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Arithmetic triangle mod n

🔗Daniel Nielsen <nielsed@...>

4/18/2011 9:58:09 PM

Taking the arithmetic (a.k.a. Pascal's) triangle mod 7 (where the numbers 0
to 6 represent "do" to "si") defines a simple set of chords in the diatonic
scale, if each chord is defined by the notes in a row of the triangle.
Likewise, JI of course stays low-limit if interpretting those small numbers
that way instead.

This <http://www.mediafire.com/?5g6w9gflkhdzd6q> is a very simple test tune
I made a couple years ago (before having heard of nearly everything
discussed on this list) when I was discovering that idea on my own. It
begins in major, then does an inversion, then minor, and in the middle plays
JI (all rows at the same time, but where a note's duration is divided by the
number of notes in the same row), and then it winds back out the same way it
came in. (It should keep octaves proper as well.)

I believe only the first 6 rows of the triangle are used in that audio file.
You can see here<http://mfi.re/imgbnc.php/24ae633c5ca01f09040e9e6393d3200aef2c88185f8411bf3a5f365587e8ab594g.jpg>that
the same pattern from the first 7 rows occurs repeatedly in the full
triangle, with some additional variations.

Anyway, I was wondering what of interest has been done with this idea. When
I did it, the results were suprisingly usual and regular to me, and it
seemed as though such patterns might be useful for some kind of standard
musical progression or perhaps something at least.

🔗Daniel Nielsen <nielsed@...>

4/18/2011 10:13:54 PM

BTW, since it wasn't clear in my message: at the time the audio file was
created, I was just using the standard arithmetic triangle without mod n.