Luna and hemithirds: Difference between revisions

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The [[7-limit]] '''hemithirds''' temperament functions as a strong extension of [[didacus]], the 2.5.7 subgroup temperament, in the range between [[25edo]] and [[31edo]] tuning, defined by tempering out [[3136/3125]] such that two of its generators (hemithird, [[~]][[28/25]], around 193.2 [[cent]]s) reach ~[[5/4]], three reach ~[[7/5]], and therefore five reach ~[[7/4]]. Hemithirds extends didacus by tempering out [[1029/1024]], such that three intervals of ~[[8/7]] reach [[3/2]], therefore finding [[4/3]] after fifteen generators in total.

'''Luna''' is a restriction of hemithirds to the [[5-limit]] that is a [[microtemperament]], supported by such high-precision tuning systems as [[118edo]] and [[441edo]]; another notable tuning of luna is [[1000edo]]. It can further be re-extended to the 7-limit in the form of [[lunatic]], but that extension is extremely complex (finding the 7th harmonic at 113 generators down).

'''Luna''' is a restriction of hemithirds to the [[5-limit]] that is a [[microtemperament]], supported by such high-precision tuning systems as [[118edo]] and [[441edo]]; another notable tuning of luna is [[1000edo]]. It can further be re-extended to the 7-limit in the form of [[lunatic]] by adding [[4375/4374]] to the comma list, but that extension is extremely complex (finding the 7th harmonic at 113 generators down).

See [[Hemimean clan #Hemithirds]] and [[Luna family #Luna]] for more information.

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 The [[7-limit]] '''hemithirds''' temperament functions as a strong extension of [[didacus]], the 2.5.7 subgroup temperament, in the range between [[25edo]] and [[31edo]] tuning, defined by tempering out [[3136/3125]] such that two of its generators (hemithird, [[~]][[28/25]], around 193.2 [[cent]]s) reach ~[[5/4]], three reach ~[[7/5]], and therefore five reach ~[[7/4]]. Hemithirds extends didacus by tempering out [[1029/1024]], such that three intervals of ~[[8/7]] reach [[3/2]], therefore finding [[4/3]] after fifteen generators in total.
-'''Luna''' is a restriction of hemithirds to the [[5-limit]] that is a [[microtemperament]], supported by such high-precision tuning systems as [[118edo]] and [[441edo]]; another notable tuning of luna is [[1000edo]]. It can further be re-extended to the 7-limit in the form of [[lunatic]], but that extension is extremely complex (finding the 7th harmonic at 113 generators down).
+'''Luna''' is a restriction of hemithirds to the [[5-limit]] that is a [[microtemperament]], supported by such high-precision tuning systems as [[118edo]] and [[441edo]]; another notable tuning of luna is [[1000edo]]. It can further be re-extended to the 7-limit in the form of [[lunatic]] by adding [[4375/4374]] to the comma list, but that extension is extremely complex (finding the 7th harmonic at 113 generators down).
 See [[Hemimean clan #Hemithirds]] and [[Luna family #Luna]] for more information.