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 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 ~~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]]. Many, though not all, ed11/4 scales have a perceptually important [[Pseudo-octave|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~~]].

The structural utility of 11/4 is apparent by being central to much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the [[octave]] and the [[tritave]].

[[Category:~~Equal~~-~~step tuning~~]]

One approach to ed11/4 tunings 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:Ed11/4| ]]

[[Category:Edonoi]]

[[Category:Lists of scales]]

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-'''Ed11/4''' is division of [[11/4]] into equal parts.
+{{Editable user page}}
+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 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 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]]. Many, though not all, ed11/4 scales have a perceptually important [[Pseudo-octave|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]].
+The structural utility of 11/4 is apparent by being central to much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the [[octave]] and the [[tritave]].
-[[Category:Equal-step tuning]]
+One approach to ed11/4 tunings 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:Ed11/4| ]] <!-- main article -->
+[[Category:Edonoi]]
+[[Category:Lists of scales]]