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  |             |          •    |     •   •    |              •  | •             | •     •  •    | •     • •    |

https://en.xen.wiki/w/Modeless_Interchange

	1L 6s	2L 5s	3L 4s	4L 3s	5L 2s	6L 1s
Bright generator range	6\7 < g < 1\1	3\7 < g < 1\2	2\7 < g < 1\3	5\7 < g < 3\4	4\7 < g < 3\5	1\7 < g < 1\6
Possible 0-2-4 chords						1:g2:g4, 1:g2:2g-3, 1:2g-5:2g-3
Ideal Δ-ratio	+2 +3, +5 +6, +1 +1	+2 +3, +4 +5, +1 +1	+1 +2, +5 +6, +1 +5	+1 +2, +5 +6, +3 +1	+2 +3, +5 +6, +1 +1	+4 +5, +6 +5, +1 +2
Optimal value of g						1.1180, 1.1146, 1.1183
in 19edo	+4+1, +1+3, +1+1 (L:s=7:2)	+5+1, +3+10, +1+1 (L:s=7:1)	+5+1, +4+5, +5+4 (L:s=5:1)	+1+2, +4+5, +6+5 (L:s=4:1)	+2+3, +5+6, +1+1 (L:s≒3:2)	+5:9, +4+5, +1+1 (L:s≒3:1)

some well known scales

LmLsLsLmLss

Scale structure
Step pattern
Brightest mode	LmLsLsLmLss
Darkest mode	ssLmLsLsLmL
Is chiral?	no
Maximum variety	4
Has strict variety?	no

SLMLSLMLSL

Scale structure
Step pattern
Brightest mode	LMLSLMLSLS
Darkest mode	SLSLMLSLML
Is chiral?	no
Maximum variety	4
Has strict variety?	no

mLLsLmLsL

Scale structure
Step pattern
Brightest mode	LH LLsLmLsLm RH LLmLsLmLs
Darkest mode	LH sLmLsLmLL RH sLmLsLLmL
Is chiral?	yes
Maximum variety	3
Has strict variety?	yes

xyzxyxyz

Scale structure
Step pattern
Brightest mode	LH xyxzyxzy RH xyxyzxyz
Darkest mode	LH zyxzyxyx RH zxyzxyxy
Is chiral?	yes
Maximum variety	4
Has strict variety?	no

aabab

Scale structure
Step pattern
Brightest mode	aabab
Darkest mode	babaa
Is chiral?	no
Maximum variety	2
Has strict variety?	yes

aghfasdgasdhfasghdsgahdfhasfhdfghasfgdhfashdfgh

aghfasdgasdhfasghdsgahdfhasfhdfghasfgdhfashdfgh

Scale structure
Step pattern
Brightest mode	LH aghfasdgasdhfasghdsgahdfhasfhdfghasfgdhfashdfgh RH afhdgfsahgfdhfsahfdhagsdhgsafhdsagdsafhgahgfdhs
Darkest mode	LH shdfghaghfasdgasdhfasghdsgahdfhasfhdfghasfgdhfa RH sdhgsafhdsagdsafhgahgfdhsafhdgfsahgfdhfsahfdhag
Is chiral?	yes
Maximum variety	37
Has strict variety?	no