User:CompactStar/Ed10/3: Difference between revisions

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== Properties ==
== Properties ==
Division of 10/3 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 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 [[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}}. Many, though not all, of these scales have a perceptually important 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 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⟨10/3⟩]] 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⟨10/3⟩]] mos.  


[[Category:Ed10/3| ]] <!-- main article -->
[[Category:Ed10/3| ]] <!-- main article -->
[[Category:Edonoi]]
[[Category:Edonoi]]
[[Category:Lists of scales]]
[[Category:Lists of scales]]

Revision as of 02:08, 25 April 2025

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

Properties

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 false octave, with various degrees of accuracy.

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 tritave and the double octave. 10/3 is also the complete ambitus of three, later five, of the church modes[clarification needed].

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⟩ mos.