[PD] Musical Algorhytmic

Mathieu Bouchard matju at sympatico.ca
Thu Dec 23 11:47:02 CET 2004

```On Wed, 15 Dec 2004, Alexandre Quessy wrote:

> Forms in musics? (A-B-A-C-A-B-A, variations on a theme and A-B-A, for
> instance)

They can be stored as integers in a list, and then applied by using [sel]
to select various subprograms, or the integer can be used to recall a
subform. Subforms can obey the same principles.

> rhytmic patterns,

Same thing, assign an integer to every drum sound. For more complexity,
more integers per note can be used, to describe velocity and whatever.
It's the same as for patterns in melody and such.

> scales, modes (Do you store only a Ionien and a ascendant melodic
> minor and derive all the other from them ?)

I see a scale as a pair of a subset of the 12-note scale together with one
note of that scale. Following that definition, it can be found that there
are 24576 of them (I think... well, sum 12!/(i-1)!(12-i)! over i).

a subset of the 12-note scale may be represented as a 12-bit integer, so
there are 2**12=4096 of them.

modes are scales modulo addition of an offset, so there are 24576/12=2048
of them. They may be represented as 11 bits, each being a toggle for the
presence of every non-initial note.

I like to look at those things using modern algebra concepts such as
group-quotients, group-actions, orbits, and so on.

> Chords,

a chord is just a scale with fewer notes than common scales, so they are
all included in the above. this is considering all notes modulo 12 so it
doesn't take into account the potential spreading of notes along the
keyboard...

I define a subscale as a subset of a scale together with the same starting
point as the bigger scale (and of course that same starting point must be
an element of the subset). Therefore, chords C, CM7 are both subscales of
the full C major scale, and furthermore, some inversions of F, FM7, Am,
Am7 also are.

_____________________________________________________________________
Mathieu Bouchard -=- Montréal QC Canada -=- http://artengine.ca/matju

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