Xenharmonic Wiki

Ed7/2: Difference between revisions

VisualWikitext
Created page with "=== Division of a fourteenth (e.g. 7/2) into n equal parts === Division of e. g. the 7:2 into equal parts can be conceived of as to directly use this interval as an equivalenc..."
 
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
mNo edit summary
 
(23 intermediate revisions by 4 users not shown)
Line 1: Line 1:
=== Division of a fourteenth (e.g. 7/2) into n equal parts ===
{{idiosyncratic terms}}
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. That e. g. the 7:2 is just about an upper limit of what may be useful as a base 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.
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.  


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:
== 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.


(Tetrad and Pentatonic - Mangan Temperament
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.


Hexa- and Heptatonic - Haneman 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).


Enneatonic plus or minus one - Baiman 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.


Hen- and dodecatonic - Sanbaiman 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?}}


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


(1L 12s and 12L 1s - Kazoe Yakuman)
=== 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


7L 6s and 6L 7s - Daichīsei and Daisharin
===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?}}


'''9L 4s''' and 4L 9s - '''Shōsūshī''' and Daisūshī
[[Category:Ed7/2| ]] <!-- main article -->
[[Category:Edonoi]]
[[Category:Lists of scales]]


10L 3s and 3L 10s - Shōsangen and Daisangen


5L 8s and 8L 5s - Ryūīsō
{{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.}}
 
2L 11s and 11L 2s - Kokushimusō
----
Retrieved from "https://en.xen.wiki/w/Ed7/2"