User:CompactStar/Ed11/5: Difference between revisions

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Division of 11/5 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 11/5 as a base though is apparent by it being the best option for "no-twos-or-threes" harmony after the extremely wide [[ed5|pentave]], as well as it being a relatively strong consonance. Many, but not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

The simplest chord ~~that is possible~~ without 2's or 3's that ~~fits in 11/5~~ is 7:11:13, so it can be viewed as the fundamental sonority of no-twos-or-threes ~~music. It is also the smallest option that is not extremely dissonant, as 5:7:11 contains a [[7/5]] tritone creating a strong dissonance~~. A neutral ninth-reduced stack of ~~three~~ [[13/7]]'s fall short of [[11/7]] by the ~~small~~ comma ~~[[847/845]]~~. Tempering out this comma ~~together with the additional comma 637/625~~ creates a [[rank-2 temperament]] in the ~~no-twos-or-threes~~ 13~~-limit~~ that can be viewed as an analog to [[meantone]]. It possesses [[MOS scale]]s of the form 1L 3s<11/5>, ~~4L 1s~~<11/5>, ~~5L 4s~~<11/5>, and ~~5L 9s~~<11/5>.

The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes musiC. A neutral ninth-reduced stack of four [[17/11]]'s fall short of [[13/11]] by the comma |0 0 -2 0 5 1 -4>. Tempering out this comma creates a [[rank-2 temperament]] in the 11.13.17 subgroup that can be viewed as an analog to [[meantone]]. It possesses [[MOS scale]]s of the form 2L 3s<11/5> (pentatonic), 2L 5s<11/5> (heptatonic), 2L 7s<11/5> (enneatonic), and 9L 2s<11/5> (hendecatonic).

== ED11/5-EDO correspondence ==

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 Division of 11/5 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 11/5 as a base though is apparent by it being the best option for "no-twos-or-threes" harmony after the extremely wide [[ed5|pentave]], as well as it being a relatively strong consonance.  Many, but not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
-The simplest chord that is possible without 2's or 3's that fits in 11/5 is 7:11:13, so it can be viewed as the fundamental sonority of no-twos-or-threes music. It is also the smallest option that is not extremely dissonant, as 5:7:11 contains a [[7/5]] tritone creating a strong dissonance. A neutral ninth-reduced stack of three [[13/7]]'s fall short of [[11/7]] by the small comma [[847/845]]. Tempering out this comma together with the additional comma 637/625 creates a [[rank-2 temperament]] in the  no-twos-or-threes 13-limit that can be viewed as an analog to [[meantone]]. It possesses [[MOS scale]]s of the form 1L 3s<11/5>, 4L 1s<11/5>, 5L 4s<11/5>, and 5L 9s<11/5>.
+The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes musiC. A neutral ninth-reduced stack of four [[17/11]]'s fall short of [[13/11]] by the comma |0 0 -2 0 5 1 -4>. Tempering out this comma creates a [[rank-2 temperament]] in the 11.13.17 subgroup that can be viewed as an analog to [[meantone]]. It possesses [[MOS scale]]s of the form 2L 3s<11/5> (pentatonic), 2L 5s<11/5> (heptatonic), 2L 7s<11/5> (enneatonic), and 9L 2s<11/5> (hendecatonic).
 == ED11/5-EDO correspondence ==