User:CompactStar/Ed11/5: Difference between revisions

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'''Ed11/5''' is division of the neutral ninth ([[11/5]]) into n equal parts.  
{{Editable user page}}
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 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.
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 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 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.


== ED11/5-EDO correspondence ==
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"
{|class="wikitable"
|-
|-
!ED11/5
! Ed11/5
!EDO
! 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]]
|-
|-
|[[8ed11/5]]
| [[40ed11/5|40]]
|[[7edo]]
| [[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]]
|-
|-
|[[16ed11/5]]
| [[50ed11/5|50]]
|[[14edo]]
| [[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]]
|-
|-
|[[24ed11/5]]
| [[60ed11/5|60]]
|[[21edo]]
| [[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]]
|-
|-
|[[25ed11/5]]
| [[70ed11/5|70]]
|[[22edo]]
| [[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]]
|-
|-
|[[33ed11/5]]
| [[80ed11/5|80]]
|[[29edo]]
| [[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]]
|-
|-
|[[50ed11/5]]
| [[90ed11/5|90]]
|[[44edo]]
| [[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]]
|}
|}
== Individual pages for ED11/5s ==
* [[2ed11/5]]
* [[3ed11/5]]
* [[4ed11/5]]
* [[5ed11/5]]
* [[6ed11/5]]
* [[7ed11/5]]
* [[8ed11/5]]
* [[9ed11/5]]
* [[10ed11/5]]
* [[13ed11/5]]
* [[14ed11/5]]


[[Category:Ed11/5]]
[[Category:Ed11/5's| ]] <!-- main article -->
[[Category:Nonoctave]]
[[Category:Lists of scales]]
[[Category:Equal-step tunings]]

Latest revision as of 17:57, 1 August 2025

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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. Many, though not all, ed11/5 have a perceptually important 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 harmonic 5 and the awkwardly narrow 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 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

Individual pages for ed11/5's

0…99
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
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