Chords of hemiwur
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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. =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 ||
Original HTML content:
<html><head><title>Chords of hemiwur</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="/W%C3%BCrschmidt%20family#Hemiwürschmidt">hemiwur temperament</a>. 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.<br />
<br />
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.<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>0-2-4<br />
</td>
<td>1-5/4-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-5<br />
</td>
<td>1-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-3-5<br />
</td>
<td>1-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-2-7<br />
</td>
<td>1-5/4-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-7<br />
</td>
<td>1-7/5-11/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-4-7<br />
</td>
<td>1-11/7-11/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-5-7<br />
</td>
<td>1-7/4-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-2-9<br />
</td>
<td>1-5/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-4-9<br />
</td>
<td>1-11/7-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-5-9<br />
</td>
<td>1-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-7-9<br />
</td>
<td>1-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-2-11<br />
</td>
<td>1-5/4-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-4-11<br />
</td>
<td>1-11/7-12/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-7-11<br />
</td>
<td>1-12/11-12/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-9-11<br />
</td>
<td>1-11/8-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-3-14<br />
</td>
<td>1-7/5-6/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-5-14<br />
</td>
<td>1-7/4-6/5<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-7-14<br />
</td>
<td>1-11/10-6/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-9-14<br />
</td>
<td>1-11/8-6/5<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-11-14<br />
</td>
<td>1-12/7-6/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-2-16<br />
</td>
<td>1-5/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-5-16<br />
</td>
<td>1-7/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-7-16<br />
</td>
<td>1-12/11-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-9-16<br />
</td>
<td>1-11/8-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-11-16<br />
</td>
<td>1-12/7-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-14-16<br />
</td>
<td>1-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-7-23<br />
</td>
<td>1-12/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-9-23<br />
</td>
<td>1-11/8-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-14-23<br />
</td>
<td>1-6/5-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-16-23<br />
</td>
<td>1-3/2-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-4-27<br />
</td>
<td>1-11/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-11-27<br />
</td>
<td>1-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-16-27<br />
</td>
<td>1-3/2-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-23-27<br />
</td>
<td>1-18/11-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-3-30<br />
</td>
<td>1-7/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-7-30<br />
</td>
<td>1-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-14-30<br />
</td>
<td>1-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-16-30<br />
</td>
<td>1-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-23-30<br />
</td>
<td>1-18/11-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-27-30<br />
</td>
<td>1-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-2-32<br />
</td>
<td>1-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-5-32<br />
</td>
<td>1-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-9-32<br />
</td>
<td>1-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-16-32<br />
</td>
<td>1-3/2-9/8<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-23-32<br />
</td>
<td>1-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-27-32<br />
</td>
<td>1-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-30-32<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>0-2-4-7<br />
</td>
<td>1-5/4-11/7-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-5-7<br />
</td>
<td>1-5/4-7/4-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-3-5-7<br />
</td>
<td>1-7/5-7/4-11/10<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-2-4-9<br />
</td>
<td>1-5/4-11/7-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-2-5-9<br />
</td>
<td>1-5/4-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-2-7-9<br />
</td>
<td>1-5/4-11/10-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-4-7-9<br />
</td>
<td>1-11/7-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-5-7-9<br />
</td>
<td>1-7/4-11/10-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-2-4-11<br />
</td>
<td>1-5/4-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-2-7-11<br />
</td>
<td>1-5/4-11/10-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-4-7-11<br />
</td>
<td>1-11/7-11/10-12/7<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-2-9-11<br />
</td>
<td>1-5/4-11/8-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-4-9-11<br />
</td>
<td>1-11/7-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-7-9-11<br />
</td>
<td>1-11/10-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-3-5-14<br />
</td>
<td>1-7/5-7/4-6/5<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-3-7-14<br />
</td>
<td>1-7/5-11/10-6/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-5-7-14<br />
</td>
<td>1-7/4-11/10-6/5<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-5-9-14<br />
</td>
<td>1-7/4-11/8-6/5<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-7-9-14<br />
</td>
<td>1-11/10-11/8-6/5<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-7-11-14<br />
</td>
<td>1-12/11-12/7-6/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-9-11-14<br />
</td>
<td>1-11/8-12/7-6/5<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-2-5-16<br />
</td>
<td>1-5/4-7/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-2-7-16<br />
</td>
<td>1-5/4-11/10-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-5-7-16<br />
</td>
<td>1-7/4-11/10-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-2-9-16<br />
</td>
<td>1-5/4-11/8-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-5-9-16<br />
</td>
<td>1-7/4-11/8-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-7-9-16<br />
</td>
<td>1-11/10-11/8-3/2<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-2-11-16<br />
</td>
<td>1-5/4-12/7-3/2<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-7-11-16<br />
</td>
<td>1-12/11-12/7-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-9-11-16<br />
</td>
<td>1-11/8-12/7-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-5-14-16<br />
</td>
<td>1-7/4-6/5-3/2<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-7-14-16<br />
</td>
<td>1-12/11-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-9-14-16<br />
</td>
<td>1-11/8-6/5-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-11-14-16<br />
</td>
<td>1-12/7-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-7-9-23<br />
</td>
<td>1-11/10-11/8-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-7-14-23<br />
</td>
<td>1-11/10-6/5-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-9-14-23<br />
</td>
<td>1-11/8-6/5-18/11<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-7-16-23<br />
</td>
<td>1-12/11-3/2-18/11<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-9-16-23<br />
</td>
<td>1-11/8-3/2-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-14-16-23<br />
</td>
<td>1-6/5-3/2-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-4-11-27<br />
</td>
<td>1-11/7-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-11-16-27<br />
</td>
<td>1-12/7-3/2-9/7<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-16-23-27<br />
</td>
<td>1-3/2-18/11-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-3-7-30<br />
</td>
<td>1-7/5-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-3-14-30<br />
</td>
<td>1-7/5-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-7-14-30<br />
</td>
<td>1-11/10-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-7-16-30<br />
</td>
<td>1-11/10-3/2-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-14-16-30<br />
</td>
<td>1-6/5-3/2-9/5<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-7-23-30<br />
</td>
<td>1-11/10-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-14-23-30<br />
</td>
<td>1-6/5-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-16-23-30<br />
</td>
<td>1-3/2-18/11-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-16-27-30<br />
</td>
<td>1-3/2-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-23-27-30<br />
</td>
<td>1-18/11-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-2-5-32<br />
</td>
<td>1-5/4-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-2-9-32<br />
</td>
<td>1-5/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-5-9-32<br />
</td>
<td>1-7/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-2-16-32<br />
</td>
<td>1-5/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-5-16-32<br />
</td>
<td>1-7/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-9-16-32<br />
</td>
<td>1-11/8-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-9-23-32<br />
</td>
<td>1-11/8-18/11-9/8<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-16-23-32<br />
</td>
<td>1-3/2-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-16-27-32<br />
</td>
<td>1-3/2-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-23-27-32<br />
</td>
<td>1-18/11-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-16-30-32<br />
</td>
<td>1-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-23-30-32<br />
</td>
<td>1-18/11-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td>0-27-30-32<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>0-2-4-7-9<br />
</td>
<td>1-5/4-11/7-11/10-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-5-7-9<br />
</td>
<td>1-5/4-7/4-11/10-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-2-4-7-11<br />
</td>
<td>1-5/4-11/7-11/10-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-2-4-9-11<br />
</td>
<td>1-5/4-11/7-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-2-7-9-11<br />
</td>
<td>1-5/4-11/10-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-4-7-9-11<br />
</td>
<td>1-11/7-11/10-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-3-5-7-14<br />
</td>
<td>1-7/5-7/4-11/10-6/5<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-5-7-9-14<br />
</td>
<td>1-7/4-11/10-11/8-6/5<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-7-9-11-14<br />
</td>
<td>1-11/10-11/8-12/7-6/5<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-2-5-7-16<br />
</td>
<td>1-5/4-7/4-11/10-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-2-5-9-16<br />
</td>
<td>1-5/4-7/4-11/8-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-2-7-9-16<br />
</td>
<td>1-5/4-11/10-11/8-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-5-7-9-16<br />
</td>
<td>1-7/4-11/10-11/8-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-2-7-11-16<br />
</td>
<td>1-5/4-11/10-12/7-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-2-9-11-16<br />
</td>
<td>1-5/4-11/8-12/7-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-7-9-11-16<br />
</td>
<td>1-11/10-11/8-12/7-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-5-7-14-16<br />
</td>
<td>1-7/4-11/10-6/5-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-5-9-14-16<br />
</td>
<td>1-7/4-11/8-6/5-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-7-9-14-16<br />
</td>
<td>1-11/10-11/8-6/5-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-7-11-14-16<br />
</td>
<td>1-12/11-12/7-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-9-11-14-16<br />
</td>
<td>1-11/8-12/7-6/5-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-7-9-14-23<br />
</td>
<td>1-11/10-11/8-6/5-18/11<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-7-9-16-23<br />
</td>
<td>1-11/10-11/8-3/2-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-7-14-16-23<br />
</td>
<td>1-11/10-6/5-3/2-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-9-14-16-23<br />
</td>
<td>1-11/8-6/5-3/2-18/11<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-3-7-14-30<br />
</td>
<td>1-7/5-11/10-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-7-14-16-30<br />
</td>
<td>1-11/10-6/5-3/2-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-7-14-23-30<br />
</td>
<td>1-11/10-6/5-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-7-16-23-30<br />
</td>
<td>1-11/10-3/2-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-14-16-23-30<br />
</td>
<td>1-6/5-3/2-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-16-23-27-30<br />
</td>
<td>1-3/2-18/11-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-2-5-9-32<br />
</td>
<td>1-5/4-7/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-2-5-16-32<br />
</td>
<td>1-5/4-7/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-2-9-16-32<br />
</td>
<td>1-5/4-11/8-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-5-9-16-32<br />
</td>
<td>1-7/4-11/8-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-9-16-23-32<br />
</td>
<td>1-11/8-3/2-18/11-9/8<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-16-23-27-32<br />
</td>
<td>1-3/2-18/11-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-16-23-30-32<br />
</td>
<td>1-3/2-18/11-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-16-27-30-32<br />
</td>
<td>1-3/2-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-23-27-30-32<br />
</td>
<td>1-18/11-9/7-9/5-9/8<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>0-2-4-7-9-11<br />
</td>
<td>1-5/4-11/7-11/10-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-5-7-9-16<br />
</td>
<td>1-5/4-7/4-11/10-11/8-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-2-7-9-11-16<br />
</td>
<td>1-5/4-11/10-11/8-12/7-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-5-7-9-14-16<br />
</td>
<td>1-7/4-11/10-11/8-6/5-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-7-9-11-14-16<br />
</td>
<td>1-11/10-11/8-12/7-6/5-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-7-9-14-16-23<br />
</td>
<td>1-11/10-11/8-6/5-3/2-18/11<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-7-14-16-23-30<br />
</td>
<td>1-11/10-6/5-3/2-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-2-5-9-16-32<br />
</td>
<td>1-5/4-7/4-11/8-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-16-23-27-30-32<br />
</td>
<td>1-3/2-18/11-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
</body></html>