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More Fun in the Waves (Part 2)

Article from Music Technology, October 1988

Following last month's explanation of computer-generated waveforms and their uses, we look at strings of waveforms working together to build complex sounds. Tom McLaughlin investigates wavetables.

Want to increase the scope of your sampled sounds or additive waveforms? Linking waveforms together will enable you to produce sounds that can be realistic or unnatural.

IN LAST MONTH'S "Fun in the Waves" we discussed designing soundwaves from scratch using computer additive synthesis. These static waveforms can often give us unique tone colours unavailable anywhere else, but unless you're satisfied with the different treatments you can obtain from them using DCFs and DCAs, they can get somewhat boring to listen to - at least when compared with sampled sounds. The natural step to making more interesting sounds is to string waveforms together, and is to building sounds what making an animated cartoon is to a sketch. This is referred to as wavetable synthesis.

This approach is applicable to any sound material that can be stored and strung together in your sampler/computer. You see, designing progressions of wavetables by additive synthesis (or other forms of constructing soundwaves within a computer) and sampling go hand in hand. They employ the same sort of technology: the storage of audio waveforms, as digitised computer "snapshots" of sound that, when played back in the order in which they were sampled or designed, will simulate or recreate moving sound. They form a sequence of acoustic events. With "cut and paste" software we can rearrange these segments of digitised sound material at will. And with total control over what we hear.

Wavetables can be constructed from samples or digitally synthesised waveforms. They can even be used together in the same wavetable, but unless you have sample rate conversion software, spend the time to tune your source sounds to a given sample rate (or vice versa) or are just darn lucky, your sampled and computer synthesised sounds are unlikely to be in tune with one another. (What about some software to make this easier, software designers?)

The principle behind wavetable synthesis is to take a collection of synthesised soundwaves or segments of pre-sampled sounds and assemble them to create a new sound. These segments can be one or several wave cycles long, but for a smooth transition (avoiding a click) between segments, start them all on positive-going zero cross points and end them on negative-going ones (or the other way around).

"New" sounds needn't be cosmic "smacks you between the eyes" sonic happenings. Indeed, a slight variation on an existing family of sounds or a different series of events to that we're familiar with can often be rewarding to use in a musical setting.

An example of this technique is a two-segment percussive sound. For the first segment find or make a segment for the general character of the sound that gives you a musical loop: a sharp harpsichord/clavinet, metallic bell-like or mellow electric piano wave, for instance. For the second find a very bright sound for the attack portion of the wavetable. You can go to town on this, depending on the type of percussive sound you want: a dull, clicky synthesised sound will complement an electric organ wave loop while a segment from a sampled cymbal will give a cutting edge to a struck string sound. If you paste the mellower segment after the bright one and loop around the second segment it will give you percussive wavetable material that can be VCA'd and VCF'd to taste.

Both segments can be as little as one wavecycle long, but since the attack portion (which only need to be a few milliseconds long) is little more than a click, it need not be in tune with the "body" of the sound.

More complex sounds can be created by plotting then programming the desired harmonic progression wave by wave using computer synthesis. Alternatively, waves can be designed at key transition points in a sound and crossfaded between them at the appropriate time scale. The latter is the preferred method as all the tedious, time-consuming calculations are carried out for you. The same goes for sampled sound material; you can take single segments of samples and treat them as if they were additive (or similarly computer generated) sound waves. If you've paid attention to starting them on a positive zero crossing and ending them on a negative zero crossing, you shouldn't have any problems with clicks between segments - which incidentally sound just like bad loop glitches.

Whether you're going to work strictly with computer synthesis, sample fragments, or a combination of the two, you should take the time to plan your wavetable or progression. It'll save you banging your head against the wall in the middle of stringing sounds together. Any way you approach this method of constructing sounds, charting things out on something, like the back of a Rizla packet will help you keep things in perspective. What sort of sound do you want to end up with? A percussive sound? Something that has a "woodwind" attack, or maybe a sound that fades in over a short amount of time for a string-type wash? You really should decide this before you begin. For the purposes of clarity we'll talk about a percussive wavetable, as it's part of a family of sounds that has a distinct attack and a tone colour that fades and becomes simpler towards the end of its duration.

For starters, get three distinct tone colour segments together. The first should be very loud, the second rather bright and of medium loudness and the third a very simple, low volume tone colour - a sine wave if you like. We'll refer to these as segments A, B and C. Since it's a percussive sound we're working on, only the second two segments actually need be in tune with each another.

My favourite trick when building percussive sounds is to use a clipped waveform for the first segment or so. As mentioned last month, when there's a greater amount of level than your computer or sampler can deal with, whether you're working with additively synthesised waveforms or sampling, the sound material will end up being clipped or distorted. The first waveform (s) of the wavetable can be purposely clipped to emulate (or in the case of mixing wave-table material with samples, enhance) the concentrated high-frequency/energy transients specific to this family of sounds.

Figure 1 shows what a three-waveform percussive wavetable will look like on a piece of paper.

Segments A and B can either be "butt" joined or crossfaded over a short period of time. On the other hand, segments B and C will give you the best results if crossfaded over a second or more. Looping around the last segment will enable you to sustain the sound even longer than you have material for and it can be faded away to nothing with your DCA and DCF just as a real percussive sound would.

You can get as involved as you wish with the number of segments in your wavetable, "butt" joining segments for an abrupt change in quality or crossfading for smoother transitions. The principle remains the same.

Constructing a wavetable of woodwind, strings, vocals and other sounds that don't have the pronounced entry of percussive sounds is a simple matter of starting your wavetable with a soft segment then crossfading to a louder, steady-state segment. The amount of time you crossfade over will, to a large extent, determine the character of your constructed sound.

Designing loops

SEAMLESS LOOPS CAN actually be designed into a progression. Yeah, you can loop around a cycle or two of many sounds and get away with it, but it will lack animation. Even the smallest amount of harmonic movement adds life to loops. Something as simple as slightly modulating the fundamental or second harmonic's amplitude makes a significant difference.

Loops can be made from sound material approximating the steady-state tone colour of a sample and crossfaded through those sounds where loops are difficult, impossible, or where loop material is nonexistent. It's a technique not unlike Roland's L/A synthesis really.

Be tasteful with the severity of harmonic movement within a loop unless you like more severe effects - gently swept harmonic cycles sound more natural to the ears. If you're working with sampled source material, try isolating segments that flow smoothly from one to another. With additive synthesis you'll want to change the levels of harmonics only a little from one to the next for a natural movement. Crossfading between members of a wavetable will give you smoother transitions, but if care is taken in the first place you may not need to resort to crossfading at all.

That said, there should be nothing to stop you constructing loops with wide variances in tone colour between segments, it's just that you're not used to hearing sounds like this. You may stumble upon some very useful sounds - especially when played back so fast that you can't hear the changes.

Making loops can be approached in two different ways. Segments that flow from one to another then back to the beginning of the loop again give a natural sound, but it can be time consuming to refine these ideal segments. A more practical method is to derive several segments that flow from one to another then reverse their order - A-B-A; A-B-C-B-A; A-B-C-D-C-B-A.

The series returning to segment A may sound strange. You'll need to reverse and invert the phase of each segment to get the most from this loop construction technique.

Loops within loops often help conceal the tell-tale loop cycles. A loop 32 segments long can have sub-loops occurring every 16, 8, 4 and 2 segments; a loop 24 segments long every 12, 8, 6, 4, 3 and 2 segments. With additive synthesis, try a slight modulation in amplitude with different harmonics having differing "sub loop" cycles.

Stereo Acoustic Events

I LIKE STEREO effects - stereo echoes, chorus effects and different reverbs on each side of a stereo mix. Before the introduction of that second audio channel we could either make things sound close up or far away: crisp 'n' clear or smothered in reverb. That was about it. With wavetable synthesis we can design stereo effects into wavetable progressions - amplitude panning, timbre panning, tuning and phase panning. A stereo effect that's easy to program into two wave-tables is a simple panning loop. (See Figure 2)

A stereo Leslie effect can be created by making the front, left and right waveforms brighter than the rear. The effect you're trying to create (best assessed when wearing a pair of headphones) is for the sound to move around your head in a circle. If you're using crossfading between segments and have the facility, experiment with different fade curves (linear, exponential and so on) for different movement effects. (See Figure 3)

Simulating PWM

SOMETHING I MISS from analogue synthesis days is playing around with pulse-width modulation. Although easily executed in a variety of manners on inexpensive analogue synths, anything resembling PWM has to be first designed and calculated, then programmed with additive synthesis - it's often a lot less work to sample an analogue synth. Far more suited to computer programming are modulations to/from/between different tone colours, phase and pitch relations. If you're going to make the effort to construct a wavetable tone progression you might as well go for something new and unusual. You just might invent the next flavour of the year. Why not try designing one wave colour to invert its phase while transforming into another colour, have all the even harmonics start sharp and the odd ones flat, modulate the pitch of specific harmonics or rapidly modulate the amplitude or phase between adjacent harmonics or harmonic clusters?


MANY THINGS WE take for granted on synthesisers and samplers turn out to be laborious or frighteningly complex programming jobs with additive synthesis. But flanging effects are no more difficult than layering the same sound on top of itself. Play them back at the same exact time and pitch and you probably won't hear anything, but playing one back slightly later or out of tune (static or modulated) with the other will produce phasing/flanging. And the effect can be very deep and wide. A new palette of flanging effects lie waiting to be discovered with a technique available on any sampler capable of playing two samples at once. Bright samples with a fair amount of harmonic movement will give the most dramatic effects. Loops give a constantly changing phase "swirl" with one slightly detuned, the severity of phase cancellations increasing the more in tune they are.


THE POWERFUL COMPUTING software of some samplers allows natural sounds to not only be digitally recorded and played back, but also analysed and resynthesised according to Fourier's theory. This is one of the most important things about sampling as it pertains to acoustic research and creative synthesis. Never before has musiciankind had the means to examine and recreate sound in such minute detail. Although on the expensive side at the moment, the computer musical instruments and software packages capable of carrying out these calculations are becoming more affordable year by year. The catch still seems to be (for most of us anyway) that unless you spend time with tuning or vari-speeding recordings of instruments when sampling, or own a system that has a comprehensive sample rate conversion program, there's very little chance that when you mix any wavetable, sampled or re-sampled sounds, they'll end up anywhere near in tune with one another to be musically useful.

You can layer different sounds after tuning them and play them back at the same time. With truly interactive sample resynthesis and wavetable software, something very much like Eventide's pitch "harmonizing" can be achieved by keeping the timing of a sample/wave progression constant while the pitch changes, by dividing the sound material up into segments, discarding or adding space between them and carrying out a crossfade from one segment to the next. The reason I bring this up is that the new age of computer musicians will not realise the full potential of our new-found sonic freedom until we can muck around with both sampled (acoustic and synthesised) and digitally created (synthesised and resynthesised) sounds.

Waveforms and Wavetables

I'LL LEAVE YOU with an esoteric approach to creating sounds from additive synthesis tables. For those of you into the nitty gritty side of things by designing additive sound waves from the bottom up, an approach to stringing together wavetables is to think in terms of chords or chord progressions. There are many chords to be found hidden within the harmonic series. Harmonic effects rarely, if ever, occurring in real life can be fashioned using wavetables. Intervals foreign to our Western music system are present that may be used to create tension within a progression. For something much more bizarre than even the most over-the-top analogue filter sweep effects, try programming a "circle of fourths or fifths" wavetable, ending up on the fundamental chord.

Progressions may be thought of in terms of block chords or counterpoint. You can experiment with the chord progression of a song's hook line or chorus to reinforce it in the mind of the listener in a subliminal fashion. There's no reason why melodies couldn't be programmed into a wavetable, even entire arrangements in four-part harmony are possible for those with enough patience.

Series - "Fun In The Waves"

This is the last part in this series. The first article in this series is:

Fun in the Waves
(MT Sep 88)

All parts in this series:

Part 1 | Part 2 (Viewing)

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Publisher: Music Technology - Music Maker Publications (UK), Future Publishing.

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Music Technology - Oct 1988



Synthesis & Sound Design


Fun In The Waves

Part 1 | Part 2 (Viewing)

Feature by Tom McLaughlin

Previous article in this issue:

> The Empire Strikes Back

Next article in this issue:

> Dr T's Fingers

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