Chords of semisept
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-12-26 20:42:31 UTC.
- The original revision id was 288529868.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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. =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 ||
Original HTML content:
<html><head><title>Chords of semisept</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Hemimean%20clan#Semisept">semisept temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, and by 176/175 valinorsmic. <br />
<br />
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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-2-9<br />
</td>
<td>1-12/7-7/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-7-9<br />
</td>
<td>1-18/11-7/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-2-11<br />
</td>
<td>1-12/7-6/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-9-11<br />
</td>
<td>1-7/5-6/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-2-12<br />
</td>
<td>1-12/7-11/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-6-12<br />
</td>
<td>1-5/4-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-10-12<br />
</td>
<td>1-11/6-11/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-6-15<br />
</td>
<td>1-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-9-15<br />
</td>
<td>1-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-2-17<br />
</td>
<td>1-12/7-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-6-17<br />
</td>
<td>1-5/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-7-17<br />
</td>
<td>1-18/11-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-10-17<br />
</td>
<td>1-11/6-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-11-17<br />
</td>
<td>1-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-15-17<br />
</td>
<td>1-7/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-2-19<br />
</td>
<td>1-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-7-19<br />
</td>
<td>1-18/11-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-9-19<br />
</td>
<td>1-7/5-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-10-19<br />
</td>
<td>1-11/6-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-12-19<br />
</td>
<td>1-11/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-17-19<br />
</td>
<td>1-3/2-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-2-21<br />
</td>
<td>1-12/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-6-21<br />
</td>
<td>1-5/4-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-9-21<br />
</td>
<td>1-7/5-11/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-10-21<br />
</td>
<td>1-11/6-11/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-11-21<br />
</td>
<td>1-6/5-11/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-12-21<br />
</td>
<td>1-11/7-11/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-15-21<br />
</td>
<td>1-7/4-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-19-21<br />
</td>
<td>1-9/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-6-27<br />
</td>
<td>1-5/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-10-27<br />
</td>
<td>1-11/6-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-12-27<br />
</td>
<td>1-11/7-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-15-27<br />
</td>
<td>1-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-17-27<br />
</td>
<td>1-3/2-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-21-27<br />
</td>
<td>1-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-7-28<br />
</td>
<td>1-18/11-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-9-28<br />
</td>
<td>1-7/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-11-28<br />
</td>
<td>1-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-17-28<br />
</td>
<td>1-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-19-28<br />
</td>
<td>1-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-21-28<br />
</td>
<td>1-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-6-34<br />
</td>
<td>1-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-7-34<br />
</td>
<td>1-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-15-34<br />
</td>
<td>1-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-17-34<br />
</td>
<td>1-3/2-9/8<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-19-34<br />
</td>
<td>1-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-27-34<br />
</td>
<td>1-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-28-34<br />
</td>
<td>1-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Tetrads"></a><!-- ws:end:WikiTextHeadingRule:2 -->Tetrads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-2-9-11<br />
</td>
<td>1-12/7-7/5-6/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-11-17<br />
</td>
<td>1-12/7-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-6-15-17<br />
</td>
<td>1-5/4-7/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-2-9-19<br />
</td>
<td>1-12/7-7/5-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-7-9-19<br />
</td>
<td>1-18/11-7/5-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-2-12-19<br />
</td>
<td>1-12/7-11/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-10-12-19<br />
</td>
<td>1-11/6-11/7-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-2-17-19<br />
</td>
<td>1-12/7-3/2-9/7<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-7-17-19<br />
</td>
<td>1-18/11-3/2-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-10-17-19<br />
</td>
<td>1-11/6-3/2-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-2-9-21<br />
</td>
<td>1-12/7-7/5-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-2-11-21<br />
</td>
<td>1-12/7-6/5-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-9-11-21<br />
</td>
<td>1-7/5-6/5-11/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-2-12-21<br />
</td>
<td>1-12/7-11/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-6-12-21<br />
</td>
<td>1-5/4-11/7-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-10-12-21<br />
</td>
<td>1-11/6-11/7-11/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-6-15-21<br />
</td>
<td>1-5/4-7/4-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-9-15-21<br />
</td>
<td>1-7/5-7/4-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-2-19-21<br />
</td>
<td>1-12/7-9/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-9-19-21<br />
</td>
<td>1-7/5-9/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-10-19-21<br />
</td>
<td>1-11/6-9/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-12-19-21<br />
</td>
<td>1-11/7-9/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-6-12-27<br />
</td>
<td>1-5/4-11/7-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-10-12-27<br />
</td>
<td>1-11/6-11/7-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-6-15-27<br />
</td>
<td>1-5/4-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-6-17-27<br />
</td>
<td>1-5/4-3/2-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-10-17-27<br />
</td>
<td>1-11/6-3/2-11/8<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-15-17-27<br />
</td>
<td>1-7/4-3/2-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-6-21-27<br />
</td>
<td>1-5/4-11/10-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-10-21-27<br />
</td>
<td>1-11/6-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-12-21-27<br />
</td>
<td>1-11/7-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-15-21-27<br />
</td>
<td>1-7/4-11/10-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-7-9-28<br />
</td>
<td>1-18/11-7/5-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-9-11-28<br />
</td>
<td>1-7/5-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-7-17-28<br />
</td>
<td>1-18/11-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-11-17-28<br />
</td>
<td>1-6/5-3/2-9/5<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-7-19-28<br />
</td>
<td>1-18/11-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-9-19-28<br />
</td>
<td>1-7/5-9/7-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-17-19-28<br />
</td>
<td>1-3/2-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-9-21-28<br />
</td>
<td>1-7/5-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-11-21-28<br />
</td>
<td>1-6/5-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-19-21-28<br />
</td>
<td>1-9/7-11/10-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-6-15-34<br />
</td>
<td>1-5/4-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-6-17-34<br />
</td>
<td>1-5/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-7-17-34<br />
</td>
<td>1-18/11-3/2-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-15-17-34<br />
</td>
<td>1-7/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-7-19-34<br />
</td>
<td>1-18/11-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-17-19-34<br />
</td>
<td>1-3/2-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-6-27-34<br />
</td>
<td>1-5/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-15-27-34<br />
</td>
<td>1-7/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-17-27-34<br />
</td>
<td>1-3/2-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-7-28-34<br />
</td>
<td>1-18/11-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-17-28-34<br />
</td>
<td>1-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-19-28-34<br />
</td>
<td>1-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Pentads"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pentads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-2-9-11-21<br />
</td>
<td>1-12/7-7/5-6/5-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-9-19-21<br />
</td>
<td>1-12/7-7/5-9/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-2-12-19-21<br />
</td>
<td>1-12/7-11/7-9/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-10-12-19-21<br />
</td>
<td>1-11/6-11/7-9/7-11/10<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-6-15-17-27<br />
</td>
<td>1-5/4-7/4-3/2-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-6-12-21-27<br />
</td>
<td>1-5/4-11/7-11/10-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-10-12-21-27<br />
</td>
<td>1-11/6-11/7-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-6-15-21-27<br />
</td>
<td>1-5/4-7/4-11/10-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-7-9-19-28<br />
</td>
<td>1-18/11-7/5-9/7-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-7-17-19-28<br />
</td>
<td>1-18/11-3/2-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-9-11-21-28<br />
</td>
<td>1-7/5-6/5-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-9-19-21-28<br />
</td>
<td>1-7/5-9/7-11/10-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-6-15-17-34<br />
</td>
<td>1-5/4-7/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-7-17-19-34<br />
</td>
<td>1-18/11-3/2-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-6-15-27-34<br />
</td>
<td>1-5/4-7/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-6-17-27-34<br />
</td>
<td>1-5/4-3/2-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-15-17-27-34<br />
</td>
<td>1-7/4-3/2-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-7-17-28-34<br />
</td>
<td>1-18/11-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-7-19-28-34<br />
</td>
<td>1-18/11-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-17-19-28-34<br />
</td>
<td>1-3/2-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Hexads"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hexads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-6-15-17-27-34<br />
</td>
<td>1-5/4-7/4-3/2-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-7-17-19-28-34<br />
</td>
<td>1-18/11-3/2-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
</body></html>