Ed7/2: Difference between revisions

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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]]. 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]]. 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 ==

[[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~~

~~'''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]]

{{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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+{{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]]. 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]]. 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:
+/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?}}
-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]]
+{{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.}}