you will see.

1785
02:15:32.070 --> 02:15:35.205
I could do a refresher, perhaps
another training session with a recap

1786
02:15:35.205 --> 02:15:38.250
and more examples. I think I am
starting to lose concentration too.

1787
02:15:38.910 --> 02:15:44.300
We need time to absorb all this. You can
look through the appendices in the slides

1788
02:15:44.300 --> 02:15:49.230
yourselves. Julie has missed her swimming
session. I really have missed it.

1789
02:15:50.430 --> 02:15:54.618
The appendices show some reflection
effects. Here I have shown the effect of

1790
02:15:54.618 --> 02:15:58.750
a wall on a sub, using virtual sources.
I am going through it very quickly.

1791
02:15:59.390 --> 02:16:01.670
You can look at it in the slides.
I think it is understandable.

1792
02:16:04.350 --> 02:16:07.590
This table about relative levels is
one I borrowed from Bob McCarthy.

1793
02:16:09.490 --> 02:16:13.086
It is a summary table. I am
going to leave you. Thank you

1794
02:16:13.086 --> 02:16:16.934
for the training, Mathieu. Sorry?
Thank you for the training.

1795
02:16:16.934 --> 02:16:20.530
I have to go. All right. In
any case, it was really good.

1796
02:16:20.850 --> 02:16:26.162
Leaving like a savage. Great,
glad to hear it. Kisses to

1797
02:16:26.162 --> 02:16:31.190
everyone. Bye, Romain. See
you soon, guys. And girls.

1798
02:16:31.950 --> 02:16:35.872
We got it. I will leave you
to look at this little table.

1799
02:16:35.872 --> 02:16:39.312
It summarises what happens
when we vary levels and

1800
02:16:39.312 --> 02:16:42.890
phase relationships, and
how each affects the other.

1801
02:16:42.990 --> 02:16:45.950
There is more detail there,
and it is very interesting.

1802
02:16:47.790 --> 02:16:50.793
Next, a little more about the
speed of sound. I said we were not

1803
02:16:50.793 --> 02:16:53.750
taking that parameter into account,
but in reality I always do.

1804
02:16:54.810 --> 02:16:57.997
It varies considerably with
temperature and altitude.

1805
02:16:57.997 --> 02:17:00.943
Looking quickly, we can
see that depending on the

1806
02:17:00.943 --> 02:17:04.370
temperature, it ranges from
325 to 349 metres per second.

1807
02:17:04.630 --> 02:17:07.915
Depending on altitude, it goes
from 340 at sea level to 295.

1808
02:17:07.915 --> 02:17:10.981
That is quite a difference.
We rarely do sound at 12,000

1809
02:17:10.981 --> 02:17:14.430
metres, but in Mexico City, for
example, I was at 2,500 metres.

1810
02:17:15.270 --> 02:17:20.957
At that point it starts to matter, so
it is at least worth considering. How do

1811
02:17:20.957 --> 02:17:26.790
you combine all of that? In Mexico City,
I imagine there was a certain altitude,

1812
02:17:26.850 --> 02:17:29.610
but also a particular temperature,
which was not 20 degrees.

1813
02:17:31.510 --> 02:17:35.410
There are two types of
calculation. The first is based

1814
02:17:35.410 --> 02:17:39.310
on temperature; the second
is based on altitude. There

1815
02:17:39.310 --> 02:17:43.210
is a third one I skipped,
based on volumetric density.

1816
02:17:43.350 --> 02:17:47.210
It is a little more complicated.
You calculate the volumetric

1817
02:17:47.210 --> 02:17:50.817
density, which is the result
of altitude and temperature:

1818
02:17:50.817 --> 02:17:54.550
roughly speaking, air pressure,
to summarise as best I can.

1819
02:17:54.790 --> 02:17:58.882
That gives us another formula, which
is quite long. Search Wikipedia for the

1820
02:17:58.882 --> 02:18:03.190
speed of sound and you will find it. Then
we can recalculate the speed of sound.

1821
02:18:04.290 --> 02:18:09.668
Is it really that fundamental?
For example, at plus ten

1822
02:18:09.668 --> 02:18:15.730
degrees and an altitude of 1,500
metres, does it really change

1823
02:18:15.730 --> 02:18:20.906
the propagation speed that much? Yes,
it does. In Mexico City, to give you an

1824
02:18:20.906 --> 02:18:26.150
idea, from memory, although I do not
remember exactly, I had values around 325

1825
02:18:26.150 --> 02:18:28.150
or 326 metres per second.

1826
02:18:30.610 --> 02:18:35.510
All my calculations change accordingly.
That is why, in my spreadsheet and

1827
02:18:35.510 --> 02:18:40.410
in the software, we always enter the
temperature and atmospheric pressure.

1828
02:18:41.170 --> 02:18:44.119
In fact, there are even more
parameters than that. This is an

1829
02:18:44.119 --> 02:18:47.551
approximate formula. I have deliberately
written an approximately-equal

1830
02:18:47.551 --> 02:18:50.790
sign. It is not the full formula.
The full formula is on Wikipedia.

1831
02:18:51.090 --> 02:18:52.750
I can show it to you if you like.

1832
02:18:55.110 --> 02:18:59.926
I will leave you to look at the
phase-difference calculation in the

1833
02:18:59.926 --> 02:19:04.670
appendix. It is a fairly simple
formula, but I have used it often.

1834
02:19:05.130 --> 02:19:08.145
You can see how it works in
the appendix. It lets you

1835
02:19:08.145 --> 02:19:11.558
calculate phase differences.
Then there are some references:

1836
02:19:11.558 --> 02:19:14.630
Bob McCarthy's Sound Systems:
Design and Optimization.

1837
02:19:14.910 --> 02:19:18.277
It is a very good book. This
one here. I use it very often.

1838
02:19:18.277 --> 02:19:21.930
There is a lot in it, and not
just about subs. We cannot see it.

1839
02:19:23.990 --> 02:19:29.580
It is this one. It blends into
your background image, so we

1840
02:19:29.580 --> 02:19:35.550
cannot see it. Your virtual
background is not working properly.

1841
02:19:37.110 --> 02:19:40.819
This one, backwards. All I
can see is Julie. Can you not

1842
02:19:40.819 --> 02:19:44.461
see me? I have no camera.
That one says Julie Courrier.

1843
02:19:44.461 --> 02:19:48.170
I have put the Bob McCarthy
book on the server as a PDF.

1844
02:19:49.550 --> 02:19:52.410
Is it the whole book? Yes, the whole book.

1845
02:19:55.500 --> 02:19:59.930
d&b TI 330 means Technical Information
330. It covers subwoofer arrays. It

1846
02:19:59.930 --> 02:20:04.300
is quite interesting and fairly short,
although it contains a few errors.

1847
02:20:05.720 --> 02:20:08.020
Then there is Dave Rat's
website. It is an old blog, but

1848
02:20:08.020 --> 02:20:10.362
there are lots of fun things
on it. Then some material on

1849
02:20:10.362 --> 02:20:12.580
Techniques du Son, and
information about the TM Array.

1850
02:20:12.700 --> 02:20:16.849
Metallica fans can have a look. There
is also a very good illustration

1851
02:20:16.849 --> 02:20:20.880
by Bob McCarthy, explaining end-fire
visually. It is very well done.

1852
02:20:21.720 --> 02:20:26.564
There are plenty of other links
I could give you, but those are

1853
02:20:26.564 --> 02:20:31.100
the main ones. I have included
them at the link I sent you.

1854
02:20:32.860 --> 02:20:36.963
That gives you an overview.
Well done. Great. Thank you

1855
02:20:36.963 --> 02:20:41.140
very much. Thank you. Great,
glad to hear it. Thank you.