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 ~~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~~.

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.

~~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.

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 ==

[[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.

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== Proposed names for 7/2-equivalent temperament collections ==

=== Joseph Ruhf’s names ===

* Tetrad and ~~Pentatonic~~ - Mangan ~~Temperament~~

* [[Tetrad]] and [[pentatonic]] - Mangan temperament

* ~~Hexa-~~ and ~~Heptatonic~~ - Haneman ~~Temperament~~

* [[Hexatonic]] and [[heptatonic]] - Haneman temperament

* Enneatonic plus or minus one - Baiman ~~Temperament~~

* Enneatonic plus or minus one - Baiman temperament

* Hen- and dodecatonic - Sanbaiman ~~Temperament)~~

* Hen- and dodecatonic - Sanbaiman temperament

* Triskaidekatonic - Yakuman ~~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?}}

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* 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?}}

===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| ]]

[[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 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.
+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.
-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.
+/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.
@@ Line 10: / Line 15: @@
 == Proposed names for 7/2-equivalent temperament collections ==
 === Joseph Ruhf’s names ===
-* Tetrad and Pentatonic - Mangan Temperament
+* [[Tetrad]] and [[pentatonic]] - Mangan temperament
-* Hexa- and Heptatonic - Haneman Temperament
+* [[Hexatonic]] and [[heptatonic]] - Haneman temperament
-* Enneatonic plus or minus one - Baiman Temperament
+* Enneatonic plus or minus one - Baiman temperament
-* Hen- and dodecatonic - Sanbaiman Temperament)
+* Hen- and dodecatonic - Sanbaiman temperament
-* Triskaidekatonic - Yakuman 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?}}
@@ Line 28: / Line 33: @@
 * 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?}}
+===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.}}