Re: trivalent scales in SCALA archive

Hi Dan,

I've just done a prelimnary search of the SCALA archive for trivalent scales.

Remarkably, though there are many of them, there is only _one_ with an even
number of notes.

It's a 12 note scale.

Here it is:

arabic1.scl | From Fortuna. Try C or G major

1/1 100 cents 200 cents 300 cents 350 cents 500 cents 600 cents 700 cents 800 cents 900
cents 1000 cents 1050 cents 2/1

Or in 24-tet:
0 2 4 6 7 10 12 14 16 18 20 21 24
steps:
2 2 2 1 3 2 2 2 2 2 1 3

Does indeed include the midpoint.

N.B. there are lots of scales also with 4 interval sizes in every interval class. Should
we call these 4-valent?

Other numbers of intervals in every class include:
5 interval sizes, 7 notes
5 sizes, 13 notes
6 sizes, 16 notes
8 sizes, 15 notes,
10 sizes, 19 notes
and 11 sizes, 19 notes.

Now for the modes:

Just searching the E.T. modes (haven't programmed it to check the modes of,
say, the Indian shruti scale yet)

This time there are quite a few 6 note scales, and some 8 note ones.

Certainly seems to support your conjecture that any trivalent scale with an even
number of notes is a mode of an e.t. scale.

More programming to do before I can check for the presence of two intervals of
the same size made up of differing combinations of L, M and S.

Robert

I've uploaded some files to
http://www.egroups.com/files/tuning/Robert+Walker/
listing all the n-valent modes and scales in the SCALA
archive for n>=2.

The files are best viewed with word wrap switched off
when you first look at them, as each new line starts a new scale
or mode.

In Wordpad:
View | Options.. | Word | No wrap.

For info about the notation used for the entries:
http://www.egroups.com/files/tuning/Robert+Walker/n-valent_modes_info.txt
and
http://www.egroups.com/files/tuning/Robert+Walker/n-valent_scales_info.txt

Next update of FTS will be able to order any list of scales according to the
"n-valency" of the entries.

Robert