User:CompactStar/Ed10/3: Difference between revisions
CompactStar (talk | contribs) Full cleanup of this page. Removed ancient references to the pre-"talk: Equal-step tuning" article name of "edXIII". 4:5:6:7 is a tetrachord so can't really be used in a similar fashion to 4:5:6 in 5-limit meantone. I suggest 2:3:6 since it is the basic chord of the 10/3.3.5 subgroup. |
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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 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. | ||
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]] MOS. | 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⟨10/3⟩]] MOS. | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||