Generic-Additive-Synthesis

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Generic-Additive-Synthesis

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Generic additive synthesis is a generalisation of additive sound synthesis.

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# Generic Additive Synthesis

Julian Rohrhuber and Juan Sebastián Lach Lau.

A generalisation of additive synthesis, as described in our article [Generic Additive Synthesis. Hints from the Early Foundational Crisis in Mathematics for Experiments in Sound Ontology](https://link.springer.com/chapter/10.1007/978-3-319-47337-6_27)

Here we provide some examples from the article and will add more in the future.

A few simple examples, using [SuperCollider](https://github.com/supercollider/supercollider):

## Simple case of concatenative frequency (phase) modulation (p. 273)

```supercollider
(
Ndef(\g, {
	var combinator = { |a, b| a <> b }; // operator: function composition
	var c = { |i| LFTri.ar(1 / i, 1 / i).range(-1, 1).max(0) }; // spectrum: time varying
	var g = { |x, i|
		SinOsc.ar(i * 40, x * 3) // basis: sine function that takes a modulated phase argument
	};
	var n = (1..12); // number of operands
	n.inject(0, { |x, i| // inject is also known as left fold. Base case is 0 here
		g.(x, i) * c.(i) + (x * (1 - c.(i))) // this is so we get 0 as the neutral element
	}) * 0.1
}).play;
)
```

[sound_examples/example_1.flac](sound_examples/example_1.flac?raw=true)

## Generic additive synthesis with a sine basis and addition (p. 271)

```supercollider
(
Ndef(\g, {

}).play;
)
```

[sound_examples/example_2.flac](sound_examples/example_2.flac?raw=true)
## Generic additive synthesis with a more complicated basis and a product combinator  (p. 271)

```supercollider
(
Ndef(\g, {
	var combinator = { |a, b| a * b }; // operator: product function
	var c = { |i| 8 / i }; // spectrum: linear
	var g = { |i| // basis: phase modulated pulses
		var cn = c.(i);
		var y1 = SinOsc.ar(120 * i, SinOsc.ar(cn * 10 * i) * (1/i));
		var y2 = LFPulse.kr(cn, 0, SinOsc.ar(cn * i, i, 0.2, 0.3));
		y1 * y2 * cn + 1
	};
	var n = (1..12); // number of operands
	var set = n.collect { |i| g.(i) }; // sequence
	LeakDC.ar(set.reduce(combinator) * (0.01 / n.size)).tanh * 0.1 ! 2 // tanh projects the final output into range
}).play;
)
```

[sound_examples/example_3.flac](sound_examples/example_3.flac?raw=true)
## Modifications of the examples from the article

### Generic additive synthesis with a sine basis and addition, interactively control the spectral shape

```supercollider
(
Ndef(\g, {
	var x = MouseX.kr(0, 50);
	var y = MouseY.kr(0, 10);
	var combinator = { |a, b| a + b }; // operator: just binary sum here
	var c = { |i|  // spectrum: jagged dynamic shape
		i = i * y + x; 
		1 / (((i % 7) + (i % 8)  + (i % 11)).max(0) + 1) 
	}; 
	var g = { |i|
		SinOsc.ar(50 * i) * (100 / i) * c.(i); // basis: sine function
	};
	var z = (1..100); // number of operands
	var set = z.collect { |i| g.(i) }; // sequence
	 // combine and scale output:
	set.reduce(combinator) ! 2 * (1 / z.size)

}).play;
)
```

[sound_examples/example_4.flac](sound_examples/example_4.flac?raw=true)

### Steno

Another example, using the [Steno](https://github.com/telephon/Steno) embedded language:

```supercollider

t = Steno.push(8); // a small 8 channel spectrum

// definition of a spectrum composition operator G
(
t.filter(\G, { |in, envir|
	var r = \rotate.kr(0);
	in = in.collect { |x| PanAz.ar(in.size, x, 2*r/in.size) }.sum;
	SinOsc.ar((100 / (\index.kr + 1)), in * 2)
});

// the last node mixes down to stereo
t.filter('.', { |in|
	Splay.ar(in) 
})
);

--GGGGG.

t.setGlobal(\index, { |i| i + 1 });

```

[sound_examples/example_5.flac](sound_examples/example_5.flac?raw=true)

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