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 | Division of 11/5 into equal parts does not necessarily imply directly using 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, 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. | ||
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 | 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>. | ||
== | |||
== Ed11/5-edo correspondence == | |||
{|class="wikitable" | {|class="wikitable" | ||
|- | |- | ||
! | ! Ed11/5 | ||
! | ! Edo | ||
|- | |- | ||
|[[8ed11/5]] | | [[8ed11/5]] | ||
|[[7edo]] | | [[7edo]] | ||
|- | |- | ||
|[[9ed11/5]] | | [[9ed11/5]] | ||
|[[8edo]] | | [[8edo]] | ||
|- | |- | ||
|[[16ed11/5]] | | [[16ed11/5]] | ||
|[[14edo]] | | [[14edo]] | ||
|- | |- | ||
|[[18ed11/5]] | | [[18ed11/5]] | ||
|[[16edo]] | | [[16edo]] | ||
|- | |- | ||
|[[24ed11/5]] | | [[24ed11/5]] | ||
|[[21edo]] | | [[21edo]] | ||
|- | |- | ||
|[[25ed11/5]] | | [[25ed11/5]] | ||
|[[22edo]] | | [[22edo]] | ||
|- | |- | ||
|[[27ed11/5]] | | [[27ed11/5]] | ||
|[[24edo]] | | [[24edo]] | ||
|- | |- | ||
|[[33ed11/5]] | | [[33ed11/5]] | ||
|[[29edo]] | | [[29edo]] | ||
|- | |- | ||
|[[50ed11/5]] | | [[50ed11/5]] | ||
|[[44edo]] | | [[44edo]] | ||
|} | |} | ||
== Individual pages for | |||
== Individual pages for ed11/5's == | |||
* [[2ed11/5]] | * [[2ed11/5]] | ||
* [[3ed11/5]] | * [[3ed11/5]] | ||
| Line 50: | Line 52: | ||
* [[14ed11/5]] | * [[14ed11/5]] | ||
* [[20ed11/5]] | * [[20ed11/5]] | ||
[[Category:Ed11/5]] | |||
[[Category:Ed11/5| ]] <!-- main article --> | |||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
Revision as of 15:53, 18 May 2024
The equal division of 11/5 (ed11/5) is a tuning obtained by dividing the 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, 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, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide harmonic 5, and the awkwardly narrow 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.
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 scales of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
Ed11/5-edo correspondence
| Ed11/5 | Edo |
|---|---|
| 8ed11/5 | 7edo |
| 9ed11/5 | 8edo |
| 16ed11/5 | 14edo |
| 18ed11/5 | 16edo |
| 24ed11/5 | 21edo |
| 25ed11/5 | 22edo |
| 27ed11/5 | 24edo |
| 33ed11/5 | 29edo |
| 50ed11/5 | 44edo |