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 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.

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:

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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 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.
 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: