[PD] pd-based procedural chord progression database..

[Mathieu Bouchard]

On Tue, 15 Aug 2006, Alexandre Quessy wrote:

> All seven modes follow the exact same spacing between degrees. There is 
> a convention using bows and circumflex accents for respectively tones 
> and semi-tones.

I prefer the digits 2 and 1, which represent the number of semitones 
between degrees. This is because they are more readily parseable by pd and 
by other computer systems.

> All other modes are just the same intervals starting at an 
> other point.

in other words, let Z denote semitone-multiple intervals, and 12Z denote 
octave-multiple intervals, then 12Z is an Ideal Subring of Z, so the 
Quotient Z/12Z is a Ring, which is the chromatic scale. Then take a subset 
of that chromatic scale that includes its zero (zero represents the 
fundamental). For example, {0,2,4,5,7,9,11}, which is made of the partial 
sums of the sequence (2,2,1,2,2,2,1), is the Ionian mode. A mode is a 
scale that contains its zero. Then define the addition of an interval and 
a scale: the resulting scale contains each sum of the interval with each 
element of the scale. The seven ecclesiastic modes appear as each of the 
sums of the Ionian mode and an interval that results in a mode (that is, 
that contains the zero).

Isn't that clearer? ;)

http://en.wikipedia.org/wiki/Ring_%28mathematics%29

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| Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
| Freelance Digital Arts Engineer, Montréal QC Canada