Luna family: Difference between revisions
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The '''luna family''' tempers out the [[ | {{Technical data page}} | ||
The '''luna family''' tempers out the [[luna comma]], 274877906944/274658203125, which has a monzo of {{monzo| 38 -2 -15 }}. It divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three. | |||
Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
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== Luna == | == Luna == | ||
{{see also|Luna and hemithirds}} | |||
[[Hemimean clan #Hemithirds|Hemithirds]], a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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; Music | ; Music | ||
* "Moongazing" from '' | * "Moongazing" from ''Lesser Groove'' (2020) [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] | [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] – atmospheric-electro, luna[25] in 1000edo by [[Xotla]] | ||
== Lunatic == | == Lunatic == | ||
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{{Mapping|legend=1| 1 4 2 21 | 0 -15 2 -113 }} | {{Mapping|legend=1| 1 4 2 21 | 0 -15 2 -113 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~262144/234375 = 193.196 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~262144/234375 = 193.196 | ||
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: mapping generators: ~2, ~200/189 | : mapping generators: ~2, ~200/189 | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~200/189 = 96.591 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~200/189 = 96.591 | ||
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: mapping generators: ~10125/7168, ~2187/1960 | : mapping generators: ~10125/7168, ~2187/1960 | ||
[[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~2187/1960 = 193.1725 | [[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~2187/1960 = 193.1725 | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Luna family| ]] <!-- main article --> | [[Category:Luna family| ]] <!-- main article --> | ||
[[Category:Luna| ]] <!-- key article --> | [[Category:Luna| ]] <!-- key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Latest revision as of 04:59, 17 July 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The luna family tempers out the luna comma, 274877906944/274658203125, which has a monzo of [38 -2 -15⟩. It divides 16/3 into fifteen parts, two of which make 5/4. It also divides 9/8 in five and 3/2 in three.
Temperaments discussed elsewhere include:
- Subneutral (+2401/2400) → Breedsmic temperaments
- Hemithirds (+3136/3125) → Hemimean clan
Luna
Hemithirds, a strong extension of didacus that tempers out 1029/1024 alongside 3136/3125, might be considered the main 7-limit extension to luna of practical interest, as 7/4 is found at only 5 generators. However, luna is an undoubted microtemperament of the 5-limit in its own right, supported by systems like 118edo and 441edo, and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.
Subgroup: 2.3.5
Comma list: 274877906944/274658203125
Mapping: [⟨1 4 2], ⟨0 -15 2]]
Optimal tuning (POTE): ~2 = 1\1, ~262144/234375 = 193.201
Optimal ET sequence: 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559
Badness: 0.020576
- Music
- "Moongazing" from Lesser Groove (2020) Bandcamp | YouTube – atmospheric-electro, luna[25] in 1000edo by Xotla
Lunatic
Subgroup: 2.3.5.7
Comma list: 4375/4374, 274877906944/274658203125
Mapping: [⟨1 4 2 21], ⟨0 -15 2 -113]]
Optimal tuning (POTE): ~2 = 1\1, ~262144/234375 = 193.196
Optimal ET sequence: 87d, 118, 323, 441, 1205, 1646
Badness: 0.037966
11-limit
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 12005/11979, 172032/171875
Mapping: [⟨1 4 2 21 14], ⟨0 -15 2 -113 -140]]
Optimal tuning (POTE): ~2 = 1\1, ~352/315 = 193.200
Optimal ET sequence: 118, 323e, 441, 559, 1000e
Badness: 0.058588
Hemiluna
Subgroup: 2.3.5.7
Comma list: 48828125/48771072, 67108864/66976875
Mapping: [⟨1 4 2 -5], ⟨0 -30 4 97]]
- mapping generators: ~2, ~200/189
Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 96.591
Optimal ET sequence: 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd
Badness: 0.179304
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 14641/14580, 131072/130977
Mapping: [⟨1 4 2 -5 7], ⟨0 -30 4 97 -44]]
Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 96.587
Optimal ET sequence: 87, 236, 323, 410
Badness: 0.100077
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580
Mapping: [⟨1 4 2 -5 7 7], ⟨0 -30 4 97 -44 -41]]
Optimal tuning (POTE): ~2 = 1\1, ~143/135 = 96.586
Optimal ET sequence: 87, 236, 323, 410
Badness: 0.046151
Semiluna
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 95703125/95551488
Mapping: [⟨2 8 4 23], ⟨0 -15 2 -54]]
- mapping generators: ~10125/7168, ~2187/1960
Optimal tuning (POTE): ~99/70 = 1\2, ~2187/1960 = 193.1725
Optimal ET sequence: 56d, 118, 292, 410
Badness: 0.192167
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 14641/14580
Mapping: [⟨2 8 4 23 14], ⟨0 -15 2 -54 -22]]
Optimal tuning (POTE): ~99/70 = 1\2, ~121/108 = 193.1732
Optimal ET sequence: 56d, 118, 292, 410
Badness: 0.067783