Luna family: Difference between revisions
Remove 13-limit luna I once added (not a great ext) |
Cleanup |
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The | The '''luna family''' tempers out the hemithirds comma aka luna comma, 274877906944/274658203125, which has a monzo of {{monzo| 38 -2 -15 }}; | ||
=Luna= | = Luna = | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 274877906944/274658203125 | |||
[[Mapping]]: [{{val| 1 4 2 }}, {{val| 0 -15 2 }}] | |||
Badness: 0.0206 | [[POTE generator]]: ~262144/234375 = 193.201 | ||
{{Val list|legend=1| 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559 }} | |||
[[Badness]]: 0.0206 | |||
= Hemithirds = | = Hemithirds = | ||
| Line 36: | Line 39: | ||
{{Val list|legend=1| 31, 87, 118 }} | {{Val list|legend=1| 31, 87, 118 }} | ||
Badness: 0.0443 | [[Badness]]: 0.0443 | ||
== 11-limit == | == 11-limit == | ||
| Line 72: | Line 75: | ||
= Lunatic = | = Lunatic = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 4375/4374, 274877906944/274658203125 | |||
[[Mapping]]: [{{val| 1 4 2 2 }}, {{val| 0 -15 2 -113 }}] | |||
{{Multival|legend=1| 15 -2 113 -38 137 268 }} | |||
[[POTE generator]]: ~262144/234375 = 193.196 | |||
Badness: 0.0380 | {{Val list|legend=1| 87d, 118, 323, 441, 1205, 1646 }} | ||
[[Badness]]: 0.0380 | |||
= Semiluna = | = Semiluna = | ||
{{see also| Canousmic temperaments #Semiluna }} | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 4802000/4782969, 95703125/95551488 | |||
[[Mapping]]: [{{val| 2 8 4 23 }}, {{val| 0 -15 2 -54 }}] | |||
Badness: 0.1922 | [[POTE generator]]: ~2187/1960 = 193.1725 | ||
{{Val list|legend=1| 56d, 118, 292, 410 }} | |||
[[Badness]]: 0.1922 | |||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 5632/5625, 9801/9800, 14641/14580 | |||
POTE generator: ~121/108 = 193.1732 | POTE generator: ~121/108 = 193.1732 | ||
Mapping: [{{val| 2 8 4 23 14 }}, {{val| 0 -15 2 -54 -22 }}] | |||
{{Val list|legend=1| 56d, 118, 292, 410 }} | |||
Badness: 0.0678 | Badness: 0.0678 | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Luna]] | [[Category:Luna]] | ||
[[Category:Hemithirds]] | [[Category:Hemithirds]] | ||
[[Category:Rank 2]] | |||
Revision as of 04:59, 6 April 2021
The luna family tempers out the hemithirds comma aka luna comma, 274877906944/274658203125, which has a monzo of [38 -2 -15⟩;
Luna
Subgroup: 2.3.5
Comma list: 274877906944/274658203125
Mapping: [⟨1 4 2], ⟨0 -15 2]]
POTE generator: ~262144/234375 = 193.201
Badness: 0.0206
Hemithirds
Subgroup: 2.3.5.7
Comma list: 1029/1024, 3136/3125
Mapping: [⟨1 4 2 2], ⟨0 -15 2 5]]
Wedgie: ⟨⟨ 15 -2 -5 -38 -50 -6 ]]
POTE generator: ~28/25 = 193.244
- [[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [11/5 -1/10 0 1/10⟩, [5/2 -1/4 0 1/4⟩]
- Eigenmonzos: 2, 7/6
- [[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [82/35 -4/35 0 2/35⟩, [20/7 -2/7 0 1/7⟩]
- Eigenmonzos: 2, 7/6
Badness: 0.0443
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 3136/3125
Mapping: [⟨1 4 2 2 7], ⟨0 -15 2 5 -22]]
POTE generator: ~28/25 = 193.227
Minimax tuning:
- 11-odd-limit
- [[1 0 0 0 0⟩, [11/9 0 0 -5/9 5/9⟩, [64/27 0 0 2/27 -2/27⟩, [79/27 0 0 5/27 -5/27⟩, [79/27 0 0 -22/27 22/27⟩]
- Eigenmonzos: 2, 11/7
Badness: 0.0190
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 625/624
Mapping: [⟨1 4 2 2 7 0], ⟨0 -15 2 5 -22 23]]
POTE generator: ~28/25 = 193.166
Badness: 0.0217
Lunatic
Subgroup: 2.3.5.7
Comma list: 4375/4374, 274877906944/274658203125
Mapping: [⟨1 4 2 2], ⟨0 -15 2 -113]]
Wedgie: ⟨⟨ 15 -2 113 -38 137 268 ]]
POTE generator: ~262144/234375 = 193.196
Badness: 0.0380
Semiluna
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 95703125/95551488
Mapping: [⟨2 8 4 23], ⟨0 -15 2 -54]]
POTE generator: ~2187/1960 = 193.1725
Badness: 0.1922
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 14641/14580
POTE generator: ~121/108 = 193.1732
Mapping: [⟨2 8 4 23 14], ⟨0 -15 2 -54 -22]]
Badness: 0.0678