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72-EDO mapped to Ztar as 5-limit lattice

🔗monz <joemonz@yahoo.com>

5/18/2001 9:32:10 PM

I've realized that the 72-EDO scale can be mapped
to the Ztar keyboard in a way which emulates a
5-limit lattice. Notes are given with both the
72-EDO degree and Monzo ASCII 72-EDO notation.

left half (closest to the "nut"):

3 C^ 45 G^ 15 D^ 57 A^ 27 E^ 69 Cv 39 F#^
52 A< 22 E< 64 B< 34 F#< 4 C#< 46 G#< 16 Eb<
29 F- 71 C- 41 G- 11 D- 53 A- 23 E- 65 B-
6 C# 48 G# 18 Eb 60 Bb 30 F 0 C 42 G
55 A+ 25 E+ 67 B+ 37 F#+ 7 C#+ 49 G#+ 19 Eb+
32 F> 2 C> 44 G> 14 D> 56 A> 26 E> 68 B>

right half:

39 F#^ 9 C#^ 51 G#^ 21 Eb^ 63 Bb^ 33 F^ 3 C^
16 Eb< 58 Bb< 28 F< 70 C< 40 G< 10 D< 52 A<
65 B- 35 F#- 5 C#- 47 G#- 17 Eb- 59 Bb- 29 F-
42 G 12 D 54 A 24 E 66 B 36 F# 6 C#
19 Eb+ 61 Bb+ 31 F+ 1 C+ 43 G+ 13 D+ 55 A+
68 B> 38 F#> 8 C#> 50 G#> 20 Eb> 62 Bb> 32 F>

I had to break the diagram in half here. The whole
thing can be seen as a unit in my revamped 72-EDO definition:
<http://tonalsoft.com/enc/number/72edo.aspx>.

At the right edge of the right half, it can be seen that
the lattice repeats, so that the full lattice covers
12 "frets", and thus with 24 "frets" the Ztar can repeat
the lattice in a higher or lower "octave", with a full
range of 2 "octaves".

Because 72-EDO is quasi-just to the 11-limit, this array
can effectively approximate a 72-tone 11-limit JI system.

Alternatively, one may tune this mapping to actual 5-limit
JI. Invoking xenharmonic bridges which allow 5-limit pitches
to be treated as higher-limit pitches, as described in
Tuning List message 1372 (Mon Mar 8, 1999 1:25 am)
</tuning/topicId_1372.html#1372>, one
may still obtain a comprehensive quasi-just 11-limit system.

-monz
http://www.monz.org
"All roads lead to n^0"