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{{idiosyncratic terms}}
The '''equal division of 7/2''' ('''ed7/2''') is a [[tuning]] obtained by dividing the [[7/2|septimal minor fourteenth (7/2)]] into a number of [[equal]] steps.  
The '''equal division of 7/2''' ('''ed7/2''') is a [[tuning]] obtained by dividing the [[7/2|septimal minor fourteenth (7/2)]] into a number of [[equal]] steps.  


== Properties ==
== Properties ==
Division of e. g. the 7:2 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. 7:2 is just about an upper limit of what may be useful as a base, which is apparent by being the absolute widest imperfect interval comfortably writable on a standard staff (which is why I have named the region of intervals between 17 and 20 degrees of 10edo after the "mangan" system of Riichi Mahjong, the proper Mangan temperament family being based on minor fourteenths) and by the fundamental complete sonority of the tonality of such a scale needing more notes than a person has fingers on one hand. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
Division of 7/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/2 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.


Incidentally, one way to treat 7/2 as an equivalence is the use of the 3:4:5:6:7:8 chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to [[5/1]], here it takes two [[4/3]] to get to the octave, (tempering out the comma 64/63). So, doing this yields 9, 13, 22 and 31 note MOS. While the notes are rather farther apart, the scheme is uncannily similar to [[Orwell]], making the temperament  the "Yakuman" that is Macro-Orwell:
7/2 may be an upper limit of what may be useful as a scale [[period]], being the widest interval comfortably writable on a standard staff.  


(Tetrad and Pentatonic - Mangan Temperament
== Joseph Ruhf's ed7/2 theory ==
{{todo|inline=1|improve synopsis}}
[[Joseph Ruhf]] has named the [[Interval region|region of intervals]] between 17 and 20 degrees of [[10edo]] after the "mangan" system of {{w|Riichi Mahjong}}, creating the ''Mangan temperament family'' whose periods are minor fourteenths (e.g. 7/2).


Hexa- and Heptatonic - Haneman Temperament
If one wishes to treat 7/2 as an equivalence, one way is the use of the 3:4:5:6:7:8 chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four [[3/2]] to get to [[5/1]], here it takes two [[4/3]] to get to the octave, ([[tempering out]] the comma [[64/63]]). So, doing this yields 9-, 13-, 22- and 31-note [[MOS scale]]s. While the notes are rather farther apart, the scheme is uncannily similar to [[orwell]]. This is the ''yakuman temperament'', named by Joseph Ruhf, that is a kind of macro-orwell.


Enneatonic plus or minus one - Baiman Temperament
== Proposed names for 7/2-equivalent temperament collections ==
=== Joseph Ruhf’s names ===
* [[Tetrad]] and [[pentatonic]] - Mangan temperament
* [[Hexatonic]] and [[heptatonic]] - Haneman temperament
* Enneatonic plus or minus one - Baiman temperament
* Hen- and dodecatonic - Sanbaiman temperament
* Triskaidekatonic - Yakuman temperament
{{todo|inline=1|clarify|comment=What do the numbers of notes mean: are they MOS scale sizes? What [[limit]] or [[subgroup]] does each temperament approximate? What [[comma]]s does each temperament temper out?}}


Hen- and dodecatonic - Sanbaiman Temperament)
== Proposed names for 7/2-equivalent MOS scales ==
''See also: [[MOS scale]].''


Triskaidekatonic - Yakuman Temperament List
=== Joseph Ruhf’s names ===
* 7L 6s - Daichīsei
* 6L 7s - Daisharin
* 9L 4s - Shōsūshī
* 4L 9s - Daisūshī
* 1L 12s and 12L 1s - Kazoe Yakuman
* 2L 11s and 11L 2s - Kokushimusō
* 5L 8s and 8L 5s - Ryūīsō


(1L 12s and 12L 1s - Kazoe Yakuman)
===Cole's names===
* 7L 11s - Pochhammeroid
{{todo|inline=1|discuss title|comment=There probably shouldn’t be instances of two MOSes having the same name. Can we come up with new names for the other one in each of those last three pairs?}}


7L 6s and 6L 7s - Daichīsei and Daisharin
[[Category:Ed7/2| ]] <!-- main article -->
 
[[Category:Edonoi]]
'''9L 4s''' and 4L 9s - '''Shōsūshī''' and Daisūshī
[[Category:Lists of scales]]
 
10L 3s and 3L 10s - Shōsangen and Daisangen


5L 8s and 8L 5s - Ryūīsō


2L 11s and 11L 2s - Kokushimusō
{{todo|inline=1|cleanup|improve readability|explain edonoi|text=Most people do not think 7/2 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}
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[[Category:Edonoi]]
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