User:CompactStar/Ed11/4: Difference between revisions

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Division of 11/4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 11/4 or another eleventh as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

Incidentally, one way to treat ~~8/3 or~~ 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].

Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].

[[Category:Equal-step tuning]]

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 Division of 11/4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 11/4 or another eleventh as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a perceptually important  pseudo (false) octave, with various degrees of accuracy.
-Incidentally, one way to treat 8/3 or 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 	161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].
+Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] 4 [[3/2]] is equated with [[5/1]], here 4 [[20/11]] is equated with [[16/11]], tempering out the comma 	161051/160000 in the 4.5.11 subgroup. Doing this yields 5, 7, 12, and 17 note MOS, coincidentally similar to [[Pythagorean tuning]].
 [[Category:Equal-step tuning]]