Harry/Chords: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 288421240 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 288485796 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-26 07:40:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288485796</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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The normal mapping for harry is har = [<2 4 7 7 9|, <0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = <2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column. | The normal mapping for harry is har = [<2 4 7 7 9|, <0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = <2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column. | ||
Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting. | Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting. There is essentially no advantage in accuracy to optimizing for [[Breed family#Jove, aka Wonder|jove temperament]] rather than harry; in addition to what jove tempers out, harry tempers out 4000/3993. However, POTE tuning, for example, shrinks the three cents of this comma to -0.0827 cents, which is hardly worth worrying about. Hence harry is one way of exploring and organizing the chords of jove, which are therefore also listed below. | ||
=Triads= | =Triads= | ||
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The normal mapping for harry is har = [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = &lt;2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. Under &quot;Chord&quot; is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.<br /> | The normal mapping for harry is har = [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = &lt;2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. Under &quot;Chord&quot; is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.<br /> | ||
<br /> | <br /> | ||
Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting.<br /> | Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting. There is essentially no advantage in accuracy to optimizing for <a class="wiki_link" href="/Breed%20family#Jove, aka Wonder">jove temperament</a> rather than harry; in addition to what jove tempers out, harry tempers out 4000/3993. However, POTE tuning, for example, shrinks the three cents of this comma to -0.0827 cents, which is hardly worth worrying about. Hence harry is one way of exploring and organizing the chords of jove, which are therefore also listed below.<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 07:40, 26 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 2011-12-26 07:40:26 UTC.
- The original revision id was 288485796.
- 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 [[Gravity family#Harry|harry temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismicmic, and by 243/242 rastmic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove. The normal mapping for harry is har = [<2 4 7 7 9|, <0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = <2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column. Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting. There is essentially no advantage in accuracy to optimizing for [[Breed family#Jove, aka Wonder|jove temperament]] rather than harry; in addition to what jove tempers out, harry tempers out 4000/3993. However, POTE tuning, for example, shrinks the three cents of this comma to -0.0827 cents, which is hardly worth worrying about. Hence harry is one way of exploring and organizing the chords of jove, which are therefore also listed below. =Triads= || Number || Chord || Transversal || Type || Complexity || || 1 || 0-201-401 || 1-9/7-7/6 || swetismic || 8 || || 2 || 0-202-401 || 1-20/11-7/6 || swetismic || 8 || || 3 || 0-202-501 || 1-20/11-10/9 || utonal || 10 || || 4 || 0-301-501 || 1-11/9-10/9 || otonal || 10 || || 5 || 0-201-502 || 1-9/7-11/7 || otonal || 10 || || 6 || 0-301-502 || 1-11/9-11/7 || utonal || 10 || || 7 || 0-201-602 || 1-9/7-3/2 || utonal || 12 || || 8 || 0-301-602 || 1-11/9-3/2 || rastmic || 12 || || 9 || 0-401-602 || 1-7/6-3/2 || otonal || 12 || || 10 || 0-201-702 || 1-9/7-10/7 || otonal || 14 || || 11 || 0-202-702 || 1-20/11-10/7 || utonal || 14 || || 12 || 0-301-702 || 1-11/9-10/7 || swetismic || 14 || || 13 || 0-401-702 || 1-7/6-10/7 || swetismic || 14 || || 14 || 0-501-702 || 1-10/9-10/7 || utonal || 14 || || 15 || 0-502-702 || 1-11/7-10/7 || otonal || 14 || || 16 || 0-201-903 || 1-9/7-11/6 || swetismic || 18 || || 17 || 0-301-903 || 1-11/9-11/6 || utonal || 18 || || 18 || 0-401-903 || 1-7/6-11/6 || otonal || 18 || || 19 || 0-502-903 || 1-11/7-11/6 || utonal || 18 || || 20 || 0-602-903 || 1-3/2-11/6 || otonal || 18 || || 21 || 0-702-903 || 1-10/7-11/6 || swetismic || 18 || || 22 || 0-301-1003 || 1-11/9-7/4 || werckismic || 20 || || 23 || 0-401-1003 || 1-7/6-7/4 || utonal || 20 || || 24 || 0-501-1003 || 1-10/9-7/4 || werckismic || 20 || || 25 || 0-502-1003 || 1-11/7-7/4 || werckismic || 20 || || 26 || 0-602-1003 || 1-3/2-7/4 || otonal || 20 || || 27 || 0-702-1003 || 1-10/7-7/4 || werckismic || 20 || || 28 || 0-202-1103 || 1-20/11-5/3 || utonal || 22 || || 29 || 0-401-1103 || 1-7/6-5/3 || otonal || 22 || || 30 || 0-501-1103 || 1-10/9-5/3 || utonal || 22 || || 31 || 0-602-1103 || 1-3/2-5/3 || otonal || 22 || || 32 || 0-702-1103 || 1-10/7-5/3 || utonal || 22 || || 33 || 0-903-1103 || 1-11/6-5/3 || otonal || 22 || || 34 || 0-201-1202 || 1-9/7-9/8 || utonal || 24 || || 35 || 0-301-1202 || 1-11/9-9/8 || rastmic || 24 || || 36 || 0-502-1202 || 1-11/7-9/8 || werckismic || 24 || || 37 || 0-602-1202 || 1-3/2-9/8 || ambitonal || 24 || || 38 || 0-702-1202 || 1-10/7-9/8 || werckismic || 24 || || 39 || 0-903-1202 || 1-11/6-9/8 || rastmic || 24 || || 40 || 0-1003-1202 || 1-7/4-9/8 || otonal || 24 || || 41 || 0-301-1503 || 1-11/9-11/8 || utonal || 30 || || 42 || 0-502-1503 || 1-11/7-11/8 || utonal || 30 || || 43 || 0-602-1503 || 1-3/2-11/8 || otonal || 30 || || 44 || 0-903-1503 || 1-11/6-11/8 || utonal || 30 || || 45 || 0-1003-1503 || 1-7/4-11/8 || otonal || 30 || || 46 || 0-1202-1503 || 1-9/8-11/8 || otonal || 30 || || 47 || 0-202-1703 || 1-20/11-5/4 || utonal || 34 || || 48 || 0-501-1703 || 1-10/9-5/4 || utonal || 34 || || 49 || 0-602-1703 || 1-3/2-5/4 || otonal || 34 || || 50 || 0-702-1703 || 1-10/7-5/4 || utonal || 34 || || 51 || 0-1003-1703 || 1-7/4-5/4 || otonal || 34 || || 52 || 0-1103-1703 || 1-5/3-5/4 || utonal || 34 || || 53 || 0-1202-1703 || 1-9/8-5/4 || otonal || 34 || || 54 || 0-1503-1703 || 1-11/8-5/4 || otonal || 34 || =Tetrads= || Number || Chord || Transversal || Type || Complexity || || 1 || 0-201-401-602 || 1-9/7-7/6-3/2 || swetismic || 12 || || 2 || 0-201-401-702 || 1-9/7-7/6-10/7 || swetismic || 14 || || 3 || 0-202-401-702 || 1-20/11-7/6-10/7 || swetismic || 14 || || 4 || 0-202-501-702 || 1-20/11-10/9-10/7 || utonal || 14 || || 5 || 0-301-501-702 || 1-11/9-10/9-10/7 || swetismic || 14 || || 6 || 0-201-502-702 || 1-9/7-11/7-10/7 || otonal || 14 || || 7 || 0-301-502-702 || 1-11/9-11/7-10/7 || swetismic || 14 || || 8 || 0-201-401-903 || 1-9/7-7/6-11/6 || swetismic || 18 || || 9 || 0-201-502-903 || 1-9/7-11/7-11/6 || swetismic || 18 || || 10 || 0-301-502-903 || 1-11/9-11/7-11/6 || utonal || 18 || || 11 || 0-201-602-903 || 1-9/7-3/2-11/6 || swetismic || 18 || || 12 || 0-301-602-903 || 1-11/9-3/2-11/6 || rastmic || 18 || || 13 || 0-401-602-903 || 1-7/6-3/2-11/6 || otonal || 18 || || 14 || 0-201-702-903 || 1-9/7-10/7-11/6 || swetismic || 18 || || 15 || 0-301-702-903 || 1-11/9-10/7-11/6 || swetismic || 18 || || 16 || 0-401-702-903 || 1-7/6-10/7-11/6 || swetismic || 18 || || 17 || 0-502-702-903 || 1-11/7-10/7-11/6 || swetismic || 18 || || 18 || 0-301-501-1003 || 1-11/9-10/9-7/4 || werckismic || 20 || || 19 || 0-301-502-1003 || 1-11/9-11/7-7/4 || werckismic || 20 || || 20 || 0-301-602-1003 || 1-11/9-3/2-7/4 || jove || 20 || || 21 || 0-401-602-1003 || 1-7/6-3/2-7/4 || ambitonal || 20 || || 22 || 0-301-702-1003 || 1-11/9-10/7-7/4 || jove || 20 || || 23 || 0-401-702-1003 || 1-7/6-10/7-7/4 || jove || 20 || || 24 || 0-501-702-1003 || 1-10/9-10/7-7/4 || werckismic || 20 || || 25 || 0-502-702-1003 || 1-11/7-10/7-7/4 || werckismic || 20 || || 26 || 0-202-401-1103 || 1-20/11-7/6-5/3 || swetismic || 22 || || 27 || 0-202-501-1103 || 1-20/11-10/9-5/3 || utonal || 22 || || 28 || 0-401-602-1103 || 1-7/6-3/2-5/3 || otonal || 22 || || 29 || 0-202-702-1103 || 1-20/11-10/7-5/3 || utonal || 22 || || 30 || 0-401-702-1103 || 1-7/6-10/7-5/3 || swetismic || 22 || || 31 || 0-501-702-1103 || 1-10/9-10/7-5/3 || utonal || 22 || || 32 || 0-401-903-1103 || 1-7/6-11/6-5/3 || otonal || 22 || || 33 || 0-602-903-1103 || 1-3/2-11/6-5/3 || otonal || 22 || || 34 || 0-702-903-1103 || 1-10/7-11/6-5/3 || swetismic || 22 || || 35 || 0-201-502-1202 || 1-9/7-11/7-9/8 || werckismic || 24 || || 36 || 0-301-502-1202 || 1-11/9-11/7-9/8 || jove || 24 || || 37 || 0-201-602-1202 || 1-9/7-3/2-9/8 || utonal || 24 || || 38 || 0-301-602-1202 || 1-11/9-3/2-9/8 || rastmic || 24 || || 39 || 0-201-702-1202 || 1-9/7-10/7-9/8 || werckismic || 24 || || 40 || 0-301-702-1202 || 1-11/9-10/7-9/8 || jove || 24 || || 41 || 0-502-702-1202 || 1-11/7-10/7-9/8 || werckismic || 24 || || 42 || 0-201-903-1202 || 1-9/7-11/6-9/8 || jove || 24 || || 43 || 0-301-903-1202 || 1-11/9-11/6-9/8 || rastmic || 24 || || 44 || 0-502-903-1202 || 1-11/7-11/6-9/8 || jove || 24 || || 45 || 0-602-903-1202 || 1-3/2-11/6-9/8 || rastmic || 24 || || 46 || 0-702-903-1202 || 1-10/7-11/6-9/8 || jove || 24 || || 47 || 0-301-1003-1202 || 1-11/9-7/4-9/8 || jove || 24 || || 48 || 0-502-1003-1202 || 1-11/7-7/4-9/8 || werckismic || 24 || || 49 || 0-602-1003-1202 || 1-3/2-7/4-9/8 || otonal || 24 || || 50 || 0-702-1003-1202 || 1-10/7-7/4-9/8 || werckismic || 24 || || 51 || 0-301-502-1503 || 1-11/9-11/7-11/8 || utonal || 30 || || 52 || 0-301-602-1503 || 1-11/9-3/2-11/8 || rastmic || 30 || || 53 || 0-301-903-1503 || 1-11/9-11/6-11/8 || utonal || 30 || || 54 || 0-502-903-1503 || 1-11/7-11/6-11/8 || utonal || 30 || || 55 || 0-602-903-1503 || 1-3/2-11/6-11/8 || ambitonal || 30 || || 56 || 0-301-1003-1503 || 1-11/9-7/4-11/8 || werckismic || 30 || || 57 || 0-502-1003-1503 || 1-11/7-7/4-11/8 || werckismic || 30 || || 58 || 0-602-1003-1503 || 1-3/2-7/4-11/8 || otonal || 30 || || 59 || 0-301-1202-1503 || 1-11/9-9/8-11/8 || rastmic || 30 || || 60 || 0-502-1202-1503 || 1-11/7-9/8-11/8 || werckismic || 30 || || 61 || 0-602-1202-1503 || 1-3/2-9/8-11/8 || otonal || 30 || || 62 || 0-903-1202-1503 || 1-11/6-9/8-11/8 || rastmic || 30 || || 63 || 0-1003-1202-1503 || 1-7/4-9/8-11/8 || otonal || 30 || || 64 || 0-202-501-1703 || 1-20/11-10/9-5/4 || utonal || 34 || || 65 || 0-202-702-1703 || 1-20/11-10/7-5/4 || utonal || 34 || || 66 || 0-501-702-1703 || 1-10/9-10/7-5/4 || utonal || 34 || || 67 || 0-501-1003-1703 || 1-10/9-7/4-5/4 || werckismic || 34 || || 68 || 0-602-1003-1703 || 1-3/2-7/4-5/4 || otonal || 34 || || 69 || 0-702-1003-1703 || 1-10/7-7/4-5/4 || werckismic || 34 || || 70 || 0-202-1103-1703 || 1-20/11-5/3-5/4 || utonal || 34 || || 71 || 0-501-1103-1703 || 1-10/9-5/3-5/4 || utonal || 34 || || 72 || 0-602-1103-1703 || 1-3/2-5/3-5/4 || ambitonal || 34 || || 73 || 0-702-1103-1703 || 1-10/7-5/3-5/4 || utonal || 34 || || 74 || 0-602-1202-1703 || 1-3/2-9/8-5/4 || otonal || 34 || || 75 || 0-702-1202-1703 || 1-10/7-9/8-5/4 || werckismic || 34 || || 76 || 0-1003-1202-1703 || 1-7/4-9/8-5/4 || otonal || 34 || || 77 || 0-602-1503-1703 || 1-3/2-11/8-5/4 || otonal || 34 || || 78 || 0-1003-1503-1703 || 1-7/4-11/8-5/4 || otonal || 34 || || 79 || 0-1202-1503-1703 || 1-9/8-11/8-5/4 || otonal || 34 || =Pentads= || Number || Chord || Transversal || Type || Complexity || || 1 || 0-201-401-602-903 || 1-9/7-7/6-3/2-11/6 || swetismic || 18 || || 2 || 0-201-401-702-903 || 1-9/7-7/6-10/7-11/6 || swetismic || 18 || || 3 || 0-201-502-702-903 || 1-9/7-11/7-10/7-11/6 || swetismic || 18 || || 4 || 0-301-502-702-903 || 1-11/9-11/7-10/7-11/6 || swetismic || 18 || || 5 || 0-301-501-702-1003 || 1-11/9-10/9-10/7-7/4 || jove || 20 || || 6 || 0-301-502-702-1003 || 1-11/9-11/7-10/7-7/4 || jove || 20 || || 7 || 0-202-401-702-1103 || 1-20/11-7/6-10/7-5/3 || swetismic || 22 || || 8 || 0-202-501-702-1103 || 1-20/11-10/9-10/7-5/3 || utonal || 22 || || 9 || 0-401-602-903-1103 || 1-7/6-3/2-11/6-5/3 || otonal || 22 || || 10 || 0-401-702-903-1103 || 1-7/6-10/7-11/6-5/3 || swetismic || 22 || || 11 || 0-201-502-702-1202 || 1-9/7-11/7-10/7-9/8 || werckismic || 24 || || 12 || 0-301-502-702-1202 || 1-11/9-11/7-10/7-9/8 || jove || 24 || || 13 || 0-201-502-903-1202 || 1-9/7-11/7-11/6-9/8 || jove || 24 || || 14 || 0-301-502-903-1202 || 1-11/9-11/7-11/6-9/8 || jove || 24 || || 15 || 0-201-602-903-1202 || 1-9/7-3/2-11/6-9/8 || jove || 24 || || 16 || 0-301-602-903-1202 || 1-11/9-3/2-11/6-9/8 || rastmic || 24 || || 17 || 0-201-702-903-1202 || 1-9/7-10/7-11/6-9/8 || jove || 24 || || 18 || 0-301-702-903-1202 || 1-11/9-10/7-11/6-9/8 || jove || 24 || || 19 || 0-502-702-903-1202 || 1-11/7-10/7-11/6-9/8 || jove || 24 || || 20 || 0-301-502-1003-1202 || 1-11/9-11/7-7/4-9/8 || jove || 24 || || 21 || 0-301-602-1003-1202 || 1-11/9-3/2-7/4-9/8 || jove || 24 || || 22 || 0-301-702-1003-1202 || 1-11/9-10/7-7/4-9/8 || jove || 24 || || 23 || 0-502-702-1003-1202 || 1-11/7-10/7-7/4-9/8 || werckismic || 24 || || 24 || 0-301-502-903-1503 || 1-11/9-11/7-11/6-11/8 || utonal || 30 || || 25 || 0-301-602-903-1503 || 1-11/9-3/2-11/6-11/8 || rastmic || 30 || || 26 || 0-301-502-1003-1503 || 1-11/9-11/7-7/4-11/8 || werckismic || 30 || || 27 || 0-301-602-1003-1503 || 1-11/9-3/2-7/4-11/8 || jove || 30 || || 28 || 0-301-502-1202-1503 || 1-11/9-11/7-9/8-11/8 || jove || 30 || || 29 || 0-301-602-1202-1503 || 1-11/9-3/2-9/8-11/8 || rastmic || 30 || || 30 || 0-301-903-1202-1503 || 1-11/9-11/6-9/8-11/8 || rastmic || 30 || || 31 || 0-502-903-1202-1503 || 1-11/7-11/6-9/8-11/8 || jove || 30 || || 32 || 0-602-903-1202-1503 || 1-3/2-11/6-9/8-11/8 || rastmic || 30 || || 33 || 0-301-1003-1202-1503 || 1-11/9-7/4-9/8-11/8 || jove || 30 || || 34 || 0-502-1003-1202-1503 || 1-11/7-7/4-9/8-11/8 || werckismic || 30 || || 35 || 0-602-1003-1202-1503 || 1-3/2-7/4-9/8-11/8 || otonal || 30 || || 36 || 0-202-501-702-1703 || 1-20/11-10/9-10/7-5/4 || utonal || 34 || || 37 || 0-501-702-1003-1703 || 1-10/9-10/7-7/4-5/4 || werckismic || 34 || || 38 || 0-202-501-1103-1703 || 1-20/11-10/9-5/3-5/4 || utonal || 34 || || 39 || 0-202-702-1103-1703 || 1-20/11-10/7-5/3-5/4 || utonal || 34 || || 40 || 0-501-702-1103-1703 || 1-10/9-10/7-5/3-5/4 || utonal || 34 || || 41 || 0-602-1003-1202-1703 || 1-3/2-7/4-9/8-5/4 || otonal || 34 || || 42 || 0-702-1003-1202-1703 || 1-10/7-7/4-9/8-5/4 || werckismic || 34 || || 43 || 0-602-1003-1503-1703 || 1-3/2-7/4-11/8-5/4 || otonal || 34 || || 44 || 0-602-1202-1503-1703 || 1-3/2-9/8-11/8-5/4 || otonal || 34 || || 45 || 0-1003-1202-1503-1703 || 1-7/4-9/8-11/8-5/4 || otonal || 34 || =Hexads= || Number || Chord || Transversal || Type || Complexity || || 1 || 0-201-502-702-903-1202 || 1-9/7-11/7-10/7-11/6-9/8 || jove || 24 || || 2 || 0-301-502-702-903-1202 || 1-11/9-11/7-10/7-11/6-9/8 || jove || 24 || || 3 || 0-301-502-702-1003-1202 || 1-11/9-11/7-10/7-7/4-9/8 || jove || 24 || || 4 || 0-301-502-903-1202-1503 || 1-11/9-11/7-11/6-9/8-11/8 || jove || 30 || || 5 || 0-301-602-903-1202-1503 || 1-11/9-3/2-11/6-9/8-11/8 || rastmic || 30 || || 6 || 0-301-502-1003-1202-1503 || 1-11/9-11/7-7/4-9/8-11/8 || jove || 30 || || 7 || 0-301-602-1003-1202-1503 || 1-11/9-3/2-7/4-9/8-11/8 || jove || 30 || || 8 || 0-202-501-702-1103-1703 || 1-20/11-10/9-10/7-5/3-5/4 || utonal || 34 || || 9 || 0-602-1003-1202-1503-1703 || 1-3/2-7/4-9/8-11/8-5/4 || otonal || 34 ||
Original HTML content:
<html><head><title>Chords of harry</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="/Gravity%20family#Harry">harry temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismicmic, and by 243/242 rastmic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove.<br />
<br />
The normal mapping for harry is har = [<2 4 7 7 9|, <0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = <2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.<br />
<br />
Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting. There is essentially no advantage in accuracy to optimizing for <a class="wiki_link" href="/Breed%20family#Jove, aka Wonder">jove temperament</a> rather than harry; in addition to what jove tempers out, harry tempers out 4000/3993. However, POTE tuning, for example, shrinks the three cents of this comma to -0.0827 cents, which is hardly worth worrying about. Hence harry is one way of exploring and organizing the chords of jove, which are therefore also listed below.<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>
<td>Complexity<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-201-401<br />
</td>
<td>1-9/7-7/6<br />
</td>
<td>swetismic<br />
</td>
<td>8<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-202-401<br />
</td>
<td>1-20/11-7/6<br />
</td>
<td>swetismic<br />
</td>
<td>8<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-202-501<br />
</td>
<td>1-20/11-10/9<br />
</td>
<td>utonal<br />
</td>
<td>10<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-301-501<br />
</td>
<td>1-11/9-10/9<br />
</td>
<td>otonal<br />
</td>
<td>10<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-201-502<br />
</td>
<td>1-9/7-11/7<br />
</td>
<td>otonal<br />
</td>
<td>10<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-301-502<br />
</td>
<td>1-11/9-11/7<br />
</td>
<td>utonal<br />
</td>
<td>10<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-201-602<br />
</td>
<td>1-9/7-3/2<br />
</td>
<td>utonal<br />
</td>
<td>12<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-301-602<br />
</td>
<td>1-11/9-3/2<br />
</td>
<td>rastmic<br />
</td>
<td>12<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-401-602<br />
</td>
<td>1-7/6-3/2<br />
</td>
<td>otonal<br />
</td>
<td>12<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-201-702<br />
</td>
<td>1-9/7-10/7<br />
</td>
<td>otonal<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-202-702<br />
</td>
<td>1-20/11-10/7<br />
</td>
<td>utonal<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-301-702<br />
</td>
<td>1-11/9-10/7<br />
</td>
<td>swetismic<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-401-702<br />
</td>
<td>1-7/6-10/7<br />
</td>
<td>swetismic<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-501-702<br />
</td>
<td>1-10/9-10/7<br />
</td>
<td>utonal<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-502-702<br />
</td>
<td>1-11/7-10/7<br />
</td>
<td>otonal<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-201-903<br />
</td>
<td>1-9/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-301-903<br />
</td>
<td>1-11/9-11/6<br />
</td>
<td>utonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-401-903<br />
</td>
<td>1-7/6-11/6<br />
</td>
<td>otonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-502-903<br />
</td>
<td>1-11/7-11/6<br />
</td>
<td>utonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-602-903<br />
</td>
<td>1-3/2-11/6<br />
</td>
<td>otonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-702-903<br />
</td>
<td>1-10/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-301-1003<br />
</td>
<td>1-11/9-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-401-1003<br />
</td>
<td>1-7/6-7/4<br />
</td>
<td>utonal<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-501-1003<br />
</td>
<td>1-10/9-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-502-1003<br />
</td>
<td>1-11/7-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-602-1003<br />
</td>
<td>1-3/2-7/4<br />
</td>
<td>otonal<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-702-1003<br />
</td>
<td>1-10/7-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-202-1103<br />
</td>
<td>1-20/11-5/3<br />
</td>
<td>utonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-401-1103<br />
</td>
<td>1-7/6-5/3<br />
</td>
<td>otonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-501-1103<br />
</td>
<td>1-10/9-5/3<br />
</td>
<td>utonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-602-1103<br />
</td>
<td>1-3/2-5/3<br />
</td>
<td>otonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-702-1103<br />
</td>
<td>1-10/7-5/3<br />
</td>
<td>utonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-903-1103<br />
</td>
<td>1-11/6-5/3<br />
</td>
<td>otonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-201-1202<br />
</td>
<td>1-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-301-1202<br />
</td>
<td>1-11/9-9/8<br />
</td>
<td>rastmic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-502-1202<br />
</td>
<td>1-11/7-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-602-1202<br />
</td>
<td>1-3/2-9/8<br />
</td>
<td>ambitonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-702-1202<br />
</td>
<td>1-10/7-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-903-1202<br />
</td>
<td>1-11/6-9/8<br />
</td>
<td>rastmic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-1003-1202<br />
</td>
<td>1-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-301-1503<br />
</td>
<td>1-11/9-11/8<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-502-1503<br />
</td>
<td>1-11/7-11/8<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-602-1503<br />
</td>
<td>1-3/2-11/8<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-903-1503<br />
</td>
<td>1-11/6-11/8<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-1003-1503<br />
</td>
<td>1-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-1202-1503<br />
</td>
<td>1-9/8-11/8<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-202-1703<br />
</td>
<td>1-20/11-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-501-1703<br />
</td>
<td>1-10/9-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-602-1703<br />
</td>
<td>1-3/2-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-702-1703<br />
</td>
<td>1-10/7-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-1003-1703<br />
</td>
<td>1-7/4-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-1103-1703<br />
</td>
<td>1-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-1202-1703<br />
</td>
<td>1-9/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-1503-1703<br />
</td>
<td>1-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<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>
<td>Complexity<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-201-401-602<br />
</td>
<td>1-9/7-7/6-3/2<br />
</td>
<td>swetismic<br />
</td>
<td>12<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-201-401-702<br />
</td>
<td>1-9/7-7/6-10/7<br />
</td>
<td>swetismic<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-202-401-702<br />
</td>
<td>1-20/11-7/6-10/7<br />
</td>
<td>swetismic<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-202-501-702<br />
</td>
<td>1-20/11-10/9-10/7<br />
</td>
<td>utonal<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-301-501-702<br />
</td>
<td>1-11/9-10/9-10/7<br />
</td>
<td>swetismic<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-201-502-702<br />
</td>
<td>1-9/7-11/7-10/7<br />
</td>
<td>otonal<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-301-502-702<br />
</td>
<td>1-11/9-11/7-10/7<br />
</td>
<td>swetismic<br />
</td>
<td>14<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-201-401-903<br />
</td>
<td>1-9/7-7/6-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-201-502-903<br />
</td>
<td>1-9/7-11/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-301-502-903<br />
</td>
<td>1-11/9-11/7-11/6<br />
</td>
<td>utonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-201-602-903<br />
</td>
<td>1-9/7-3/2-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-301-602-903<br />
</td>
<td>1-11/9-3/2-11/6<br />
</td>
<td>rastmic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-401-602-903<br />
</td>
<td>1-7/6-3/2-11/6<br />
</td>
<td>otonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-201-702-903<br />
</td>
<td>1-9/7-10/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-301-702-903<br />
</td>
<td>1-11/9-10/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-401-702-903<br />
</td>
<td>1-7/6-10/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-502-702-903<br />
</td>
<td>1-11/7-10/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-301-501-1003<br />
</td>
<td>1-11/9-10/9-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-301-502-1003<br />
</td>
<td>1-11/9-11/7-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-301-602-1003<br />
</td>
<td>1-11/9-3/2-7/4<br />
</td>
<td>jove<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-401-602-1003<br />
</td>
<td>1-7/6-3/2-7/4<br />
</td>
<td>ambitonal<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-301-702-1003<br />
</td>
<td>1-11/9-10/7-7/4<br />
</td>
<td>jove<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-401-702-1003<br />
</td>
<td>1-7/6-10/7-7/4<br />
</td>
<td>jove<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-501-702-1003<br />
</td>
<td>1-10/9-10/7-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-502-702-1003<br />
</td>
<td>1-11/7-10/7-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-202-401-1103<br />
</td>
<td>1-20/11-7/6-5/3<br />
</td>
<td>swetismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-202-501-1103<br />
</td>
<td>1-20/11-10/9-5/3<br />
</td>
<td>utonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-401-602-1103<br />
</td>
<td>1-7/6-3/2-5/3<br />
</td>
<td>otonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-202-702-1103<br />
</td>
<td>1-20/11-10/7-5/3<br />
</td>
<td>utonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-401-702-1103<br />
</td>
<td>1-7/6-10/7-5/3<br />
</td>
<td>swetismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-501-702-1103<br />
</td>
<td>1-10/9-10/7-5/3<br />
</td>
<td>utonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-401-903-1103<br />
</td>
<td>1-7/6-11/6-5/3<br />
</td>
<td>otonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-602-903-1103<br />
</td>
<td>1-3/2-11/6-5/3<br />
</td>
<td>otonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-702-903-1103<br />
</td>
<td>1-10/7-11/6-5/3<br />
</td>
<td>swetismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-201-502-1202<br />
</td>
<td>1-9/7-11/7-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-301-502-1202<br />
</td>
<td>1-11/9-11/7-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-201-602-1202<br />
</td>
<td>1-9/7-3/2-9/8<br />
</td>
<td>utonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-301-602-1202<br />
</td>
<td>1-11/9-3/2-9/8<br />
</td>
<td>rastmic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-201-702-1202<br />
</td>
<td>1-9/7-10/7-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-301-702-1202<br />
</td>
<td>1-11/9-10/7-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-502-702-1202<br />
</td>
<td>1-11/7-10/7-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-201-903-1202<br />
</td>
<td>1-9/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-301-903-1202<br />
</td>
<td>1-11/9-11/6-9/8<br />
</td>
<td>rastmic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-502-903-1202<br />
</td>
<td>1-11/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-602-903-1202<br />
</td>
<td>1-3/2-11/6-9/8<br />
</td>
<td>rastmic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-702-903-1202<br />
</td>
<td>1-10/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-301-1003-1202<br />
</td>
<td>1-11/9-7/4-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-502-1003-1202<br />
</td>
<td>1-11/7-7/4-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-602-1003-1202<br />
</td>
<td>1-3/2-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-702-1003-1202<br />
</td>
<td>1-10/7-7/4-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-301-502-1503<br />
</td>
<td>1-11/9-11/7-11/8<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-301-602-1503<br />
</td>
<td>1-11/9-3/2-11/8<br />
</td>
<td>rastmic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-301-903-1503<br />
</td>
<td>1-11/9-11/6-11/8<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-502-903-1503<br />
</td>
<td>1-11/7-11/6-11/8<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-602-903-1503<br />
</td>
<td>1-3/2-11/6-11/8<br />
</td>
<td>ambitonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-301-1003-1503<br />
</td>
<td>1-11/9-7/4-11/8<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-502-1003-1503<br />
</td>
<td>1-11/7-7/4-11/8<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-602-1003-1503<br />
</td>
<td>1-3/2-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-301-1202-1503<br />
</td>
<td>1-11/9-9/8-11/8<br />
</td>
<td>rastmic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-502-1202-1503<br />
</td>
<td>1-11/7-9/8-11/8<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-602-1202-1503<br />
</td>
<td>1-3/2-9/8-11/8<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-903-1202-1503<br />
</td>
<td>1-11/6-9/8-11/8<br />
</td>
<td>rastmic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-1003-1202-1503<br />
</td>
<td>1-7/4-9/8-11/8<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-202-501-1703<br />
</td>
<td>1-20/11-10/9-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-202-702-1703<br />
</td>
<td>1-20/11-10/7-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td>0-501-702-1703<br />
</td>
<td>1-10/9-10/7-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>67<br />
</td>
<td>0-501-1003-1703<br />
</td>
<td>1-10/9-7/4-5/4<br />
</td>
<td>werckismic<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>68<br />
</td>
<td>0-602-1003-1703<br />
</td>
<td>1-3/2-7/4-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>69<br />
</td>
<td>0-702-1003-1703<br />
</td>
<td>1-10/7-7/4-5/4<br />
</td>
<td>werckismic<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>70<br />
</td>
<td>0-202-1103-1703<br />
</td>
<td>1-20/11-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>71<br />
</td>
<td>0-501-1103-1703<br />
</td>
<td>1-10/9-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>72<br />
</td>
<td>0-602-1103-1703<br />
</td>
<td>1-3/2-5/3-5/4<br />
</td>
<td>ambitonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>73<br />
</td>
<td>0-702-1103-1703<br />
</td>
<td>1-10/7-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>74<br />
</td>
<td>0-602-1202-1703<br />
</td>
<td>1-3/2-9/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>75<br />
</td>
<td>0-702-1202-1703<br />
</td>
<td>1-10/7-9/8-5/4<br />
</td>
<td>werckismic<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>76<br />
</td>
<td>0-1003-1202-1703<br />
</td>
<td>1-7/4-9/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>77<br />
</td>
<td>0-602-1503-1703<br />
</td>
<td>1-3/2-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>78<br />
</td>
<td>0-1003-1503-1703<br />
</td>
<td>1-7/4-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>79<br />
</td>
<td>0-1202-1503-1703<br />
</td>
<td>1-9/8-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<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>
<td>Complexity<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-201-401-602-903<br />
</td>
<td>1-9/7-7/6-3/2-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-201-401-702-903<br />
</td>
<td>1-9/7-7/6-10/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-201-502-702-903<br />
</td>
<td>1-9/7-11/7-10/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-301-502-702-903<br />
</td>
<td>1-11/9-11/7-10/7-11/6<br />
</td>
<td>swetismic<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-301-501-702-1003<br />
</td>
<td>1-11/9-10/9-10/7-7/4<br />
</td>
<td>jove<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-301-502-702-1003<br />
</td>
<td>1-11/9-11/7-10/7-7/4<br />
</td>
<td>jove<br />
</td>
<td>20<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-202-401-702-1103<br />
</td>
<td>1-20/11-7/6-10/7-5/3<br />
</td>
<td>swetismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-202-501-702-1103<br />
</td>
<td>1-20/11-10/9-10/7-5/3<br />
</td>
<td>utonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-401-602-903-1103<br />
</td>
<td>1-7/6-3/2-11/6-5/3<br />
</td>
<td>otonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-401-702-903-1103<br />
</td>
<td>1-7/6-10/7-11/6-5/3<br />
</td>
<td>swetismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-201-502-702-1202<br />
</td>
<td>1-9/7-11/7-10/7-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-301-502-702-1202<br />
</td>
<td>1-11/9-11/7-10/7-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-201-502-903-1202<br />
</td>
<td>1-9/7-11/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-301-502-903-1202<br />
</td>
<td>1-11/9-11/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-201-602-903-1202<br />
</td>
<td>1-9/7-3/2-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-301-602-903-1202<br />
</td>
<td>1-11/9-3/2-11/6-9/8<br />
</td>
<td>rastmic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-201-702-903-1202<br />
</td>
<td>1-9/7-10/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-301-702-903-1202<br />
</td>
<td>1-11/9-10/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-502-702-903-1202<br />
</td>
<td>1-11/7-10/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-301-502-1003-1202<br />
</td>
<td>1-11/9-11/7-7/4-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-301-602-1003-1202<br />
</td>
<td>1-11/9-3/2-7/4-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-301-702-1003-1202<br />
</td>
<td>1-11/9-10/7-7/4-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-502-702-1003-1202<br />
</td>
<td>1-11/7-10/7-7/4-9/8<br />
</td>
<td>werckismic<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-301-502-903-1503<br />
</td>
<td>1-11/9-11/7-11/6-11/8<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-301-602-903-1503<br />
</td>
<td>1-11/9-3/2-11/6-11/8<br />
</td>
<td>rastmic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-301-502-1003-1503<br />
</td>
<td>1-11/9-11/7-7/4-11/8<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-301-602-1003-1503<br />
</td>
<td>1-11/9-3/2-7/4-11/8<br />
</td>
<td>jove<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-301-502-1202-1503<br />
</td>
<td>1-11/9-11/7-9/8-11/8<br />
</td>
<td>jove<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-301-602-1202-1503<br />
</td>
<td>1-11/9-3/2-9/8-11/8<br />
</td>
<td>rastmic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-301-903-1202-1503<br />
</td>
<td>1-11/9-11/6-9/8-11/8<br />
</td>
<td>rastmic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-502-903-1202-1503<br />
</td>
<td>1-11/7-11/6-9/8-11/8<br />
</td>
<td>jove<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-602-903-1202-1503<br />
</td>
<td>1-3/2-11/6-9/8-11/8<br />
</td>
<td>rastmic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-301-1003-1202-1503<br />
</td>
<td>1-11/9-7/4-9/8-11/8<br />
</td>
<td>jove<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-502-1003-1202-1503<br />
</td>
<td>1-11/7-7/4-9/8-11/8<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-602-1003-1202-1503<br />
</td>
<td>1-3/2-7/4-9/8-11/8<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-202-501-702-1703<br />
</td>
<td>1-20/11-10/9-10/7-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-501-702-1003-1703<br />
</td>
<td>1-10/9-10/7-7/4-5/4<br />
</td>
<td>werckismic<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-202-501-1103-1703<br />
</td>
<td>1-20/11-10/9-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-202-702-1103-1703<br />
</td>
<td>1-20/11-10/7-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-501-702-1103-1703<br />
</td>
<td>1-10/9-10/7-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-602-1003-1202-1703<br />
</td>
<td>1-3/2-7/4-9/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-702-1003-1202-1703<br />
</td>
<td>1-10/7-7/4-9/8-5/4<br />
</td>
<td>werckismic<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-602-1003-1503-1703<br />
</td>
<td>1-3/2-7/4-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-602-1202-1503-1703<br />
</td>
<td>1-3/2-9/8-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-1003-1202-1503-1703<br />
</td>
<td>1-7/4-9/8-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<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>
<td>Complexity<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-201-502-702-903-1202<br />
</td>
<td>1-9/7-11/7-10/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-301-502-702-903-1202<br />
</td>
<td>1-11/9-11/7-10/7-11/6-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-301-502-702-1003-1202<br />
</td>
<td>1-11/9-11/7-10/7-7/4-9/8<br />
</td>
<td>jove<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-301-502-903-1202-1503<br />
</td>
<td>1-11/9-11/7-11/6-9/8-11/8<br />
</td>
<td>jove<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-301-602-903-1202-1503<br />
</td>
<td>1-11/9-3/2-11/6-9/8-11/8<br />
</td>
<td>rastmic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-301-502-1003-1202-1503<br />
</td>
<td>1-11/9-11/7-7/4-9/8-11/8<br />
</td>
<td>jove<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-301-602-1003-1202-1503<br />
</td>
<td>1-11/9-3/2-7/4-9/8-11/8<br />
</td>
<td>jove<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-202-501-702-1103-1703<br />
</td>
<td>1-20/11-10/9-10/7-5/3-5/4<br />
</td>
<td>utonal<br />
</td>
<td>34<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-602-1003-1202-1503-1703<br />
</td>
<td>1-3/2-7/4-9/8-11/8-5/4<br />
</td>
<td>otonal<br />
</td>
<td>34<br />
</td>
</tr>
</table>
</body></html>