Chords of hemiwur: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[Würschmidt_family#Hemiwürschmidt|hemiwur temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 121/120 are biyatismic, by 176/175 valinorsmic, and by 385/384 keenanismic. Chords requiring any two of the above are labeled zeus.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-01 01:26:30 UTC</tt>.<br>
: The original revision id was <tt>288950695</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Würschmidt family#Hemiwürschmidt|hemiwur temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 121/120 are biyatismic, by 176/175 valinorsmic, and by 385/384 keenanismic. Chords requiring any two of the above are labeled zeus.


Hemiwur has MOS of size 6, 7, 13, 19, 25, 31, 37 and 68. The largest chords on these lists have complexity 32, and so would require the 37 note MOS, but there are many chords of much lower complexity, so that the 13-note MOS, for instance, has a couple of hexads, plus many more pentads, tetrads and triads.
Hemiwur has MOS of size 6, 7, 13, 19, 25, 31, 37 and 68. The largest chords on these lists have complexity 32, and so would require the 37 note MOS, but there are many chords of much lower complexity, so that the 13-note MOS, for instance, has a couple of hexads, plus many more pentads, tetrads and triads.


=Triads=
=Triads=
|| Number || Chord || Transversal || Type ||
 
|| 1 || 0-2-4 || 1-5/4-11/7 || valinorsmic ||
{| class="wikitable"
|| 2 || 0-2-5 || 1-5/4-7/4 || otonal ||
|-
|| 3 || 0-3-5 || 1-7/5-7/4 || utonal ||
| | Number
|| 4 || 0-2-7 || 1-5/4-11/10 || valinorsmic ||
| | Chord
|| 5 || 0-3-7 || 1-7/5-11/10 || otonal ||
| | Transversal
|| 6 || 0-4-7 || 1-11/7-11/10 || utonal ||
| | Type
|| 7 || 0-5-7 || 1-7/4-11/10 || valinorsmic ||
|-
|| 8 || 0-2-9 || 1-5/4-11/8 || otonal ||
| | 1
|| 9 || 0-4-9 || 1-11/7-11/8 || utonal ||
| | 0-2-4
|| 10 || 0-5-9 || 1-7/4-11/8 || otonal ||
| | 1-5/4-11/7
|| 11 || 0-7-9 || 1-11/10-11/8 || utonal ||
| | valinorsmic
|| 12 || 0-2-11 || 1-5/4-12/7 || keenanismic ||
|-
|| 13 || 0-4-11 || 1-11/7-12/7 || otonal ||
| | 2
|| 14 || 0-7-11 || 1-12/11-12/7 || utonal ||
| | 0-2-5
|| 15 || 0-9-11 || 1-11/8-12/7 || keenanismic ||
| | 1-5/4-7/4
|| 16 || 0-3-14 || 1-7/5-6/5 || otonal ||
| | otonal
|| 17 || 0-5-14 || 1-7/4-6/5 || keenanismic ||
|-
|| 18 || 0-7-14 || 1-11/10-6/5 || otonal ||
| | 3
|| 19 || 0-9-14 || 1-11/8-6/5 || keenanismic ||
| | 0-3-5
|| 20 || 0-11-14 || 1-12/7-6/5 || utonal ||
| | 1-7/5-7/4
|| 21 || 0-2-16 || 1-5/4-3/2 || otonal ||
| | utonal
|| 22 || 0-5-16 || 1-7/4-3/2 || otonal ||
|-
|| 23 || 0-7-16 || 1-12/11-3/2 || utonal ||
| | 4
|| 24 || 0-9-16 || 1-11/8-3/2 || otonal ||
| | 0-2-7
|| 25 || 0-11-16 || 1-12/7-3/2 || utonal ||
| | 1-5/4-11/10
|| 26 || 0-14-16 || 1-6/5-3/2 || utonal ||
| | valinorsmic
|| 27 || 0-7-23 || 1-12/11-18/11 || otonal ||
|-
|| 28 || 0-9-23 || 1-11/8-18/11 || biyatismic ||
| | 5
|| 29 || 0-14-23 || 1-6/5-18/11 || biyatismic ||
| | 0-3-7
|| 30 || 0-16-23 || 1-3/2-18/11 || utonal ||
| | 1-7/5-11/10
|| 31 || 0-4-27 || 1-11/7-9/7 || otonal ||
| | otonal
|| 32 || 0-11-27 || 1-12/7-9/7 || otonal ||
|-
|| 33 || 0-16-27 || 1-3/2-9/7 || utonal ||
| | 6
|| 34 || 0-23-27 || 1-18/11-9/7 || utonal ||
| | 0-4-7
|| 35 || 0-3-30 || 1-7/5-9/5 || otonal ||
| | 1-11/7-11/10
|| 36 || 0-7-30 || 1-11/10-9/5 || otonal ||
| | utonal
|| 37 || 0-14-30 || 1-6/5-9/5 || otonal ||
|-
|| 38 || 0-16-30 || 1-3/2-9/5 || utonal ||
| | 7
|| 39 || 0-23-30 || 1-18/11-9/5 || utonal ||
| | 0-5-7
|| 40 || 0-27-30 || 1-9/7-9/5 || utonal ||
| | 1-7/4-11/10
|| 41 || 0-2-32 || 1-5/4-9/8 || otonal ||
| | valinorsmic
|| 42 || 0-5-32 || 1-7/4-9/8 || otonal ||
|-
|| 43 || 0-9-32 || 1-11/8-9/8 || otonal ||
| | 8
|| 44 || 0-16-32 || 1-3/2-9/8 || ambitonal ||
| | 0-2-9
|| 45 || 0-23-32 || 1-18/11-9/8 || utonal ||
| | 1-5/4-11/8
|| 46 || 0-27-32 || 1-9/7-9/8 || utonal ||
| | otonal
|| 47 || 0-30-32 || 1-9/5-9/8 || utonal ||
|-
| | 9
| | 0-4-9
| | 1-11/7-11/8
| | utonal
|-
| | 10
| | 0-5-9
| | 1-7/4-11/8
| | otonal
|-
| | 11
| | 0-7-9
| | 1-11/10-11/8
| | utonal
|-
| | 12
| | 0-2-11
| | 1-5/4-12/7
| | keenanismic
|-
| | 13
| | 0-4-11
| | 1-11/7-12/7
| | otonal
|-
| | 14
| | 0-7-11
| | 1-12/11-12/7
| | utonal
|-
| | 15
| | 0-9-11
| | 1-11/8-12/7
| | keenanismic
|-
| | 16
| | 0-3-14
| | 1-7/5-6/5
| | otonal
|-
| | 17
| | 0-5-14
| | 1-7/4-6/5
| | keenanismic
|-
| | 18
| | 0-7-14
| | 1-11/10-6/5
| | otonal
|-
| | 19
| | 0-9-14
| | 1-11/8-6/5
| | keenanismic
|-
| | 20
| | 0-11-14
| | 1-12/7-6/5
| | utonal
|-
| | 21
| | 0-2-16
| | 1-5/4-3/2
| | otonal
|-
| | 22
| | 0-5-16
| | 1-7/4-3/2
| | otonal
|-
| | 23
| | 0-7-16
| | 1-12/11-3/2
| | utonal
|-
| | 24
| | 0-9-16
| | 1-11/8-3/2
| | otonal
|-
| | 25
| | 0-11-16
| | 1-12/7-3/2
| | utonal
|-
| | 26
| | 0-14-16
| | 1-6/5-3/2
| | utonal
|-
| | 27
| | 0-7-23
| | 1-12/11-18/11
| | otonal
|-
| | 28
| | 0-9-23
| | 1-11/8-18/11
| | biyatismic
|-
| | 29
| | 0-14-23
| | 1-6/5-18/11
| | biyatismic
|-
| | 30
| | 0-16-23
| | 1-3/2-18/11
| | utonal
|-
| | 31
| | 0-4-27
| | 1-11/7-9/7
| | otonal
|-
| | 32
| | 0-11-27
| | 1-12/7-9/7
| | otonal
|-
| | 33
| | 0-16-27
| | 1-3/2-9/7
| | utonal
|-
| | 34
| | 0-23-27
| | 1-18/11-9/7
| | utonal
|-
| | 35
| | 0-3-30
| | 1-7/5-9/5
| | otonal
|-
| | 36
| | 0-7-30
| | 1-11/10-9/5
| | otonal
|-
| | 37
| | 0-14-30
| | 1-6/5-9/5
| | otonal
|-
| | 38
| | 0-16-30
| | 1-3/2-9/5
| | utonal
|-
| | 39
| | 0-23-30
| | 1-18/11-9/5
| | utonal
|-
| | 40
| | 0-27-30
| | 1-9/7-9/5
| | utonal
|-
| | 41
| | 0-2-32
| | 1-5/4-9/8
| | otonal
|-
| | 42
| | 0-5-32
| | 1-7/4-9/8
| | otonal
|-
| | 43
| | 0-9-32
| | 1-11/8-9/8
| | otonal
|-
| | 44
| | 0-16-32
| | 1-3/2-9/8
| | ambitonal
|-
| | 45
| | 0-23-32
| | 1-18/11-9/8
| | utonal
|-
| | 46
| | 0-27-32
| | 1-9/7-9/8
| | utonal
|-
| | 47
| | 0-30-32
| | 1-9/5-9/8
| | utonal
|}


=Tetrads=
=Tetrads=
|| Number || Chord || Transversal || Type ||
 
|| 1 || 0-2-4-7 || 1-5/4-11/7-11/10 || valinorsmic ||
{| class="wikitable"
|| 2 || 0-2-5-7 || 1-5/4-7/4-11/10 || valinorsmic ||
|-
|| 3 || 0-3-5-7 || 1-7/5-7/4-11/10 || valinorsmic ||
| | Number
|| 4 || 0-2-4-9 || 1-5/4-11/7-11/8 || valinorsmic ||
| | Chord
|| 5 || 0-2-5-9 || 1-5/4-7/4-11/8 || otonal ||
| | Transversal
|| 6 || 0-2-7-9 || 1-5/4-11/10-11/8 || valinorsmic ||
| | Type
|| 7 || 0-4-7-9 || 1-11/7-11/10-11/8 || utonal ||
|-
|| 8 || 0-5-7-9 || 1-7/4-11/10-11/8 || valinorsmic ||
| | 1
|| 9 || 0-2-4-11 || 1-5/4-11/7-12/7 || zeus ||
| | 0-2-4-7
|| 10 || 0-2-7-11 || 1-5/4-11/10-12/7 || zeus ||
| | 1-5/4-11/7-11/10
|| 11 || 0-4-7-11 || 1-11/7-11/10-12/7 || biyatismic ||
| | valinorsmic
|| 12 || 0-2-9-11 || 1-5/4-11/8-12/7 || keenanismic ||
|-
|| 13 || 0-4-9-11 || 1-11/7-11/8-12/7 || zeus ||
| | 2
|| 14 || 0-7-9-11 || 1-11/10-11/8-12/7 || zeus ||
| | 0-2-5-7
|| 15 || 0-3-5-14 || 1-7/5-7/4-6/5 || keenanismic ||
| | 1-5/4-7/4-11/10
|| 16 || 0-3-7-14 || 1-7/5-11/10-6/5 || otonal ||
| | valinorsmic
|| 17 || 0-5-7-14 || 1-7/4-11/10-6/5 || zeus ||
|-
|| 18 || 0-5-9-14 || 1-7/4-11/8-6/5 || keenanismic ||
| | 3
|| 19 || 0-7-9-14 || 1-11/10-11/8-6/5 || zeus ||
| | 0-3-5-7
|| 20 || 0-7-11-14 || 1-12/11-12/7-6/5 || utonal ||
| | 1-7/5-7/4-11/10
|| 21 || 0-9-11-14 || 1-11/8-12/7-6/5 || keenanismic ||
| | valinorsmic
|| 22 || 0-2-5-16 || 1-5/4-7/4-3/2 || otonal ||
|-
|| 23 || 0-2-7-16 || 1-5/4-11/10-3/2 || zeus ||
| | 4
|| 24 || 0-5-7-16 || 1-7/4-11/10-3/2 || zeus ||
| | 0-2-4-9
|| 25 || 0-2-9-16 || 1-5/4-11/8-3/2 || otonal ||
| | 1-5/4-11/7-11/8
|| 26 || 0-5-9-16 || 1-7/4-11/8-3/2 || otonal ||
| | valinorsmic
|| 27 || 0-7-9-16 || 1-11/10-11/8-3/2 || biyatismic ||
|-
|| 28 || 0-2-11-16 || 1-5/4-12/7-3/2 || keenanismic ||
| | 5
|| 29 || 0-7-11-16 || 1-12/11-12/7-3/2 || utonal ||
| | 0-2-5-9
|| 30 || 0-9-11-16 || 1-11/8-12/7-3/2 || zeus ||
| | 1-5/4-7/4-11/8
|| 31 || 0-5-14-16 || 1-7/4-6/5-3/2 || keenanismic ||
| | otonal
|| 32 || 0-7-14-16 || 1-12/11-6/5-3/2 || utonal ||
|-
|| 33 || 0-9-14-16 || 1-11/8-6/5-3/2 || zeus ||
| | 6
|| 34 || 0-11-14-16 || 1-12/7-6/5-3/2 || utonal ||
| | 0-2-7-9
|| 35 || 0-7-9-23 || 1-11/10-11/8-18/11 || biyatismic ||
| | 1-5/4-11/10-11/8
|| 36 || 0-7-14-23 || 1-11/10-6/5-18/11 || biyatismic ||
| | valinorsmic
|| 37 || 0-9-14-23 || 1-11/8-6/5-18/11 || zeus ||
|-
|| 38 || 0-7-16-23 || 1-12/11-3/2-18/11 || ambitonal ||
| | 7
|| 39 || 0-9-16-23 || 1-11/8-3/2-18/11 || biyatismic ||
| | 0-4-7-9
|| 40 || 0-14-16-23 || 1-6/5-3/2-18/11 || biyatismic ||
| | 1-11/7-11/10-11/8
|| 41 || 0-4-11-27 || 1-11/7-12/7-9/7 || otonal ||
| | utonal
|| 42 || 0-11-16-27 || 1-12/7-3/2-9/7 || ambitonal ||
|-
|| 43 || 0-16-23-27 || 1-3/2-18/11-9/7 || utonal ||
| | 8
|| 44 || 0-3-7-30 || 1-7/5-11/10-9/5 || otonal ||
| | 0-5-7-9
|| 45 || 0-3-14-30 || 1-7/5-6/5-9/5 || otonal ||
| | 1-7/4-11/10-11/8
|| 46 || 0-7-14-30 || 1-11/10-6/5-9/5 || otonal ||
| | valinorsmic
|| 47 || 0-7-16-30 || 1-11/10-3/2-9/5 || biyatismic ||
|-
|| 48 || 0-14-16-30 || 1-6/5-3/2-9/5 || ambitonal ||
| | 9
|| 49 || 0-7-23-30 || 1-11/10-18/11-9/5 || biyatismic ||
| | 0-2-4-11
|| 50 || 0-14-23-30 || 1-6/5-18/11-9/5 || biyatismic ||
| | 1-5/4-11/7-12/7
|| 51 || 0-16-23-30 || 1-3/2-18/11-9/5 || utonal ||
| | zeus
|| 52 || 0-16-27-30 || 1-3/2-9/7-9/5 || utonal ||
|-
|| 53 || 0-23-27-30 || 1-18/11-9/7-9/5 || utonal ||
| | 10
|| 54 || 0-2-5-32 || 1-5/4-7/4-9/8 || otonal ||
| | 0-2-7-11
|| 55 || 0-2-9-32 || 1-5/4-11/8-9/8 || otonal ||
| | 1-5/4-11/10-12/7
|| 56 || 0-5-9-32 || 1-7/4-11/8-9/8 || otonal ||
| | zeus
|| 57 || 0-2-16-32 || 1-5/4-3/2-9/8 || otonal ||
|-
|| 58 || 0-5-16-32 || 1-7/4-3/2-9/8 || otonal ||
| | 11
|| 59 || 0-9-16-32 || 1-11/8-3/2-9/8 || otonal ||
| | 0-4-7-11
|| 60 || 0-9-23-32 || 1-11/8-18/11-9/8 || biyatismic ||
| | 1-11/7-11/10-12/7
|| 61 || 0-16-23-32 || 1-3/2-18/11-9/8 || utonal ||
| | biyatismic
|| 62 || 0-16-27-32 || 1-3/2-9/7-9/8 || utonal ||
|-
|| 63 || 0-23-27-32 || 1-18/11-9/7-9/8 || utonal ||
| | 12
|| 64 || 0-16-30-32 || 1-3/2-9/5-9/8 || utonal ||
| | 0-2-9-11
|| 65 || 0-23-30-32 || 1-18/11-9/5-9/8 || utonal ||
| | 1-5/4-11/8-12/7
|| 66 || 0-27-30-32 || 1-9/7-9/5-9/8 || utonal ||
| | keenanismic
|-
| | 13
| | 0-4-9-11
| | 1-11/7-11/8-12/7
| | zeus
|-
| | 14
| | 0-7-9-11
| | 1-11/10-11/8-12/7
| | zeus
|-
| | 15
| | 0-3-5-14
| | 1-7/5-7/4-6/5
| | keenanismic
|-
| | 16
| | 0-3-7-14
| | 1-7/5-11/10-6/5
| | otonal
|-
| | 17
| | 0-5-7-14
| | 1-7/4-11/10-6/5
| | zeus
|-
| | 18
| | 0-5-9-14
| | 1-7/4-11/8-6/5
| | keenanismic
|-
| | 19
| | 0-7-9-14
| | 1-11/10-11/8-6/5
| | zeus
|-
| | 20
| | 0-7-11-14
| | 1-12/11-12/7-6/5
| | utonal
|-
| | 21
| | 0-9-11-14
| | 1-11/8-12/7-6/5
| | keenanismic
|-
| | 22
| | 0-2-5-16
| | 1-5/4-7/4-3/2
| | otonal
|-
| | 23
| | 0-2-7-16
| | 1-5/4-11/10-3/2
| | zeus
|-
| | 24
| | 0-5-7-16
| | 1-7/4-11/10-3/2
| | zeus
|-
| | 25
| | 0-2-9-16
| | 1-5/4-11/8-3/2
| | otonal
|-
| | 26
| | 0-5-9-16
| | 1-7/4-11/8-3/2
| | otonal
|-
| | 27
| | 0-7-9-16
| | 1-11/10-11/8-3/2
| | biyatismic
|-
| | 28
| | 0-2-11-16
| | 1-5/4-12/7-3/2
| | keenanismic
|-
| | 29
| | 0-7-11-16
| | 1-12/11-12/7-3/2
| | utonal
|-
| | 30
| | 0-9-11-16
| | 1-11/8-12/7-3/2
| | zeus
|-
| | 31
| | 0-5-14-16
| | 1-7/4-6/5-3/2
| | keenanismic
|-
| | 32
| | 0-7-14-16
| | 1-12/11-6/5-3/2
| | utonal
|-
| | 33
| | 0-9-14-16
| | 1-11/8-6/5-3/2
| | zeus
|-
| | 34
| | 0-11-14-16
| | 1-12/7-6/5-3/2
| | utonal
|-
| | 35
| | 0-7-9-23
| | 1-11/10-11/8-18/11
| | biyatismic
|-
| | 36
| | 0-7-14-23
| | 1-11/10-6/5-18/11
| | biyatismic
|-
| | 37
| | 0-9-14-23
| | 1-11/8-6/5-18/11
| | zeus
|-
| | 38
| | 0-7-16-23
| | 1-12/11-3/2-18/11
| | ambitonal
|-
| | 39
| | 0-9-16-23
| | 1-11/8-3/2-18/11
| | biyatismic
|-
| | 40
| | 0-14-16-23
| | 1-6/5-3/2-18/11
| | biyatismic
|-
| | 41
| | 0-4-11-27
| | 1-11/7-12/7-9/7
| | otonal
|-
| | 42
| | 0-11-16-27
| | 1-12/7-3/2-9/7
| | ambitonal
|-
| | 43
| | 0-16-23-27
| | 1-3/2-18/11-9/7
| | utonal
|-
| | 44
| | 0-3-7-30
| | 1-7/5-11/10-9/5
| | otonal
|-
| | 45
| | 0-3-14-30
| | 1-7/5-6/5-9/5
| | otonal
|-
| | 46
| | 0-7-14-30
| | 1-11/10-6/5-9/5
| | otonal
|-
| | 47
| | 0-7-16-30
| | 1-11/10-3/2-9/5
| | biyatismic
|-
| | 48
| | 0-14-16-30
| | 1-6/5-3/2-9/5
| | ambitonal
|-
| | 49
| | 0-7-23-30
| | 1-11/10-18/11-9/5
| | biyatismic
|-
| | 50
| | 0-14-23-30
| | 1-6/5-18/11-9/5
| | biyatismic
|-
| | 51
| | 0-16-23-30
| | 1-3/2-18/11-9/5
| | utonal
|-
| | 52
| | 0-16-27-30
| | 1-3/2-9/7-9/5
| | utonal
|-
| | 53
| | 0-23-27-30
| | 1-18/11-9/7-9/5
| | utonal
|-
| | 54
| | 0-2-5-32
| | 1-5/4-7/4-9/8
| | otonal
|-
| | 55
| | 0-2-9-32
| | 1-5/4-11/8-9/8
| | otonal
|-
| | 56
| | 0-5-9-32
| | 1-7/4-11/8-9/8
| | otonal
|-
| | 57
| | 0-2-16-32
| | 1-5/4-3/2-9/8
| | otonal
|-
| | 58
| | 0-5-16-32
| | 1-7/4-3/2-9/8
| | otonal
|-
| | 59
| | 0-9-16-32
| | 1-11/8-3/2-9/8
| | otonal
|-
| | 60
| | 0-9-23-32
| | 1-11/8-18/11-9/8
| | biyatismic
|-
| | 61
| | 0-16-23-32
| | 1-3/2-18/11-9/8
| | utonal
|-
| | 62
| | 0-16-27-32
| | 1-3/2-9/7-9/8
| | utonal
|-
| | 63
| | 0-23-27-32
| | 1-18/11-9/7-9/8
| | utonal
|-
| | 64
| | 0-16-30-32
| | 1-3/2-9/5-9/8
| | utonal
|-
| | 65
| | 0-23-30-32
| | 1-18/11-9/5-9/8
| | utonal
|-
| | 66
| | 0-27-30-32
| | 1-9/7-9/5-9/8
| | utonal
|}


=Pentads=
=Pentads=
|| Number || Chord || Transversal || Type ||
 
|| 1 || 0-2-4-7-9 || 1-5/4-11/7-11/10-11/8 || valinorsmic ||
{| class="wikitable"
|| 2 || 0-2-5-7-9 || 1-5/4-7/4-11/10-11/8 || valinorsmic ||
|-
|| 3 || 0-2-4-7-11 || 1-5/4-11/7-11/10-12/7 || zeus ||
| | Number
|| 4 || 0-2-4-9-11 || 1-5/4-11/7-11/8-12/7 || zeus ||
| | Chord
|| 5 || 0-2-7-9-11 || 1-5/4-11/10-11/8-12/7 || zeus ||
| | Transversal
|| 6 || 0-4-7-9-11 || 1-11/7-11/10-11/8-12/7 || zeus ||
| | Type
|| 7 || 0-3-5-7-14 || 1-7/5-7/4-11/10-6/5 || zeus ||
|-
|| 8 || 0-5-7-9-14 || 1-7/4-11/10-11/8-6/5 || zeus ||
| | 1
|| 9 || 0-7-9-11-14 || 1-11/10-11/8-12/7-6/5 || zeus ||
| | 0-2-4-7-9
|| 10 || 0-2-5-7-16 || 1-5/4-7/4-11/10-3/2 || zeus ||
| | 1-5/4-11/7-11/10-11/8
|| 11 || 0-2-5-9-16 || 1-5/4-7/4-11/8-3/2 || otonal ||
| | valinorsmic
|| 12 || 0-2-7-9-16 || 1-5/4-11/10-11/8-3/2 || zeus ||
|-
|| 13 || 0-5-7-9-16 || 1-7/4-11/10-11/8-3/2 || zeus ||
| | 2
|| 14 || 0-2-7-11-16 || 1-5/4-11/10-12/7-3/2 || zeus ||
| | 0-2-5-7-9
|| 15 || 0-2-9-11-16 || 1-5/4-11/8-12/7-3/2 || zeus ||
| | 1-5/4-7/4-11/10-11/8
|| 16 || 0-7-9-11-16 || 1-11/10-11/8-12/7-3/2 || zeus ||
| | valinorsmic
|| 17 || 0-5-7-14-16 || 1-7/4-11/10-6/5-3/2 || zeus ||
|-
|| 18 || 0-5-9-14-16 || 1-7/4-11/8-6/5-3/2 || zeus ||
| | 3
|| 19 || 0-7-9-14-16 || 1-11/10-11/8-6/5-3/2 || zeus ||
| | 0-2-4-7-11
|| 20 || 0-7-11-14-16 || 1-12/11-12/7-6/5-3/2 || utonal ||
| | 1-5/4-11/7-11/10-12/7
|| 21 || 0-9-11-14-16 || 1-11/8-12/7-6/5-3/2 || zeus ||
| | zeus
|| 22 || 0-7-9-14-23 || 1-11/10-11/8-6/5-18/11 || zeus ||
|-
|| 23 || 0-7-9-16-23 || 1-11/10-11/8-3/2-18/11 || biyatismic ||
| | 4
|| 24 || 0-7-14-16-23 || 1-11/10-6/5-3/2-18/11 || biyatismic ||
| | 0-2-4-9-11
|| 25 || 0-9-14-16-23 || 1-11/8-6/5-3/2-18/11 || zeus ||
| | 1-5/4-11/7-11/8-12/7
|| 26 || 0-3-7-14-30 || 1-7/5-11/10-6/5-9/5 || otonal ||
| | zeus
|| 27 || 0-7-14-16-30 || 1-11/10-6/5-3/2-9/5 || biyatismic ||
|-
|| 28 || 0-7-14-23-30 || 1-11/10-6/5-18/11-9/5 || biyatismic ||
| | 5
|| 29 || 0-7-16-23-30 || 1-11/10-3/2-18/11-9/5 || biyatismic ||
| | 0-2-7-9-11
|| 30 || 0-14-16-23-30 || 1-6/5-3/2-18/11-9/5 || biyatismic ||
| | 1-5/4-11/10-11/8-12/7
|| 31 || 0-16-23-27-30 || 1-3/2-18/11-9/7-9/5 || utonal ||
| | zeus
|| 32 || 0-2-5-9-32 || 1-5/4-7/4-11/8-9/8 || otonal ||
|-
|| 33 || 0-2-5-16-32 || 1-5/4-7/4-3/2-9/8 || otonal ||
| | 6
|| 34 || 0-2-9-16-32 || 1-5/4-11/8-3/2-9/8 || otonal ||
| | 0-4-7-9-11
|| 35 || 0-5-9-16-32 || 1-7/4-11/8-3/2-9/8 || otonal ||
| | 1-11/7-11/10-11/8-12/7
|| 36 || 0-9-16-23-32 || 1-11/8-3/2-18/11-9/8 || biyatismic ||
| | zeus
|| 37 || 0-16-23-27-32 || 1-3/2-18/11-9/7-9/8 || utonal ||
|-
|| 38 || 0-16-23-30-32 || 1-3/2-18/11-9/5-9/8 || utonal ||
| | 7
|| 39 || 0-16-27-30-32 || 1-3/2-9/7-9/5-9/8 || utonal ||
| | 0-3-5-7-14
|| 40 || 0-23-27-30-32 || 1-18/11-9/7-9/5-9/8 || utonal ||
| | 1-7/5-7/4-11/10-6/5
| | zeus
|-
| | 8
| | 0-5-7-9-14
| | 1-7/4-11/10-11/8-6/5
| | zeus
|-
| | 9
| | 0-7-9-11-14
| | 1-11/10-11/8-12/7-6/5
| | zeus
|-
| | 10
| | 0-2-5-7-16
| | 1-5/4-7/4-11/10-3/2
| | zeus
|-
| | 11
| | 0-2-5-9-16
| | 1-5/4-7/4-11/8-3/2
| | otonal
|-
| | 12
| | 0-2-7-9-16
| | 1-5/4-11/10-11/8-3/2
| | zeus
|-
| | 13
| | 0-5-7-9-16
| | 1-7/4-11/10-11/8-3/2
| | zeus
|-
| | 14
| | 0-2-7-11-16
| | 1-5/4-11/10-12/7-3/2
| | zeus
|-
| | 15
| | 0-2-9-11-16
| | 1-5/4-11/8-12/7-3/2
| | zeus
|-
| | 16
| | 0-7-9-11-16
| | 1-11/10-11/8-12/7-3/2
| | zeus
|-
| | 17
| | 0-5-7-14-16
| | 1-7/4-11/10-6/5-3/2
| | zeus
|-
| | 18
| | 0-5-9-14-16
| | 1-7/4-11/8-6/5-3/2
| | zeus
|-
| | 19
| | 0-7-9-14-16
| | 1-11/10-11/8-6/5-3/2
| | zeus
|-
| | 20
| | 0-7-11-14-16
| | 1-12/11-12/7-6/5-3/2
| | utonal
|-
| | 21
| | 0-9-11-14-16
| | 1-11/8-12/7-6/5-3/2
| | zeus
|-
| | 22
| | 0-7-9-14-23
| | 1-11/10-11/8-6/5-18/11
| | zeus
|-
| | 23
| | 0-7-9-16-23
| | 1-11/10-11/8-3/2-18/11
| | biyatismic
|-
| | 24
| | 0-7-14-16-23
| | 1-11/10-6/5-3/2-18/11
| | biyatismic
|-
| | 25
| | 0-9-14-16-23
| | 1-11/8-6/5-3/2-18/11
| | zeus
|-
| | 26
| | 0-3-7-14-30
| | 1-7/5-11/10-6/5-9/5
| | otonal
|-
| | 27
| | 0-7-14-16-30
| | 1-11/10-6/5-3/2-9/5
| | biyatismic
|-
| | 28
| | 0-7-14-23-30
| | 1-11/10-6/5-18/11-9/5
| | biyatismic
|-
| | 29
| | 0-7-16-23-30
| | 1-11/10-3/2-18/11-9/5
| | biyatismic
|-
| | 30
| | 0-14-16-23-30
| | 1-6/5-3/2-18/11-9/5
| | biyatismic
|-
| | 31
| | 0-16-23-27-30
| | 1-3/2-18/11-9/7-9/5
| | utonal
|-
| | 32
| | 0-2-5-9-32
| | 1-5/4-7/4-11/8-9/8
| | otonal
|-
| | 33
| | 0-2-5-16-32
| | 1-5/4-7/4-3/2-9/8
| | otonal
|-
| | 34
| | 0-2-9-16-32
| | 1-5/4-11/8-3/2-9/8
| | otonal
|-
| | 35
| | 0-5-9-16-32
| | 1-7/4-11/8-3/2-9/8
| | otonal
|-
| | 36
| | 0-9-16-23-32
| | 1-11/8-3/2-18/11-9/8
| | biyatismic
|-
| | 37
| | 0-16-23-27-32
| | 1-3/2-18/11-9/7-9/8
| | utonal
|-
| | 38
| | 0-16-23-30-32
| | 1-3/2-18/11-9/5-9/8
| | utonal
|-
| | 39
| | 0-16-27-30-32
| | 1-3/2-9/7-9/5-9/8
| | utonal
|-
| | 40
| | 0-23-27-30-32
| | 1-18/11-9/7-9/5-9/8
| | utonal
|}


=Hexads=
=Hexads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4-7-9-11 || 1-5/4-11/7-11/10-11/8-12/7 || zeus ||
|| 2 || 0-2-5-7-9-16 || 1-5/4-7/4-11/10-11/8-3/2 || zeus ||
|| 3 || 0-2-7-9-11-16 || 1-5/4-11/10-11/8-12/7-3/2 || zeus ||
|| 4 || 0-5-7-9-14-16 || 1-7/4-11/10-11/8-6/5-3/2 || zeus ||
|| 5 || 0-7-9-11-14-16 || 1-11/10-11/8-12/7-6/5-3/2 || zeus ||
|| 6 || 0-7-9-14-16-23 || 1-11/10-11/8-6/5-3/2-18/11 || zeus ||
|| 7 || 0-7-14-16-23-30 || 1-11/10-6/5-3/2-18/11-9/5 || biyatismic ||
|| 8 || 0-2-5-9-16-32 || 1-5/4-7/4-11/8-3/2-9/8 || otonal ||
|| 9 || 0-16-23-27-30-32 || 1-3/2-18/11-9/7-9/5-9/8 || utonal ||
</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chords of hemiwur&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; of 11-limit &lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiwürschmidt"&gt;hemiwur temperament&lt;/a&gt;. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 121/120 are biyatismic, by 176/175 valinorsmic, and by 385/384 keenanismic. Chords requiring any two of the above are labeled zeus.&lt;br /&gt;
&lt;br /&gt;
Hemiwur has MOS of size 6, 7, 13, 19, 25, 31, 37 and 68. The largest chords on these lists have complexity 32, and so would require the 37 note MOS, but there are many chords of much lower complexity, so that the 13-note MOS, for instance, has a couple of hexads, plus many more pentads, tetrads and triads.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Triads&lt;/h1&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Number&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Chord&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Transversal&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Type&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/11-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/11-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/11-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-23-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-23-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-27-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/7-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ambitonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-23-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-27-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/7-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-30-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Tetrads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Tetrads&lt;/h1&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Number&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Chord&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Transversal&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Type&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-4-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-5-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-7/4-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-4-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/7-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-7-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/10-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-7-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/10-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-7-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/10-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-4-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/7-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-7-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/10-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-7-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/10-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/8-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/8-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-5-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-7/4-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-7-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-11/10-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-7-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/10-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-9-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/8-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-11-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/11-12/7-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-11-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-12/7-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-7-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/10-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-7-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/10-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-9-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/8-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-9-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/8-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-11-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-12/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-11-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/11-12/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-11-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-12/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;keenanismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/11-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-14-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-6/5-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-14-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-6/5-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-16-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/11-3/2-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ambitonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-16-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-3/2-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-16-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-3/2-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-11-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-12/7-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-16-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-3/2-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ambitonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-23-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-18/11-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-7-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-11/10-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-14-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-6/5-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-14-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-6/5-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-16-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-3/2-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-16-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-3/2-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ambitonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-23-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-23-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-23-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-27-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-9/7-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-23-27-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-9-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/8-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-9-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/8-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-16-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-16-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-16-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-23-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-18/11-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-23-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-18/11-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;62&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-27-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-9/7-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-23-27-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-30-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-23-30-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;66&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-27-30-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/7-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Pentads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pentads&lt;/h1&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Number&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Chord&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Transversal&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Type&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-4-7-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/7-11/10-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-7-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/10-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;valinorsmic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-4-7-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/7-11/10-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-4-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/7-11/8-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-7-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/10-11/8-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-4-7-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/10-11/8-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-5-7-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-7/4-11/10-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-7-9-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/10-11/8-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-11-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-12/7-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-7-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/10-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-9-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/8-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-7-9-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/10-11/8-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-7-9-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/10-11/8-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-7-11-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/10-12/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-9-11-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/8-12/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-11-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-12/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-7-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/10-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-9-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/8-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-11-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/11-12/7-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-11-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-12/7-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-14-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-6/5-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-16-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-3/2-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-14-16-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-6/5-3/2-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-14-16-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-6/5-3/2-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-3-7-14-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-11/10-6/5-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-14-16-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-6/5-3/2-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-14-23-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-6/5-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-16-23-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-3/2-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-16-23-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-3/2-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-23-27-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-18/11-9/7-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-9-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/8-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-16-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-9-16-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/8-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-9-16-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/8-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-16-23-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/8-3/2-18/11-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-23-27-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-18/11-9/7-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-23-30-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-18/11-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-27-30-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-9/7-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-23-27-30-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Hexads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hexads&lt;/h1&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Number&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Chord&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Transversal&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Type&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-4-7-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/7-11/10-11/8-12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-7-9-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/10-11/8-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-7-9-11-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/10-11/8-12/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-7-9-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-11/10-11/8-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-11-14-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-12/7-6/5-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-14-16-23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-11/8-6/5-3/2-18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;zeus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-14-16-23-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-6/5-3/2-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;biyatismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-5-9-16-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/8-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-23-27-30-32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-18/11-9/7-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
{| class="wikitable"
|-
| | Number
| | Chord
| | Transversal
| | Type
|-
| | 1
| | 0-2-4-7-9-11
| | 1-5/4-11/7-11/10-11/8-12/7
| | zeus
|-
| | 2
| | 0-2-5-7-9-16
| | 1-5/4-7/4-11/10-11/8-3/2
| | zeus
|-
| | 3
| | 0-2-7-9-11-16
| | 1-5/4-11/10-11/8-12/7-3/2
| | zeus
|-
| | 4
| | 0-5-7-9-14-16
| | 1-7/4-11/10-11/8-6/5-3/2
| | zeus
|-
| | 5
| | 0-7-9-11-14-16
| | 1-11/10-11/8-12/7-6/5-3/2
| | zeus
|-
| | 6
| | 0-7-9-14-16-23
| | 1-11/10-11/8-6/5-3/2-18/11
| | zeus
|-
| | 7
| | 0-7-14-16-23-30
| | 1-11/10-6/5-3/2-18/11-9/5
| | biyatismic
|-
| | 8
| | 0-2-5-9-16-32
| | 1-5/4-7/4-11/8-3/2-9/8
| | otonal
|-
| | 9
| | 0-16-23-27-30-32
| | 1-3/2-18/11-9/7-9/5-9/8
| | utonal
|}

Revision as of 00:00, 17 July 2018

Below are listed the dyadic chords of 11-limit hemiwur temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 121/120 are biyatismic, by 176/175 valinorsmic, and by 385/384 keenanismic. Chords requiring any two of the above are labeled zeus.

Hemiwur has MOS of size 6, 7, 13, 19, 25, 31, 37 and 68. The largest chords on these lists have complexity 32, and so would require the 37 note MOS, but there are many chords of much lower complexity, so that the 13-note MOS, for instance, has a couple of hexads, plus many more pentads, tetrads and triads.

Triads

Number Chord Transversal Type
1 0-2-4 1-5/4-11/7 valinorsmic
2 0-2-5 1-5/4-7/4 otonal
3 0-3-5 1-7/5-7/4 utonal
4 0-2-7 1-5/4-11/10 valinorsmic
5 0-3-7 1-7/5-11/10 otonal
6 0-4-7 1-11/7-11/10 utonal
7 0-5-7 1-7/4-11/10 valinorsmic
8 0-2-9 1-5/4-11/8 otonal
9 0-4-9 1-11/7-11/8 utonal
10 0-5-9 1-7/4-11/8 otonal
11 0-7-9 1-11/10-11/8 utonal
12 0-2-11 1-5/4-12/7 keenanismic
13 0-4-11 1-11/7-12/7 otonal
14 0-7-11 1-12/11-12/7 utonal
15 0-9-11 1-11/8-12/7 keenanismic
16 0-3-14 1-7/5-6/5 otonal
17 0-5-14 1-7/4-6/5 keenanismic
18 0-7-14 1-11/10-6/5 otonal
19 0-9-14 1-11/8-6/5 keenanismic
20 0-11-14 1-12/7-6/5 utonal
21 0-2-16 1-5/4-3/2 otonal
22 0-5-16 1-7/4-3/2 otonal
23 0-7-16 1-12/11-3/2 utonal
24 0-9-16 1-11/8-3/2 otonal
25 0-11-16 1-12/7-3/2 utonal
26 0-14-16 1-6/5-3/2 utonal
27 0-7-23 1-12/11-18/11 otonal
28 0-9-23 1-11/8-18/11 biyatismic
29 0-14-23 1-6/5-18/11 biyatismic
30 0-16-23 1-3/2-18/11 utonal
31 0-4-27 1-11/7-9/7 otonal
32 0-11-27 1-12/7-9/7 otonal
33 0-16-27 1-3/2-9/7 utonal
34 0-23-27 1-18/11-9/7 utonal
35 0-3-30 1-7/5-9/5 otonal
36 0-7-30 1-11/10-9/5 otonal
37 0-14-30 1-6/5-9/5 otonal
38 0-16-30 1-3/2-9/5 utonal
39 0-23-30 1-18/11-9/5 utonal
40 0-27-30 1-9/7-9/5 utonal
41 0-2-32 1-5/4-9/8 otonal
42 0-5-32 1-7/4-9/8 otonal
43 0-9-32 1-11/8-9/8 otonal
44 0-16-32 1-3/2-9/8 ambitonal
45 0-23-32 1-18/11-9/8 utonal
46 0-27-32 1-9/7-9/8 utonal
47 0-30-32 1-9/5-9/8 utonal

Tetrads

Number Chord Transversal Type
1 0-2-4-7 1-5/4-11/7-11/10 valinorsmic
2 0-2-5-7 1-5/4-7/4-11/10 valinorsmic
3 0-3-5-7 1-7/5-7/4-11/10 valinorsmic
4 0-2-4-9 1-5/4-11/7-11/8 valinorsmic
5 0-2-5-9 1-5/4-7/4-11/8 otonal
6 0-2-7-9 1-5/4-11/10-11/8 valinorsmic
7 0-4-7-9 1-11/7-11/10-11/8 utonal
8 0-5-7-9 1-7/4-11/10-11/8 valinorsmic
9 0-2-4-11 1-5/4-11/7-12/7 zeus
10 0-2-7-11 1-5/4-11/10-12/7 zeus
11 0-4-7-11 1-11/7-11/10-12/7 biyatismic
12 0-2-9-11 1-5/4-11/8-12/7 keenanismic
13 0-4-9-11 1-11/7-11/8-12/7 zeus
14 0-7-9-11 1-11/10-11/8-12/7 zeus
15 0-3-5-14 1-7/5-7/4-6/5 keenanismic
16 0-3-7-14 1-7/5-11/10-6/5 otonal
17 0-5-7-14 1-7/4-11/10-6/5 zeus
18 0-5-9-14 1-7/4-11/8-6/5 keenanismic
19 0-7-9-14 1-11/10-11/8-6/5 zeus
20 0-7-11-14 1-12/11-12/7-6/5 utonal
21 0-9-11-14 1-11/8-12/7-6/5 keenanismic
22 0-2-5-16 1-5/4-7/4-3/2 otonal
23 0-2-7-16 1-5/4-11/10-3/2 zeus
24 0-5-7-16 1-7/4-11/10-3/2 zeus
25 0-2-9-16 1-5/4-11/8-3/2 otonal
26 0-5-9-16 1-7/4-11/8-3/2 otonal
27 0-7-9-16 1-11/10-11/8-3/2 biyatismic
28 0-2-11-16 1-5/4-12/7-3/2 keenanismic
29 0-7-11-16 1-12/11-12/7-3/2 utonal
30 0-9-11-16 1-11/8-12/7-3/2 zeus
31 0-5-14-16 1-7/4-6/5-3/2 keenanismic
32 0-7-14-16 1-12/11-6/5-3/2 utonal
33 0-9-14-16 1-11/8-6/5-3/2 zeus
34 0-11-14-16 1-12/7-6/5-3/2 utonal
35 0-7-9-23 1-11/10-11/8-18/11 biyatismic
36 0-7-14-23 1-11/10-6/5-18/11 biyatismic
37 0-9-14-23 1-11/8-6/5-18/11 zeus
38 0-7-16-23 1-12/11-3/2-18/11 ambitonal
39 0-9-16-23 1-11/8-3/2-18/11 biyatismic
40 0-14-16-23 1-6/5-3/2-18/11 biyatismic
41 0-4-11-27 1-11/7-12/7-9/7 otonal
42 0-11-16-27 1-12/7-3/2-9/7 ambitonal
43 0-16-23-27 1-3/2-18/11-9/7 utonal
44 0-3-7-30 1-7/5-11/10-9/5 otonal
45 0-3-14-30 1-7/5-6/5-9/5 otonal
46 0-7-14-30 1-11/10-6/5-9/5 otonal
47 0-7-16-30 1-11/10-3/2-9/5 biyatismic
48 0-14-16-30 1-6/5-3/2-9/5 ambitonal
49 0-7-23-30 1-11/10-18/11-9/5 biyatismic
50 0-14-23-30 1-6/5-18/11-9/5 biyatismic
51 0-16-23-30 1-3/2-18/11-9/5 utonal
52 0-16-27-30 1-3/2-9/7-9/5 utonal
53 0-23-27-30 1-18/11-9/7-9/5 utonal
54 0-2-5-32 1-5/4-7/4-9/8 otonal
55 0-2-9-32 1-5/4-11/8-9/8 otonal
56 0-5-9-32 1-7/4-11/8-9/8 otonal
57 0-2-16-32 1-5/4-3/2-9/8 otonal
58 0-5-16-32 1-7/4-3/2-9/8 otonal
59 0-9-16-32 1-11/8-3/2-9/8 otonal
60 0-9-23-32 1-11/8-18/11-9/8 biyatismic
61 0-16-23-32 1-3/2-18/11-9/8 utonal
62 0-16-27-32 1-3/2-9/7-9/8 utonal
63 0-23-27-32 1-18/11-9/7-9/8 utonal
64 0-16-30-32 1-3/2-9/5-9/8 utonal
65 0-23-30-32 1-18/11-9/5-9/8 utonal
66 0-27-30-32 1-9/7-9/5-9/8 utonal

Pentads

Number Chord Transversal Type
1 0-2-4-7-9 1-5/4-11/7-11/10-11/8 valinorsmic
2 0-2-5-7-9 1-5/4-7/4-11/10-11/8 valinorsmic
3 0-2-4-7-11 1-5/4-11/7-11/10-12/7 zeus
4 0-2-4-9-11 1-5/4-11/7-11/8-12/7 zeus
5 0-2-7-9-11 1-5/4-11/10-11/8-12/7 zeus
6 0-4-7-9-11 1-11/7-11/10-11/8-12/7 zeus
7 0-3-5-7-14 1-7/5-7/4-11/10-6/5 zeus
8 0-5-7-9-14 1-7/4-11/10-11/8-6/5 zeus
9 0-7-9-11-14 1-11/10-11/8-12/7-6/5 zeus
10 0-2-5-7-16 1-5/4-7/4-11/10-3/2 zeus
11 0-2-5-9-16 1-5/4-7/4-11/8-3/2 otonal
12 0-2-7-9-16 1-5/4-11/10-11/8-3/2 zeus
13 0-5-7-9-16 1-7/4-11/10-11/8-3/2 zeus
14 0-2-7-11-16 1-5/4-11/10-12/7-3/2 zeus
15 0-2-9-11-16 1-5/4-11/8-12/7-3/2 zeus
16 0-7-9-11-16 1-11/10-11/8-12/7-3/2 zeus
17 0-5-7-14-16 1-7/4-11/10-6/5-3/2 zeus
18 0-5-9-14-16 1-7/4-11/8-6/5-3/2 zeus
19 0-7-9-14-16 1-11/10-11/8-6/5-3/2 zeus
20 0-7-11-14-16 1-12/11-12/7-6/5-3/2 utonal
21 0-9-11-14-16 1-11/8-12/7-6/5-3/2 zeus
22 0-7-9-14-23 1-11/10-11/8-6/5-18/11 zeus
23 0-7-9-16-23 1-11/10-11/8-3/2-18/11 biyatismic
24 0-7-14-16-23 1-11/10-6/5-3/2-18/11 biyatismic
25 0-9-14-16-23 1-11/8-6/5-3/2-18/11 zeus
26 0-3-7-14-30 1-7/5-11/10-6/5-9/5 otonal
27 0-7-14-16-30 1-11/10-6/5-3/2-9/5 biyatismic
28 0-7-14-23-30 1-11/10-6/5-18/11-9/5 biyatismic
29 0-7-16-23-30 1-11/10-3/2-18/11-9/5 biyatismic
30 0-14-16-23-30 1-6/5-3/2-18/11-9/5 biyatismic
31 0-16-23-27-30 1-3/2-18/11-9/7-9/5 utonal
32 0-2-5-9-32 1-5/4-7/4-11/8-9/8 otonal
33 0-2-5-16-32 1-5/4-7/4-3/2-9/8 otonal
34 0-2-9-16-32 1-5/4-11/8-3/2-9/8 otonal
35 0-5-9-16-32 1-7/4-11/8-3/2-9/8 otonal
36 0-9-16-23-32 1-11/8-3/2-18/11-9/8 biyatismic
37 0-16-23-27-32 1-3/2-18/11-9/7-9/8 utonal
38 0-16-23-30-32 1-3/2-18/11-9/5-9/8 utonal
39 0-16-27-30-32 1-3/2-9/7-9/5-9/8 utonal
40 0-23-27-30-32 1-18/11-9/7-9/5-9/8 utonal

Hexads

Number Chord Transversal Type
1 0-2-4-7-9-11 1-5/4-11/7-11/10-11/8-12/7 zeus
2 0-2-5-7-9-16 1-5/4-7/4-11/10-11/8-3/2 zeus
3 0-2-7-9-11-16 1-5/4-11/10-11/8-12/7-3/2 zeus
4 0-5-7-9-14-16 1-7/4-11/10-11/8-6/5-3/2 zeus
5 0-7-9-11-14-16 1-11/10-11/8-12/7-6/5-3/2 zeus
6 0-7-9-14-16-23 1-11/10-11/8-6/5-3/2-18/11 zeus
7 0-7-14-16-23-30 1-11/10-6/5-3/2-18/11-9/5 biyatismic
8 0-2-5-9-16-32 1-5/4-7/4-11/8-3/2-9/8 otonal
9 0-16-23-27-30-32 1-3/2-18/11-9/7-9/5-9/8 utonal
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