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Royalmilktea

Joined 10 April 2021
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Created page with "== Proposed temperament names == === 11 June 2021 === ==== Haze ==== Subgroup: 2.3.5.7 Comma list: 67108864/66430125, 4375/4374 Mapping: [⟨3 5 6 5],..."
 
Cmloegcmluin (talk | contribs)
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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
 
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=== 11 June 2021 ===
=== 11 June 2021 ===


==== [[Misty family|Haze]] ====
==== [[Misty family|Haze (99&12d)]] ====


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 67108864/66430125, 4375/4374
Commas: 67108864/66430125, 4375/4374


Mapping: [⟨3 5 6 5], ⟨0 1 -4 23]]
Mapping: [⟨3 5 6 5], ⟨0 1 -4 23]]
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
=== 29 June 2021 ===
==== [[Schismic-Pythagorean equivalence continuum|Quasi-twelve]] ====
Subgroup: 2.3.5
Commas: [146 -76 -11⟩
Mapping: [⟨1 -3 34], ⟨0 11 -76]]
POTE generator: 500.180
{{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
=== 13 August 2021 ===
==== [[31-comma temperaments#Birds|Bards (11-limit)]] ====
Subgroup: 2.3.5.7.11
Commas: 385/384, 1331/1323, 3136/3125, 3773/3750
Mapping: [⟨31 49 72 87 107], ⟨0 1 0 0 1]]
POTE generator: 5.5612
{{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
==== [[31-comma temperaments#Birds|Bards (13-limit)]] ====
Subgroup: 2.3.5.7.11.13
Commas: 352/351, 1573/1568, 1716/1715, 3146/3125
Mapping: [⟨31 49 72 87 107 115], ⟨0 1 0 0 1 -2]]
POTE generator: 5.7001
{{Optimal ET sequence|legend=1|31, 62f, 93ef, 124f, 155f, 186, 217e, 248e}}
Temperament finder: link won't show up for some reason idk
=== 20 October 2021 ===
==== [[Schismatic family|Novtant]] ====
Subgroup: 2.3.5.7
Commas: 32805/32768, 40353607/40310784
Mapping: [⟨9 14 23 25], ⟨0 1 -8 1]]
POTE generator: 35.0760
{{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
==== [[Schismatic family|Novtant (11-limit)]] ====
Subgroup: 2.3.5.7.11
Commas: 441/440, 32805/32768, 40353607/40310784
Mapping: [⟨9 14 23 25 28], ⟨0 1 -8 1 12]]
POTE generator: 34.9487
{{Optimal ET sequence|legend=1|36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e}}
==== [[Schismatic family|Novtant (13-limit)]] ====
Subgroup: 2.3.5.7.11.13
Commas: 441/440, 729/728, 3584/3575, 4096/4095
Mapping: [⟨9 14 23 25 28 32], ⟨0 1 -8 1 12 5]]
POTE generator: 34.9421
{{Optimal ET sequence|legend=1|36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e}}
==== [[Schismatic family|Novtant (17-limit)]] ====
Subgroup: 2.3.5.7.11.13.17
Commas: 441/440, 729/728, 936/935, 1156/1155, 3584/3575, 4096/4095
Mapping: [⟨9 14 23 25 28 32 36], ⟨0 1 -8 1 12 5 3]]
POTE generator: 34.9435
{{Optimal ET sequence|legend=1|36e, 72cee, 135e, 171, 207, 243ce, 342e, 378, 414c, 549e}}
=== 15 September 2022 ===
==== Quartmedian/Timetracker ====
Quartmedian: in reference to [[Sextile]], Timetracker in reference to [[World calendar]], I haven't chosen which name is better.
Subgroup: 2.3.5
Commas: [101 -52 -8>
Mapping: [<4 7 5] <0 -2 13]]
POTE generator: 98.9569
{{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
==== Gregory ====
Extension of Quartmedian, in reference to [[400edo]].
Subgroup: 2.3.5.7
Commas: [2 6 -11 5>, [21 -8 -6 2>, [-19 14 -5 3>, [40 -22 -1 -1>
Mapping: [<4 7 5 1] <0 -2 13 31]]
POTE generator: 98.9914
{{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
==== Gregory (11-limit) ====
Subgroup: 2.3.5.7.11
Commas: 5632/5625, 9801/9800, 200704/200475, [6 2 -6 -2 3>
Mapping: [<4 7 5 1 -2] <0 -2 13 31 48]]
POTE generator: 98.9908
{{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
==== Gregory (13-limit) ====
Subgroup: 2.3.5.7.11.13
Commas: 1716/1715, 2080/2079, 21632/21609, 40656/40625
Mapping: [<4 7 5 1 -2 -5] <0 -2 13 31 48 60]]
POTE generator: 99.0023
{{Optimal ET sequence|legend=1|12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce}}
==== Gregory (17-limit) ====
Subgroup: 2.3.5.7.11.13.17
Commas: 936/935, 3757/3750, 11271/11264, 77571/77440
Mapping: [<4 7 5 1 -2 -5 18] <0 -2 13 31 48 60 -5]]
POTE generator: 99.0004
{{Optimal ET sequence|legend=1|12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce}}
==== Gregory (19-limit) ====
Subgroup: 2.3.5.7.11.13.17.19
Commas: 2926/2925, 5985/5984, 6175/6171, 37544/37485
Mapping: [<4 7 5 1 -2 -5 18 16] <0 -2 13 31 48 60 -5 3]]
POTE generator: 98.9979
{{Optimal ET sequence|legend=1|12f, 24deff, 376deff, 388f, 400, 412e, 424cdeeff, 788f, 800, 812ce}}
=== 24 September 2022 ===
==== Bimonzismic ====
[[Monzismic|Bimonzismic]] splits the octave in two and tempers out the [[Unnoticeable commas|euzenius]] comma.
Subgroup: 2.3.5.7
Commas: [54 -37 2⟩, 78125000/78121827, [51 -24 -8 2⟩
Mapping: [⟨2 4 20 77] ⟨0 -2 -37 -172]]
POTE generator: 249.0179
{{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
==== Trimonzismic ====
Trimonzismic splits the octave in three and tempers out the [[Landscape comma|landscape]] comma.
Subgroup: 2.3.5.7
Commas: [54 -37 2⟩, 250047/250000, [50, -31, -4, 3⟩
Mapping: [⟨3 4 -7 -18] ⟨0 2 37 70]]
POTE generator: 150.9822
{{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
==== Septimonzismic ====
Septimonzismic splits the octave in seven and tempers out the [[akjaysma]].
Subgroup: 2.3.5.7
Commas: [54 -37 2⟩, [47 -7 -7 -7⟩, [-7 30 -9 -7⟩
Mapping: [⟨7 12 33 2] ⟨0 -2 -37 39]]
POTE generator: 77.5892
{{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
=== 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 ==
=== 7 August 2021 ===
==== The Milky Way ====
===== Milkyway (Rank 4 parent temperament, named so after me :)) =====
Subgroup: 2.5.7.17.19
Comma: 476/475 (The difference between 28/25 and 19/17)
Mapping:
[⟨1 0 0 0 2],
[⟨0 1 0 0 -2],
[⟨0 0 1 0 1],
[⟨0 0 0 1 1]]
POTE generators: 2/1, ~5/1 = 2787.1374, ~7/1 = 3368.7049, ~17/1 = 4904.4999
{{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
===== Orion (Rank 3) =====
Subgroup: 2.5.7.17.19
Commas: 476/475, 1445/1444, 2128/2125, 3136/3125
Mapping:
[⟨1 0 -3 0 -1],
[⟨0 2 5 0 1],
[⟨0 0 0 1 1]]
POTE generators: 2/1, ~56/25 = 1393.7535, ~17/1 = 4905.0728
{{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
===== Epsilon (Rank 2) =====
Subgroup: 2.5.7.17.19
Commas: 343/340, 476/475, 1225/1216, 2401/2375
Mapping: [⟨1 2 2 2 2], [⟨0 2 5 13 14]]
POTE generators: ~28/25 = 192.6270
{{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
===== Luyten (Rank 2) =====
Subgroup: 2.5.7.17.19
Commas: 476/475, 32768/32585
Mapping: [⟨1 2 2 2 2], [⟨0 2 5 -18 -17]]
POTE generators: ~28/25 = 194.0839
{{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
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