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 ~~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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 == 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 ==
+{{idiosyncratic terms}}
+{{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.