Luna family: Difference between revisions

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The '''luna family''' tempers out the ~~hemithirds comma aka~~ luna comma, 274877906944/274658203125, which has a monzo of {{monzo| 38 -2 -15 }}.

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:

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== Luna ==

[[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

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; Music

* "Moongazing" from ''~~Lessor~~ 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]]

* "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 ==

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~~{{Multival|legend=1| 15 -2 113 -38 137 268 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~262144/234375 = 193.196

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: mapping generators: ~2, ~200/189

~~{{Multival|legend=1| 30 -4 -97 -76 -238 -214 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~200/189 = 96.591

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: mapping generators: ~10125/7168, ~2187/1960

~~{{Multival|legend=1| 30 -4 108 -76 87 262 }}~~

[[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~2187/1960 = 193.1725

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[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Luna family| ]]

[[Category:Luna| ]]

[[Category:Rank 2]]

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-The '''luna family''' tempers out the hemithirds comma aka luna comma, 274877906944/274658203125, which has a monzo of {{monzo| 38 -2 -15 }}.
+{{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:
@@ Line 6: / Line 7: @@
 == 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
@@ Line 19: / Line 24: @@
 ; Music
-* "Moongazing" from ''Lessor 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]]
+* "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 ==
@@ Line 27: / Line 32: @@
 {{Mapping|legend=1| 1 4 2 21 | 0 -15 2 -113 }}
-{{Multival|legend=1| 15 -2 113 -38 137 268 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~262144/234375 = 193.196
@@ Line 57: / Line 60: @@
 : mapping generators: ~2, ~200/189
-{{Multival|legend=1| 30 -4 -97 -76 -238 -214 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~200/189 = 96.591
@@ Line 100: / Line 101: @@
 : mapping generators: ~10125/7168, ~2187/1960
-{{Multival|legend=1| 30 -4 108 -76 87 262 }}
 [[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~2187/1960 = 193.1725
@@ Line 123: / Line 122: @@
 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Luna family| ]] <!-- main article -->
 [[Category:Luna| ]] <!-- key article -->
 [[Category:Rank 2]]