Chords of semisept: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[Hemimean_clan#Semisept|semisept temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, and by 176/175 valinorsmic.  
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>2011-12-26 20:42:31 UTC</tt>.<br>
: The original revision id was <tt>288529868</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 [[Hemimean clan#Semisept|semisept temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, and by 176/175 valinorsmic.  


Semisept has MOS of size 5, 8, 13, 18, 31, 49 and 80. Some amount triadic and tetradic harmony shows itself by the 13-note MOS and much more with 18 notes. The swetismic tetrad with complexity 11 is worthy of particular note.
Semisept has MOS of size 5, 8, 13, 18, 31, 49 and 80. Some amount triadic and tetradic harmony shows itself by the 13-note MOS and much more with 18 notes. The swetismic tetrad with complexity 11 is worthy of particular note.


=Triads=
=Triads=
|| Number || Chord || Transversal || Type ||
 
|| 1 || 0-2-9 || 1-12/7-7/5 || swetismic ||
{| class="wikitable"
|| 2 || 0-7-9 || 1-18/11-7/5 || swetismic ||
|-
|| 3 || 0-2-11 || 1-12/7-6/5 || utonal ||
| | Number
|| 4 || 0-9-11 || 1-7/5-6/5 || otonal ||
| | Chord
|| 5 || 0-2-12 || 1-12/7-11/7 || otonal ||
| | Transversal
|| 6 || 0-6-12 || 1-5/4-11/7 || valinorsmic ||
| | Type
|| 7 || 0-10-12 || 1-11/6-11/7 || utonal ||
|-
|| 8 || 0-6-15 || 1-5/4-7/4 || otonal ||
| | 1
|| 9 || 0-9-15 || 1-7/5-7/4 || utonal ||
| | 0-2-9
|| 10 || 0-2-17 || 1-12/7-3/2 || utonal ||
| | 1-12/7-7/5
|| 11 || 0-6-17 || 1-5/4-3/2 || otonal ||
| | swetismic
|| 12 || 0-7-17 || 1-18/11-3/2 || utonal ||
|-
|| 13 || 0-10-17 || 1-11/6-3/2 || otonal ||
| | 2
|| 14 || 0-11-17 || 1-6/5-3/2 || utonal ||
| | 0-7-9
|| 15 || 0-15-17 || 1-7/4-3/2 || otonal ||
| | 1-18/11-7/5
|| 16 || 0-2-19 || 1-12/7-9/7 || otonal ||
| | swetismic
|| 17 || 0-7-19 || 1-18/11-9/7 || utonal ||
|-
|| 18 || 0-9-19 || 1-7/5-9/7 || swetismic ||
| | 3
|| 19 || 0-10-19 || 1-11/6-9/7 || swetismic ||
| | 0-2-11
|| 20 || 0-12-19 || 1-11/7-9/7 || otonal ||
| | 1-12/7-6/5
|| 21 || 0-17-19 || 1-3/2-9/7 || utonal ||
| | utonal
|| 22 || 0-2-21 || 1-12/7-11/10 || swetismic ||
|-
|| 23 || 0-6-21 || 1-5/4-11/10 || valinorsmic ||
| | 4
|| 24 || 0-9-21 || 1-7/5-11/10 || otonal ||
| | 0-9-11
|| 25 || 0-10-21 || 1-11/6-11/10 || utonal ||
| | 1-7/5-6/5
|| 26 || 0-11-21 || 1-6/5-11/10 || otonal ||
| | otonal
|| 27 || 0-12-21 || 1-11/7-11/10 || utonal ||
|-
|| 28 || 0-15-21 || 1-7/4-11/10 || valinorsmic ||
| | 5
|| 29 || 0-19-21 || 1-9/7-11/10 || swetismic ||
| | 0-2-12
|| 30 || 0-6-27 || 1-5/4-11/8 || otonal ||
| | 1-12/7-11/7
|| 31 || 0-10-27 || 1-11/6-11/8 || utonal ||
| | otonal
|| 32 || 0-12-27 || 1-11/7-11/8 || utonal ||
|-
|| 33 || 0-15-27 || 1-7/4-11/8 || otonal ||
| | 6
|| 34 || 0-17-27 || 1-3/2-11/8 || otonal ||
| | 0-6-12
|| 35 || 0-21-27 || 1-11/10-11/8 || utonal ||
| | 1-5/4-11/7
|| 36 || 0-7-28 || 1-18/11-9/5 || utonal ||
| | valinorsmic
|| 37 || 0-9-28 || 1-7/5-9/5 || otonal ||
|-
|| 38 || 0-11-28 || 1-6/5-9/5 || otonal ||
| | 7
|| 39 || 0-17-28 || 1-3/2-9/5 || utonal ||
| | 0-10-12
|| 40 || 0-19-28 || 1-9/7-9/5 || utonal ||
| | 1-11/6-11/7
|| 41 || 0-21-28 || 1-11/10-9/5 || otonal ||
| | utonal
|| 42 || 0-6-34 || 1-5/4-9/8 || otonal ||
|-
|| 43 || 0-7-34 || 1-18/11-9/8 || utonal ||
| | 8
|| 44 || 0-15-34 || 1-7/4-9/8 || otonal ||
| | 0-6-15
|| 45 || 0-17-34 || 1-3/2-9/8 || ambitonal ||
| | 1-5/4-7/4
|| 46 || 0-19-34 || 1-9/7-9/8 || utonal ||
| | otonal
|| 47 || 0-27-34 || 1-11/8-9/8 || otonal ||
|-
|| 48 || 0-28-34 || 1-9/5-9/8 || utonal ||
| | 9
| | 0-9-15
| | 1-7/5-7/4
| | utonal
|-
| | 10
| | 0-2-17
| | 1-12/7-3/2
| | utonal
|-
| | 11
| | 0-6-17
| | 1-5/4-3/2
| | otonal
|-
| | 12
| | 0-7-17
| | 1-18/11-3/2
| | utonal
|-
| | 13
| | 0-10-17
| | 1-11/6-3/2
| | otonal
|-
| | 14
| | 0-11-17
| | 1-6/5-3/2
| | utonal
|-
| | 15
| | 0-15-17
| | 1-7/4-3/2
| | otonal
|-
| | 16
| | 0-2-19
| | 1-12/7-9/7
| | otonal
|-
| | 17
| | 0-7-19
| | 1-18/11-9/7
| | utonal
|-
| | 18
| | 0-9-19
| | 1-7/5-9/7
| | swetismic
|-
| | 19
| | 0-10-19
| | 1-11/6-9/7
| | swetismic
|-
| | 20
| | 0-12-19
| | 1-11/7-9/7
| | otonal
|-
| | 21
| | 0-17-19
| | 1-3/2-9/7
| | utonal
|-
| | 22
| | 0-2-21
| | 1-12/7-11/10
| | swetismic
|-
| | 23
| | 0-6-21
| | 1-5/4-11/10
| | valinorsmic
|-
| | 24
| | 0-9-21
| | 1-7/5-11/10
| | otonal
|-
| | 25
| | 0-10-21
| | 1-11/6-11/10
| | utonal
|-
| | 26
| | 0-11-21
| | 1-6/5-11/10
| | otonal
|-
| | 27
| | 0-12-21
| | 1-11/7-11/10
| | utonal
|-
| | 28
| | 0-15-21
| | 1-7/4-11/10
| | valinorsmic
|-
| | 29
| | 0-19-21
| | 1-9/7-11/10
| | swetismic
|-
| | 30
| | 0-6-27
| | 1-5/4-11/8
| | otonal
|-
| | 31
| | 0-10-27
| | 1-11/6-11/8
| | utonal
|-
| | 32
| | 0-12-27
| | 1-11/7-11/8
| | utonal
|-
| | 33
| | 0-15-27
| | 1-7/4-11/8
| | otonal
|-
| | 34
| | 0-17-27
| | 1-3/2-11/8
| | otonal
|-
| | 35
| | 0-21-27
| | 1-11/10-11/8
| | utonal
|-
| | 36
| | 0-7-28
| | 1-18/11-9/5
| | utonal
|-
| | 37
| | 0-9-28
| | 1-7/5-9/5
| | otonal
|-
| | 38
| | 0-11-28
| | 1-6/5-9/5
| | otonal
|-
| | 39
| | 0-17-28
| | 1-3/2-9/5
| | utonal
|-
| | 40
| | 0-19-28
| | 1-9/7-9/5
| | utonal
|-
| | 41
| | 0-21-28
| | 1-11/10-9/5
| | otonal
|-
| | 42
| | 0-6-34
| | 1-5/4-9/8
| | otonal
|-
| | 43
| | 0-7-34
| | 1-18/11-9/8
| | utonal
|-
| | 44
| | 0-15-34
| | 1-7/4-9/8
| | otonal
|-
| | 45
| | 0-17-34
| | 1-3/2-9/8
| | ambitonal
|-
| | 46
| | 0-19-34
| | 1-9/7-9/8
| | utonal
|-
| | 47
| | 0-27-34
| | 1-11/8-9/8
| | otonal
|-
| | 48
| | 0-28-34
| | 1-9/5-9/8
| | utonal
|}


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


=Pentads=
=Pentads=
|| Number || Chord || Transversal || Type ||
 
|| 1 || 0-2-9-11-21 || 1-12/7-7/5-6/5-11/10 || swetismic ||
{| class="wikitable"
|| 2 || 0-2-9-19-21 || 1-12/7-7/5-9/7-11/10 || swetismic ||
|-
|| 3 || 0-2-12-19-21 || 1-12/7-11/7-9/7-11/10 || swetismic ||
| | Number
|| 4 || 0-10-12-19-21 || 1-11/6-11/7-9/7-11/10 || swetismic ||
| | Chord
|| 5 || 0-6-15-17-27 || 1-5/4-7/4-3/2-11/8 || otonal ||
| | Transversal
|| 6 || 0-6-12-21-27 || 1-5/4-11/7-11/10-11/8 || valinorsmic ||
| | Type
|| 7 || 0-10-12-21-27 || 1-11/6-11/7-11/10-11/8 || utonal ||
|-
|| 8 || 0-6-15-21-27 || 1-5/4-7/4-11/10-11/8 || valinorsmic ||
| | 1
|| 9 || 0-7-9-19-28 || 1-18/11-7/5-9/7-9/5 || swetismic ||
| | 0-2-9-11-21
|| 10 || 0-7-17-19-28 || 1-18/11-3/2-9/7-9/5 || utonal ||
| | 1-12/7-7/5-6/5-11/10
|| 11 || 0-9-11-21-28 || 1-7/5-6/5-11/10-9/5 || otonal ||
| | swetismic
|| 12 || 0-9-19-21-28 || 1-7/5-9/7-11/10-9/5 || swetismic ||
|-
|| 13 || 0-6-15-17-34 || 1-5/4-7/4-3/2-9/8 || otonal ||
| | 2
|| 14 || 0-7-17-19-34 || 1-18/11-3/2-9/7-9/8 || utonal ||
| | 0-2-9-19-21
|| 15 || 0-6-15-27-34 || 1-5/4-7/4-11/8-9/8 || otonal ||
| | 1-12/7-7/5-9/7-11/10
|| 16 || 0-6-17-27-34 || 1-5/4-3/2-11/8-9/8 || otonal ||
| | swetismic
|| 17 || 0-15-17-27-34 || 1-7/4-3/2-11/8-9/8 || otonal ||
|-
|| 18 || 0-7-17-28-34 || 1-18/11-3/2-9/5-9/8 || utonal ||
| | 3
|| 19 || 0-7-19-28-34 || 1-18/11-9/7-9/5-9/8 || utonal ||
| | 0-2-12-19-21
|| 20 || 0-17-19-28-34 || 1-3/2-9/7-9/5-9/8 || utonal ||
| | 1-12/7-11/7-9/7-11/10
| | swetismic
|-
| | 4
| | 0-10-12-19-21
| | 1-11/6-11/7-9/7-11/10
| | swetismic
|-
| | 5
| | 0-6-15-17-27
| | 1-5/4-7/4-3/2-11/8
| | otonal
|-
| | 6
| | 0-6-12-21-27
| | 1-5/4-11/7-11/10-11/8
| | valinorsmic
|-
| | 7
| | 0-10-12-21-27
| | 1-11/6-11/7-11/10-11/8
| | utonal
|-
| | 8
| | 0-6-15-21-27
| | 1-5/4-7/4-11/10-11/8
| | valinorsmic
|-
| | 9
| | 0-7-9-19-28
| | 1-18/11-7/5-9/7-9/5
| | swetismic
|-
| | 10
| | 0-7-17-19-28
| | 1-18/11-3/2-9/7-9/5
| | utonal
|-
| | 11
| | 0-9-11-21-28
| | 1-7/5-6/5-11/10-9/5
| | otonal
|-
| | 12
| | 0-9-19-21-28
| | 1-7/5-9/7-11/10-9/5
| | swetismic
|-
| | 13
| | 0-6-15-17-34
| | 1-5/4-7/4-3/2-9/8
| | otonal
|-
| | 14
| | 0-7-17-19-34
| | 1-18/11-3/2-9/7-9/8
| | utonal
|-
| | 15
| | 0-6-15-27-34
| | 1-5/4-7/4-11/8-9/8
| | otonal
|-
| | 16
| | 0-6-17-27-34
| | 1-5/4-3/2-11/8-9/8
| | otonal
|-
| | 17
| | 0-15-17-27-34
| | 1-7/4-3/2-11/8-9/8
| | otonal
|-
| | 18
| | 0-7-17-28-34
| | 1-18/11-3/2-9/5-9/8
| | utonal
|-
| | 19
| | 0-7-19-28-34
| | 1-18/11-9/7-9/5-9/8
| | utonal
|-
| | 20
| | 0-17-19-28-34
| | 1-3/2-9/7-9/5-9/8
| | utonal
|}


=Hexads=
=Hexads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-6-15-17-27-34 || 1-5/4-7/4-3/2-11/8-9/8 || otonal ||
|| 2 || 0-7-17-19-28-34 || 1-18/11-3/2-9/7-9/5-9/8 || 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 semisept&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="/Hemimean%20clan#Semisept"&gt;semisept temperament&lt;/a&gt;. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, and by 176/175 valinorsmic. &lt;br /&gt;
&lt;br /&gt;
Semisept has MOS of size 5, 8, 13, 18, 31, 49 and 80. Some amount triadic and tetradic harmony shows itself by the 13-note MOS and much more with 18 notes. The swetismic tetrad with complexity 11 is worthy of particular note.&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;0-2-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-7-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-2-11&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;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-11&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;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-11/7&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;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-12&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;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/7&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;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-15&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;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-15&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;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-17&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;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-17&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;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2&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;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-3/2&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;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-17&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;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-17&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;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-19&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;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-19&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;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-10-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-12-19&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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-17-19&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;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-6-21&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;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-21&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;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/10&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;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-11/10&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;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-12-21&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;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-21&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;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-19-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-6-27&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;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/8&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;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-12-27&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;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-27&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;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-17-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-11/8&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;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-21-27&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;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-28&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;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-28&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;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-28&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;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-17-28&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;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-19-28&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;0-21-28&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;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-34&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;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-34&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;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-34&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;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-17-34&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;46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-19-34&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;0-27-34&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;48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-28-34&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;0-2-9-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-7/5-6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-2-11-17&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;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-15-17&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;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-9-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-7/5-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-7-9-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-7/5-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-2-12-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-11/7-9/7&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;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-12-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/7-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-2-17-19&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;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-17-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2-9/7&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;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-17-19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-3/2-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-2-9-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-7/5-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-2-11-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-6/5-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-9-11-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-6/5-11/10&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;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-12-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-11/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-6-12-21&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;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-12-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/7-11/10&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;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-15-21&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;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-15-21&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;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-2-19-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-9/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-9-19-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-9/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-10-19-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-9/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-12-19-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-9/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-6-12-27&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;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-12-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/7-11/8&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;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-15-27&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;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-17-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2-11/8&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;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-17-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-3/2-11/8&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;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-17-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-3/2-11/8&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;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-21-27&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;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-21-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/10-11/8&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;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-12-21-27&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;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-21-27&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;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-7/5-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-9-11-28&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;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-17-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2-9/5&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;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-17-28&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;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-19-28&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;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-19-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-9/7-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-17-19-28&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;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-21-28&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;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-11-21-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-11/10-9/5&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;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-19-21-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/7-11/10-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-6-15-34&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;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-17-34&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;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-17-34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2-9/8&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;0-15-17-34&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;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-19-34&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;48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-17-19-34&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;49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-27-34&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;50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-27-34&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;51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-17-27-34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-11/8-9/8&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;52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-28-34&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;53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-17-28-34&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;54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-19-28-34&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;0-2-9-11-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-7/5-6/5-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-2-9-19-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-7/5-9/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-2-12-19-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-12/7-11/7-9/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-10-12-19-21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/7-9/7-11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-6-15-17-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-3/2-11/8&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;0-6-12-21-27&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;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-12-21-27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/7-11/10-11/8&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;0-6-15-21-27&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;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-9-19-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-7/5-9/7-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-7-17-19-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2-9/7-9/5&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;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-11-21-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-6/5-11/10-9/5&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;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-19-21-28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-9/7-11/10-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&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;0-6-15-17-34&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;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-17-19-34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2-9/7-9/8&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;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-15-27-34&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;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-6-17-27-34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2-11/8-9/8&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;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-17-27-34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/4-3/2-11/8-9/8&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;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-17-28-34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2-9/5-9/8&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;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-19-28-34&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;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-17-19-28-34&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;/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;0-6-15-17-27-34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-3/2-11/8-9/8&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;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-7-17-19-28-34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2-9/7-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
{| class="wikitable"
|-
| | Number
| | Chord
| | Transversal
| | Type
|-
| | 1
| | 0-6-15-17-27-34
| | 1-5/4-7/4-3/2-11/8-9/8
| | otonal
|-
| | 2
| | 0-7-17-19-28-34
| | 1-18/11-3/2-9/7-9/5-9/8
| | utonal
|}

Revision as of 00:00, 17 July 2018

Below are listed the dyadic chords of 11-limit semisept temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, and by 176/175 valinorsmic.

Semisept has MOS of size 5, 8, 13, 18, 31, 49 and 80. Some amount triadic and tetradic harmony shows itself by the 13-note MOS and much more with 18 notes. The swetismic tetrad with complexity 11 is worthy of particular note.

Triads

Number Chord Transversal Type
1 0-2-9 1-12/7-7/5 swetismic
2 0-7-9 1-18/11-7/5 swetismic
3 0-2-11 1-12/7-6/5 utonal
4 0-9-11 1-7/5-6/5 otonal
5 0-2-12 1-12/7-11/7 otonal
6 0-6-12 1-5/4-11/7 valinorsmic
7 0-10-12 1-11/6-11/7 utonal
8 0-6-15 1-5/4-7/4 otonal
9 0-9-15 1-7/5-7/4 utonal
10 0-2-17 1-12/7-3/2 utonal
11 0-6-17 1-5/4-3/2 otonal
12 0-7-17 1-18/11-3/2 utonal
13 0-10-17 1-11/6-3/2 otonal
14 0-11-17 1-6/5-3/2 utonal
15 0-15-17 1-7/4-3/2 otonal
16 0-2-19 1-12/7-9/7 otonal
17 0-7-19 1-18/11-9/7 utonal
18 0-9-19 1-7/5-9/7 swetismic
19 0-10-19 1-11/6-9/7 swetismic
20 0-12-19 1-11/7-9/7 otonal
21 0-17-19 1-3/2-9/7 utonal
22 0-2-21 1-12/7-11/10 swetismic
23 0-6-21 1-5/4-11/10 valinorsmic
24 0-9-21 1-7/5-11/10 otonal
25 0-10-21 1-11/6-11/10 utonal
26 0-11-21 1-6/5-11/10 otonal
27 0-12-21 1-11/7-11/10 utonal
28 0-15-21 1-7/4-11/10 valinorsmic
29 0-19-21 1-9/7-11/10 swetismic
30 0-6-27 1-5/4-11/8 otonal
31 0-10-27 1-11/6-11/8 utonal
32 0-12-27 1-11/7-11/8 utonal
33 0-15-27 1-7/4-11/8 otonal
34 0-17-27 1-3/2-11/8 otonal
35 0-21-27 1-11/10-11/8 utonal
36 0-7-28 1-18/11-9/5 utonal
37 0-9-28 1-7/5-9/5 otonal
38 0-11-28 1-6/5-9/5 otonal
39 0-17-28 1-3/2-9/5 utonal
40 0-19-28 1-9/7-9/5 utonal
41 0-21-28 1-11/10-9/5 otonal
42 0-6-34 1-5/4-9/8 otonal
43 0-7-34 1-18/11-9/8 utonal
44 0-15-34 1-7/4-9/8 otonal
45 0-17-34 1-3/2-9/8 ambitonal
46 0-19-34 1-9/7-9/8 utonal
47 0-27-34 1-11/8-9/8 otonal
48 0-28-34 1-9/5-9/8 utonal

Tetrads

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

Pentads

Number Chord Transversal Type
1 0-2-9-11-21 1-12/7-7/5-6/5-11/10 swetismic
2 0-2-9-19-21 1-12/7-7/5-9/7-11/10 swetismic
3 0-2-12-19-21 1-12/7-11/7-9/7-11/10 swetismic
4 0-10-12-19-21 1-11/6-11/7-9/7-11/10 swetismic
5 0-6-15-17-27 1-5/4-7/4-3/2-11/8 otonal
6 0-6-12-21-27 1-5/4-11/7-11/10-11/8 valinorsmic
7 0-10-12-21-27 1-11/6-11/7-11/10-11/8 utonal
8 0-6-15-21-27 1-5/4-7/4-11/10-11/8 valinorsmic
9 0-7-9-19-28 1-18/11-7/5-9/7-9/5 swetismic
10 0-7-17-19-28 1-18/11-3/2-9/7-9/5 utonal
11 0-9-11-21-28 1-7/5-6/5-11/10-9/5 otonal
12 0-9-19-21-28 1-7/5-9/7-11/10-9/5 swetismic
13 0-6-15-17-34 1-5/4-7/4-3/2-9/8 otonal
14 0-7-17-19-34 1-18/11-3/2-9/7-9/8 utonal
15 0-6-15-27-34 1-5/4-7/4-11/8-9/8 otonal
16 0-6-17-27-34 1-5/4-3/2-11/8-9/8 otonal
17 0-15-17-27-34 1-7/4-3/2-11/8-9/8 otonal
18 0-7-17-28-34 1-18/11-3/2-9/5-9/8 utonal
19 0-7-19-28-34 1-18/11-9/7-9/5-9/8 utonal
20 0-17-19-28-34 1-3/2-9/7-9/5-9/8 utonal

Hexads

Number Chord Transversal Type
1 0-6-15-17-27-34 1-5/4-7/4-3/2-11/8-9/8 otonal
2 0-7-17-19-28-34 1-18/11-3/2-9/7-9/5-9/8 utonal
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