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gd update

🔗Carl Lumma <carl@lumma.org>

6/9/2002 9:21:27 PM

I've added several scales (now there are 36), updated the Scala files,
added a mean variety column to the spreadsheet.

Excel 2000 Spreadsheet:
http://lumma.org/gd/results.xls

Zip archive of the Scala files used:
http://lumma.org/gd/scl.zip

Explanation of the columns in the spreadsheet:
http://lumma.org/gd/spec.txt

Examples of the "diatonic harmony" metric:
http://lumma.org/gd/diatonic-prop-test.xls

I've been trying to scan for scales that share a common rank-order
matrix. The only ones I know of right now are rothenberg and
balzano-20. That's right, Rothenberg, then Balzano, then Dan Stearns
discovered this scale, all for different reasons. For R., it was
a search of subsets of 31-tET with high stability and efficiency.
For Balzano -- well, I won't go into it here. Stearns points out that
there are 11:13:15, 1/(15:13:11) chords on scale degrees 1-3-5. It
ranks high on my list because the 8ths are either 5:3 and 7:4. You'll
get more out of the 31-tET version for those, but the 20-tET version
gets you higher Lumma stability.

As far as ranking the scales, the top ten according to the "diatonic
harmony" property are:

08_octatonic
10_blackwood
06_hexatonic
07_diatonic
07_qm(2)
07_hungarian-minor
06_super7
05_pentatonic
10_sym-major
10_pent-major

That's not bad, I'd say. The next two are:

09_balzano-20 / 09_rothenberg
08_nova

This excludes Paul Hahn's trichordal scales and my subset-13 scale,
having their high scores from the 12:7, which is arguably not
singable in two-part harmony.

For the next version, I hope to improve the modal transposition
property (s - i isn't very good), find some method of creating a
combined score out of the four, and robustly check for rank-order
doubles.

-Carl