User:Akselai/SandBox
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├──┼─┼╫┼───────┤ ├──┼─┼╫┼───────┤
| 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
| Scale structure | |
| Step pattern | |
| Brightest mode | LmLsLsLmLss |
| Darkest mode | ssLmLsLsLmL |
| Is chiral? | no |
| Maximum variety | 4 |
| Has strict variety? | no |
| Scale structure | |
| Step pattern | |
| Brightest mode | LMLSLMLSLS |
| Darkest mode | SLSLMLSLML |
| Is chiral? | no |
| Maximum variety | 4 |
| Has strict variety? | no |
| 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 |
| 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 |
| Scale structure | |
| Step pattern | |
| Brightest mode | aabab |
| Darkest mode | babaa |
| Is chiral? | no |
| Maximum variety | 2 |
| Has strict variety? | yes |
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 |
the most useless temperament(s) in all of xen history
Rank-2
Microphone
- See also: 44th-octave temperaments
This temperament additionally tempers out the parismina [1 -26 0 2 10⟩, which is even smaller than the blare comma. Surprisingly, this temperament admits an optimal generator very close to 3/2.
Subgroup: 2.9.7.11 (lol wrong!! should have been 2.3.7.11 instead)
Comma list: [-52 2 0 10 6⟩, [1 -26 0 2 10⟩
Sval mapping: [⟨44 88 175 75], ⟨0 2 -2 3]]
- CTE: ~64/63 = 1\44 = 27.273, ~[25 0 0 -5 -3⟩ = 701.953
Optimal ET sequence: 176, 484, 660, 836, 1012, 1848, 4708, 6556, 11264, 17820, 29084, 46904, 75988, 122892
Badness (Smith): 2.466 × 10-3