The Chart

(I know I've talked about this here before, but I haven't really explained it much, so here it goes...)

In most of my non-12et compositions, which tend to be tonal with occasional fits of atonality, I have a few versions os a system of pitch mapping. The one I use the most uses 31 pitch classes (i.e. note names with quarter tones included) mapped to 41 degrees in 72 equal temperament, based on Miracle tuning, to approximate 11-limit JI.

The list below is an example of such a roadmap, using pitches in 53 equal temperament, 34 in all, assigned to 19 pitch classes. The pitches without a note name are alternates of another a 1/53-octave comma away, thus G# is normally 3, but can also be 2, and A is either 8 or 9, 8 by default. This is, of course, Hanson/kleismic tuning. The approximated ratios listed on each line are 5-limit-plus-13 with factors no more than 36.

(This table should be viewed in a monospaced font.)

0 G 1/1
2
3 G# 27/26 26/25 25/24
5 16/15
6 Ab 27/25 13/12
8 A 10/9
9 9/8
11 A# 15/13
12
14 Bb 6/5
16 16/13
17 B 5/4
19 32/25
20 Cb 13/10
22 C 4/3
23 27/20
25 C# 18/13 25/18
26
28 Db 36/25 13/9
30
31 D 3/2
33 D# 20/13
34 25/16
36 Eb 8/5
37 13/8
39 E 5/3
41
42 Fb 26/15
44 16/9
45 F 9/5
47 F# 24/13
48 15/8
50 Gb 25/13
51
53 G 2/1

There are two "orphaned" JI ratios that do map to 53 but not to 34; these are listed below. (In 31-41-72, the Partchian ratios 11/10 and 20/11 fit in with 72 but not 41.)

13 32/27
40 27/16

I'm working on a PDF of different schemes; so far I have this, 19-53-72, 22-50-72 and, of course, 31-41-72.

~D. ¶¦¬{> http://dannywier.ucoz.com