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 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).

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 and 125/121 creates a [[rank-2 temperament]] in the 5.11.13.17 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 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).
+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 and 125/121 creates a [[rank-2 temperament]] in the 5.11.13.17 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 ==