User:CompactStar/Ed10/3: Difference between revisions

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The '''equal division of 10/3''' ('''ed10/3''') is a [[tuning]] obtained by dividing the [[10/3|just major thirteenth (10/3)]] into a number of [[equal]] steps.

== Properties ==

Division of 10:3 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 10:3 or another thirteenth as a base though, is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[EDT|tritave]] and the [[Ed4|double octave]]~~. 10/3 is also the complete ambitus of three, later five, of the church modes~~. Many, though not all, ~~of these~~ scales have a perceptually important ~~pseudo (~~false) octave, with various degrees of accuracy.

Division of 10/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed10/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.

~~Incidentally, one way to treat~~ 10/3 ~~as an equivalence~~ is the ~~use~~ of the ~~2:3:6 chord~~ as ~~the fundamental complete sonority in~~ a ~~very similar way~~ to the ~~4:5:6 chord in meantone. Whereas in meantone it takes four~~ [[3/2]] ~~to get to~~ [[5/4~~]], here it takes eight [[3~~/1]] ~~to get to [[3/2]] (tempering out the comma 5000000/4782969 in~~ 10/3~~.3.5 subgroup). This [[regular temperament]] yields monolarge MOS with 1-12 notes~~, ~~followed by a 13-note [[12L 1s (10/3-equivalent)|12L 1s&lang;10/3&rang;]] MOS~~.

The structural significance of 10/3 or another thirteenth is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1|tritave]] and the [[4/1|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes{{clarify}}.

One approach to ed10/3 tunings is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in the 5-limit). This [[regular temperament]] yields monolarge mos with 1–12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)|12L 1s&lang;10/3&rang;]] mos.

[[Category:Ed10/3| ]]

[[Category:Edonoi]]

[[Category:Lists of scales]]

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+{{Editable user page}}
 The '''equal division of 10/3''' ('''ed10/3''') is a [[tuning]] obtained by dividing the [[10/3|just major thirteenth (10/3)]] into a number of [[equal]] steps.
 == Properties ==
-Division of 10:3 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 10:3 or another thirteenth as a base though, is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[EDT|tritave]] and the [[Ed4|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
+Division of 10/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed10/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.
-Incidentally, one way to treat 10/3 as an equivalence is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in 10/3.3.5 subgroup). This [[regular temperament]] yields monolarge MOS with 1-12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)|12L 1s&lang;10/3&rang;]] MOS.
+The structural significance of 10/3 or another thirteenth is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1|tritave]] and the [[4/1|double octave]]. 10/3 is also the complete ambitus of three, later five, of the church modes{{clarify}}.
+One approach to ed10/3 tunings is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes eight [[3/1]] to get to [[3/2]] (tempering out the comma 5000000/4782969 in the 5-limit). This [[regular temperament]] yields monolarge mos with 1–12 notes, followed by a 13-note [[12L 1s (10/3-equivalent)|12L 1s&lang;10/3&rang;]] mos.
+[[Category:Ed10/3| ]] <!-- main article -->
 [[Category:Edonoi]]
+[[Category:Lists of scales]]