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]]. Many, though not all, ed11/5 have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy. | |||
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 == | |||
{|class="wikitable" | |||
|- | |||
! 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]] | |||
|} | |||
== Individual pages for ed11/5's == | |||
{| class="wikitable center-all" | |||
|+ style=white-space:nowrap | 0…99 | |||
| [[0ed11/5|0]] | |||
| [[1ed11/5|1]] | |||
| [[2ed11/5|2]] | |||
| [[3ed11/5|3]] | |||
| [[4ed11/5|4]] | |||
| [[5ed11/5|5]] | |||
| [[6ed11/5|6]] | |||
| [[7ed11/5|7]] | |||
| [[8ed11/5|8]] | |||
| [[9ed11/5|9]] | |||
|- | |||
| [[10ed11/5|10]] | |||
| [[11ed11/5|11]] | |||
| [[12ed11/5|12]] | |||
| [[13ed11/5|13]] | |||
| [[14ed11/5|14]] | |||
| [[15ed11/5|15]] | |||
| [[16ed11/5|16]] | |||
| [[17ed11/5|17]] | |||
| [[18ed11/5|18]] | |||
| [[19ed11/5|19]] | |||
|- | |||
| [[20ed11/5|20]] | |||
| [[21ed11/5|21]] | |||
| [[22ed11/5|22]] | |||
| [[23ed11/5|23]] | |||
| [[24ed11/5|24]] | |||
| [[25ed11/5|25]] | |||
| [[26ed11/5|26]] | |||
| [[27ed11/5|27]] | |||
| [[28ed11/5|28]] | |||
| [[29ed11/5|29]] | |||
|- | |||
| [[30ed11/5|30]] | |||
| [[31ed11/5|31]] | |||
| [[32ed11/5|32]] | |||
| [[33ed11/5|33]] | |||
| [[34ed11/5|34]] | |||
| [[35ed11/5|35]] | |||
| [[36ed11/5|36]] | |||
| [[37ed11/5|37]] | |||
| [[38ed11/5|38]] | |||
| [[39ed11/5|39]] | |||
|- | |||
| [[40ed11/5|40]] | |||
| [[41ed11/5|41]] | |||
| [[42ed11/5|42]] | |||
| [[43ed11/5|43]] | |||
| [[44ed11/5|44]] | |||
| [[45ed11/5|45]] | |||
| [[46ed11/5|46]] | |||
| [[47ed11/5|47]] | |||
| [[48ed11/5|48]] | |||
| [[49ed11/5|49]] | |||
|- | |||
| [[50ed11/5|50]] | |||
| [[51ed11/5|51]] | |||
| [[52ed11/5|52]] | |||
| [[53ed11/5|53]] | |||
| [[54ed11/5|54]] | |||
| [[55ed11/5|55]] | |||
| [[56ed11/5|56]] | |||
| [[57ed11/5|57]] | |||
| [[58ed11/5|58]] | |||
| [[59ed11/5|59]] | |||
|- | |||
| [[60ed11/5|60]] | |||
| [[61ed11/5|61]] | |||
| [[62ed11/5|62]] | |||
| [[63ed11/5|63]] | |||
| [[64ed11/5|64]] | |||
| [[65ed11/5|65]] | |||
| [[66ed11/5|66]] | |||
| [[67ed11/5|67]] | |||
| [[68ed11/5|68]] | |||
| [[69ed11/5|69]] | |||
|- | |||
| [[70ed11/5|70]] | |||
| [[71ed11/5|71]] | |||
| [[72ed11/5|72]] | |||
| [[73ed11/5|73]] | |||
| [[74ed11/5|74]] | |||
| [[75ed11/5|75]] | |||
| [[76ed11/5|76]] | |||
| [[77ed11/5|77]] | |||
| [[78ed11/5|78]] | |||
| [[79ed11/5|79]] | |||
|- | |||
| [[80ed11/5|80]] | |||
| [[81ed11/5|81]] | |||
| [[82ed11/5|82]] | |||
| [[83ed11/5|83]] | |||
| [[84ed11/5|84]] | |||
| [[85ed11/5|85]] | |||
| [[86ed11/5|86]] | |||
| [[87ed11/5|87]] | |||
| [[88ed11/5|88]] | |||
| [[89ed11/5|89]] | |||
|- | |||
| [[90ed11/5|90]] | |||
| [[91ed11/5|91]] | |||
| [[92ed11/5|92]] | |||
| [[93ed11/5|93]] | |||
| [[94ed11/5|94]] | |||
| [[95ed11/5|95]] | |||
| [[96ed11/5|96]] | |||
| [[97ed11/5|97]] | |||
| [[98ed11/5|98]] | |||
| [[99ed11/5|99]] | |||
|} | |||
[[Category:Ed11/5's| ]] <!-- main article --> | |||
[[Category:Lists of scales]] | |||