View source for Ed7/2

{{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. 

== Properties ==
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.

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. 

== 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).

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.

== 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?}}

== Proposed names for 7/2-equivalent MOS scales ==
''See also: [[MOS scale]].''

=== 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

===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?}}

[[Category:Ed7/2| ]] <!-- main article -->
[[Category:Edonoi]]
[[Category:Lists of scales]]


{{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.}}