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 == | == Properties == | ||
Division of 11/4 into equal parts | 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]] | 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]] | [[Category:Equal-step tuning]] | ||
Revision as of 16:23, 18 May 2024
The equal division of 11/4 (ed11/4) is a tuning obtained by dividing the 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.
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 scales, coincidentally similar to Pythagorean tuning.