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

[Kyle Klipowicz]

Only if you study abstract algebra (and I think that musicians are a
subset of mathematicians less than the converse).  :-)

~Kyle

On 8/15/06, Mathieu Bouchard <matju at artengine.ca> wrote:
> 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
>
>   _ _ __ ___ _____ ________ _____________ _____________________ ...
> | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
> | Freelance Digital Arts Engineer, Montréal QC Canada
>
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>
>


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