Bohpier/Chords
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Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod. Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords. In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the [[sensamagic chords]] exist in strict Bohlen-Pierce. =Triads= || Number || Chord || Transversal || Type || || 1 || 0-1-4 || 1-12/11-7/5 || swetismic || || 2 || 0-3-4 || 1-9/7-7/5 || swetismic || || 3 || 0-3-6 || 1-9/7-5/3 || sensamagic || || 4 || 0-1-7 || 1-12/11-20/11 || otonal || || 5 || 0-3-7 || 1-9/7-9/5 || utonal || || 6 || 0-4-7 || 1-7/5-9/5 || otonal || || 7 || 0-6-7 || 1-5/3-20/11 || utonal || || 8 || 0-3-10 || 1-9/7-7/6 || sensamagic || || 9 || 0-4-10 || 1-7/5-7/6 || utonal || || 10 || 0-6-10 || 1-5/3-7/6 || otonal || || 11 || 0-7-10 || 1-9/5-7/6 || sensamagic || || 12 || 0-1-11 || 1-12/11-14/11 || otonal || || 13 || 0-4-11 || 1-7/5-14/11 || utonal || || 14 || 0-7-11 || 1-20/11-14/11 || otonal || || 15 || 0-10-11 || 1-7/6-14/11 || utonal || || 16 || 0-1-12 || 1-12/11-11/8 || hemimin || || 17 || 0-6-12 || 1-5/3-11/8 || ptolemismic || || 18 || 0-11-12 || 1-14/11-11/8 || hemimin || || 19 || 0-1-13 || 1-12/11-3/2 || utonal || || 20 || 0-3-13 || 1-9/7-3/2 || utonal || || 21 || 0-6-13 || 1-5/3-3/2 || otonal || || 22 || 0-7-13 || 1-9/5-3/2 || utonal || || 23 || 0-10-13 || 1-7/6-3/2 || otonal || || 24 || 0-12-13 || 1-11/8-3/2 || otonal || || 25 || 0-1-14 || 1-12/11-18/11 || otonal || || 26 || 0-3-14 || 1-9/7-18/11 || utonal || || 27 || 0-4-14 || 1-7/5-18/11 || swetismic || || 28 || 0-7-14 || 1-9/5-18/11 || utonal || || 29 || 0-10-14 || 1-7/6-18/11 || swetismic || || 30 || 0-11-14 || 1-14/11-18/11 || otonal || || 31 || 0-13-14 || 1-3/2-18/11 || utonal || || 32 || 0-6-19 || 1-5/3-5/4 || utonal || || 33 || 0-7-19 || 1-20/11-5/4 || utonal || || 34 || 0-12-19 || 1-11/8-5/4 || otonal || || 35 || 0-13-19 || 1-3/2-5/4 || otonal || || 36 || 0-4-23 || 1-7/5-7/4 || utonal || || 37 || 0-10-23 || 1-7/6-7/4 || utonal || || 38 || 0-11-23 || 1-14/11-7/4 || utonal || || 39 || 0-12-23 || 1-11/8-7/4 || otonal || || 40 || 0-13-23 || 1-3/2-7/4 || otonal || || 41 || 0-19-23 || 1-5/4-7/4 || otonal || || 42 || 0-3-26 || 1-9/7-9/8 || utonal || || 43 || 0-7-26 || 1-9/5-9/8 || utonal || || 44 || 0-12-26 || 1-11/8-9/8 || otonal || || 45 || 0-13-26 || 1-3/2-9/8 || ambitonal || || 46 || 0-14-26 || 1-18/11-9/8 || utonal || || 47 || 0-19-26 || 1-5/4-9/8 || otonal || || 48 || 0-23-26 || 1-7/4-9/8 || otonal || =Tetrads= || Number || Chord || Transversal || Type || || 1 || 0-1-4-7 || 1-12/11-7/5-9/5 || octarod || || 2 || 0-3-4-7 || 1-9/7-7/5-9/5 || swetismic || || 3 || 0-3-6-7 || 1-9/7-5/3-9/5 || octarod || || 4 || 0-3-4-10 || 1-9/7-7/5-7/6 || octarod || || 5 || 0-3-6-10 || 1-9/7-5/3-7/6 || sensamagic || || 6 || 0-3-7-10 || 1-9/7-9/5-7/6 || sensamagic || || 7 || 0-4-7-10 || 1-7/5-9/5-7/6 || sensamagic || || 8 || 0-6-7-10 || 1-5/3-9/5-7/6 || octarod || || 9 || 0-1-4-11 || 1-12/11-7/5-14/11 || octarod || || 10 || 0-1-7-11 || 1-12/11-20/11-14/11 || otonal || || 11 || 0-4-7-11 || 1-7/5-9/5-14/11 || ptolemismic || || 12 || 0-4-10-11 || 1-7/5-7/6-14/11 || utonal || || 13 || 0-7-10-11 || 1-9/5-7/6-14/11 || octarod || || 14 || 0-1-11-12 || 1-12/11-14/11-11/8 || hemimin || || 15 || 0-3-6-13 || 1-9/7-5/3-3/2 || sensamagic || || 16 || 0-1-7-13 || 1-12/11-9/5-3/2 || ptolemismic || || 17 || 0-3-7-13 || 1-9/7-9/5-3/2 || utonal || || 18 || 0-6-7-13 || 1-5/3-9/5-3/2 || ptolemismic || || 19 || 0-3-10-13 || 1-9/7-7/6-3/2 || sensamagic || || 20 || 0-6-10-13 || 1-5/3-7/6-3/2 || otonal || || 21 || 0-7-10-13 || 1-9/5-7/6-3/2 || sensamagic || || 22 || 0-1-12-13 || 1-12/11-11/8-3/2 || hemimin || || 23 || 0-6-12-13 || 1-5/3-11/8-3/2 || ptolemismic || || 24 || 0-1-4-14 || 1-12/11-7/5-18/11 || swetismic || || 25 || 0-3-4-14 || 1-9/7-7/5-18/11 || swetismic || || 26 || 0-1-7-14 || 1-12/11-20/11-18/11 || otonal || || 27 || 0-3-7-14 || 1-9/7-9/5-18/11 || utonal || || 28 || 0-4-7-14 || 1-7/5-9/5-18/11 || octarod || || 29 || 0-3-10-14 || 1-9/7-7/6-18/11 || octarod || || 30 || 0-4-10-14 || 1-7/5-7/6-18/11 || swetismic || || 31 || 0-7-10-14 || 1-9/5-7/6-18/11 || octarod || || 32 || 0-1-11-14 || 1-12/11-14/11-18/11 || otonal || || 33 || 0-4-11-14 || 1-7/5-14/11-18/11 || octarod || || 34 || 0-7-11-14 || 1-20/11-14/11-18/11 || otonal || || 35 || 0-10-11-14 || 1-7/6-14/11-18/11 || swetismic || || 36 || 0-1-13-14 || 1-12/11-3/2-18/11 || ambitonal || || 37 || 0-3-13-14 || 1-9/7-3/2-18/11 || utonal || || 38 || 0-7-13-14 || 1-9/5-3/2-18/11 || utonal || || 39 || 0-10-13-14 || 1-7/6-3/2-18/11 || swetismic || || 40 || 0-6-7-19 || 1-5/3-20/11-5/4 || utonal || || 41 || 0-6-12-19 || 1-5/3-11/8-5/4 || ptolemismic || || 42 || 0-6-13-19 || 1-5/3-3/2-5/4 || ambitonal || || 43 || 0-7-13-19 || 1-9/5-3/2-5/4 || ptolemismic || || 44 || 0-12-13-19 || 1-11/8-3/2-5/4 || otonal || || 45 || 0-4-10-23 || 1-7/5-7/6-7/4 || utonal || || 46 || 0-4-11-23 || 1-7/5-14/11-7/4 || utonal || || 47 || 0-10-11-23 || 1-7/6-14/11-7/4 || utonal || || 48 || 0-11-12-23 || 1-14/11-11/8-7/4 || hemimin || || 49 || 0-10-13-23 || 1-7/6-3/2-7/4 || ambitonal || || 50 || 0-12-13-23 || 1-11/8-3/2-7/4 || otonal || || 51 || 0-12-19-23 || 1-11/8-5/4-7/4 || otonal || || 52 || 0-13-19-23 || 1-3/2-5/4-7/4 || otonal || || 53 || 0-3-7-26 || 1-9/7-9/5-9/8 || utonal || || 54 || 0-3-13-26 || 1-9/7-3/2-9/8 || utonal || || 55 || 0-7-13-26 || 1-9/5-3/2-9/8 || utonal || || 56 || 0-12-13-26 || 1-11/8-3/2-9/8 || otonal || || 57 || 0-3-14-26 || 1-9/7-18/11-9/8 || utonal || || 58 || 0-7-14-26 || 1-9/5-18/11-9/8 || utonal || || 59 || 0-13-14-26 || 1-3/2-18/11-9/8 || utonal || || 60 || 0-7-19-26 || 1-9/5-5/4-9/8 || ptolemismic || || 61 || 0-12-19-26 || 1-11/8-5/4-9/8 || otonal || || 62 || 0-13-19-26 || 1-3/2-5/4-9/8 || otonal || || 63 || 0-12-23-26 || 1-11/8-7/4-9/8 || otonal || || 64 || 0-13-23-26 || 1-3/2-7/4-9/8 || otonal || || 65 || 0-19-23-26 || 1-5/4-7/4-9/8 || otonal || =Pentads= || Number || Chord || Transversal || Type || || 1 || 0-3-4-7-10 || 1-9/7-7/5-9/5-7/6 || octarod || || 2 || 0-3-6-7-10 || 1-9/7-5/3-9/5-7/6 || octarod || || 3 || 0-1-4-7-11 || 1-12/11-7/5-9/5-14/11 || octarod || || 4 || 0-4-7-10-11 || 1-7/5-9/5-7/6-14/11 || octarod || || 5 || 0-3-6-7-13 || 1-9/7-5/3-9/5-3/2 || octarod || || 6 || 0-3-6-10-13 || 1-9/7-5/3-7/6-3/2 || sensamagic || || 7 || 0-3-7-10-13 || 1-9/7-9/5-7/6-3/2 || sensamagic || || 8 || 0-6-7-10-13 || 1-5/3-9/5-7/6-3/2 || octarod || || 9 || 0-1-4-7-14 || 1-12/11-7/5-9/5-18/11 || octarod || || 10 || 0-3-4-7-14 || 1-9/7-7/5-9/5-18/11 || octarod || || 11 || 0-3-4-10-14 || 1-9/7-7/5-7/6-18/11 || octarod || || 12 || 0-3-7-10-14 || 1-9/7-9/5-7/6-18/11 || octarod || || 13 || 0-4-7-10-14 || 1-7/5-9/5-7/6-18/11 || octarod || || 14 || 0-1-4-11-14 || 1-12/11-7/5-14/11-18/11 || octarod || || 15 || 0-1-7-11-14 || 1-12/11-20/11-14/11-18/11 || otonal || || 16 || 0-4-7-11-14 || 1-7/5-9/5-14/11-18/11 || octarod || || 17 || 0-4-10-11-14 || 1-7/5-7/6-14/11-18/11 || octarod || || 18 || 0-7-10-11-14 || 1-9/5-7/6-14/11-18/11 || octarod || || 19 || 0-1-7-13-14 || 1-12/11-9/5-3/2-18/11 || ptolemismic || || 20 || 0-3-7-13-14 || 1-9/7-9/5-3/2-18/11 || utonal || || 21 || 0-3-10-13-14 || 1-9/7-7/6-3/2-18/11 || octarod || || 22 || 0-7-10-13-14 || 1-9/5-7/6-3/2-18/11 || octarod || || 23 || 0-6-7-13-19 || 1-5/3-9/5-3/2-5/4 || ptolemismic || || 24 || 0-6-12-13-19 || 1-5/3-11/8-3/2-5/4 || ptolemismic || || 25 || 0-4-10-11-23 || 1-7/5-7/6-14/11-7/4 || utonal || || 26 || 0-12-13-19-23 || 1-11/8-3/2-5/4-7/4 || otonal || || 27 || 0-3-7-13-26 || 1-9/7-9/5-3/2-9/8 || utonal || || 28 || 0-3-7-14-26 || 1-9/7-9/5-18/11-9/8 || utonal || || 29 || 0-3-13-14-26 || 1-9/7-3/2-18/11-9/8 || utonal || || 30 || 0-7-13-14-26 || 1-9/5-3/2-18/11-9/8 || utonal || || 31 || 0-7-13-19-26 || 1-9/5-3/2-5/4-9/8 || ptolemismic || || 32 || 0-12-13-19-26 || 1-11/8-3/2-5/4-9/8 || otonal || || 33 || 0-12-13-23-26 || 1-11/8-3/2-7/4-9/8 || otonal || || 34 || 0-12-19-23-26 || 1-11/8-5/4-7/4-9/8 || otonal || || 35 || 0-13-19-23-26 || 1-3/2-5/4-7/4-9/8 || otonal || =Hexads= || Number || Chord || Transversal || Type || || 1 || 0-3-6-7-10-13 || 1-9/7-5/3-9/5-7/6-3/2 || octarod || || 2 || 0-3-4-7-10-14 || 1-9/7-7/5-9/5-7/6-18/11 || octarod || || 3 || 0-1-4-7-11-14 || 1-12/11-7/5-9/5-14/11-18/11 || octarod || || 4 || 0-4-7-10-11-14 || 1-7/5-9/5-7/6-14/11-18/11 || octarod || || 5 || 0-3-7-10-13-14 || 1-9/7-9/5-7/6-3/2-18/11 || octarod || || 6 || 0-3-7-13-14-26 || 1-9/7-9/5-3/2-18/11-9/8 || utonal || || 7 || 0-12-13-19-23-26 || 1-11/8-3/2-5/4-7/4-9/8 || otonal ||
Original HTML content:
<html><head><title>Chords of bohpier</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="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<br />
<br />
Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />
<br />
In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the <a class="wiki_link" href="/sensamagic%20chords">sensamagic chords</a> exist in strict Bohlen-Pierce.<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>0-1-4<br />
</td>
<td>1-12/11-7/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-3-4<br />
</td>
<td>1-9/7-7/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-3-6<br />
</td>
<td>1-9/7-5/3<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-1-7<br />
</td>
<td>1-12/11-20/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-7<br />
</td>
<td>1-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-4-7<br />
</td>
<td>1-7/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-6-7<br />
</td>
<td>1-5/3-20/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-3-10<br />
</td>
<td>1-9/7-7/6<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-4-10<br />
</td>
<td>1-7/5-7/6<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-6-10<br />
</td>
<td>1-5/3-7/6<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-7-10<br />
</td>
<td>1-9/5-7/6<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-1-11<br />
</td>
<td>1-12/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-4-11<br />
</td>
<td>1-7/5-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-7-11<br />
</td>
<td>1-20/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-10-11<br />
</td>
<td>1-7/6-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-1-12<br />
</td>
<td>1-12/11-11/8<br />
</td>
<td>hemimin<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-6-12<br />
</td>
<td>1-5/3-11/8<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-11-12<br />
</td>
<td>1-14/11-11/8<br />
</td>
<td>hemimin<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-1-13<br />
</td>
<td>1-12/11-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-3-13<br />
</td>
<td>1-9/7-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-6-13<br />
</td>
<td>1-5/3-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-7-13<br />
</td>
<td>1-9/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-10-13<br />
</td>
<td>1-7/6-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-12-13<br />
</td>
<td>1-11/8-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-1-14<br />
</td>
<td>1-12/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-3-14<br />
</td>
<td>1-9/7-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-4-14<br />
</td>
<td>1-7/5-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-7-14<br />
</td>
<td>1-9/5-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-10-14<br />
</td>
<td>1-7/6-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-11-14<br />
</td>
<td>1-14/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-13-14<br />
</td>
<td>1-3/2-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-6-19<br />
</td>
<td>1-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-7-19<br />
</td>
<td>1-20/11-5/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-12-19<br />
</td>
<td>1-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-13-19<br />
</td>
<td>1-3/2-5/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-4-23<br />
</td>
<td>1-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-10-23<br />
</td>
<td>1-7/6-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-11-23<br />
</td>
<td>1-14/11-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-12-23<br />
</td>
<td>1-11/8-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-13-23<br />
</td>
<td>1-3/2-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-19-23<br />
</td>
<td>1-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-3-26<br />
</td>
<td>1-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-7-26<br />
</td>
<td>1-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-12-26<br />
</td>
<td>1-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-13-26<br />
</td>
<td>1-3/2-9/8<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-14-26<br />
</td>
<td>1-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-19-26<br />
</td>
<td>1-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-23-26<br />
</td>
<td>1-7/4-9/8<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>0-1-4-7<br />
</td>
<td>1-12/11-7/5-9/5<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-3-4-7<br />
</td>
<td>1-9/7-7/5-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-3-6-7<br />
</td>
<td>1-9/7-5/3-9/5<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-3-4-10<br />
</td>
<td>1-9/7-7/5-7/6<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-6-10<br />
</td>
<td>1-9/7-5/3-7/6<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-3-7-10<br />
</td>
<td>1-9/7-9/5-7/6<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-4-7-10<br />
</td>
<td>1-7/5-9/5-7/6<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-6-7-10<br />
</td>
<td>1-5/3-9/5-7/6<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-1-4-11<br />
</td>
<td>1-12/11-7/5-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-1-7-11<br />
</td>
<td>1-12/11-20/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-4-7-11<br />
</td>
<td>1-7/5-9/5-14/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-4-10-11<br />
</td>
<td>1-7/5-7/6-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-7-10-11<br />
</td>
<td>1-9/5-7/6-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-1-11-12<br />
</td>
<td>1-12/11-14/11-11/8<br />
</td>
<td>hemimin<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-3-6-13<br />
</td>
<td>1-9/7-5/3-3/2<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-1-7-13<br />
</td>
<td>1-12/11-9/5-3/2<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-3-7-13<br />
</td>
<td>1-9/7-9/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-6-7-13<br />
</td>
<td>1-5/3-9/5-3/2<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-3-10-13<br />
</td>
<td>1-9/7-7/6-3/2<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-6-10-13<br />
</td>
<td>1-5/3-7/6-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-7-10-13<br />
</td>
<td>1-9/5-7/6-3/2<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-1-12-13<br />
</td>
<td>1-12/11-11/8-3/2<br />
</td>
<td>hemimin<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-6-12-13<br />
</td>
<td>1-5/3-11/8-3/2<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-1-4-14<br />
</td>
<td>1-12/11-7/5-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-3-4-14<br />
</td>
<td>1-9/7-7/5-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-1-7-14<br />
</td>
<td>1-12/11-20/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-3-7-14<br />
</td>
<td>1-9/7-9/5-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-4-7-14<br />
</td>
<td>1-7/5-9/5-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-3-10-14<br />
</td>
<td>1-9/7-7/6-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-4-10-14<br />
</td>
<td>1-7/5-7/6-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-7-10-14<br />
</td>
<td>1-9/5-7/6-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-1-11-14<br />
</td>
<td>1-12/11-14/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-4-11-14<br />
</td>
<td>1-7/5-14/11-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-7-11-14<br />
</td>
<td>1-20/11-14/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-10-11-14<br />
</td>
<td>1-7/6-14/11-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-1-13-14<br />
</td>
<td>1-12/11-3/2-18/11<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-3-13-14<br />
</td>
<td>1-9/7-3/2-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-7-13-14<br />
</td>
<td>1-9/5-3/2-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-10-13-14<br />
</td>
<td>1-7/6-3/2-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-6-7-19<br />
</td>
<td>1-5/3-20/11-5/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-6-12-19<br />
</td>
<td>1-5/3-11/8-5/4<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-6-13-19<br />
</td>
<td>1-5/3-3/2-5/4<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-7-13-19<br />
</td>
<td>1-9/5-3/2-5/4<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-12-13-19<br />
</td>
<td>1-11/8-3/2-5/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-4-10-23<br />
</td>
<td>1-7/5-7/6-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-4-11-23<br />
</td>
<td>1-7/5-14/11-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-10-11-23<br />
</td>
<td>1-7/6-14/11-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-11-12-23<br />
</td>
<td>1-14/11-11/8-7/4<br />
</td>
<td>hemimin<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-10-13-23<br />
</td>
<td>1-7/6-3/2-7/4<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-12-13-23<br />
</td>
<td>1-11/8-3/2-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-12-19-23<br />
</td>
<td>1-11/8-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-13-19-23<br />
</td>
<td>1-3/2-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-3-7-26<br />
</td>
<td>1-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-3-13-26<br />
</td>
<td>1-9/7-3/2-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-7-13-26<br />
</td>
<td>1-9/5-3/2-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-12-13-26<br />
</td>
<td>1-11/8-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-3-14-26<br />
</td>
<td>1-9/7-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-7-14-26<br />
</td>
<td>1-9/5-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-13-14-26<br />
</td>
<td>1-3/2-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-7-19-26<br />
</td>
<td>1-9/5-5/4-9/8<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-12-19-26<br />
</td>
<td>1-11/8-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-13-19-26<br />
</td>
<td>1-3/2-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-12-23-26<br />
</td>
<td>1-11/8-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-13-23-26<br />
</td>
<td>1-3/2-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-19-23-26<br />
</td>
<td>1-5/4-7/4-9/8<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>0-3-4-7-10<br />
</td>
<td>1-9/7-7/5-9/5-7/6<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-3-6-7-10<br />
</td>
<td>1-9/7-5/3-9/5-7/6<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-1-4-7-11<br />
</td>
<td>1-12/11-7/5-9/5-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-4-7-10-11<br />
</td>
<td>1-7/5-9/5-7/6-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-6-7-13<br />
</td>
<td>1-9/7-5/3-9/5-3/2<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-3-6-10-13<br />
</td>
<td>1-9/7-5/3-7/6-3/2<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-3-7-10-13<br />
</td>
<td>1-9/7-9/5-7/6-3/2<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-6-7-10-13<br />
</td>
<td>1-5/3-9/5-7/6-3/2<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-1-4-7-14<br />
</td>
<td>1-12/11-7/5-9/5-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-3-4-7-14<br />
</td>
<td>1-9/7-7/5-9/5-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-3-4-10-14<br />
</td>
<td>1-9/7-7/5-7/6-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-3-7-10-14<br />
</td>
<td>1-9/7-9/5-7/6-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-4-7-10-14<br />
</td>
<td>1-7/5-9/5-7/6-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-1-4-11-14<br />
</td>
<td>1-12/11-7/5-14/11-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-1-7-11-14<br />
</td>
<td>1-12/11-20/11-14/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-4-7-11-14<br />
</td>
<td>1-7/5-9/5-14/11-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-4-10-11-14<br />
</td>
<td>1-7/5-7/6-14/11-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-7-10-11-14<br />
</td>
<td>1-9/5-7/6-14/11-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-1-7-13-14<br />
</td>
<td>1-12/11-9/5-3/2-18/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-3-7-13-14<br />
</td>
<td>1-9/7-9/5-3/2-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-3-10-13-14<br />
</td>
<td>1-9/7-7/6-3/2-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-7-10-13-14<br />
</td>
<td>1-9/5-7/6-3/2-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-6-7-13-19<br />
</td>
<td>1-5/3-9/5-3/2-5/4<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-6-12-13-19<br />
</td>
<td>1-5/3-11/8-3/2-5/4<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-4-10-11-23<br />
</td>
<td>1-7/5-7/6-14/11-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-12-13-19-23<br />
</td>
<td>1-11/8-3/2-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-3-7-13-26<br />
</td>
<td>1-9/7-9/5-3/2-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-3-7-14-26<br />
</td>
<td>1-9/7-9/5-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-3-13-14-26<br />
</td>
<td>1-9/7-3/2-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-7-13-14-26<br />
</td>
<td>1-9/5-3/2-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-7-13-19-26<br />
</td>
<td>1-9/5-3/2-5/4-9/8<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-12-13-19-26<br />
</td>
<td>1-11/8-3/2-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-12-13-23-26<br />
</td>
<td>1-11/8-3/2-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-12-19-23-26<br />
</td>
<td>1-11/8-5/4-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-13-19-23-26<br />
</td>
<td>1-3/2-5/4-7/4-9/8<br />
</td>
<td>otonal<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>0-3-6-7-10-13<br />
</td>
<td>1-9/7-5/3-9/5-7/6-3/2<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-3-4-7-10-14<br />
</td>
<td>1-9/7-7/5-9/5-7/6-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-1-4-7-11-14<br />
</td>
<td>1-12/11-7/5-9/5-14/11-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-4-7-10-11-14<br />
</td>
<td>1-7/5-9/5-7/6-14/11-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-7-10-13-14<br />
</td>
<td>1-9/7-9/5-7/6-3/2-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-3-7-13-14-26<br />
</td>
<td>1-9/7-9/5-3/2-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-12-13-19-23-26<br />
</td>
<td>1-11/8-3/2-5/4-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
</table>
</body></html>