Xenharmonic Wiki

Royalmilktea

Joined 10 April 2021
← Older edit
VisualWikitext
Royalmilktea (talk | contribs)
autopatrolled, emailconfirmed
64 edits
mozismic temperaments
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
 
(2 intermediate revisions by one other user not shown)
Line 13: Line 13:
POTE generator: ~3/2 = 703.050
POTE generator: ~3/2 = 703.050


Vals: 12d, 87d, 99, 111d, 186d, 198
{{Optimal ET sequence|legend=1|12d, 87d, 99, 111d, 186d, 198}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=4375%3A4374+%5B26%2C-12%2C-3%2C0%3E&page=2&limit=7
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=4375%3A4374+%5B26%2C-12%2C-3%2C0%3E&page=2&limit=7
Line 28: Line 28:
POTE generator: 500.180
POTE generator: 500.180


Vals: 12, 547, 559, 1106, 1118, 1665, 1677
{{Optimal ET sequence|legend=1|12, 547, 559, 1106, 1118, 1665, 1677}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B146%2C-76%2C-11%3E&page=2&limit=5
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B146%2C-76%2C-11%3E&page=2&limit=5
Line 43: Line 43:
POTE generator: 5.5612
POTE generator: 5.5612


Vals: 31, 62, 93e, 124, 155, 186, 217e
{{Optimal ET sequence|legend=1|31, 62, 93e, 124, 155, 186, 217e}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=385%3A384+%5B72%2C0%2C-31%2C0%2C0%3E+%5B-87%2C0%2C0%2C31%2C0%3E&page=2&limit=11
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=385%3A384+%5B72%2C0%2C-31%2C0%2C0%3E+%5B-87%2C0%2C0%2C31%2C0%3E&page=2&limit=11
Line 56: Line 56:
POTE generator: 5.7001
POTE generator: 5.7001


Vals: 31, 62f, 93ef, 124f, 155f, 186, 217e, 248e
{{Optimal ET sequence|legend=1|31, 62f, 93ef, 124f, 155f, 186, 217e, 248e}}


Temperament finder: link won't show up for some reason idk
Temperament finder: link won't show up for some reason idk
Line 71: Line 71:
POTE generator: 35.0760
POTE generator: 35.0760


Vals: 36, 135, 171, 207, 342, 378, 513, 549, 684, 855
{{Optimal ET sequence|legend=1|36, 135, 171, 207, 342, 378, 513, 549, 684, 855}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-11%2C-9%2C0%2C9%3E+%5B-15%2C8%2C1%2C0%3E&page=2&limit=7
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-11%2C-9%2C0%2C9%3E+%5B-15%2C8%2C1%2C0%3E&page=2&limit=7
Line 84: Line 84:
POTE generator: 34.9487
POTE generator: 34.9487


Vals: 36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e
{{Optimal ET sequence|legend=1|36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e}}


==== [[Schismatic family|Novtant (13-limit)]] ====
==== [[Schismatic family|Novtant (13-limit)]] ====
Line 95: Line 95:
POTE generator: 34.9421
POTE generator: 34.9421


Vals: 36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e
{{Optimal ET sequence|legend=1|36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e}}


==== [[Schismatic family|Novtant (17-limit)]] ====
==== [[Schismatic family|Novtant (17-limit)]] ====
Line 106: Line 106:
POTE generator: 34.9435
POTE generator: 34.9435


Vals: 36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e
{{Optimal ET sequence|legend=1|36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e}}


=== 15 September 2022 ===
=== 15 September 2022 ===
Line 121: Line 121:
POTE generator: 98.9569
POTE generator: 98.9569


Vals: 12, 24, 364, 376, 388, 400, 752, 764, 1152
{{Optimal ET sequence|legend=1|12, 24, 364, 376, 388, 400, 752, 764, 1152}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B101%2C-52%2C-8%3E&page=2&limit=5
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B101%2C-52%2C-8%3E&page=2&limit=5
Line 136: Line 136:
POTE generator: 98.9914
POTE generator: 98.9914


Vals: 12, 24d, 36d, 364d, 376d, 388, 400, 412, 424cd, 788
{{Optimal ET sequence|legend=1|12, 24d, 36d, 364d, 376d, 388, 400, 412, 424cd, 788}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B101%2C-52%2C-8%2C0%3E+%5B2%2C6%2C-11%2C5%3E&page=2&limit=7
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B101%2C-52%2C-8%2C0%3E+%5B2%2C6%2C-11%2C5%3E&page=2&limit=7
Line 149: Line 149:
POTE generator: 98.9908
POTE generator: 98.9908


Vals: 12, 24de, 376de, 388, 400, 412e, 424cdee, 776de, 788, 800
{{Optimal ET sequence|legend=1|12, 24de, 376de, 388, 400, 412e, 424cdee, 776de, 788, 800}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=9801%3A9800+%5B101%2C-52%2C-8%2C0%2C0%3E+%5B2%2C6%2C-11%2C5%2C0%3E&page=2&limit=11
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=9801%3A9800+%5B101%2C-52%2C-8%2C0%2C0%3E+%5B2%2C6%2C-11%2C5%2C0%3E&page=2&limit=11
Line 162: Line 162:
POTE generator: 99.0023
POTE generator: 99.0023


Vals: 12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce
{{Optimal ET sequence|legend=1|12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce}}


==== Gregory (17-limit) ====
==== Gregory (17-limit) ====
Line 173: Line 173:
POTE generator: 99.0004
POTE generator: 99.0004


Vals: 12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce
{{Optimal ET sequence|legend=1|12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce}}


==== Gregory (19-limit) ====
==== Gregory (19-limit) ====
Line 184: Line 184:
POTE generator: 98.9979
POTE generator: 98.9979


Vals: 12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce
{{Optimal ET sequence|legend=1|12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce}}


=== 24 September 2022 ===
=== 24 September 2022 ===
Line 199: Line 199:
POTE generator: 249.0179
POTE generator: 249.0179


Vals: 612, 1224, 2342, 2954, 3566, 4178, 5908, 6520, 7132, 9474
{{Optimal ET sequence|legend=1|612, 1224, 2342, 2954, 3566, 4178, 5908, 6520, 7132, 9474}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B54%2C-37%2C2%2C0%3E+%5B3%2C-13%2C10%2C-2%3E&page=2&limit=7
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B54%2C-37%2C2%2C0%3E+%5B3%2C-13%2C10%2C-2%3E&page=2&limit=7
Line 214: Line 214:
POTE generator: 150.9822
POTE generator: 150.9822


Vals: 159, 453, 612, 1065, 1224, 1677, 1836, 2289, 2742, 2901
{{Optimal ET sequence|legend=1|159, 453, 612, 1065, 1224, 1677, 1836, 2289, 2742, 2901}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-4%2C6%2C-6%2C3%3E+%5B54%2C-37%2C2%2C0%3E&page=2&limit=7
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-4%2C6%2C-6%2C3%3E+%5B54%2C-37%2C2%2C0%3E&page=2&limit=7
Line 229: Line 229:
POTE generator: 77.5892
POTE generator: 77.5892


Vals: 665, 1624, 2289, 2954, 3619, 4578, 5243, 5908, 6573, 8197
{{Optimal ET sequence|legend=1|665, 1624, 2289, 2954, 3619, 4578, 5243, 5908, 6573, 8197}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B54%2C-37%2C2%2C0%3E+%5B47%2C-7%2C-7%2C-7%3E&page=2&limit=7
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B54%2C-37%2C2%2C0%3E+%5B47%2C-7%2C-7%2C-7%3E&page=2&limit=7
=== 2 October 2022 ===
==== Nelindro ====
Nelindro is named akin to the [[Nelinda|nelindic temperament]] because its period is also 4/1.
Subgroup: 4.7.10
Comma list: 2100875/2097152
Mapping: [⟨1 0 4], ⟨0 3 -5]]
POTE generator: ~490/256 = 1122.8167
{{Optimal ET sequence|legend=1|[[15ED4|c15]], [[47ed4|c47]], [[109ed4|c109]], [[171ed4|c171]], [[233ed4|c233]]}}
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-12%2C5%2C3%3E&page=2&limit=4_7_10
==== Nelindro (4.7.10.13 subgroup) ====
Subgroup: 4.7.10.13
Comma list: 640/637, 15625/15379, 21875/21632, 214375/212992
Mapping: [⟨1 0 4 7], ⟨0 3 -5 -11]]
POTE generator: ~490/256 = 1123.3566
{{Optimal ET sequence|legend=1|[[15ED4|c15]], [[47ed4|c47]], [[79ed4|c79]], [[109ed4|c109]], [[141ed4|c141]]}}
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-12%2C5%2C3%2C0%3E+640%3A637&page=2&limit=4_7_10_13
=== 3 October 2022 ===
==== Excavator (5/2.8.11 subgroup) ====
This temperament is akin to major decimophonic that is laid out in the [[nelinda]] page.
Subgroup: 5/2.8.11
Comma list: 537109375/536870912
Mapping: [⟨1 2 1], ⟨0 1 6]]
POTE generator: ~32/25 = 427.5097
{{Optimal ET sequence|legend=1|26, 52, 89, 115, 141, 167, 193, 256, 282, 308}}
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B11%2C-6%2C1%3E&page=2&limit=5%2F2_8_11
==== Excavator (5/2.8.11.14 subgroup) ====
Subgroup: 5/2.8.11.14
Comma list: 176/175, 537109375/536870912, 236328125/234881024, 103984375/102760448
Mapping: [⟨1 2 1 1], ⟨0 1 6 7]]
POTE generator: ~14/11 = 426.6693
{{Optimal ET sequence|legend=1|4, 11, 15, 22, 26, 30, 37, 41, 52, 67}}
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-2%2C1%2C1%2C-1%3E+%5B11%2C-6%2C1%2C0%3E&page=2&limit=5%2F2_8_11_14


== Proposed temperament families/realms ==
== Proposed temperament families/realms ==
Line 256: Line 316:
POTE generators: 2/1, ~5/1 = 2787.1374, ~7/1 = 3368.7049, ~17/1 = 4904.4999
POTE generators: 2/1, ~5/1 = 2787.1374, ~7/1 = 3368.7049, ~17/1 = 4904.4999


Vals: 12, 25, 31, 37, 43, 56, 68, 93
{{Optimal ET sequence|legend=1|12, 25, 31, 37, 43, 56, 68, 93}}


Temperament finder for all temperament that temper out 476/475: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475&page=2&limit=2_5_7_17_19
Temperament finder for all temperament that temper out 476/475: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475&page=2&limit=2_5_7_17_19
Line 275: Line 335:
POTE generators: 2/1, ~56/25 = 1393.7535, ~17/1 = 4905.0728
POTE generators: 2/1, ~56/25 = 1393.7535, ~17/1 = 4905.0728


Vals: 12, 25, 31, 37, 43, 50, 56, 68, 93
{{Optimal ET sequence|legend=1|12, 25, 31, 37, 43, 50, 56, 68, 93}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475+3136%3A3125+1445%3A1444+2128%3A2125&page=2&limit=2_5_7_17_19
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475+3136%3A3125+1445%3A1444+2128%3A2125&page=2&limit=2_5_7_17_19
Line 288: Line 348:
POTE generators: ~28/25 = 192.6270
POTE generators: ~28/25 = 192.6270


Vals: 6h, 19gh, 25, 31, 37gh, 50, 56
{{Optimal ET sequence|legend=1|6h, 19gh, 25, 31, 37gh, 50, 56}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475+3136%3A3125+343%3A340&page=2&limit=2_5_7_17_19
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475+3136%3A3125+343%3A340&page=2&limit=2_5_7_17_19
Line 301: Line 361:
POTE generators: ~28/25 = 194.0839
POTE generators: ~28/25 = 194.0839


Vals: 6g, 31, 37, 68, 74, 99, 105
{{Optimal ET sequence|legend=1|6g, 31, 37, 68, 74, 99, 105}}


Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475+3136%3A3125+34391%3A34295+32768%3A32585&page=2&limit=2_5_7_17_19
Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=476%3A475+3136%3A3125+34391%3A34295+32768%3A32585&page=2&limit=2_5_7_17_19
Retrieved from "https://en.xen.wiki/w/User:Royalmilktea"