Chords of magic: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 288236008 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 288251266 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-22 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-22 23:42:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288251266</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/225, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic+, the nonce name Graham Breed's [[http://x31eq.com/temper/|Temperament Finder]] gives to it. Finally, anything requiring three independent commas among those discussed above is labeled magic. | Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/225, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic+, the nonce name Graham Breed's [[http://x31eq.com/temper/|Temperament Finder]] gives to it. Finally, anything requiring three independent commas among those discussed above is labeled magic. | ||
Magic has MOS of sizes 7, 10, 13, 16, 19 and 22 notes. | Magic has MOS of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven note MOS is not without a few harmonic resources, and the larger MOS do much better. | ||
=Triads= | =Triads= | ||
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Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/225, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic+, the nonce name Graham Breed's <a class="wiki_link_ext" href="http://x31eq.com/temper/" rel="nofollow">Temperament Finder</a> gives to it. Finally, anything requiring three independent commas among those discussed above is labeled magic.<br /> | Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/225, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic+, the nonce name Graham Breed's <a class="wiki_link_ext" href="http://x31eq.com/temper/" rel="nofollow">Temperament Finder</a> gives to it. Finally, anything requiring three independent commas among those discussed above is labeled magic.<br /> | ||
<br /> | <br /> | ||
Magic has MOS of sizes 7, 10, 13, 16, 19 and 22 notes. | Magic has MOS of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven note MOS is not without a few harmonic resources, and the larger MOS do much better.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1> | ||
Revision as of 23:42, 22 December 2011
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 2011-12-22 23:42:31 UTC.
- The original revision id was 288251266.
- 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 [[Magic|magic temperament]]. Typing the chords requires consideration of the fact that magic conflates 10/9 and 11/10 and so also 9/5 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 10/9 and 9/5. Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/225, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic+, the nonce name Graham Breed's [[http://x31eq.com/temper/|Temperament Finder]] gives to it. Finally, anything requiring three independent commas among those discussed above is labeled magic. Magic has MOS of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven note MOS is not without a few harmonic resources, and the larger MOS do much better. =Triads= || Number || Chord || Transversal || Type || || 1 || 0-1-2 || 1-5/4-14/9 || marvel || || 2 || 0-2-4 || 1-14/9-6/5 || sensamagic || || 3 || 0-1-5 || 1-5/4-3/2 || otonal || || 4 || 0-4-5 || 1-6/5-3/2 || utonal || || 5 || 0-2-7 || 1-14/9-7/6 || utonal || || 6 || 0-5-7 || 1-3/2-7/6 || otonal || || 7 || 0-1-8 || 1-5/4-16/11 || keenanismic || || 8 || 0-4-8 || 1-6/5-16/11 || ptolemismic || || 9 || 0-7-8 || 1-7/6-16/11 || keenanismic || || 10 || 0-1-9 || 1-5/4-20/11 || utonal || || 11 || 0-2-9 || 1-14/9-9/5 || sensamagic || || 12 || 0-4-9 || 1-6/5-9/5 || otonal || || 13 || 0-5-9 || 1-3/2-9/5 || utonal || || 14 || 0-7-9 || 1-7/6-9/5 || sensamagic || || 15 || 0-8-9 || 1-16/11-20/11 || otonal || || 16 || 0-1-10 || 1-5/4-9/8 || otonal || || 17 || 0-2-10 || 1-14/9-9/8 || pentacircle || || 18 || 0-5-10 || 1-3/2-9/8 || ambitonal || || 19 || 0-8-10 || 1-16/11-9/8 || pentacircle || || 20 || 0-9-10 || 1-9/5-9/8 || utonal || || 21 || 0-1-11 || 1-5/4-7/5 || marvel || || 22 || 0-2-11 || 1-14/9-7/5 || utonal || || 23 || 0-4-11 || 1-6/5-7/5 || otonal || || 24 || 0-7-11 || 1-7/6-7/5 || utonal || || 25 || 0-9-11 || 1-9/5-7/5 || otonal || || 26 || 0-10-11 || 1-9/8-7/5 || marvel || || 27 || 0-1-12 || 1-5/4-7/4 || otonal || || 28 || 0-2-12 || 1-14/9-7/4 || utonal || || 29 || 0-4-12 || 1-6/5-7/4 || keenanismic || || 30 || 0-5-12 || 1-3/2-7/4 || otonal || || 31 || 0-7-12 || 1-7/6-7/4 || utonal || || 32 || 0-8-12 || 1-16/11-7/4 || keenanismic || || 33 || 0-10-12 || 1-9/8-7/4 || otonal || || 34 || 0-11-12 || 1-7/5-7/4 || utonal || || 35 || 0-1-13 || 1-5/4-12/11 || keenanismic || || 36 || 0-2-13 || 1-14/9-12/11 || swetismic || || 37 || 0-4-13 || 1-6/5-12/11 || utonal || || 38 || 0-5-13 || 1-3/2-12/11 || utonal || || 39 || 0-8-13 || 1-16/11-12/11 || otonal || || 40 || 0-9-13 || 1-20/11-12/11 || otonal || || 41 || 0-11-13 || 1-7/5-12/11 || swetismic || || 42 || 0-12-13 || 1-7/4-12/11 || keenanismic || || 43 || 0-5-18 || 1-3/2-18/11 || utonal || || 44 || 0-7-18 || 1-7/6-18/11 || swetismic || || 45 || 0-8-18 || 1-16/11-18/11 || otonal || || 46 || 0-9-18 || 1-9/5-18/11 || utonal || || 47 || 0-10-18 || 1-9/8-18/11 || utonal || || 48 || 0-11-18 || 1-7/5-18/11 || swetismic || || 49 || 0-13-18 || 1-12/11-18/11 || otonal || || 50 || 0-2-20 || 1-14/9-14/11 || utonal || || 51 || 0-7-20 || 1-7/6-14/11 || utonal || || 52 || 0-8-20 || 1-16/11-14/11 || otonal || || 53 || 0-9-20 || 1-20/11-14/11 || otonal || || 54 || 0-10-20 || 1-9/8-14/11 || pentacircle || || 55 || 0-11-20 || 1-7/5-14/11 || utonal || || 56 || 0-12-20 || 1-7/4-14/11 || utonal || || 57 || 0-13-20 || 1-12/11-14/11 || otonal || || 58 || 0-18-20 || 1-18/11-14/11 || otonal || =Tetrads= || Number || Chord || Transversal || Type || || 1 || 0-1-2-9 || 1-5/4-14/9-9/5 || magic || || 2 || 0-2-4-9 || 1-14/9-6/5-9/5 || sensamagic || || 3 || 0-1-5-9 || 1-5/4-3/2-9/5 || ptolemismic || || 4 || 0-4-5-9 || 1-6/5-3/2-9/5 || ambitonal || || 5 || 0-2-7-9 || 1-14/9-7/6-9/5 || sensamagic || || 6 || 0-5-7-9 || 1-3/2-7/6-9/5 || sensamagic || || 7 || 0-1-8-9 || 1-5/4-16/11-9/5 || supermagic+ || || 8 || 0-4-8-9 || 1-6/5-16/11-9/5 || ptolemismic || || 9 || 0-7-8-9 || 1-7/6-16/11-9/5 || magic || || 10 || 0-1-2-10 || 1-5/4-14/9-9/8 || apollo || || 11 || 0-1-5-10 || 1-5/4-3/2-9/8 || otonal || || 12 || 0-1-8-10 || 1-5/4-16/11-9/8 || sensamagic11 || || 13 || 0-1-9-10 || 1-5/4-9/5-9/8 || ptolemismic || || 14 || 0-2-9-10 || 1-14/9-9/5-9/8 || sensamagic11 || || 15 || 0-5-9-10 || 1-3/2-9/5-9/8 || utonal || || 16 || 0-8-9-10 || 1-16/11-9/5-9/8 || apollo || || 17 || 0-1-2-11 || 1-5/4-14/9-7/5 || marvel || || 18 || 0-2-4-11 || 1-14/9-6/5-7/5 || sensamagic || || 19 || 0-2-7-11 || 1-14/9-7/6-7/5 || utonal || || 20 || 0-1-9-11 || 1-5/4-9/5-7/5 || apollo || || 21 || 0-2-9-11 || 1-14/9-9/5-7/5 || sensamagic || || 22 || 0-4-9-11 || 1-6/5-9/5-7/5 || otonal || || 23 || 0-7-9-11 || 1-7/6-9/5-7/5 || sensamagic || || 24 || 0-1-10-11 || 1-5/4-9/8-7/5 || marvel || || 25 || 0-2-10-11 || 1-14/9-9/8-7/5 || apollo || || 26 || 0-9-10-11 || 1-9/5-9/8-7/5 || marvel || || 27 || 0-1-2-12 || 1-5/4-14/9-7/4 || marvel || || 28 || 0-2-4-12 || 1-14/9-6/5-7/4 || sensamagic11 || || 29 || 0-1-5-12 || 1-5/4-3/2-7/4 || otonal || || 30 || 0-4-5-12 || 1-6/5-3/2-7/4 || keenanismic || || 31 || 0-2-7-12 || 1-14/9-7/6-7/4 || utonal || || 32 || 0-5-7-12 || 1-3/2-7/6-7/4 || ambitonal || || 33 || 0-1-8-12 || 1-5/4-16/11-7/4 || keenanismic || || 34 || 0-4-8-12 || 1-6/5-16/11-7/4 || supermagic+ || || 35 || 0-7-8-12 || 1-7/6-16/11-7/4 || keenanismic || || 36 || 0-1-10-12 || 1-5/4-9/8-7/4 || otonal || || 37 || 0-2-10-12 || 1-14/9-9/8-7/4 || pentacircle || || 38 || 0-5-10-12 || 1-3/2-9/8-7/4 || otonal || || 39 || 0-8-10-12 || 1-16/11-9/8-7/4 || sensamagic11 || || 40 || 0-1-11-12 || 1-5/4-7/5-7/4 || marvel || || 41 || 0-2-11-12 || 1-14/9-7/5-7/4 || utonal || || 42 || 0-4-11-12 || 1-6/5-7/5-7/4 || keenanismic || || 43 || 0-7-11-12 || 1-7/6-7/5-7/4 || utonal || || 44 || 0-10-11-12 || 1-9/8-7/5-7/4 || marvel || || 45 || 0-1-2-13 || 1-5/4-14/9-12/11 || unimarvel || || 46 || 0-2-4-13 || 1-14/9-6/5-12/11 || octarod || || 47 || 0-1-5-13 || 1-5/4-3/2-12/11 || keenanismic || || 48 || 0-4-5-13 || 1-6/5-3/2-12/11 || utonal || || 49 || 0-1-8-13 || 1-5/4-16/11-12/11 || keenanismic || || 50 || 0-4-8-13 || 1-6/5-16/11-12/11 || ptolemismic || || 51 || 0-1-9-13 || 1-5/4-9/5-12/11 || supermagic+ || || 52 || 0-2-9-13 || 1-14/9-9/5-12/11 || octarod || || 53 || 0-4-9-13 || 1-6/5-9/5-12/11 || ptolemismic || || 54 || 0-5-9-13 || 1-3/2-9/5-12/11 || ptolemismic || || 55 || 0-8-9-13 || 1-16/11-20/11-12/11 || otonal || || 56 || 0-1-11-13 || 1-5/4-7/5-12/11 || unimarvel || || 57 || 0-2-11-13 || 1-14/9-7/5-12/11 || swetismic || || 58 || 0-4-11-13 || 1-6/5-7/5-12/11 || octarod || || 59 || 0-9-11-13 || 1-9/5-7/5-12/11 || octarod || || 60 || 0-1-12-13 || 1-5/4-7/4-12/11 || keenanismic || || 61 || 0-2-12-13 || 1-14/9-7/4-12/11 || unimarvel || || 62 || 0-4-12-13 || 1-6/5-7/4-12/11 || supermagic+ || || 63 || 0-5-12-13 || 1-3/2-7/4-12/11 || keenanismic || || 64 || 0-8-12-13 || 1-16/11-7/4-12/11 || keenanismic || || 65 || 0-11-12-13 || 1-7/5-7/4-12/11 || unimarvel || || 66 || 0-5-7-18 || 1-3/2-7/6-18/11 || swetismic || || 67 || 0-7-8-18 || 1-7/6-16/11-18/11 || unimarvel || || 68 || 0-5-9-18 || 1-3/2-9/5-18/11 || utonal || || 69 || 0-7-9-18 || 1-7/6-9/5-18/11 || octarod || || 70 || 0-8-9-18 || 1-16/11-20/11-18/11 || otonal || || 71 || 0-5-10-18 || 1-3/2-9/8-18/11 || utonal || || 72 || 0-8-10-18 || 1-16/11-9/8-18/11 || pentacircle || || 73 || 0-9-10-18 || 1-9/5-9/8-18/11 || utonal || || 74 || 0-7-11-18 || 1-7/6-7/5-18/11 || swetismic || || 75 || 0-9-11-18 || 1-9/5-7/5-18/11 || octarod || || 76 || 0-10-11-18 || 1-9/8-7/5-18/11 || unimarvel || || 77 || 0-5-13-18 || 1-3/2-12/11-18/11 || ambitonal || || 78 || 0-8-13-18 || 1-16/11-12/11-18/11 || otonal || || 79 || 0-9-13-18 || 1-20/11-12/11-18/11 || otonal || || 80 || 0-11-13-18 || 1-7/5-12/11-18/11 || swetismic || || 81 || 0-2-7-20 || 1-14/9-7/6-14/11 || utonal || || 82 || 0-7-8-20 || 1-7/6-16/11-14/11 || keenanismic || || 83 || 0-2-9-20 || 1-14/9-9/5-14/11 || octarod || || 84 || 0-7-9-20 || 1-7/6-9/5-14/11 || octarod || || 85 || 0-8-9-20 || 1-16/11-20/11-14/11 || otonal || || 86 || 0-2-10-20 || 1-14/9-9/8-14/11 || pentacircle || || 87 || 0-8-10-20 || 1-16/11-9/8-14/11 || pentacircle || || 88 || 0-9-10-20 || 1-9/5-9/8-14/11 || apollo || || 89 || 0-2-11-20 || 1-14/9-7/5-14/11 || utonal || || 90 || 0-7-11-20 || 1-7/6-7/5-14/11 || utonal || || 91 || 0-9-11-20 || 1-9/5-7/5-14/11 || ptolemismic || || 92 || 0-10-11-20 || 1-9/8-7/5-14/11 || apollo || || 93 || 0-2-12-20 || 1-14/9-7/4-14/11 || utonal || || 94 || 0-7-12-20 || 1-7/6-7/4-14/11 || utonal || || 95 || 0-8-12-20 || 1-16/11-7/4-14/11 || keenanismic || || 96 || 0-10-12-20 || 1-9/8-7/4-14/11 || pentacircle || || 97 || 0-11-12-20 || 1-7/5-7/4-14/11 || utonal || || 98 || 0-2-13-20 || 1-14/9-12/11-14/11 || swetismic || || 99 || 0-8-13-20 || 1-16/11-12/11-14/11 || otonal || || 100 || 0-9-13-20 || 1-20/11-12/11-14/11 || otonal || || 101 || 0-11-13-20 || 1-7/5-12/11-14/11 || octarod || || 102 || 0-12-13-20 || 1-7/4-12/11-14/11 || keenanismic || || 103 || 0-7-18-20 || 1-7/6-18/11-14/11 || swetismic || || 104 || 0-8-18-20 || 1-16/11-18/11-14/11 || otonal || || 105 || 0-9-18-20 || 1-20/11-18/11-14/11 || otonal || || 106 || 0-10-18-20 || 1-9/8-18/11-14/11 || pentacircle || || 107 || 0-11-18-20 || 1-7/5-18/11-14/11 || octarod || || 108 || 0-13-18-20 || 1-12/11-18/11-14/11 || otonal || =Pentads= || Number || Chord || Transversal || Type || || 1 || 0-1-2-9-10 || 1-5/4-14/9-9/5-9/8 || magic || || 2 || 0-1-5-9-10 || 1-5/4-3/2-9/5-9/8 || ptolemismic || || 3 || 0-1-8-9-10 || 1-5/4-16/11-9/5-9/8 || magic || || 4 || 0-1-2-9-11 || 1-5/4-14/9-9/5-7/5 || magic || || 5 || 0-2-4-9-11 || 1-14/9-6/5-9/5-7/5 || sensamagic || || 6 || 0-2-7-9-11 || 1-14/9-7/6-9/5-7/5 || sensamagic || || 7 || 0-1-2-10-11 || 1-5/4-14/9-9/8-7/5 || apollo || || 8 || 0-1-9-10-11 || 1-5/4-9/5-9/8-7/5 || apollo || || 9 || 0-2-9-10-11 || 1-14/9-9/5-9/8-7/5 || magic || || 10 || 0-1-2-10-12 || 1-5/4-14/9-9/8-7/4 || apollo || || 11 || 0-1-5-10-12 || 1-5/4-3/2-9/8-7/4 || otonal || || 12 || 0-1-8-10-12 || 1-5/4-16/11-9/8-7/4 || sensamagic11 || || 13 || 0-1-2-11-12 || 1-5/4-14/9-7/5-7/4 || marvel || || 14 || 0-2-4-11-12 || 1-14/9-6/5-7/5-7/4 || sensamagic11 || || 15 || 0-2-7-11-12 || 1-14/9-7/6-7/5-7/4 || utonal || || 16 || 0-1-10-11-12 || 1-5/4-9/8-7/5-7/4 || marvel || || 17 || 0-2-10-11-12 || 1-14/9-9/8-7/5-7/4 || apollo || || 18 || 0-1-2-9-13 || 1-5/4-14/9-9/5-12/11 || magic || || 19 || 0-2-4-9-13 || 1-14/9-6/5-9/5-12/11 || octarod || || 20 || 0-1-5-9-13 || 1-5/4-3/2-9/5-12/11 || supermagic+ || || 21 || 0-4-5-9-13 || 1-6/5-3/2-9/5-12/11 || ptolemismic || || 22 || 0-1-8-9-13 || 1-5/4-16/11-9/5-12/11 || supermagic+ || || 23 || 0-4-8-9-13 || 1-6/5-16/11-9/5-12/11 || ptolemismic || || 24 || 0-1-2-11-13 || 1-5/4-14/9-7/5-12/11 || unimarvel || || 25 || 0-2-4-11-13 || 1-14/9-6/5-7/5-12/11 || octarod || || 26 || 0-1-9-11-13 || 1-5/4-9/5-7/5-12/11 || magic || || 27 || 0-2-9-11-13 || 1-14/9-9/5-7/5-12/11 || octarod || || 28 || 0-4-9-11-13 || 1-6/5-9/5-7/5-12/11 || octarod || || 29 || 0-1-2-12-13 || 1-5/4-14/9-7/4-12/11 || unimarvel || || 30 || 0-2-4-12-13 || 1-14/9-6/5-7/4-12/11 || magic || || 31 || 0-1-5-12-13 || 1-5/4-3/2-7/4-12/11 || keenanismic || || 32 || 0-4-5-12-13 || 1-6/5-3/2-7/4-12/11 || supermagic+ || || 33 || 0-1-8-12-13 || 1-5/4-16/11-7/4-12/11 || keenanismic || || 34 || 0-4-8-12-13 || 1-6/5-16/11-7/4-12/11 || supermagic+ || || 35 || 0-1-11-12-13 || 1-5/4-7/5-7/4-12/11 || unimarvel || || 36 || 0-2-11-12-13 || 1-14/9-7/5-7/4-12/11 || unimarvel || || 37 || 0-4-11-12-13 || 1-6/5-7/5-7/4-12/11 || magic || || 38 || 0-5-7-9-18 || 1-3/2-7/6-9/5-18/11 || octarod || || 39 || 0-7-8-9-18 || 1-7/6-16/11-9/5-18/11 || magic || || 40 || 0-5-9-10-18 || 1-3/2-9/5-9/8-18/11 || utonal || || 41 || 0-8-9-10-18 || 1-16/11-9/5-9/8-18/11 || apollo || || 42 || 0-7-9-11-18 || 1-7/6-9/5-7/5-18/11 || octarod || || 43 || 0-9-10-11-18 || 1-9/5-9/8-7/5-18/11 || magic || || 44 || 0-5-9-13-18 || 1-3/2-9/5-12/11-18/11 || ptolemismic || || 45 || 0-8-9-13-18 || 1-16/11-20/11-12/11-18/11 || otonal || || 46 || 0-9-11-13-18 || 1-9/5-7/5-12/11-18/11 || octarod || || 47 || 0-2-7-9-20 || 1-14/9-7/6-9/5-14/11 || octarod || || 48 || 0-7-8-9-20 || 1-7/6-16/11-9/5-14/11 || magic || || 49 || 0-2-9-10-20 || 1-14/9-9/5-9/8-14/11 || magic || || 50 || 0-8-9-10-20 || 1-16/11-9/5-9/8-14/11 || apollo || || 51 || 0-2-7-11-20 || 1-14/9-7/6-7/5-14/11 || utonal || || 52 || 0-2-9-11-20 || 1-14/9-9/5-7/5-14/11 || octarod || || 53 || 0-7-9-11-20 || 1-7/6-9/5-7/5-14/11 || octarod || || 54 || 0-2-10-11-20 || 1-14/9-9/8-7/5-14/11 || apollo || || 55 || 0-9-10-11-20 || 1-9/5-9/8-7/5-14/11 || apollo || || 56 || 0-2-7-12-20 || 1-14/9-7/6-7/4-14/11 || utonal || || 57 || 0-7-8-12-20 || 1-7/6-16/11-7/4-14/11 || keenanismic || || 58 || 0-2-10-12-20 || 1-14/9-9/8-7/4-14/11 || pentacircle || || 59 || 0-8-10-12-20 || 1-16/11-9/8-7/4-14/11 || sensamagic11 || || 60 || 0-2-11-12-20 || 1-14/9-7/5-7/4-14/11 || utonal || || 61 || 0-7-11-12-20 || 1-7/6-7/5-7/4-14/11 || utonal || || 62 || 0-10-11-12-20 || 1-9/8-7/5-7/4-14/11 || apollo || || 63 || 0-2-9-13-20 || 1-14/9-9/5-12/11-14/11 || octarod || || 64 || 0-8-9-13-20 || 1-16/11-20/11-12/11-14/11 || otonal || || 65 || 0-2-11-13-20 || 1-14/9-7/5-12/11-14/11 || octarod || || 66 || 0-9-11-13-20 || 1-9/5-7/5-12/11-14/11 || octarod || || 67 || 0-2-12-13-20 || 1-14/9-7/4-12/11-14/11 || unimarvel || || 68 || 0-8-12-13-20 || 1-16/11-7/4-12/11-14/11 || keenanismic || || 69 || 0-11-12-13-20 || 1-7/5-7/4-12/11-14/11 || magic || || 70 || 0-7-8-18-20 || 1-7/6-16/11-18/11-14/11 || unimarvel || || 71 || 0-7-9-18-20 || 1-7/6-9/5-18/11-14/11 || octarod || || 72 || 0-8-9-18-20 || 1-16/11-20/11-18/11-14/11 || otonal || || 73 || 0-8-10-18-20 || 1-16/11-9/8-18/11-14/11 || pentacircle || || 74 || 0-9-10-18-20 || 1-9/5-9/8-18/11-14/11 || apollo || || 75 || 0-7-11-18-20 || 1-7/6-7/5-18/11-14/11 || octarod || || 76 || 0-9-11-18-20 || 1-9/5-7/5-18/11-14/11 || octarod || || 77 || 0-10-11-18-20 || 1-9/8-7/5-18/11-14/11 || magic || || 78 || 0-8-13-18-20 || 1-16/11-12/11-18/11-14/11 || otonal || || 79 || 0-9-13-18-20 || 1-20/11-12/11-18/11-14/11 || otonal || || 80 || 0-11-13-18-20 || 1-7/5-12/11-18/11-14/11 || octarod || =Hexads= || Number || Chord || Transversal || Type || || 1 || 0-1-2-9-10-11 || 1-5/4-14/9-9/5-9/8-7/5 || magic || || 2 || 0-1-2-10-11-12 || 1-5/4-14/9-9/8-7/5-7/4 || apollo || || 3 || 0-1-2-9-11-13 || 1-5/4-14/9-9/5-7/5-12/11 || magic || || 4 || 0-2-4-9-11-13 || 1-14/9-6/5-9/5-7/5-12/11 || octarod || || 5 || 0-1-2-11-12-13 || 1-5/4-14/9-7/5-7/4-12/11 || unimarvel || || 6 || 0-2-4-11-12-13 || 1-14/9-6/5-7/5-7/4-12/11 || magic || || 7 || 0-2-7-9-11-20 || 1-14/9-7/6-9/5-7/5-14/11 || octarod || || 8 || 0-2-9-10-11-20 || 1-14/9-9/5-9/8-7/5-14/11 || magic || || 9 || 0-2-7-11-12-20 || 1-14/9-7/6-7/5-7/4-14/11 || utonal || || 10 || 0-2-10-11-12-20 || 1-14/9-9/8-7/5-7/4-14/11 || apollo || || 11 || 0-2-9-11-13-20 || 1-14/9-9/5-7/5-12/11-14/11 || octarod || || 12 || 0-2-11-12-13-20 || 1-14/9-7/5-7/4-12/11-14/11 || magic || || 13 || 0-7-8-9-18-20 || 1-7/6-16/11-9/5-18/11-14/11 || magic || || 14 || 0-8-9-10-18-20 || 1-16/11-9/5-9/8-18/11-14/11 || apollo || || 15 || 0-7-9-11-18-20 || 1-7/6-9/5-7/5-18/11-14/11 || octarod || || 16 || 0-9-10-11-18-20 || 1-9/5-9/8-7/5-18/11-14/11 || magic || || 17 || 0-8-9-13-18-20 || 1-16/11-20/11-12/11-18/11-14/11 || otonal || || 18 || 0-9-11-13-18-20 || 1-9/5-7/5-12/11-18/11-14/11 || octarod ||
Original HTML content:
<html><head><title>Chords of magic</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="/Magic">magic temperament</a>. Typing the chords requires consideration of the fact that magic conflates 10/9 and 11/10 and so also 9/5 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 10/9 and 9/5.<br />
<br />
Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/225, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic+, the nonce name Graham Breed's <a class="wiki_link_ext" href="http://x31eq.com/temper/" rel="nofollow">Temperament Finder</a> gives to it. Finally, anything requiring three independent commas among those discussed above is labeled magic.<br />
<br />
Magic has MOS of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven note MOS is not without a few harmonic resources, and the larger MOS do much better.<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>0-1-2<br />
</td>
<td>1-5/4-14/9<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-4<br />
</td>
<td>1-14/9-6/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-1-5<br />
</td>
<td>1-5/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-4-5<br />
</td>
<td>1-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-2-7<br />
</td>
<td>1-14/9-7/6<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-5-7<br />
</td>
<td>1-3/2-7/6<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-1-8<br />
</td>
<td>1-5/4-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-4-8<br />
</td>
<td>1-6/5-16/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-7-8<br />
</td>
<td>1-7/6-16/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-1-9<br />
</td>
<td>1-5/4-20/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-2-9<br />
</td>
<td>1-14/9-9/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-4-9<br />
</td>
<td>1-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-5-9<br />
</td>
<td>1-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-7-9<br />
</td>
<td>1-7/6-9/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-8-9<br />
</td>
<td>1-16/11-20/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-1-10<br />
</td>
<td>1-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-2-10<br />
</td>
<td>1-14/9-9/8<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-5-10<br />
</td>
<td>1-3/2-9/8<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-8-10<br />
</td>
<td>1-16/11-9/8<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-9-10<br />
</td>
<td>1-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-1-11<br />
</td>
<td>1-5/4-7/5<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-2-11<br />
</td>
<td>1-14/9-7/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-4-11<br />
</td>
<td>1-6/5-7/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-7-11<br />
</td>
<td>1-7/6-7/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-9-11<br />
</td>
<td>1-9/5-7/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-10-11<br />
</td>
<td>1-9/8-7/5<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-1-12<br />
</td>
<td>1-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-2-12<br />
</td>
<td>1-14/9-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-4-12<br />
</td>
<td>1-6/5-7/4<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-5-12<br />
</td>
<td>1-3/2-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-7-12<br />
</td>
<td>1-7/6-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-8-12<br />
</td>
<td>1-16/11-7/4<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-10-12<br />
</td>
<td>1-9/8-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-11-12<br />
</td>
<td>1-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-1-13<br />
</td>
<td>1-5/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-2-13<br />
</td>
<td>1-14/9-12/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-4-13<br />
</td>
<td>1-6/5-12/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-5-13<br />
</td>
<td>1-3/2-12/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-8-13<br />
</td>
<td>1-16/11-12/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-9-13<br />
</td>
<td>1-20/11-12/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-11-13<br />
</td>
<td>1-7/5-12/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-12-13<br />
</td>
<td>1-7/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-5-18<br />
</td>
<td>1-3/2-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-7-18<br />
</td>
<td>1-7/6-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-8-18<br />
</td>
<td>1-16/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-9-18<br />
</td>
<td>1-9/5-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-10-18<br />
</td>
<td>1-9/8-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-11-18<br />
</td>
<td>1-7/5-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-13-18<br />
</td>
<td>1-12/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-2-20<br />
</td>
<td>1-14/9-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-7-20<br />
</td>
<td>1-7/6-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-8-20<br />
</td>
<td>1-16/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-9-20<br />
</td>
<td>1-20/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-10-20<br />
</td>
<td>1-9/8-14/11<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-11-20<br />
</td>
<td>1-7/5-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-12-20<br />
</td>
<td>1-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-13-20<br />
</td>
<td>1-12/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-18-20<br />
</td>
<td>1-18/11-14/11<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>0-1-2-9<br />
</td>
<td>1-5/4-14/9-9/5<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-4-9<br />
</td>
<td>1-14/9-6/5-9/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-1-5-9<br />
</td>
<td>1-5/4-3/2-9/5<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-4-5-9<br />
</td>
<td>1-6/5-3/2-9/5<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-2-7-9<br />
</td>
<td>1-14/9-7/6-9/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-5-7-9<br />
</td>
<td>1-3/2-7/6-9/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-1-8-9<br />
</td>
<td>1-5/4-16/11-9/5<br />
</td>
<td>supermagic+<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-4-8-9<br />
</td>
<td>1-6/5-16/11-9/5<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-7-8-9<br />
</td>
<td>1-7/6-16/11-9/5<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-1-2-10<br />
</td>
<td>1-5/4-14/9-9/8<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-1-5-10<br />
</td>
<td>1-5/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-1-8-10<br />
</td>
<td>1-5/4-16/11-9/8<br />
</td>
<td>sensamagic11<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-1-9-10<br />
</td>
<td>1-5/4-9/5-9/8<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-2-9-10<br />
</td>
<td>1-14/9-9/5-9/8<br />
</td>
<td>sensamagic11<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-5-9-10<br />
</td>
<td>1-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-8-9-10<br />
</td>
<td>1-16/11-9/5-9/8<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-1-2-11<br />
</td>
<td>1-5/4-14/9-7/5<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-2-4-11<br />
</td>
<td>1-14/9-6/5-7/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-2-7-11<br />
</td>
<td>1-14/9-7/6-7/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-1-9-11<br />
</td>
<td>1-5/4-9/5-7/5<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-2-9-11<br />
</td>
<td>1-14/9-9/5-7/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-4-9-11<br />
</td>
<td>1-6/5-9/5-7/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-7-9-11<br />
</td>
<td>1-7/6-9/5-7/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-1-10-11<br />
</td>
<td>1-5/4-9/8-7/5<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-2-10-11<br />
</td>
<td>1-14/9-9/8-7/5<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-9-10-11<br />
</td>
<td>1-9/5-9/8-7/5<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-1-2-12<br />
</td>
<td>1-5/4-14/9-7/4<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-2-4-12<br />
</td>
<td>1-14/9-6/5-7/4<br />
</td>
<td>sensamagic11<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-1-5-12<br />
</td>
<td>1-5/4-3/2-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-4-5-12<br />
</td>
<td>1-6/5-3/2-7/4<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-2-7-12<br />
</td>
<td>1-14/9-7/6-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-5-7-12<br />
</td>
<td>1-3/2-7/6-7/4<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-1-8-12<br />
</td>
<td>1-5/4-16/11-7/4<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-4-8-12<br />
</td>
<td>1-6/5-16/11-7/4<br />
</td>
<td>supermagic+<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-7-8-12<br />
</td>
<td>1-7/6-16/11-7/4<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-1-10-12<br />
</td>
<td>1-5/4-9/8-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-2-10-12<br />
</td>
<td>1-14/9-9/8-7/4<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-5-10-12<br />
</td>
<td>1-3/2-9/8-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-8-10-12<br />
</td>
<td>1-16/11-9/8-7/4<br />
</td>
<td>sensamagic11<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-1-11-12<br />
</td>
<td>1-5/4-7/5-7/4<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-2-11-12<br />
</td>
<td>1-14/9-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-4-11-12<br />
</td>
<td>1-6/5-7/5-7/4<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-7-11-12<br />
</td>
<td>1-7/6-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-10-11-12<br />
</td>
<td>1-9/8-7/5-7/4<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-1-2-13<br />
</td>
<td>1-5/4-14/9-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-2-4-13<br />
</td>
<td>1-14/9-6/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-1-5-13<br />
</td>
<td>1-5/4-3/2-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-4-5-13<br />
</td>
<td>1-6/5-3/2-12/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-1-8-13<br />
</td>
<td>1-5/4-16/11-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-4-8-13<br />
</td>
<td>1-6/5-16/11-12/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-1-9-13<br />
</td>
<td>1-5/4-9/5-12/11<br />
</td>
<td>supermagic+<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-2-9-13<br />
</td>
<td>1-14/9-9/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-4-9-13<br />
</td>
<td>1-6/5-9/5-12/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-5-9-13<br />
</td>
<td>1-3/2-9/5-12/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-8-9-13<br />
</td>
<td>1-16/11-20/11-12/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-1-11-13<br />
</td>
<td>1-5/4-7/5-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-2-11-13<br />
</td>
<td>1-14/9-7/5-12/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-4-11-13<br />
</td>
<td>1-6/5-7/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-9-11-13<br />
</td>
<td>1-9/5-7/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-1-12-13<br />
</td>
<td>1-5/4-7/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-2-12-13<br />
</td>
<td>1-14/9-7/4-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-4-12-13<br />
</td>
<td>1-6/5-7/4-12/11<br />
</td>
<td>supermagic+<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-5-12-13<br />
</td>
<td>1-3/2-7/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-8-12-13<br />
</td>
<td>1-16/11-7/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-11-12-13<br />
</td>
<td>1-7/5-7/4-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td>0-5-7-18<br />
</td>
<td>1-3/2-7/6-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>67<br />
</td>
<td>0-7-8-18<br />
</td>
<td>1-7/6-16/11-18/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>68<br />
</td>
<td>0-5-9-18<br />
</td>
<td>1-3/2-9/5-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>69<br />
</td>
<td>0-7-9-18<br />
</td>
<td>1-7/6-9/5-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>70<br />
</td>
<td>0-8-9-18<br />
</td>
<td>1-16/11-20/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>71<br />
</td>
<td>0-5-10-18<br />
</td>
<td>1-3/2-9/8-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>72<br />
</td>
<td>0-8-10-18<br />
</td>
<td>1-16/11-9/8-18/11<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>73<br />
</td>
<td>0-9-10-18<br />
</td>
<td>1-9/5-9/8-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>74<br />
</td>
<td>0-7-11-18<br />
</td>
<td>1-7/6-7/5-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>75<br />
</td>
<td>0-9-11-18<br />
</td>
<td>1-9/5-7/5-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>76<br />
</td>
<td>0-10-11-18<br />
</td>
<td>1-9/8-7/5-18/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>77<br />
</td>
<td>0-5-13-18<br />
</td>
<td>1-3/2-12/11-18/11<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>78<br />
</td>
<td>0-8-13-18<br />
</td>
<td>1-16/11-12/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>79<br />
</td>
<td>0-9-13-18<br />
</td>
<td>1-20/11-12/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>80<br />
</td>
<td>0-11-13-18<br />
</td>
<td>1-7/5-12/11-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>81<br />
</td>
<td>0-2-7-20<br />
</td>
<td>1-14/9-7/6-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>82<br />
</td>
<td>0-7-8-20<br />
</td>
<td>1-7/6-16/11-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>83<br />
</td>
<td>0-2-9-20<br />
</td>
<td>1-14/9-9/5-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>84<br />
</td>
<td>0-7-9-20<br />
</td>
<td>1-7/6-9/5-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>85<br />
</td>
<td>0-8-9-20<br />
</td>
<td>1-16/11-20/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>86<br />
</td>
<td>0-2-10-20<br />
</td>
<td>1-14/9-9/8-14/11<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>87<br />
</td>
<td>0-8-10-20<br />
</td>
<td>1-16/11-9/8-14/11<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>88<br />
</td>
<td>0-9-10-20<br />
</td>
<td>1-9/5-9/8-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>89<br />
</td>
<td>0-2-11-20<br />
</td>
<td>1-14/9-7/5-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>90<br />
</td>
<td>0-7-11-20<br />
</td>
<td>1-7/6-7/5-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>91<br />
</td>
<td>0-9-11-20<br />
</td>
<td>1-9/5-7/5-14/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>92<br />
</td>
<td>0-10-11-20<br />
</td>
<td>1-9/8-7/5-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>93<br />
</td>
<td>0-2-12-20<br />
</td>
<td>1-14/9-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>94<br />
</td>
<td>0-7-12-20<br />
</td>
<td>1-7/6-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>95<br />
</td>
<td>0-8-12-20<br />
</td>
<td>1-16/11-7/4-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>96<br />
</td>
<td>0-10-12-20<br />
</td>
<td>1-9/8-7/4-14/11<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>97<br />
</td>
<td>0-11-12-20<br />
</td>
<td>1-7/5-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>98<br />
</td>
<td>0-2-13-20<br />
</td>
<td>1-14/9-12/11-14/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>99<br />
</td>
<td>0-8-13-20<br />
</td>
<td>1-16/11-12/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>100<br />
</td>
<td>0-9-13-20<br />
</td>
<td>1-20/11-12/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>101<br />
</td>
<td>0-11-13-20<br />
</td>
<td>1-7/5-12/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>102<br />
</td>
<td>0-12-13-20<br />
</td>
<td>1-7/4-12/11-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>103<br />
</td>
<td>0-7-18-20<br />
</td>
<td>1-7/6-18/11-14/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>104<br />
</td>
<td>0-8-18-20<br />
</td>
<td>1-16/11-18/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>105<br />
</td>
<td>0-9-18-20<br />
</td>
<td>1-20/11-18/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>106<br />
</td>
<td>0-10-18-20<br />
</td>
<td>1-9/8-18/11-14/11<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>107<br />
</td>
<td>0-11-18-20<br />
</td>
<td>1-7/5-18/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>108<br />
</td>
<td>0-13-18-20<br />
</td>
<td>1-12/11-18/11-14/11<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>0-1-2-9-10<br />
</td>
<td>1-5/4-14/9-9/5-9/8<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-1-5-9-10<br />
</td>
<td>1-5/4-3/2-9/5-9/8<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-1-8-9-10<br />
</td>
<td>1-5/4-16/11-9/5-9/8<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-1-2-9-11<br />
</td>
<td>1-5/4-14/9-9/5-7/5<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-2-4-9-11<br />
</td>
<td>1-14/9-6/5-9/5-7/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-2-7-9-11<br />
</td>
<td>1-14/9-7/6-9/5-7/5<br />
</td>
<td>sensamagic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-1-2-10-11<br />
</td>
<td>1-5/4-14/9-9/8-7/5<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-1-9-10-11<br />
</td>
<td>1-5/4-9/5-9/8-7/5<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-2-9-10-11<br />
</td>
<td>1-14/9-9/5-9/8-7/5<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-1-2-10-12<br />
</td>
<td>1-5/4-14/9-9/8-7/4<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-1-5-10-12<br />
</td>
<td>1-5/4-3/2-9/8-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-1-8-10-12<br />
</td>
<td>1-5/4-16/11-9/8-7/4<br />
</td>
<td>sensamagic11<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-1-2-11-12<br />
</td>
<td>1-5/4-14/9-7/5-7/4<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-2-4-11-12<br />
</td>
<td>1-14/9-6/5-7/5-7/4<br />
</td>
<td>sensamagic11<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-2-7-11-12<br />
</td>
<td>1-14/9-7/6-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-1-10-11-12<br />
</td>
<td>1-5/4-9/8-7/5-7/4<br />
</td>
<td>marvel<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-2-10-11-12<br />
</td>
<td>1-14/9-9/8-7/5-7/4<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-1-2-9-13<br />
</td>
<td>1-5/4-14/9-9/5-12/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-2-4-9-13<br />
</td>
<td>1-14/9-6/5-9/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-1-5-9-13<br />
</td>
<td>1-5/4-3/2-9/5-12/11<br />
</td>
<td>supermagic+<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-4-5-9-13<br />
</td>
<td>1-6/5-3/2-9/5-12/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-1-8-9-13<br />
</td>
<td>1-5/4-16/11-9/5-12/11<br />
</td>
<td>supermagic+<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-4-8-9-13<br />
</td>
<td>1-6/5-16/11-9/5-12/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-1-2-11-13<br />
</td>
<td>1-5/4-14/9-7/5-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-2-4-11-13<br />
</td>
<td>1-14/9-6/5-7/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-1-9-11-13<br />
</td>
<td>1-5/4-9/5-7/5-12/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-2-9-11-13<br />
</td>
<td>1-14/9-9/5-7/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-4-9-11-13<br />
</td>
<td>1-6/5-9/5-7/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-1-2-12-13<br />
</td>
<td>1-5/4-14/9-7/4-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-2-4-12-13<br />
</td>
<td>1-14/9-6/5-7/4-12/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-1-5-12-13<br />
</td>
<td>1-5/4-3/2-7/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-4-5-12-13<br />
</td>
<td>1-6/5-3/2-7/4-12/11<br />
</td>
<td>supermagic+<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-1-8-12-13<br />
</td>
<td>1-5/4-16/11-7/4-12/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-4-8-12-13<br />
</td>
<td>1-6/5-16/11-7/4-12/11<br />
</td>
<td>supermagic+<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-1-11-12-13<br />
</td>
<td>1-5/4-7/5-7/4-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-2-11-12-13<br />
</td>
<td>1-14/9-7/5-7/4-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-4-11-12-13<br />
</td>
<td>1-6/5-7/5-7/4-12/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-5-7-9-18<br />
</td>
<td>1-3/2-7/6-9/5-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-7-8-9-18<br />
</td>
<td>1-7/6-16/11-9/5-18/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-5-9-10-18<br />
</td>
<td>1-3/2-9/5-9/8-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-8-9-10-18<br />
</td>
<td>1-16/11-9/5-9/8-18/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-7-9-11-18<br />
</td>
<td>1-7/6-9/5-7/5-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-9-10-11-18<br />
</td>
<td>1-9/5-9/8-7/5-18/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-5-9-13-18<br />
</td>
<td>1-3/2-9/5-12/11-18/11<br />
</td>
<td>ptolemismic<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-8-9-13-18<br />
</td>
<td>1-16/11-20/11-12/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-9-11-13-18<br />
</td>
<td>1-9/5-7/5-12/11-18/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-2-7-9-20<br />
</td>
<td>1-14/9-7/6-9/5-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-7-8-9-20<br />
</td>
<td>1-7/6-16/11-9/5-14/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-2-9-10-20<br />
</td>
<td>1-14/9-9/5-9/8-14/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-8-9-10-20<br />
</td>
<td>1-16/11-9/5-9/8-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-2-7-11-20<br />
</td>
<td>1-14/9-7/6-7/5-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-2-9-11-20<br />
</td>
<td>1-14/9-9/5-7/5-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-7-9-11-20<br />
</td>
<td>1-7/6-9/5-7/5-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-2-10-11-20<br />
</td>
<td>1-14/9-9/8-7/5-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-9-10-11-20<br />
</td>
<td>1-9/5-9/8-7/5-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-2-7-12-20<br />
</td>
<td>1-14/9-7/6-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-7-8-12-20<br />
</td>
<td>1-7/6-16/11-7/4-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-2-10-12-20<br />
</td>
<td>1-14/9-9/8-7/4-14/11<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-8-10-12-20<br />
</td>
<td>1-16/11-9/8-7/4-14/11<br />
</td>
<td>sensamagic11<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-2-11-12-20<br />
</td>
<td>1-14/9-7/5-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-7-11-12-20<br />
</td>
<td>1-7/6-7/5-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-10-11-12-20<br />
</td>
<td>1-9/8-7/5-7/4-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-2-9-13-20<br />
</td>
<td>1-14/9-9/5-12/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-8-9-13-20<br />
</td>
<td>1-16/11-20/11-12/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-2-11-13-20<br />
</td>
<td>1-14/9-7/5-12/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td>0-9-11-13-20<br />
</td>
<td>1-9/5-7/5-12/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>67<br />
</td>
<td>0-2-12-13-20<br />
</td>
<td>1-14/9-7/4-12/11-14/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>68<br />
</td>
<td>0-8-12-13-20<br />
</td>
<td>1-16/11-7/4-12/11-14/11<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>69<br />
</td>
<td>0-11-12-13-20<br />
</td>
<td>1-7/5-7/4-12/11-14/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>70<br />
</td>
<td>0-7-8-18-20<br />
</td>
<td>1-7/6-16/11-18/11-14/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>71<br />
</td>
<td>0-7-9-18-20<br />
</td>
<td>1-7/6-9/5-18/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>72<br />
</td>
<td>0-8-9-18-20<br />
</td>
<td>1-16/11-20/11-18/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>73<br />
</td>
<td>0-8-10-18-20<br />
</td>
<td>1-16/11-9/8-18/11-14/11<br />
</td>
<td>pentacircle<br />
</td>
</tr>
<tr>
<td>74<br />
</td>
<td>0-9-10-18-20<br />
</td>
<td>1-9/5-9/8-18/11-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>75<br />
</td>
<td>0-7-11-18-20<br />
</td>
<td>1-7/6-7/5-18/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>76<br />
</td>
<td>0-9-11-18-20<br />
</td>
<td>1-9/5-7/5-18/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>77<br />
</td>
<td>0-10-11-18-20<br />
</td>
<td>1-9/8-7/5-18/11-14/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>78<br />
</td>
<td>0-8-13-18-20<br />
</td>
<td>1-16/11-12/11-18/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>79<br />
</td>
<td>0-9-13-18-20<br />
</td>
<td>1-20/11-12/11-18/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>80<br />
</td>
<td>0-11-13-18-20<br />
</td>
<td>1-7/5-12/11-18/11-14/11<br />
</td>
<td>octarod<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>0-1-2-9-10-11<br />
</td>
<td>1-5/4-14/9-9/5-9/8-7/5<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-1-2-10-11-12<br />
</td>
<td>1-5/4-14/9-9/8-7/5-7/4<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-1-2-9-11-13<br />
</td>
<td>1-5/4-14/9-9/5-7/5-12/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-2-4-9-11-13<br />
</td>
<td>1-14/9-6/5-9/5-7/5-12/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-1-2-11-12-13<br />
</td>
<td>1-5/4-14/9-7/5-7/4-12/11<br />
</td>
<td>unimarvel<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-2-4-11-12-13<br />
</td>
<td>1-14/9-6/5-7/5-7/4-12/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-2-7-9-11-20<br />
</td>
<td>1-14/9-7/6-9/5-7/5-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-2-9-10-11-20<br />
</td>
<td>1-14/9-9/5-9/8-7/5-14/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-2-7-11-12-20<br />
</td>
<td>1-14/9-7/6-7/5-7/4-14/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-2-10-11-12-20<br />
</td>
<td>1-14/9-9/8-7/5-7/4-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-2-9-11-13-20<br />
</td>
<td>1-14/9-9/5-7/5-12/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-2-11-12-13-20<br />
</td>
<td>1-14/9-7/5-7/4-12/11-14/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-7-8-9-18-20<br />
</td>
<td>1-7/6-16/11-9/5-18/11-14/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-8-9-10-18-20<br />
</td>
<td>1-16/11-9/5-9/8-18/11-14/11<br />
</td>
<td>apollo<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-7-9-11-18-20<br />
</td>
<td>1-7/6-9/5-7/5-18/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-9-10-11-18-20<br />
</td>
<td>1-9/5-9/8-7/5-18/11-14/11<br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-8-9-13-18-20<br />
</td>
<td>1-16/11-20/11-12/11-18/11-14/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-9-11-13-18-20<br />
</td>
<td>1-9/5-7/5-12/11-18/11-14/11<br />
</td>
<td>octarod<br />
</td>
</tr>
</table>
</body></html>