39edo: Difference between revisions
→Theory: this is quasisuper, not 7-limit superpyth |
+subsets and supersets; +ups and downs notation (copypasted from 46edo). Collapse the armodue notation table |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro | {{EDO intro}} | ||
== Theory == | == Theory == | ||
39edo's [[3/2|perfect fifth]] is 5.8 cents sharp. Together with its best [[5/4|classical major third]] which is the familiar 400 cents of [[12edo]], we get a system which [[tempering out|tempers out]] the [[diesis]], 128/125, and the [[amity comma]], 1600000/1594323. We have two choices for a map for [[7/1|7]], but the sharp one works better with the [[3/1|3]] and [[5/1|5]], which adds [[64/63]] and [[126/125]] to the list. Tempering out both 128/125 and 64/63 makes 39et, in some few ways, allied to 12et in [[support]]ing [[augene]], and is in fact, an excellent choice for an augene tuning, but one difference is that 39et has a fine [[11/1|11]], and adding it to consideration we find that the equal temperament tempers out [[99/98]] and [[121/120]] also. This choice for 39et is the 39d [[val]] {{val| 39 62 91 '''110''' 135 }}. | 39edo's [[3/2|perfect fifth]] is 5.8 cents sharp. Together with its best [[5/4|classical major third]] which is the familiar 400 cents of [[12edo]], we get a system which [[tempering out|tempers out]] the [[diesis]], 128/125, and the [[amity comma]], 1600000/1594323. We have two choices for a map for [[7/1|7]], but the sharp one works better with the [[3/1|3]] and [[5/1|5]], which adds [[64/63]] and [[126/125]] to the list. Tempering out both 128/125 and 64/63 makes 39et, in some few ways, allied to 12et in [[support]]ing [[augene]], and is in fact, an excellent choice for an augene tuning, but one difference is that 39et has a fine [[11/1|11]], and adding it to consideration we find that the equal temperament tempers out [[99/98]] and [[121/120]] also. This choice for 39et is the 39d [[val]] {{val| 39 62 91 '''110''' 135 }}. | ||
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|39}} | {{Harmonics in equal|39}} | ||
=== Subsets and supersets === | |||
Since 39 factors into {{factorization|39}}, 39edo contains [[3edo]] and [[13edo]] as subsets. | |||
== Intervals == | == Intervals == | ||
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== Notation == | == Notation == | ||
=== Ups and downs notation === | |||
Using [[Helmholtz-Ellis notation|Helmholtz–Ellis]] accidentals, 39edo can also be notated using [[ups and downs notation]]: | |||
{{Sharpness-sharp5}} | |||
Here, a sharp raises by five steps, and a flat lowers by five steps, so single and double arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with three arrows. | |||
=== Armodue notation === | === Armodue notation === | ||
; Armodue nomenclature 5;2 relation | ; Armodue nomenclature 5;2 relation | ||
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* '''v''' = Semiflat (1/5-tone down) | * '''v''' = Semiflat (1/5-tone down) | ||
{| class="wikitable center-all right-3 left-5" | {| class="wikitable center-all right-3 left-5 mw-collapsible mw-collapsed" | ||
|- | |- | ||
! colspan="2" | # | ! colspan="2" | # | ||
! Cents | ! Cents | ||
! Armodue | ! Armodue Notation | ||
! Associated Ratios | ! Associated Ratios | ||
|- | |- | ||