Luna and hemithirds/Chords
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 2011-12-29 10:30:00 UTC.
- The original revision id was 288736208.
- The revision comment was:
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Original Wikitext content:
Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Gamelismic clan#Hemithirds|hemithirds temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic. Hemithirds has MOS of size 6, 7, 13, 19, 25, 31, 56 and 87. It may be seen that adding essentially tempered chords to the mix allows for a notably richer range of harmonies even for the 13 note MOS. =Triads= || Number || Chord || Transversal || Type || || 1 || 0-2-5 || 1-5/4-7/4 || otonal || || 2 || 0-3-5 || 1-7/5-7/4 || utonal || || 3 || 0-2-7 || 1-5/4-12/11 || keenanismic || || 4 || 0-5-7 || 1-7/4-12/11 || keenanismic || || 5 || 0-3-8 || 1-7/5-11/9 || werckismic || || 6 || 0-5-8 || 1-7/4-11/9 || werckismic || || 7 || 0-7-15 || 1-12/11-4/3 || utonal || || 8 || 0-8-15 || 1-11/9-4/3 || otonal || || 9 || 0-2-17 || 1-5/4-5/3 || utonal || || 10 || 0-15-17 || 1-4/3-5/3 || otonal || || 11 || 0-3-20 || 1-7/5-7/6 || utonal || || 12 || 0-5-20 || 1-7/4-7/6 || utonal || || 13 || 0-15-20 || 1-4/3-7/6 || otonal || || 14 || 0-17-20 || 1-5/3-7/6 || otonal || || 15 || 0-2-22 || 1-5/4-16/11 || keenanismic || || 16 || 0-5-22 || 1-7/4-16/11 || keenanismic || || 17 || 0-7-22 || 1-12/11-16/11 || otonal || || 18 || 0-15-22 || 1-4/3-16/11 || utonal || || 19 || 0-17-22 || 1-5/3-16/11 || keenanismic || || 20 || 0-20-22 || 1-7/6-16/11 || keenanismic || || 21 || 0-2-24 || 1-5/4-20/11 || utonal || || 22 || 0-7-24 || 1-12/11-20/11 || otonal || || 23 || 0-17-24 || 1-5/3-20/11 || utonal || || 24 || 0-22-24 || 1-16/11-20/11 || otonal || || 25 || 0-3-27 || 1-7/5-14/11 || utonal || || 26 || 0-5-27 || 1-7/4-14/11 || utonal || || 27 || 0-7-27 || 1-12/11-14/11 || otonal || || 28 || 0-20-27 || 1-7/6-14/11 || utonal || || 29 || 0-22-27 || 1-16/11-14/11 || otonal || || 30 || 0-24-27 || 1-20/11-14/11 || otonal || || 31 || 0-3-30 || 1-7/5-16/9 || werckismic || || 32 || 0-8-30 || 1-11/9-16/9 || otonal || || 33 || 0-15-30 || 1-4/3-16/9 || ambitonal || || 34 || 0-22-30 || 1-16/11-16/9 || utonal || || 35 || 0-27-30 || 1-14/11-16/9 || werckismic || || 36 || 0-2-32 || 1-5/4-10/9 || utonal || || 37 || 0-5-32 || 1-7/4-10/9 || werckismic || || 38 || 0-8-32 || 1-11/9-10/9 || otonal || || 39 || 0-15-32 || 1-4/3-10/9 || otonal || || 40 || 0-17-32 || 1-5/3-10/9 || utonal || || 41 || 0-24-32 || 1-20/11-10/9 || utonal || || 42 || 0-27-32 || 1-14/11-10/9 || werckismic || || 43 || 0-30-32 || 1-16/9-10/9 || otonal || || 44 || 0-3-35 || 1-7/5-14/9 || utonal || || 45 || 0-5-35 || 1-7/4-14/9 || utonal || || 46 || 0-8-35 || 1-11/9-14/9 || otonal || || 47 || 0-15-35 || 1-4/3-14/9 || otonal || || 48 || 0-20-35 || 1-7/6-14/9 || utonal || || 49 || 0-27-35 || 1-14/11-14/9 || utonal || || 50 || 0-30-35 || 1-16/9-14/9 || otonal || || 51 || 0-32-35 || 1-10/9-14/9 || otonal || =Tetrads= || Number || Chord || Transversal || Type || || 1 || 0-2-5-7 || 1-5/4-7/4-12/11 || keenanismic || || 2 || 0-3-5-8 || 1-7/5-7/4-11/9 || werckismic || || 3 || 0-3-5-20 || 1-7/5-7/4-7/6 || utonal || || 4 || 0-15-17-20 || 1-4/3-5/3-7/6 || otonal || || 5 || 0-2-5-22 || 1-5/4-7/4-16/11 || keenanismic || || 6 || 0-2-7-22 || 1-5/4-12/11-16/11 || keenanismic || || 7 || 0-5-7-22 || 1-7/4-12/11-16/11 || keenanismic || || 8 || 0-7-15-22 || 1-12/11-4/3-16/11 || ambitonal || || 9 || 0-2-17-22 || 1-5/4-5/3-16/11 || keenanismic || || 10 || 0-15-17-22 || 1-4/3-5/3-16/11 || keenanismic || || 11 || 0-5-20-22 || 1-7/4-7/6-16/11 || keenanismic || || 12 || 0-15-20-22 || 1-4/3-7/6-16/11 || keenanismic || || 13 || 0-17-20-22 || 1-5/3-7/6-16/11 || keenanismic || || 14 || 0-2-7-24 || 1-5/4-12/11-20/11 || keenanismic || || 15 || 0-2-17-24 || 1-5/4-5/3-20/11 || utonal || || 16 || 0-2-22-24 || 1-5/4-16/11-20/11 || keenanismic || || 17 || 0-7-22-24 || 1-12/11-16/11-20/11 || otonal || || 18 || 0-17-22-24 || 1-5/3-16/11-20/11 || keenanismic || || 19 || 0-3-5-27 || 1-7/5-7/4-14/11 || utonal || || 20 || 0-5-7-27 || 1-7/4-12/11-14/11 || keenanismic || || 21 || 0-3-20-27 || 1-7/5-7/6-14/11 || utonal || || 22 || 0-5-20-27 || 1-7/4-7/6-14/11 || utonal || || 23 || 0-5-22-27 || 1-7/4-16/11-14/11 || keenanismic || || 24 || 0-7-22-27 || 1-12/11-16/11-14/11 || otonal || || 25 || 0-20-22-27 || 1-7/6-16/11-14/11 || keenanismic || || 26 || 0-7-24-27 || 1-12/11-20/11-14/11 || otonal || || 27 || 0-22-24-27 || 1-16/11-20/11-14/11 || otonal || || 28 || 0-3-8-30 || 1-7/5-11/9-16/9 || werckismic || || 29 || 0-8-15-30 || 1-11/9-4/3-16/9 || otonal || || 30 || 0-15-22-30 || 1-4/3-16/11-16/9 || utonal || || 31 || 0-3-27-30 || 1-7/5-14/11-16/9 || werckismic || || 32 || 0-22-27-30 || 1-16/11-14/11-16/9 || werckismic || || 33 || 0-2-5-32 || 1-5/4-7/4-10/9 || werckismic || || 34 || 0-5-8-32 || 1-7/4-11/9-10/9 || werckismic || || 35 || 0-8-15-32 || 1-11/9-4/3-10/9 || otonal || || 36 || 0-2-17-32 || 1-5/4-5/3-10/9 || utonal || || 37 || 0-15-17-32 || 1-4/3-5/3-10/9 || ambitonal || || 38 || 0-2-24-32 || 1-5/4-20/11-10/9 || utonal || || 39 || 0-17-24-32 || 1-5/3-20/11-10/9 || utonal || || 40 || 0-5-27-32 || 1-7/4-14/11-10/9 || werckismic || || 41 || 0-24-27-32 || 1-20/11-14/11-10/9 || werckismic || || 42 || 0-8-30-32 || 1-11/9-16/9-10/9 || otonal || || 43 || 0-15-30-32 || 1-4/3-16/9-10/9 || otonal || || 44 || 0-27-30-32 || 1-14/11-16/9-10/9 || werckismic || || 45 || 0-3-5-35 || 1-7/5-7/4-14/9 || utonal || || 46 || 0-3-8-35 || 1-7/5-11/9-14/9 || werckismic || || 47 || 0-5-8-35 || 1-7/4-11/9-14/9 || werckismic || || 48 || 0-8-15-35 || 1-11/9-4/3-14/9 || otonal || || 49 || 0-3-20-35 || 1-7/5-7/6-14/9 || utonal || || 50 || 0-5-20-35 || 1-7/4-7/6-14/9 || utonal || || 51 || 0-15-20-35 || 1-4/3-7/6-14/9 || ambitonal || || 52 || 0-3-27-35 || 1-7/5-14/11-14/9 || utonal || || 53 || 0-5-27-35 || 1-7/4-14/11-14/9 || utonal || || 54 || 0-20-27-35 || 1-7/6-14/11-14/9 || utonal || || 55 || 0-3-30-35 || 1-7/5-16/9-14/9 || werckismic || || 56 || 0-8-30-35 || 1-11/9-16/9-14/9 || otonal || || 57 || 0-15-30-35 || 1-4/3-16/9-14/9 || otonal || || 58 || 0-27-30-35 || 1-14/11-16/9-14/9 || werckismic || || 59 || 0-5-32-35 || 1-7/4-10/9-14/9 || werckismic || || 60 || 0-8-32-35 || 1-11/9-10/9-14/9 || otonal || || 61 || 0-15-32-35 || 1-4/3-10/9-14/9 || otonal || || 62 || 0-27-32-35 || 1-14/11-10/9-14/9 || werckismic || || 63 || 0-30-32-35 || 1-16/9-10/9-14/9 || otonal || =Pentads= || Number || Chord || Transversal || Type || || 1 || 0-2-5-7-22 || 1-5/4-7/4-12/11-16/11 || keenanismic || || 2 || 0-15-17-20-22 || 1-4/3-5/3-7/6-16/11 || keenanismic || || 3 || 0-2-7-22-24 || 1-5/4-12/11-16/11-20/11 || keenanismic || || 4 || 0-2-17-22-24 || 1-5/4-5/3-16/11-20/11 || keenanismic || || 5 || 0-3-5-20-27 || 1-7/5-7/4-7/6-14/11 || utonal || || 6 || 0-5-7-22-27 || 1-7/4-12/11-16/11-14/11 || keenanismic || || 7 || 0-5-20-22-27 || 1-7/4-7/6-16/11-14/11 || keenanismic || || 8 || 0-7-22-24-27 || 1-12/11-16/11-20/11-14/11 || otonal || || 9 || 0-2-17-24-32 || 1-5/4-5/3-20/11-10/9 || utonal || || 10 || 0-8-15-30-32 || 1-11/9-4/3-16/9-10/9 || otonal || || 11 || 0-3-5-8-35 || 1-7/5-7/4-11/9-14/9 || werckismic || || 12 || 0-3-5-20-35 || 1-7/5-7/4-7/6-14/9 || utonal || || 13 || 0-3-5-27-35 || 1-7/5-7/4-14/11-14/9 || utonal || || 14 || 0-3-20-27-35 || 1-7/5-7/6-14/11-14/9 || utonal || || 15 || 0-5-20-27-35 || 1-7/4-7/6-14/11-14/9 || utonal || || 16 || 0-3-8-30-35 || 1-7/5-11/9-16/9-14/9 || werckismic || || 17 || 0-8-15-30-35 || 1-11/9-4/3-16/9-14/9 || otonal || || 18 || 0-3-27-30-35 || 1-7/5-14/11-16/9-14/9 || werckismic || || 19 || 0-5-8-32-35 || 1-7/4-11/9-10/9-14/9 || werckismic || || 20 || 0-8-15-32-35 || 1-11/9-4/3-10/9-14/9 || otonal || || 21 || 0-5-27-32-35 || 1-7/4-14/11-10/9-14/9 || werckismic || || 22 || 0-8-30-32-35 || 1-11/9-16/9-10/9-14/9 || otonal || || 23 || 0-15-30-32-35 || 1-4/3-16/9-10/9-14/9 || otonal || || 24 || 0-27-30-32-35 || 1-14/11-16/9-10/9-14/9 || werckismic || =Hexads= || Number || Chord || Transversal || Type || || 1 || 0-3-5-20-27-35 || 1-7/5-7/4-7/6-14/11-14/9 || utonal || || 2 || 0-8-15-30-32-35 || 1-11/9-4/3-16/9-10/9-14/9 || otonal ||
Original HTML content:
<html><head><title>Chords of hemithirds</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="/Gamelismic%20clan#Hemithirds">hemithirds temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.<br />
<br />
Hemithirds has MOS of size 6, 7, 13, 19, 25, 31, 56 and 87. It may be seen that adding essentially tempered chords to the mix allows for a notably richer range of harmonies even for the 13 note MOS.<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>0-2-5<br />
</td>
<td>1-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-3-5<br />
</td>
<td>1-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-2-7<br />
</td>
<td>1-5/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-5-7<br />
</td>
<td>1-7/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-8<br />
</td>
<td>1-7/5-11/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-5-8<br />
</td>
<td>1-7/4-11/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-7-15<br />
</td>
<td>1-12/11-4/3<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-8-15<br />
</td>
<td>1-11/9-4/3<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-2-17<br />
</td>
<td>1-5/4-5/3<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-15-17<br />
</td>
<td>1-4/3-5/3<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-3-20<br />
</td>
<td>1-7/5-7/6<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-5-20<br />
</td>
<td>1-7/4-7/6<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-15-20<br />
</td>
<td>1-4/3-7/6<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-17-20<br />
</td>
<td>1-5/3-7/6<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-2-22<br />
</td>
<td>1-5/4-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-5-22<br />
</td>
<td>1-7/4-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-7-22<br />
</td>
<td>1-12/11-16/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-15-22<br />
</td>
<td>1-4/3-16/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-17-22<br />
</td>
<td>1-5/3-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-20-22<br />
</td>
<td>1-7/6-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-2-24<br />
</td>
<td>1-5/4-20/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-7-24<br />
</td>
<td>1-12/11-20/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-17-24<br />
</td>
<td>1-5/3-20/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-22-24<br />
</td>
<td>1-16/11-20/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-3-27<br />
</td>
<td>1-7/5-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-5-27<br />
</td>
<td>1-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-7-27<br />
</td>
<td>1-12/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-20-27<br />
</td>
<td>1-7/6-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-22-27<br />
</td>
<td>1-16/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-24-27<br />
</td>
<td>1-20/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-3-30<br />
</td>
<td>1-7/5-16/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-8-30<br />
</td>
<td>1-11/9-16/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-15-30<br />
</td>
<td>1-4/3-16/9<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-22-30<br />
</td>
<td>1-16/11-16/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-27-30<br />
</td>
<td>1-14/11-16/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-2-32<br />
</td>
<td>1-5/4-10/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-5-32<br />
</td>
<td>1-7/4-10/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-8-32<br />
</td>
<td>1-11/9-10/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-15-32<br />
</td>
<td>1-4/3-10/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-17-32<br />
</td>
<td>1-5/3-10/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-24-32<br />
</td>
<td>1-20/11-10/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-27-32<br />
</td>
<td>1-14/11-10/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-30-32<br />
</td>
<td>1-16/9-10/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-3-35<br />
</td>
<td>1-7/5-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-5-35<br />
</td>
<td>1-7/4-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-8-35<br />
</td>
<td>1-11/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-15-35<br />
</td>
<td>1-4/3-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-20-35<br />
</td>
<td>1-7/6-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-27-35<br />
</td>
<td>1-14/11-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-30-35<br />
</td>
<td>1-16/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-32-35<br />
</td>
<td>1-10/9-14/9<br />
</td>
<td>otonal<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>0-2-5-7<br />
</td>
<td>1-5/4-7/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-3-5-8<br />
</td>
<td>1-7/5-7/4-11/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-3-5-20<br />
</td>
<td>1-7/5-7/4-7/6<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-15-17-20<br />
</td>
<td>1-4/3-5/3-7/6<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-2-5-22<br />
</td>
<td>1-5/4-7/4-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-2-7-22<br />
</td>
<td>1-5/4-12/11-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-5-7-22<br />
</td>
<td>1-7/4-12/11-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-7-15-22<br />
</td>
<td>1-12/11-4/3-16/11<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-2-17-22<br />
</td>
<td>1-5/4-5/3-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-15-17-22<br />
</td>
<td>1-4/3-5/3-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-5-20-22<br />
</td>
<td>1-7/4-7/6-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-15-20-22<br />
</td>
<td>1-4/3-7/6-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-17-20-22<br />
</td>
<td>1-5/3-7/6-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-2-7-24<br />
</td>
<td>1-5/4-12/11-20/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-2-17-24<br />
</td>
<td>1-5/4-5/3-20/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-2-22-24<br />
</td>
<td>1-5/4-16/11-20/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-7-22-24<br />
</td>
<td>1-12/11-16/11-20/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-17-22-24<br />
</td>
<td>1-5/3-16/11-20/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-3-5-27<br />
</td>
<td>1-7/5-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-5-7-27<br />
</td>
<td>1-7/4-12/11-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-3-20-27<br />
</td>
<td>1-7/5-7/6-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-5-20-27<br />
</td>
<td>1-7/4-7/6-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-5-22-27<br />
</td>
<td>1-7/4-16/11-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-7-22-27<br />
</td>
<td>1-12/11-16/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-20-22-27<br />
</td>
<td>1-7/6-16/11-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-7-24-27<br />
</td>
<td>1-12/11-20/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-22-24-27<br />
</td>
<td>1-16/11-20/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-3-8-30<br />
</td>
<td>1-7/5-11/9-16/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-8-15-30<br />
</td>
<td>1-11/9-4/3-16/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-15-22-30<br />
</td>
<td>1-4/3-16/11-16/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-3-27-30<br />
</td>
<td>1-7/5-14/11-16/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-22-27-30<br />
</td>
<td>1-16/11-14/11-16/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-2-5-32<br />
</td>
<td>1-5/4-7/4-10/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-5-8-32<br />
</td>
<td>1-7/4-11/9-10/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-8-15-32<br />
</td>
<td>1-11/9-4/3-10/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-2-17-32<br />
</td>
<td>1-5/4-5/3-10/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-15-17-32<br />
</td>
<td>1-4/3-5/3-10/9<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-2-24-32<br />
</td>
<td>1-5/4-20/11-10/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-17-24-32<br />
</td>
<td>1-5/3-20/11-10/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-5-27-32<br />
</td>
<td>1-7/4-14/11-10/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-24-27-32<br />
</td>
<td>1-20/11-14/11-10/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-8-30-32<br />
</td>
<td>1-11/9-16/9-10/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-15-30-32<br />
</td>
<td>1-4/3-16/9-10/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-27-30-32<br />
</td>
<td>1-14/11-16/9-10/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-3-5-35<br />
</td>
<td>1-7/5-7/4-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-3-8-35<br />
</td>
<td>1-7/5-11/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-5-8-35<br />
</td>
<td>1-7/4-11/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-8-15-35<br />
</td>
<td>1-11/9-4/3-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-3-20-35<br />
</td>
<td>1-7/5-7/6-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-5-20-35<br />
</td>
<td>1-7/4-7/6-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-15-20-35<br />
</td>
<td>1-4/3-7/6-14/9<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-3-27-35<br />
</td>
<td>1-7/5-14/11-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-5-27-35<br />
</td>
<td>1-7/4-14/11-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-20-27-35<br />
</td>
<td>1-7/6-14/11-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-3-30-35<br />
</td>
<td>1-7/5-16/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-8-30-35<br />
</td>
<td>1-11/9-16/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-15-30-35<br />
</td>
<td>1-4/3-16/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-27-30-35<br />
</td>
<td>1-14/11-16/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-5-32-35<br />
</td>
<td>1-7/4-10/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-8-32-35<br />
</td>
<td>1-11/9-10/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-15-32-35<br />
</td>
<td>1-4/3-10/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-27-32-35<br />
</td>
<td>1-14/11-10/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-30-32-35<br />
</td>
<td>1-16/9-10/9-14/9<br />
</td>
<td>otonal<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>0-2-5-7-22<br />
</td>
<td>1-5/4-7/4-12/11-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-15-17-20-22<br />
</td>
<td>1-4/3-5/3-7/6-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-2-7-22-24<br />
</td>
<td>1-5/4-12/11-16/11-20/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-2-17-22-24<br />
</td>
<td>1-5/4-5/3-16/11-20/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-5-20-27<br />
</td>
<td>1-7/5-7/4-7/6-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-5-7-22-27<br />
</td>
<td>1-7/4-12/11-16/11-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-5-20-22-27<br />
</td>
<td>1-7/4-7/6-16/11-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-7-22-24-27<br />
</td>
<td>1-12/11-16/11-20/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-2-17-24-32<br />
</td>
<td>1-5/4-5/3-20/11-10/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-8-15-30-32<br />
</td>
<td>1-11/9-4/3-16/9-10/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-3-5-8-35<br />
</td>
<td>1-7/5-7/4-11/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-3-5-20-35<br />
</td>
<td>1-7/5-7/4-7/6-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-3-5-27-35<br />
</td>
<td>1-7/5-7/4-14/11-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-3-20-27-35<br />
</td>
<td>1-7/5-7/6-14/11-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-5-20-27-35<br />
</td>
<td>1-7/4-7/6-14/11-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-3-8-30-35<br />
</td>
<td>1-7/5-11/9-16/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-8-15-30-35<br />
</td>
<td>1-11/9-4/3-16/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-3-27-30-35<br />
</td>
<td>1-7/5-14/11-16/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-5-8-32-35<br />
</td>
<td>1-7/4-11/9-10/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-8-15-32-35<br />
</td>
<td>1-11/9-4/3-10/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-5-27-32-35<br />
</td>
<td>1-7/4-14/11-10/9-14/9<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-8-30-32-35<br />
</td>
<td>1-11/9-16/9-10/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-15-30-32-35<br />
</td>
<td>1-4/3-16/9-10/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-27-30-32-35<br />
</td>
<td>1-14/11-16/9-10/9-14/9<br />
</td>
<td>werckismic<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>0-3-5-20-27-35<br />
</td>
<td>1-7/5-7/4-7/6-14/11-14/9<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-8-15-30-32-35<br />
</td>
<td>1-11/9-4/3-16/9-10/9-14/9<br />
</td>
<td>otonal<br />
</td>
</tr>
</table>
</body></html>