User:IlL/Building JI scales

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Some nice JI scales I want to try

Primodal

Nejis

3:6 might be good for neji versions of 11edo, 13edo, 18edo, 23edo

13neji 13(4:8)

55/52 29/26 61/52 16/13 17/13 18/13 19/13 20/13 21/13 89/52 47/26 99/52 2/1

13neji /19

20/19 21/19 89/76 47/38 25/19 26/19 55/38 29/19 61/38 65/38 34/19 36/19 2/1

Nice buzzy effects in higher register.

13neji 37(2:4)

39/37 41/37 87/74 46/37 97/74 51/37 54/37 57/37 60/37 63/37 133/74 70/37 74/37

14neji /13

55/52 115/104 15/13 16/13 67/52 35/26 37/26 3/2 81/52 85/52 45/26 47/26 99/52 2/1

14neji /19

20/19 21/19 22/19 23/19 97/76 51/38 27/19 3/2 30/19 63/38 33/19 69/38 36/19 38/19

17neji /13

27/26 113/104 59/52 61/52 16/13 33/26 69/52 18/13 75/52 3/2 41/26 85/52 22/13 23/13 24/13 25/13 2/1

17neji /23

24/23 25/23 26/23 27/23 28/23 59/46 61/46 32/23 33/23 3/2 72/46 75/46 39/23 81/46 42/23 44/23 2/1

22neji /17

35/34 145/136 75/68 77/68 159/136 41/34 5/4 175/136 45/34 93/68 24/17 99/68 205/136 53/34 109/68 113/68 29/17 30/17 31/17 32/17 33/17 2/1

With less complex intervals:

35/34 36/34 75/68 77/68 80/68 41/34 5/4 87/68 45/34 93/68 24/17 99/68 205/136 53/34 109/68 113/68 29/17 30/17 31/17 32/17 33/17 2/1

26neji /17

35/34 18/17 37/34 19/17 39/34 20/17 41/34 21/17 43/34 22/17 91/68 93/68 24/17 99/68 51/34 26/17 107/68 55/34 113/68 29/17 119/68 61/34 63/34 65/34 33/17 34/17

Zhea's nejis

17neji 53(2:4): 106:110:115:120:125:130:135:141:147:153:159:166:173:180:188:195:203:212

Over-2 7-note scales

The simplest (i.e. involving the lowest distinct harmonics) 7-note /2 overtone scale is 1/1 9/8 5/4 11/8 3/2 13/8 7/4 2/1. We can consider this as our basic scale. To keep using a 7-note framework, let's consider the seventh 7/4~15/8 a fuzzy note, much like Bb~B in medieval diatonic music.

[A similar analysis could be done to get heptatonic scales in other primodalities.]

Let's chromatically modify some of the notes to more complex overtones (/2^n) near these.

Level 1 chromaticisms are modifications that come from overtones 32 or lower. The modifications range from about a semitone, to about a quarter tone.

seconds: 17~9~19 (m2~M2~A2)

thirds: 19~5 (m3~M3)

fourths: 21~11~23 (sub4~sup4~A4)

fifths: 3

sixths: 25~13~27 (m6~n6~M6)

sevenths: 7~29~15~31 (subm7~supm7~M7)

Level 2 chromaticisms come from overtones 64 or lower.

seconds: 33~17~35~9~37~19 (m2~n2~M2~godzilla generator~A2)

thirds: 37~19~39~5~41 (m3~n3~M3~M3)

fourths: 21~43~11~45~23~47

fifths: 47~3~49

sixths: 49~25~51~13~53~27~55

sevenths: 55~7~57~29~15~61~31~63

Since some of the intervals don't easily fit into heptatonic categories (such as 37/32), we could consider alternate scale structures for using these...

Some scales

Mellow /8 mixolydian

9/8 5/4 43/32 3/2 27/16 29/16 2/1

A bit 7edo-esque

9/8 5/4 39/32 3/2 27/16 29/16 2/1

Some 3/2-equivalent CSes

(found by Praveen)

  • 1/1 11/10 6/5 5/4 11/8 3/2
  • 1/1 25/24 7/6 5/4 7/5 3/2
  • 1/1 21/20 8/7 6/5 5/4 21/16 10/7 3/2
  • 441/440 tempered out: 1/1 21/20 11/10 8/7 6/5 5/4 21/16 11/8 10/7 3/2
  • hexanic: 1/1 21/20 35/32 8/7 6/5 5/4 21/16 48/35 10/7 3/2
  • major: 1/1 25/24 7/6 6/5 5/4 7/5 35/24 3/2
  • minor: 1/1 25/24 15/14 6/5 5/4 9/7 75/56 3/2
  • augmented: 1/1 15/14 7/6 5/4 9/7 35/24 3/2
  • the 29 string model: 1/1 21/20 8/7 6/5 5/4 21/16 10/7 3/2 or 1/1 25/24 7/6 6/5 5/4 7/5 35/24 3/2
  • the 37 string model: 1/1 21/20 35/32 8/7 6/5 5/4 21/16 48/35 10/7 3/2 or 1/1 25/24 15/14 7/6 6/5 5/4 9/7 7/5 35/24 3/2