User:Akselai/SandBox

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3:4:6 truncated linear fractal scales

Order	Number of steps	Step visualization	Chord	Intervals < 1/16
0	1	├───────────────────────────────────────────────────────────────┤	1:2	1
1	2	├────────────────────┼──────────────────────────────────────────┤	3:4:6	1/3 2/3
2	4	├──────┼─────────────┼─────────────┼────────────────────────────┤	9:10:12:14:18	1/9 2/9 4/9
3	8	├─┼────┼────┼────────┼────┼────────┼────────┼───────────────────┤	27:28:30:32:36:38:42:46:54	2/27 4/27 8/27
4	15	├─┼─┼──┼─┼──┼──┼─────┼─┼──┼──┼─────┼──┼─────┼─────┼─────────────┤	81:84:86:90:92:96:100:108:110:114:118:126:130:138:146:162	8/81 16/81
5	20	├─┼─┼──┼─┼──┼──┼─┼───┼─┼──┼──┼─┼───┼──┼─┼───┼─┼───┼───┼─────────┤	243:252:258:270:276:288:300:308:324:330:342: 354:362:378:390:398:414:422:438:454:486	16/243 32/243
6	26	├─┼─┼──┼─┼──┼──┼─┼┼──┼─┼──┼──┼─┼┼──┼──┼─┼┼──┼─┼┼──┼┼──┼──┼──────┤	729:756:774:810:828:864:900:924:940:972:990:1026:1062:1086:1102: 1134:1170:1194:1210:1242:1266:1282:1314:1330:1362:1394:1458	64/729
7	27	├─┼─┼──┼─┼──┼──┼─┼┼──┼─┼──┼──┼─┼┼──┼──┼─┼┼──┼─┼┼──┼┼──┼──┼─┼────┤	2187:2268:2322:2430:2484:2592:2700:2772:2820:2916:2970:3078:3186:3258: 3306:3402:3510:3582:3630:3726:3798:3846:3942:3990:4086:4182:4246:4374	none

order = 8
ratio = [0, 1/3] 
# the "shape" of the ratio, only input integers please. 
# [a, b] corresponds to the ratio 1:2^{a/(a+b)}:2,
# [a, b, c] corresponds to the ratio 1:2^{a/(a+b+c)}:2^{(a+b)/(a+b+c)}:2, etc.

c = [0, 1]
if order == 0:
    c = []
for i in range(0, order-1):
    b = []
    for j in range(len(c)-1):
        if (c[j+1]-c[j] > 1/16):
            b.append([c[j] + x*(c[j+1]-c[j]) for x in ratio])
        else:
            b.append([c[j]])
    b.append([1])
    c = [x for xs in b for x in xs]
c = [1+x for x in c]
print([i / gcd(c) for i in c])
print([c[i+1]-c[i] for i in range(len(c)-1)])

Numbered Musical Notation

WT13C XII Prelude Example (Diamond MOS accidentals)
(ovb = 2/1 ("octave") lower)
[13edo]   [21221212]          [6\13 higher than written]

     ||       |             |               |              |            · ·· | · ·    · ···  | ·             |              |
     ||  1234 | 5 3 6 4 3 1 |&812 -123 4567 |&8 6 4 6 7 6  | 5345 6 7&8 1 23 | 4 2 &8 2 3218 | 1 7 5 7 &8765 | 7 4 2 6 5432 |
  3  ||: ════ | ――― ――― ――― | ══― ════ ════ | ――― ――― ―――  | ════ ――═══ ――══ | ―――  ――― ════ | ――― ―――  ════ | ――― ――― ════ |
     ||       |             | ·             |              |                 |               |               |              |
  -  ||  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ etc.
     ||       |             |               |              |                 |               |               |              |
  4  ||: 0    | 1   2   3   | 4   2   &8    | 2   6  ♮8 12 | 3·     2   1 7  |&8·     3 1    | 5·   &8  6    | 2·    5 3    |
     ||  ovb  |             |          ·    |     ·   ――══ |        ―   ―――  | ·      ―      | ·     ―  ·    | ·     ―      |
     ||       |             |               |         ·    |              ·  |               |       ·       |       · ·    |