[sdiy] The ideal quantizer, was: Music

[Ingo Debus]

Am 23.02.2011 um 05:51 schrieb David G. Dixon:

>> Just run all the white keys from E to E, and voila!  The E  
>> phrygian mode.
>
> ...
>
> Sorry, I didn't mean to bore the entire list with that little bit  
> of music
> theory.  I thought I was sending a private message to Scott.  My  
> bad.  :)

I find this subject very interesting.
I've been wondering for quite some time how a good universal  
quantizer would look like. This would be a module which takes  
continuous (pitch cv) input and outputs pitch control voltages  
according to a scale. It would take as few parameters as possible and  
give as many musically useful results as possible while not omitting  
musically useful results.

Ok, the other project I'm working on is a perpetuum mobile ;-)

One approach is, have 12 switches. Switch on means note of the  
chromatic scale belongs to target scale. This gives you (2^12)-1  
possibilities (-1 because all switches off doesn't make sense). It's  
obvious that there must be a lot of scales that are less useful.  
OTOH, you're restricted to scales that are subsets of the chromatic  
scale, and repeat (at least) every octave. Also, unless you already  
know how a "musically useful" scale looks like, you'll have a hard  
time finding good results by randomly toggling the switches.

What I'm thinking of is:
Parameter 1: "big" interval. This is the interval at which the scale  
repeats. Usually set to one octave.
Parameter 2: "little" interval. This is the interval of the equal- 
tempered "super-scale" which the target scale is a subset of. For  
western scales this is set to a semitone.
Parameter 3: number of notes per "big" interval (usually octave). Set  
to 7 for diatonic scales, to 5 for pentatonic, to 6 for whole-tone  
scale and so on.

Further parameters could be "transpose" and "mode". "Transpose" would  
be just an offset at the output. It's questionable if "mode" is  
required at all. In David's example, C ionian, D dorian and so on all  
share the same notes. A "mode" parameter could perhaps sweep from C  
ionian to C dorian to C phrygian and so on.

Still another parameter (or parameters) is needed, perhaps called  
"unevenness". In a heptatonic scale there are five whole tone  
intervals and two semitone intervals between neighbouring notes. This  
parameter could determine how far apart the two semitone intervals  
are placed. Increasing this parameter further, minor thirds would be  
introduced, along with more semitone intervals. In the extreme  
position, the heptatonic scale would look like C-C#-D-D#-E-F-F#-C.

The goal is, finding nice scales without having to know a lot about  
music theory. Any ideas?

Ingo