EE2F2 - Music Technology

9. Additive Synthesis & Digital Techniques

‘Traditional’ Synthesis

Subtractive Synthesis Covered last week in the lecture and lab

Additive Synthesis A technique used in both analogue and digital forms Still the subject of current research

FM Synthesis Early digital synthesis technique Still used in the synthesisers in cheaper soundcards

Advanced digital techniques How it’s done today – more in the next two sessions

Subtractive Synthesis Limitations

Subtractive techniques can be used to synthesise a wide variety of waveforms from very simple sources

For synthesising natural sounds, it has several drawbacks

It isn’t always obvious how to synthesise the timbre (there can be several ways)

The result is usually only an approximation to the timbre you wanted

Some timbres are impossible to imitate using a simple subtractive synthesiser

Additive Synthesis

Recognising that all waveforms are just combinations of sine waves, an alternative synthesis technique seems obvious…

Just add together multiple sine waves Mix them at the correct levels and you

can synthesise any spectrum (i.e. create an arbitrary timbre)

Simple Additive Synthesis

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5

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15

20

2 3 4 5 6

1 2 3 4 5 60

5

10

15

20

Remember the oboe?

Taking the first six frequencies individually (fundamental plus first five

harmonics)

+ + + + + =

+

Limitations of the simple synthesiser Just adding sine waves together gives a ‘static’

sound Real sounds evolve with time and vary with pitch

and velocity The individual levels of the sine waves depend,

therefore on pitch and velocity and they also change with time

i.e. They all have different envelopes To synthesise this, in an additive synthesiser

each sine wave goes through its own VCA controlled by its own envelope generator

Block Diagram

Env. Gens.L.F.O.

Outputmixer

Trigger

VCOs VCAs

NB. In addition to the envelope generators, an LFO is usually included, just like the subtractive synthesiser.

The VCA gain is set by its E.G. and the keyboard output (and LFO)

Pros & Cons Pros

Any combination of harmonics is possible With the right balance, realistic sounds can be

produced Modern computer analysis techniques can extract the

required parameters from a recorded sound Cons

The number of harmonics is limited to the number of sine-wave generators

The complexity of the envelopes is limited It’s difficult to program by hand

NB. All these drawbacks can be addressed using a modern, computerised equivalent

Current Research

Traditional analogue synthesis

Modern computer based synthesis

Small number of partials (six or less).

Large (unlimited?) number of partials.

Each partial has a fixed frequency.

Arbitrary frequency envelopes are possible.

Amplitude of partials controlled by simple ADSR

envelopes.

Amplitude envelopes are arbitrarily complex.

Sounds are passable synthetic versions of real

instruments.

Sounds are indistinguishable from the original.

Modern Additive SynthesisFlute example(CERL Sound Group, Illinois)

Unlimited number of partials

Highly realistic

‘Morphable’Synth FluteSynth CelloSynth

Cello/Flute

Early Digital Synthesis Synthesisers using digital processors to generate

sound emerged during the late 70s and early 80s Common characteristics compared with modern

instruments Slow processors Low memory

Algorithms for generating sound had to be computationally simple and undemanding of memory

The most successful entirely digital technique was FM synthesis – popularised by the Yamaha DX7 (1983)

Frequency Modulation Principles A low frequency oscillator

modulating a VCO produces a vibrato effect

If the modulating frequency is an audio frequency, a complex spectrum is produced

The spectrum can be calculated using Bessel functions

It depends on the magnitude of the modulation

VCO

Osc.

f

f

FM Synthesis - Operators An FM synthesiser consists of

a number of operators Each operator consists of:

A digitally controlled oscillator (DCO)

An amplifier An envelope generator

For basic FM, two operators are needed – one acting as a modulator and one as a carrier

DCO

AmpEnv. Gen.

A single operator

Frequency Control Input

Audio Output

FM Synthesis – Algorithms Each operator has

an (optional) input and an output

Exactly how the several operators in the synth are ‘wired’ together is not fixed

Different configurations can be used – these are called algorithms

1 2 3 4 Additive

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4Paired

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4Stacked

Programming FM Synthesisers Sound made by a modulator-carrier pair of operators

varies dramatically with the modulation index To program an FM synthesiser you need to:

Choose the right algorithm Set-up the operators

Without detailed mathematical analysis, getting it right is a matter of:

Trial and error Experience and patient experimentation In fact, most users never bothered!

However, the range of sounds possible by varying only a few tens of parameters is (probably) unsurpassed

Pros & Cons Pros

Very small number of parameters Wide range of sounds possible Requires very simple processing (sine wave generation

and a bit of multiplication) Unique sound is still emulated by modern synthesisers

Cons VERY difficult to program even with computer assistance Difficult for even a computer to figure out the best

algorithm and the parameters needed to resynthesise a sound

The sounds are still unrealistic

Advanced Digital Techniques Today, processing power and memory

capacities have multiplied by thousands since the early digital synthesisers

Processing speeds mean that far more elaborate additive techniques are possible

Memory capacity means that digital recordings of real instruments can be stored for real-time playback

This can provide the most realistic sounding instruments (and, also the least!) using a family of techniques based on sampling

Summary Subtractive synthesis

Start with a rich waveform, subtract unwanted harmonics Not too difficult to program but will never sound realistic

Additive synthesis Construct a timbre by adding sine waves Can sound like the real thing, but only if enough partials can be

used Virtually useless for generating novel sounds

FM synthesis Construct a timbre using frequency modulated sine waves Can generate realistic or novel sounds using relatively few

parameters VERY hard to program!

Sampling Next time!