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Tonal Attractors And Complex Sounds

Regretfully, some e-music newbies don't always see the need to tune their VCO's before doing a performance : their reasoning
is that they are only interested in exploring weird and complex noises, not perpetuating sirupy tonal stuff!

Well, whatever style of e-music you are practicing,  you will always need a yardstick base to define your tones intricate ratios relationships.

To achieve that goal, several scales are at your disposal : diatonic, just-tonic, modal progressions by whole
tones or by fifths, Stockhausen's 51 notes per octave scale, the Hertz scale and so on...

It is no coincidence, that the best e-music compositions often incorporate a judicious mix of complex "tonal-centric-like" tones with complex sound clusters and noises. As an example, "Silver Apple Of The Moon", by Morton Subotnick, is a classic piece of electronic
music composition : it is not rigourously tonal per se, but exhibits a distinctive tonal "flavor".

Obviously, there are numerous advantages to tune your oscillators to a known initial frequency beforehand, for you can quickly react
to any scale change in a flexible way. Indeed, by using your VCO's various processing inputs - along with
feedback, linear FM, non-linear modulations and DC bias voltages - you can quickly transpose a tonal sequence into
complex tones, without touching the VCO initial frequency knob.

Ratios of relationships

In tonal music, tones are organized according to their ratios of relationships towards a tonal center attraction
defined by a given key.
According to Hermann Helmholtz, when a tone in the scale is sounded at the same time with a reference tone in C,
the tone with the highest pitch number ratio will always be in strong consonance with the reference tone.
(see Table of consonances/dissonances hereunder).

Obviously, the perfect chord consonance is the Unison (ratio 1:1) with an intensity of influence of 100.
Then, comes the Octave (ratio 1:2), the Fifth (ratio 2:3) and the Major Third (ratio 4:5).

On the "roughness" side, the best dissonant tones, are the ones with a low pitch number ratio and a weak intensity of influence :
D, D+, E+,Eb-, Bb, Ab, Gb are the top contenders exhibiting various degrees of "repulsion" towards a tonal center in C...

Helmholtz defines these differences poetically: "Two consonant tones flow always quietly, side-by-side, in an undisturbed stream :
Two dissonant tones exhibit a roughness by cutting one another up into separate pulses of tones"...

The above sentence says it all : these are all the ingredients that we need to create a successful e-music composition...

Mapping Canyons and Valleys

In our journey to discovery, let's do some mental trekking through the deep Canyons and Valleys of Helmholtz
consonance/dissonance terrain mapping.

This chart - which complements the table we have seen earlier-shows, in a visual way, the intensity of influence
of a given note in the scale when it is sounded at the same time with another tone in C.

In this example, the height and the width of the Canyons, are proportional to the amount of consonances produced by the
addition of the two partial tones : i.e tones in consonance occupy a much bigger "space".
(Notice that the pairs of upper partials are always erected over one another).

But, as dramatic as these Canyons appear, they are not that useful to us synthesists. The key to building
complex dissonant sounds resides elsewhere : in the quiet and unexplored green bucolic valleys hidden away from prying eyes.

I invite you to explore these gentle slopes, and discover their marvelous sonic secrets.

Andre Stordeur