User:CompactStar/Ed11/5: Difference between revisions

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The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5|neutral ninth (11/5)]] into a certain number of [[equal]] steps.

Division of 11/5 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 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1|harmonic 5]], and the awkwardly narrow [[7/5|small septimal tritone]]. It is also a relatively strong consonance. Many, though not all, ~~of these scales~~ have a perceptually important false octave, with various degrees of accuracy.

Division of 11/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed11/5 have a perceptually important [[Pseudo-octave|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 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.

The structural utility of 11/5 is apparent by it being the high ninth of a [[just]] dominant 11th chord, being the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1|harmonic 5]] and the awkwardly narrow [[7/5|small septimal tritone]], and being a relatively strong [[consonance]] by most metrics.

The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it might be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.

== Ed11/5-edo correspondence ==

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 The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5|neutral ninth (11/5)]] into a certain number of [[equal]] steps.
-Division of 11/5 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 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1|harmonic 5]], and the awkwardly narrow [[7/5|small septimal tritone]]. It is also a relatively strong consonance. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.
+Division of 11/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed11/5 have a perceptually important [[Pseudo-octave|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 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
+The structural utility of 11/5 is apparent by it being the high ninth of a [[just]] dominant 11th chord, being the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1|harmonic 5]] and the awkwardly narrow [[7/5|small septimal tritone]], and being a relatively strong [[consonance]] by most metrics.
+The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it might be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
 == Ed11/5-edo correspondence ==