User:CompactStar/Ed11/4: Difference between revisions

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'''~~Ed11~~/4''' is ~~division of~~ [[11/4]] ~~into~~ equal ~~parts~~.

The '''equal division of 11/4''' ('''ed11/4''') is a [[tuning]] obtained by dividing the [[11/4|undecimal semi-augmented eleventh (11/4)]] in a certain number of [[equal]] steps.

== Properties ==

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 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the octave and the tritave. Many, though not all, of these scales have a perceptually important ~~pseudo (~~false) octave, with various degrees of accuracy.

Division of 11/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of 11/4 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the [[octave]] and the [[tritave]]. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

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]].

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]] a stack of four [[3/2]]'s is equated with [[5/1]], here a stack of four [[20/11]]'s 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 scale]]s, coincidentally similar to [[Pythagorean tuning]].

[[Category:Equal-step tuning]]

@@ Line 1: / Line 1: @@
-'''Ed11/4''' is division of [[11/4]] into equal parts.
+The '''equal division of 11/4''' ('''ed11/4''') is a [[tuning]] obtained by dividing the [[11/4|undecimal semi-augmented eleventh (11/4)]] in a certain number of [[equal]] steps.
 == Properties ==
-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 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the octave and the tritave. Many, though not all, of these scales have a perceptually important  pseudo (false) octave, with various degrees of accuracy.
+Division of 11/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. The utility of 11/4 as a base though, is apparent by being used at the base of so much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the [[octave]] and the [[tritave]]. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.
-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]].
+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]] a stack of four [[3/2]]'s is equated with [[5/1]], here a stack of four [[20/11]]'s 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 scale]]s, coincidentally similar to [[Pythagorean tuning]].
 [[Category:Equal-step tuning]]