User:CompactStar/Ed11/4: Difference between revisions

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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 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.

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~~ 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]].

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]].

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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+{{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 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.
+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 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]].
+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]].
+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]]