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== Properties ==
== Properties ==
Division of 7/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. 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 [[Joseph Ruhf]] has 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]]. The question of equivalence has not even been posed yet. 7/2 may be an upper limit of what may be useful as a scale [[period]], being the absolute widest imperfect interval comfortably writable on a standard staff.  


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:
Due to the above, [[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). The fundamental complete sonority of the tonality of such a scale needs more notes than a person has fingers on one hand. Many, though not all, of these scales have a perceptually important [[Pseudo-octave|pseudo (false) octave]], with various degrees of accuracy.


Tetrad and Pentatonic - Mangan 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.


Hexa- and Heptatonic - Haneman Temperament
== Proposed names for 7/2-equivalent temperament families ==
''See also: [[MOS scale]].''


Enneatonic plus or minus one - Baiman Temperament
=== Joseph Ruhf’s names ===
* Tetrad and Pentatonic - Mangan Temperament
* Hexa- 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
{{todo|inline=1|review|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?}}


(1L 12s and 12L 1s - Kazoe Yakuman)
7L 6s and 6L 7s - Daichīsei and Daisharin
'''9L 4s''' and 4L 9s - '''Shōsūshī''' and Daisūshī
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 layout}}
[[Category:Ed7/2| ]] <!-- main article -->
[[Category:Ed7/2| ]] <!-- main article -->
[[Category:Edonoi]]
[[Category:Edonoi]]
[[Category:Lists of scales]]
[[Category:Lists of scales]]

Revision as of 07:54, 9 January 2025

The equal division of 7/2 (ed7/2) is a tuning obtained by dividing the 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. The question of equivalence has not even been posed yet. 7/2 may be an upper limit of what may be useful as a scale period, being the absolute widest imperfect interval comfortably writable on a standard staff.

Due to the above, Joseph Ruhf has named the region of intervals between 17 and 20 degrees of 10edo after the "mangan" system of Riichi Mahjong, creating the Mangan temperament family whose periods are minor fourteenths (e.g. 7/2). The fundamental complete sonority of the tonality of such a scale needs 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.

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 scales. 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 families

See also: MOS scale.

Joseph Ruhf’s names

  • Tetrad and Pentatonic - Mangan Temperament
  • Hexa- and Heptatonic - Haneman Temperament
  • Enneatonic plus or minus one - Baiman Temperament
  • Hen- and dodecatonic - Sanbaiman Temperament)
  • Triskaidekatonic - Yakuman Temperament
Todo: clarify

What do the numbers of notes mean: are they MOS scale sizes? What limit or subgroup does each temperament approximate? What commas 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
Todo: review

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?

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