Ed7/2: Difference between revisions

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== 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| ]]

[[Category:Edonoi]]

[[Category:Lists of scales]]

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 == 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)
-L 6s and 6L 7s - Daichīsei and Daisharin
-'''9L 4s''' and 4L 9s - '''Shōsūshī''' and Daisūshī
-L 3s and 3L 10s - Shōsangen and Daisangen
-L 8s and 8L 5s - Ryūīsō
-L 11s and 11L 2s - Kokushimusō
-{{todo|inline=1|cleanup|improve layout}}
 [[Category:Ed7/2| ]] <!-- main article -->
 [[Category:Edonoi]]
 [[Category:Lists of scales]]