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M-AUDIO TimewARP 2600 User Guide

Copyright © 2004, by Way Out Ware, Inc.. All rights reserved.
No part of this work may be reproduced or transmitted in any form or by any means, electronic or
mechanical, from or to any form of media, without the prior written permission of Way Out Ware, Inc..
Requests for permission to reproduce any part of this work should be addressed to : Way Out Ware,
Inc., attn: Copyright Adminstration, info@wayoutware.com.
User Guide
English
Table Of Contents
1.1 The ARP 2600, 1970 - 1981 and Onward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 How this Manual is Organized. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 How To Use This Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Digidesign Pro Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2 MIDI Communication and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3.1 Signals and Sounds
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Attributes of Signals
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Attributes of Auditory Events
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4 How Signals and Sounds Go Together... Sort of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.5 Modules and Methods for Generating Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3.6 Modules and Methods for Processing/Modifying Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.7 Controlling One Module by Means of Another . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
4.1 Top Row Control Panel Buttons and Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
4.2 Preamp/Gain Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
4.3 Voltage-Controlled Oscillators (VCO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
4.4 Voltage Controlled Filter (VCF)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.5 Envelope Generators
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.6 Voltage Controlled Amplifier (VCA)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.7 Mix/Pan/Reverb Output Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4.8 Envelope Follower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
4.9 Ring Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
4.10 Noise Generator (NG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
4.11 Voltage Processors (VP)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.12 The Sample & Hold Module (S/H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.13 The Internal Clock /Electronic Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.14 The Virtual Keyboard
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.1 Table of Alternate Keyboard Tunings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
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TimewARP • User Guide
English
English

1 The TimewARP 2600 Manual

1.1 The ARP 2600, 1970 - 1981 and Onward

The ARP 2600 was the second product of ARP Instruments. It was released in 1970, and continued until the
manufacturer ceased operations in 1981.
Its design combined modularity (for studio flexibility, and for instructional use) and integration (for real-time
performance). Functionally, the ARP 2600 was completely modular: any signal output could be routed to any
signal input, with a patch cord. Operationally, the ARP 2600 was integrated, using internally-wired default signal
paths that made it possible to create a wide range of keyboard patches by simply opening up slide attenuators,
as though sitting in front of a mixing console.
The ARP 2600 earned an early reputation for stability, and for flexibility exceeding that of its competitor, the
Minimoog. Used 2600’s in good condition command premium prices on eBay today and businesses around the
country make a living reconditioning, rebuilding, and customizing 30-year-old units.
Among rock musicians, the ARP 2600 was used by Stevie Wonder, Pete Townsend, Joe Zawinul, Edgar Winter, Paul
Bley, Roger Powell, Jean-Michel Jarre, Mike Oldfield, Herbie Hancock, and many, many others.
Its modular design, and the popularity of its Owner’s Manual, made the ARP 2600 a widely used teaching
instrument in many schools and music conservatories around the country and internationally.
We are proud to bring you this software emulation of the 2600. Have fun with it, learn from it, but above all, make
noise with it.

1.2 Foreword

Unfasten the seat belts of your mind. The TimewARP 2600 will be an astonishing, exhilarating, and enlightening
experience.
Creating this manual has been an astonishing, exhilarating, and enlightening experience for me. How many are
ever given the chance to revisit an earlier life, an earlier project, a project like the ARP 2600 Manual, decades later,
and get it right? It’s time travel. I’m grateful to Way Out Ware for providing me that opportunity.
When, at Alan R. Pearlman’s invitation, I began work on the original 2600 manual in September of 1970, the 2600
itself barely existed. For the first two months, I was writing “blind”—without a machine in front of me. My first
hands-on experience with a synthesizer had been only six months earlier (it was a Putney VCS3).
I finished the text in March of 1971, Margaret Friend created the graphics, and the Owner’s Manual for the ARP
2600 began what turned out to be a surprisingly long career. In spite of the many defects that my inexperience
contributed—the gaps in coverage, and outright errors—it became quite popular. To this day, it still gets an
occasional respectable mention in the analog-synthesis community.
When Way Out Ware’s Jim Heintz called in early 2004 to tell me about the TimewARP 2600, a lot of time had
passed. Regarding software synthesizers, I had grown weary and cynical. Analog-modeling software had been
a decade-long disappointment; some products did interesting things but not the things that real analog modules
do. Jim, however, had already encountered, thought about, and solved these problems. He owned a real 2600.
He really aimed at getting it right and would not be satisfied with anything less. It was a pleasure, finally, to accept
his invitation to do an Owner’s Manual.
It’s now clear that Way Out Ware has set a new standard for software-based audio synthesis. The behavior of the
TimewARP 2600 software—both module-by-module and integrated into patches—is effectively indistinguishable
from that of the analog hardware that it emulates.
Soaring and swooping through the free air of analog synthesis—a world of nothing but sliders and cords and
continuously evolving patch configuration—was a capstone course at the Boston School of Electronic Music in
the 1970’s. That is the world that the TimewARP 2600, for a new generation of musicians in a new millennium
(that means you), provides access to: it is the first—and I believe only—software synthesizer to support real-time
performance by sliders and patchcords alone.
So here it is: your new Owner’s Manual, for the new TimewARP 2600.
Unfasten the seat belts of your mind. How else can you hope to experience time travel? How else can you enjoy
free flight?
Jim Michmerhuizen
Jim Michmerhuizen is the author of the original ARP 2600 Manual and Founder and Director of the Boston
School of Electronic Music.
4

1.3 How this Manual is Organized

This is not a textbook; it’s a survival manual.
Chapter 2 is about installing and configuring the software so you can get up and running.
Chapter 3 is a brief introduction to the vocabulary and methods of classical analog synthesis, so that we can
understand each other throughout the rest of the book.
Chapter 4 is a module-by-module reference, including the digital extensions made possible by the fact that the
TimewARP 2600 is software—a piece of computer behavior—rather than a collection of electronic hardware.
Chapter 5 is not in this book, but is a collection of patches, with accompanying documentation, located in a separate
document file called Patchman.pdf found on the distribution CD (or as a download from www.wayoutware.com).
The patches and commentary are keyed to the numbered chapters, sections, and subsections of this manual.
Some of the patches form a tutorial sequence, and some illustrate vocabulary lessons and concepts.

1.4 How To Use This Manual

You’ll probably need to do a quick run through of Chapter 2 as you install the TimewARP 2600 and learn some of
the basic setup operations. After that, you can pretty much mix and match, according to your experience.
If you’re new to audio synthesis, you’ll want to walk through the tutorial patch sequence in Patchman.pdf, referring
back to Chapter 3 for concepts and Chapter 4 for detailed module specifications while you explore, and learn to
control, the vast range and patch repertoire of the TimewARP 2600 software synthesizer.
If you already have some experience with audio synthesis, you might go directly to Chapter 4 for the detailed
module-by-module specifications of the TimewARP 2600. If you know and love the original ARP 2600 itself, take
particular note of section 4.1, where we describe what you can do with the TimewARP 2600 that you could not do
with its analog ancestor. These digital extensions include patch load/save, additional VCO sine-wave outputs,
dual-channel signal input, automatic Y-connections at all signal outputs, sixteen keyboard micro-tuning options,
MIDI Beat Clock synchronization, and MIDI controller mapping (with subranges) for all the panel sliders.
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TimewARP • User Guide
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2 System Requirements, Installation, Configuration, Setup and Usage
In this chapter you will find all of the platform-dependent information you need in order to install and operate your
TimewARP 2600 software synthesizer.
The TimewARP 2600 provides an extended set of digitally-based features that no hardware-based analog
synthesizer can offer. We describe the most important of these in section 2.2.

2.1 Digidesign Pro Tools

This release of the TimewARP 2600 is an RTAS plug-in and runs only under Digidesign Pro Tools 6.1 and later
versions, on either Apple OS X or Windows XP. On either of these platforms, the requirements for the TimewARP
2600 are essentially those of Pro Tools itself.
2.1.1 System Requirements
These are the same as Pro Tools itself, including enough memory to satisfy the practical needs of the TimewARP
2600 software.
2.1.1.1 Disk Space and RAM
The executable file occupies 6.1MB on disc, and the RAM requirements when running are the same as the Pro
Tools minimums.
2.1.1.2 System Clock
The TimewARP 2600 performs all signal generation and processing in real time. In complex polyphonic patches,
this may put a considerable load on your CPU. You may have difficulty with a clock speed less than 800MHz;
higher clock rates will increase the number of polyphonic voices you can use, and the complexity of the patches
available.
2.1.2 Installation
Installation on either platform is accomplished by very simple standardized installation sequences. You must, of
course, have a current installation of Pro Tools on your target computer.
2.1.2.1 Mac OS X
Insert the distribution CD or download the .dmg installer file from www.wayoutware.com. Double-click the .dmg
installer to initiate installation.
If you agreed to the license, a TimewARP 2600 installer icon appears. Double-click it to initiate the installation
process.
When finished, start Pro Tools and proceed to 2.1.3.1.
2.1.2.2 Windows XP
Insert the distribution CD or download the installer file from www.wayoutware.com. Run the .exe installer file.
If you agreed to the license, follow the installer instructions.
When finished, start Pro Tools and proceed to 2.1.3.1.
2.1.3 Setups
2.1.3.1 Real-time Instrument for Performance and Recording
The TimewARP 2600 can transform your computer into a real-time instrument for live performance or recording.
To set this up, create an audio track in Pro Tools. Select either mono or stereo in the track-creation window; this
will determine, in turn, the channel options offered by the TimewARP 2600 for this track.
In the mix window display for this track, at the track-inserts block up at the top, click on the first insert selector.
Choose the TimewARP 2600 plug-in from the appropriate menu.
Now create another track, but in the track creation dialog, choose MIDI track instead of audio track, and route the
track output to the TimewARP 2600.
As input for the new track, select your MIDI keyboard device, and enable the track for recording. Pro Tools will
route all incoming MIDI events from your MIDI keyboard device to the TimewARP 2600 plug-in.
If your MIDI keyboard has any additional MIDI control devices (sliders, knobs, buttons, etc.), you can assign these
to any TimewARP 2600 sliders, knobs and switches that you choose. For details, see section 2.2.
6
2.1.3.2 Processing Audio Signals
The TimewARP 2600 can be used to process audio signals in a similar manner to a reverb or other effects plug-
in.
To set this up, create an audio track or select a track already recorded in Pro Tools. (If this is a new track, select
either mono or stereo in the track-creation window; this will determine, in turn, the channel options offered by the
TimewARP 2600 for this track.)
In the mix window display for this track, at the track-inserts block up at the top, click on the first available insert
selector. Choose the TimewARP 2600 plug-in from the appropriate menu.
If the current track is mono, the TimewARP 2600 for this track will be configured for one channel of input, and you can
select between mono and stereo output. If the current track is stereo, the TimewARP 2600 insert will automatically
be configured for stereo throughout. Confirm this, when the synthesizer panel comes up, by observing that the
preamp module in the upper left corner has two channel outputs rather than just one.
If you are processing an existing track, press play on the transport control to hear the audio being processed by
the TimewARP 2600 in real time. You need to select an appropriate TimewARP 2600 patch (such as those in the
Voice or Guitar Effects categories in the Factory group) to successfully process audio this way.
If you are processing a live track, enable the track’s record mode, and then audio from your input will be fed
through the TimewARP 2600. You need to select an appropriate TimewARP 2600 patch (such as those in the Voice
or Guitar Effects categories in the Factory group) to successfully process audio this way.
2.1.3.3 MIDI Tracks
Running as a track plug-in, the TimewARP 2600 can process prerecorded MIDI tracks.
To do this, set up two tracks just as you did above in section 2.1.3.1: an audio track that is running the TimewARP
2600 as a track insert, and a MIDI track whose output is routed to the TimewARP 2600.
When you play this track (use the Pro Tools transport window to play, rewind, pause the MIDI sequence, etc.), the
MIDI events stored in the track sequence will be routed to the TimewARP 2600. MIDI note-events will become
key depressions at the virtual keyboard; MIDI pitch-bend will turn the virtual keyboard pitch-bend knob; and
MIDI controllers that are mapped to TimewARP 2600 sliders, knobs or switches (see section 2.2) will move those
controls.
2.1.4 Selecting Patches
The TimewARP 2600 gives you a three-level hierarchy for storing and organizing your patches. All Patches are
sorted into various Categories, which are in turn sorted into major Groups. Each of the three patch selection
buttons generates a drop-down list associated with one layer in this hierarchy.
Groups, Categories, and Patches can also be selected by keyboard shortcuts. The up/down arrow keys on the
computer keyboard select Patches, the left/right arrow keys move between Categories, and using the control key
with the left/right arrow keys moves between Groups.
2.1.5 Making Patch Connections
Use the mouse to connect any output to any input jack. Position the cursor at any signal output, click and hold
down the mouse button, and drag the patch cord to any signal input. To remove a patch cord, drag either end
away from its signal jack.
The TimewARP 2600 will not connect two outputs or two inputs together. If you drag from one jack to another but
no patch cord appears, it may be that both jacks are inputs or both are outputs.
The TimewARP 2600 will allow Y-connections, distributing a single output signal to multiple destinations by holding
the control key down while clicking an output that already has a cable connected to it. A second cable will appear
attached to the cursor, which can then be plugged into another input.
2.1.6 Using the Sliders and Knobs
To adjust a slider or knob, drag it with the mouse. For increased resolution, hold down the command (Apple) or
control (Windows) key during the drag operation.
If you pause for a moment over a slider, a display will pop up with the numerical value and name of the parameter
it controls.
If you have MIDI controller hardware, you can easily connect it to the sliders, knobs or switches; see section
2.2.2.
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TimewARP • User Guide
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2.1.7 Using the Virtual Keyboard Display
The graphic TimewARP 2600 keyboard display responds directly to mouse events; click on any key to create a MIDI
“keydown” signal. This is useful when you are creating and tuning a new patch, if you don’t have a hardware
MIDI keyboard handy.
The virtual keyboard also displays—as key depressions—incoming MIDI note-events. Use this to monitor your
external MIDI keyboard connection and activity.
2.1.8 Polyphonic Operation
The TimewARP 2600 can respond to as many as eight simultaneous keydown events. Use the Voices dropdown
(see section 4.1.1.2) to set the number of voices.
2.1.9 Saving and Loading Patches
You may save patches using the Save or Save As buttons or load patches with the Patch Manager (see section 4.1
below). There is no limit to the number of patches you can create and save. To enable the Save button, the Lock
button (padlock icon) must be in the unlocked mode.
You may wish to create a bank of “template” patches, generic versions of often-used configurations.
The TimewARP 2600 responds to MIDI bank-select and patch-select commands.

2.2 MIDI Communication and Control

2.2.1 Slider, Knob and Switch Control
You may control any slider, knob or switch on the TimewARP 2600 plug-in with any MIDI controller. If you have a
hardware control surface, or if your MIDI keyboard has slider or knob control devices, you can use them to control
any combination of sliders, knobs or switches in a patch.
Any connections you set up are global to the TimewARP 2600—you can store them independently of any specific
patch (see section 4.1.2.1 below).
To connect a slider, knob, or switch to an external MIDI controller, hold down the control (Mac) or shift (Windows)
key and click on the slider, knob or switch image. The responding dialog box offers you both global and patch-
specific connections.
2.2.1.1 Global MIDI Map Settings
Select the controller number, either by directly typing it in, or by moving the physical control on the MIDI device you
intend to use.
Set the response curve, polarity, and range. The response curve may be linear, or exponential, or logarithmic. The
polarity is either direct or inverted. To set the Control Range, drag either end of the bar inward. Whenever the bar
covers less than the entire controller range, you may also drag it to the right or left, to adjust the range offset.
You may, if you wish, assign the same external control to several TimewARP 2600 sliders or knobs, and set a
different curve, polarity, and range for each one. In this way, you can create patches and configurations of the
TimewARP 2600 that are specifically adapted for expressive performance either live or in the studio.
2.2.1.2 Patch-Specific Settings
Besides globally assigning a slider, knob or switch to a MIDI controller, you may also assign the slider or knob to
be controlled by the velocity and/or aftertouch parameters of incoming keyboard events. (These assignments are
not global; they are stored with individual patches.)
In real time, these controller values are summed with the current global control values to determine the real-time
value of the slider. So, by careful tuning beforehand, you can have both keyboard expression and hardware
knob/slider control at the same time.
2.2.2 MIDI Patch Selection
In each group of patches, the first 128 are available to standard incoming MIDI patch-selection commands.
Patch categories don’t affect this numbering. For example, if the first category in a group has 127 patches, then
the second category will have just one patch available for MIDI patch selection.
Groups themselves can be selected with MIDI bank-select commands.
8

3 The Craft of Audio Synthesis

This chapter is about the facts—physical, mathematical, and auditory—that make the TimewARP 2600, and the hardware
that it emulates, possible. We have to spend a few minutes here distinguishing between physical signals, and the sounds
that people hear in the presence of certain kinds of signals.
This is important because synthesizer equipment can only deal with signals—physical commotion of one sort and another.
When you are fiddling with synthesizer equipment, you are generating and modifying signals for the sake of the interesting
(we hope) sounds you hear when those signals reach your eardrums.

3.1 Signals and Sounds

A signal is something happening: a waving flashlight, or ambulance siren, referee flag dropping, winking at a friend. Tiny
disturbances of the air around us are signals for our ears; we hear them as noise, or singing, or sirens, shrieks, growls,
whatever.
The signal is the physical disturbance in the air, the movement of the eardrum. The sound is your perception of the signal:
“Hello!”
3.1.1 Analog and Digital Representations of Signals
The signals we are concerned with in sound synthesis are audio signals: more or less regular variations in air pressure, at
our eardrums, repeating at rates of between 20 and 20,000 times in one second.
Such signals are straightforward physical processes which can be recorded and reproduced. One way to do that is to look
at the pattern of air-pressure variation, and model it in some other medium. During the past century this has been done
with grooves in a phonograph record, magnetic fields along a length of tape or wire, and other media. The usual scenario
is: with one or more microphones, generate an electronic model of the vibrating air, then use the electronic signal to drive
a magnetic recording head, or amplifier, or LP recording lathe. Throughout such processing, the signals we deal with are
directly analogous to each other; except for the change in medium from air to voltage to magnetic field strength or stylus
position, the signals are identical. Graphed or charted, they even look the same. This is analog recording.
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TimewARP • User Guide
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Another way to record such a signal is, with high-speed digital circuits, to measure the underlying medium many times each
second, and store the measured numbers. This is digital recording.
Since the TimewARP 2600 is not constructed of electronic circuits, concepts such as “voltage” don’t apply here. The TimewARP
2600 is software, a complex piece of computer behavior. The signal medium for the original ARP 2600 was electrical
pressure, measured in volts. The signal medium for the TimewARP 2600 is simply number sequences. We use those
numbers the way the original machine used electrical pressure; where the original Owner’s Manual used the word “voltage”
we will just say “signal” or “signal level,” and in the module specifications we will refer to “virtual Volts” or “vV.”

3.2 Attributes of Signals

The simplest possible signal is a sine wave. It’s like the back-and-forth motion of a point on a circle as the circle rotates. A
lot of the mathematics of sine waves is based on that rotating-circle idea; you don’t have to get involved in that unless you’re
curious about it, but it’s helpful to train your imagination by picturing the basic sine-wave graph as a slightly stretched coil
spring like a “slinky.”
The motion of a pendulum, or of a tuning fork, swinging back and forth as they slowly come to rest, is a decaying sine
wave.
A sine wave signal has exactly three attributes: its frequency, its amplitude, and its phase. It has no other characteristics at
all. (The decaying swing of the pendulum or the tuning fork does have one other attribute: the amount of energy/amplitude
that it loses on each swing. It’s not a “pure” sine wave.)
3.2.1 Fundamental Attributes
Picture a point on that rotating circle, leaving a trail behind as it rotates, like an airplane propeller. Picture the trail, stretched
out behind like a coil spring, and ask yourself:
3.2.1.1 Amplitude: what’s the diameter of this imaginary circle?
3.2.1.2 Frequency: how fast is it rotating?
3.2.1.3 Phase: when does it start a new cycle?
10
3.2.2 Complex Attributes
Most of the activity that reaches our ears every day is far more complex than just a sine wave. Banging on a
garbage can creates a much more complicated sort of vibration than tapping a tuning fork.
But any kind of motion that isn’t a sine wave can still be analyzed as a collection of sine waves. This is called
Fourier analysis, after the man who discovered that it was possible, and proved—mathematically—that it always
worked.
This goes both ways: any complex signal can also be constructed from a collection of sine waves with the
appropriate attributes: amplitude, frequency, and phase relationships.
In fact, any kind of motion—any repeating pattern of the sort that we are interested in here as “sound waves”—
can be examined and analyzed under two different headings:
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3.2.2.1 Waveshape, and Time-Domain Attributes
Any repeating motion can be diagrammed in a graph where the horizontal axis is a period of time and the vertical
one is the motion itself, back and forth. This is the time-domain view of a signal:
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3.2.2.2 Spectrum, and Frequency-Domain Attributes
Instead of looking at a signal as something in motion through a period of time, we can look at the collection of
sine-wave components of the signal. In such graphs, the horizontal axis is a frequency range (instead of a time
period), and we indicate each spectrum component with a single vertical line in the graph. The height of the line
indicates the strength of the component at that frequency. This is the frequency-domain, or spectral-domain, view
of a signal.
It is the distribution and relative strength of spectral components that we experience as the tone-color of a sound
or sounds. “Bright,” “dull,” “sharp,” “tinny,” “heavy,” and so on—these are all descriptive words for the spectral
attributes of sounds.
3.2.2.2.1 Harmonic Series
The spectral view of any periodic signal has components at simple multiples of the signal frequency. For example,
suppose we examine a sawtooth wave at a frequency of 110Hz. It will have components at 110, 220, 330, 440,
and so on.
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A simple number sequence like this is called a harmonic series. It is interesting to think about musically; the
smaller numbers in the series all form simple musical intervals: octaves, fifths, fourths, and thirds.
Most musical instruments generate harmonic spectra. Some have more, some have fewer harmonics, and there
are wide spectral variations even within a single instrument depending on how it is played. In general, whatever
the actual spectral components are, they will always form a harmonic series.
In audio synthesis, you will use oscillators to generate pitched tones that have a harmonic spectrum.
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3.2.2.2.2 Inharmonic Series
Inharmonic, in this context, means “not forming a harmonic series.” Some waveforms do not repeat themselves
at a regular interval; the spectra of such waves will have components at strange non-integral frequency ratios, or
they may have shifting spectral components that die out and reappear. Some percussion instruments, such as
kettledrums, or bells, have inharmonic spectral components.
In audio synthesis, you can use various modulation techniques—such as AM and FM—to generate inharmonic
spectra.
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3.2.3 Attributes of Random Signals
A completely random signal—noise—actually has a continuous spectrum: it does not consist of isolated sine
waves in a harmonic series, nor even in an inharmonic series. A noise spectrum is a continuum of frequency
components; in order to describe it, we have to talk about how much energy is in each band in this continuum.
One kind of noise may have high-frequency energy, while another has low-frequency energy.
In audio synthesis, noise is an extraordinarily useful signal. Filters can be used to shape a noise spectrum into
almost anything—even pitched sounds.
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