Diaschismic/Chords

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This revision was by author genewardsmith and made on 2011-12-25 15:19:36 UTC.
The original revision id was 288444650.
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Original Wikitext content:

Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Diaschismic+family#Diaschismic|diaschismic temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 441/440 are labeled werckismic, by 176/175 valinorsmic, by 896/891 pentacircle, and by 126/125 starling. Those requiring tempering by any two of 126/125, 176/175 or 441/440 are labeled thrush, and by both 896/891 and 441/440 pele.

The normal mapping for diaschismic is dia = [<2 0 11 31 45|, <0 1 -2 -8 -12|]. From this we may derive a val v = dia[1] - 100 dia[2] = <2 -100 211 831 1245| which we may use to sort and normalize the chords of diaschismic. 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.

Diaschsmic has MOS of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.

=Triads=
|| Number || Chord || Transversal || Type || Complexity ||
|| 1 || 0-104-208 || 1-4/3-16/9 || ambitonal || 4 ||
|| 2 || 0-104-311 || 1-4/3-5/3 || otonal || 6 ||
|| 3 || 0-207-311 || 1-5/4-5/3 || utonal || 6 ||
|| 4 || 0-104-413 || 1-4/3-10/9 || otonal || 8 ||
|| 5 || 0-207-413 || 1-5/4-10/9 || utonal || 8 ||
|| 6 || 0-208-413 || 1-16/9-10/9 || otonal || 8 ||
|| 7 || 0-311-413 || 1-5/3-10/9 || utonal || 8 ||
|| 8 || 0-207-414 || 1-5/4-11/7 || valinorsmic || 8 ||
|| 9 || 0-208-414 || 1-16/9-11/7 || pentacircle || 8 ||
|| 10 || 0-207-620 || 1-5/4-7/5 || starling || 12 ||
|| 11 || 0-208-620 || 1-16/9-7/5 || werckismic || 12 ||
|| 12 || 0-311-620 || 1-5/3-7/5 || starling || 12 ||
|| 13 || 0-413-620 || 1-10/9-7/5 || starling || 12 ||
|| 14 || 0-414-620 || 1-11/7-7/5 || werckismic || 12 ||
|| 15 || 0-207-827 || 1-5/4-7/4 || otonal || 16 ||
|| 16 || 0-413-827 || 1-10/9-7/4 || werckismic || 16 ||
|| 17 || 0-414-827 || 1-11/7-7/4 || werckismic || 16 ||
|| 18 || 0-620-827 || 1-7/5-7/4 || utonal || 16 ||
|| 19 || 0-104-929 || 1-4/3-7/6 || otonal || 18 ||
|| 20 || 0-311-929 || 1-5/3-7/6 || otonal || 18 ||
|| 21 || 0-620-929 || 1-7/5-7/6 || utonal || 18 ||
|| 22 || 0-827-929 || 1-7/4-7/6 || utonal || 18 ||
|| 23 || 0-207-1032 || 1-5/4-11/10 || valinorsmic || 20 ||
|| 24 || 0-414-1032 || 1-11/7-11/10 || utonal || 20 ||
|| 25 || 0-620-1032 || 1-7/5-11/10 || otonal || 20 ||
|| 26 || 0-827-1032 || 1-7/4-11/10 || valinorsmic || 20 ||
|| 27 || 0-104-1033 || 1-4/3-14/9 || otonal || 20 ||
|| 28 || 0-208-1033 || 1-16/9-14/9 || otonal || 20 ||
|| 29 || 0-413-1033 || 1-10/9-14/9 || otonal || 20 ||
|| 30 || 0-620-1033 || 1-7/5-14/9 || utonal || 20 ||
|| 31 || 0-827-1033 || 1-7/4-14/9 || utonal || 20 ||
|| 32 || 0-929-1033 || 1-7/6-14/9 || utonal || 20 ||
|| 33 || 0-207-1239 || 1-5/4-11/8 || otonal || 24 ||
|| 34 || 0-208-1239 || 1-16/9-11/8 || pentacircle || 24 ||
|| 35 || 0-414-1239 || 1-11/7-11/8 || utonal || 24 ||
|| 36 || 0-827-1239 || 1-7/4-11/8 || otonal || 24 ||
|| 37 || 0-1032-1239 || 1-11/10-11/8 || utonal || 24 ||
|| 38 || 0-1033-1239 || 1-14/9-11/8 || pentacircle || 24 ||
|| 39 || 0-104-1343 || 1-4/3-11/6 || otonal || 26 ||
|| 40 || 0-311-1343 || 1-5/3-11/6 || otonal || 26 ||
|| 41 || 0-414-1343 || 1-11/7-11/6 || utonal || 26 ||
|| 42 || 0-929-1343 || 1-7/6-11/6 || otonal || 26 ||
|| 43 || 0-1032-1343 || 1-11/10-11/6 || utonal || 26 ||
|| 44 || 0-1239-1343 || 1-11/8-11/6 || utonal || 26 ||
|| 45 || 0-104-1445 || 1-4/3-11/9 || otonal || 28 ||
|| 46 || 0-208-1445 || 1-16/9-11/9 || otonal || 28 ||
|| 47 || 0-413-1445 || 1-10/9-11/9 || otonal || 28 ||
|| 48 || 0-414-1445 || 1-11/7-11/9 || utonal || 28 ||
|| 49 || 0-620-1445 || 1-7/5-11/9 || werckismic || 28 ||
|| 50 || 0-827-1445 || 1-7/4-11/9 || werckismic || 28 ||
|| 51 || 0-1032-1445 || 1-11/10-11/9 || utonal || 28 ||
|| 52 || 0-1033-1445 || 1-14/9-11/9 || otonal || 28 ||
|| 53 || 0-1239-1445 || 1-11/8-11/9 || utonal || 28 ||
|| 54 || 0-1343-1445 || 1-11/6-11/9 || utonal || 28 ||

=Tetrads=
|| Number || Chord || Transversal || Type || Complexity ||
|| 1 || 0-104-208-413 || 1-4/3-16/9-10/9 || otonal || 8 ||
|| 2 || 0-104-311-413 || 1-4/3-5/3-10/9 || ambitonal || 8 ||
|| 3 || 0-207-311-413 || 1-5/4-5/3-10/9 || utonal || 8 ||
|| 4 || 0-207-311-620 || 1-5/4-5/3-7/5 || starling || 12 ||
|| 5 || 0-207-413-620 || 1-5/4-10/9-7/5 || starling || 12 ||
|| 6 || 0-208-413-620 || 1-16/9-10/9-7/5 || thrush || 12 ||
|| 7 || 0-311-413-620 || 1-5/3-10/9-7/5 || starling || 12 ||
|| 8 || 0-207-414-620 || 1-5/4-11/7-7/5 || thrush || 12 ||
|| 9 || 0-208-414-620 || 1-16/9-11/7-7/5 || pele || 12 ||
|| 10 || 0-207-413-827 || 1-5/4-10/9-7/4 || werckismic || 16 ||
|| 11 || 0-207-414-827 || 1-5/4-11/7-7/4 || thrush || 16 ||
|| 12 || 0-207-620-827 || 1-5/4-7/5-7/4 || starling || 16 ||
|| 13 || 0-413-620-827 || 1-10/9-7/5-7/4 || thrush || 16 ||
|| 14 || 0-414-620-827 || 1-11/7-7/5-7/4 || werckismic || 16 ||
|| 15 || 0-104-311-929 || 1-4/3-5/3-7/6 || otonal || 18 ||
|| 16 || 0-311-620-929 || 1-5/3-7/5-7/6 || starling || 18 ||
|| 17 || 0-620-827-929 || 1-7/5-7/4-7/6 || utonal || 18 ||
|| 18 || 0-207-414-1032 || 1-5/4-11/7-11/10 || valinorsmic || 20 ||
|| 19 || 0-207-620-1032 || 1-5/4-7/5-11/10 || thrush || 20 ||
|| 20 || 0-414-620-1032 || 1-11/7-7/5-11/10 || werckismic || 20 ||
|| 21 || 0-207-827-1032 || 1-5/4-7/4-11/10 || valinorsmic || 20 ||
|| 22 || 0-414-827-1032 || 1-11/7-7/4-11/10 || thrush || 20 ||
|| 23 || 0-620-827-1032 || 1-7/5-7/4-11/10 || valinorsmic || 20 ||
|| 24 || 0-104-208-1033 || 1-4/3-16/9-14/9 || otonal || 20 ||
|| 25 || 0-104-413-1033 || 1-4/3-10/9-14/9 || otonal || 20 ||
|| 26 || 0-208-413-1033 || 1-16/9-10/9-14/9 || otonal || 20 ||
|| 27 || 0-208-620-1033 || 1-16/9-7/5-14/9 || werckismic || 20 ||
|| 28 || 0-413-620-1033 || 1-10/9-7/5-14/9 || starling || 20 ||
|| 29 || 0-413-827-1033 || 1-10/9-7/4-14/9 || werckismic || 20 ||
|| 30 || 0-620-827-1033 || 1-7/5-7/4-14/9 || utonal || 20 ||
|| 31 || 0-104-929-1033 || 1-4/3-7/6-14/9 || ambitonal || 20 ||
|| 32 || 0-620-929-1033 || 1-7/5-7/6-14/9 || utonal || 20 ||
|| 33 || 0-827-929-1033 || 1-7/4-7/6-14/9 || utonal || 20 ||
|| 34 || 0-207-414-1239 || 1-5/4-11/7-11/8 || valinorsmic || 24 ||
|| 35 || 0-208-414-1239 || 1-16/9-11/7-11/8 || pentacircle || 24 ||
|| 36 || 0-207-827-1239 || 1-5/4-7/4-11/8 || otonal || 24 ||
|| 37 || 0-414-827-1239 || 1-11/7-7/4-11/8 || werckismic || 24 ||
|| 38 || 0-207-1032-1239 || 1-5/4-11/10-11/8 || valinorsmic || 24 ||
|| 39 || 0-414-1032-1239 || 1-11/7-11/10-11/8 || utonal || 24 ||
|| 40 || 0-827-1032-1239 || 1-7/4-11/10-11/8 || valinorsmic || 24 ||
|| 41 || 0-208-1033-1239 || 1-16/9-14/9-11/8 || pentacircle || 24 ||
|| 42 || 0-827-1033-1239 || 1-7/4-14/9-11/8 || pentacircle || 24 ||
|| 43 || 0-104-311-1343 || 1-4/3-5/3-11/6 || otonal || 26 ||
|| 44 || 0-104-929-1343 || 1-4/3-7/6-11/6 || otonal || 26 ||
|| 45 || 0-311-929-1343 || 1-5/3-7/6-11/6 || otonal || 26 ||
|| 46 || 0-414-1032-1343 || 1-11/7-11/10-11/6 || utonal || 26 ||
|| 47 || 0-414-1239-1343 || 1-11/7-11/8-11/6 || utonal || 26 ||
|| 48 || 0-1032-1239-1343 || 1-11/10-11/8-11/6 || utonal || 26 ||
|| 49 || 0-104-208-1445 || 1-4/3-16/9-11/9 || otonal || 28 ||
|| 50 || 0-104-413-1445 || 1-4/3-10/9-11/9 || otonal || 28 ||
|| 51 || 0-208-413-1445 || 1-16/9-10/9-11/9 || otonal || 28 ||
|| 52 || 0-208-414-1445 || 1-16/9-11/7-11/9 || pentacircle || 28 ||
|| 53 || 0-208-620-1445 || 1-16/9-7/5-11/9 || werckismic || 28 ||
|| 54 || 0-413-620-1445 || 1-10/9-7/5-11/9 || thrush || 28 ||
|| 55 || 0-414-620-1445 || 1-11/7-7/5-11/9 || werckismic || 28 ||
|| 56 || 0-413-827-1445 || 1-10/9-7/4-11/9 || werckismic || 28 ||
|| 57 || 0-414-827-1445 || 1-11/7-7/4-11/9 || werckismic || 28 ||
|| 58 || 0-620-827-1445 || 1-7/5-7/4-11/9 || werckismic || 28 ||
|| 59 || 0-414-1032-1445 || 1-11/7-11/10-11/9 || utonal || 28 ||
|| 60 || 0-620-1032-1445 || 1-7/5-11/10-11/9 || werckismic || 28 ||
|| 61 || 0-827-1032-1445 || 1-7/4-11/10-11/9 || thrush || 28 ||
|| 62 || 0-104-1033-1445 || 1-4/3-14/9-11/9 || otonal || 28 ||
|| 63 || 0-208-1033-1445 || 1-16/9-14/9-11/9 || otonal || 28 ||
|| 64 || 0-413-1033-1445 || 1-10/9-14/9-11/9 || otonal || 28 ||
|| 65 || 0-620-1033-1445 || 1-7/5-14/9-11/9 || werckismic || 28 ||
|| 66 || 0-827-1033-1445 || 1-7/4-14/9-11/9 || werckismic || 28 ||
|| 67 || 0-208-1239-1445 || 1-16/9-11/8-11/9 || pentacircle || 28 ||
|| 68 || 0-414-1239-1445 || 1-11/7-11/8-11/9 || utonal || 28 ||
|| 69 || 0-827-1239-1445 || 1-7/4-11/8-11/9 || werckismic || 28 ||
|| 70 || 0-1032-1239-1445 || 1-11/10-11/8-11/9 || utonal || 28 ||
|| 71 || 0-1033-1239-1445 || 1-14/9-11/8-11/9 || pentacircle || 28 ||
|| 72 || 0-104-1343-1445 || 1-4/3-11/6-11/9 || ambitonal || 28 ||
|| 73 || 0-414-1343-1445 || 1-11/7-11/6-11/9 || utonal || 28 ||
|| 74 || 0-1032-1343-1445 || 1-11/10-11/6-11/9 || utonal || 28 ||
|| 75 || 0-1239-1343-1445 || 1-11/8-11/6-11/9 || utonal || 28 ||

=Pentads=
|| Number || Chord || Transversal || Type || Complexity ||
|| 1 || 0-207-311-413-620 || 1-5/4-5/3-10/9-7/5 || starling || 12 ||
|| 2 || 0-207-413-620-827 || 1-5/4-10/9-7/5-7/4 || thrush || 16 ||
|| 3 || 0-207-414-620-827 || 1-5/4-11/7-7/5-7/4 || thrush || 16 ||
|| 4 || 0-207-414-620-1032 || 1-5/4-11/7-7/5-11/10 || thrush || 20 ||
|| 5 || 0-207-414-827-1032 || 1-5/4-11/7-7/4-11/10 || thrush || 20 ||
|| 6 || 0-207-620-827-1032 || 1-5/4-7/5-7/4-11/10 || thrush || 20 ||
|| 7 || 0-414-620-827-1032 || 1-11/7-7/5-7/4-11/10 || thrush || 20 ||
|| 8 || 0-104-208-413-1033 || 1-4/3-16/9-10/9-14/9 || otonal || 20 ||
|| 9 || 0-208-413-620-1033 || 1-16/9-10/9-7/5-14/9 || thrush || 20 ||
|| 10 || 0-413-620-827-1033 || 1-10/9-7/5-7/4-14/9 || thrush || 20 ||
|| 11 || 0-620-827-929-1033 || 1-7/5-7/4-7/6-14/9 || utonal || 20 ||
|| 12 || 0-207-414-827-1239 || 1-5/4-11/7-7/4-11/8 || thrush || 24 ||
|| 13 || 0-207-414-1032-1239 || 1-5/4-11/7-11/10-11/8 || valinorsmic || 24 ||
|| 14 || 0-207-827-1032-1239 || 1-5/4-7/4-11/10-11/8 || valinorsmic || 24 ||
|| 15 || 0-414-827-1032-1239 || 1-11/7-7/4-11/10-11/8 || thrush || 24 ||
|| 16 || 0-104-311-929-1343 || 1-4/3-5/3-7/6-11/6 || otonal || 26 ||
|| 17 || 0-414-1032-1239-1343 || 1-11/7-11/10-11/8-11/6 || utonal || 26 ||
|| 18 || 0-104-208-413-1445 || 1-4/3-16/9-10/9-11/9 || otonal || 28 ||
|| 19 || 0-208-413-620-1445 || 1-16/9-10/9-7/5-11/9 || thrush || 28 ||
|| 20 || 0-208-414-620-1445 || 1-16/9-11/7-7/5-11/9 || pele || 28 ||
|| 21 || 0-413-620-827-1445 || 1-10/9-7/5-7/4-11/9 || thrush || 28 ||
|| 22 || 0-414-620-827-1445 || 1-11/7-7/5-7/4-11/9 || werckismic || 28 ||
|| 23 || 0-414-620-1032-1445 || 1-11/7-7/5-11/10-11/9 || werckismic || 28 ||
|| 24 || 0-414-827-1032-1445 || 1-11/7-7/4-11/10-11/9 || thrush || 28 ||
|| 25 || 0-620-827-1032-1445 || 1-7/5-7/4-11/10-11/9 || thrush || 28 ||
|| 26 || 0-104-208-1033-1445 || 1-4/3-16/9-14/9-11/9 || otonal || 28 ||
|| 27 || 0-104-413-1033-1445 || 1-4/3-10/9-14/9-11/9 || otonal || 28 ||
|| 28 || 0-208-413-1033-1445 || 1-16/9-10/9-14/9-11/9 || otonal || 28 ||
|| 29 || 0-208-620-1033-1445 || 1-16/9-7/5-14/9-11/9 || werckismic || 28 ||
|| 30 || 0-413-620-1033-1445 || 1-10/9-7/5-14/9-11/9 || thrush || 28 ||
|| 31 || 0-413-827-1033-1445 || 1-10/9-7/4-14/9-11/9 || werckismic || 28 ||
|| 32 || 0-620-827-1033-1445 || 1-7/5-7/4-14/9-11/9 || werckismic || 28 ||
|| 33 || 0-208-414-1239-1445 || 1-16/9-11/7-11/8-11/9 || pentacircle || 28 ||
|| 34 || 0-414-827-1239-1445 || 1-11/7-7/4-11/8-11/9 || werckismic || 28 ||
|| 35 || 0-414-1032-1239-1445 || 1-11/7-11/10-11/8-11/9 || utonal || 28 ||
|| 36 || 0-827-1032-1239-1445 || 1-7/4-11/10-11/8-11/9 || thrush || 28 ||
|| 37 || 0-208-1033-1239-1445 || 1-16/9-14/9-11/8-11/9 || pentacircle || 28 ||
|| 38 || 0-827-1033-1239-1445 || 1-7/4-14/9-11/8-11/9 || pele || 28 ||
|| 39 || 0-414-1032-1343-1445 || 1-11/7-11/10-11/6-11/9 || utonal || 28 ||
|| 40 || 0-414-1239-1343-1445 || 1-11/7-11/8-11/6-11/9 || utonal || 28 ||
|| 41 || 0-1032-1239-1343-1445 || 1-11/10-11/8-11/6-11/9 || utonal || 28 ||

=Hexads=
|| Number || Chord || Transversal || Type || Complexity ||
|| 1 || 0-207-414-620-827-1032 || 1-5/4-11/7-7/5-7/4-11/10 || thrush || 20 ||
|| 2 || 0-207-414-827-1032-1239 || 1-5/4-11/7-7/4-11/10-11/8 || thrush || 24 ||
|| 3 || 0-414-620-827-1032-1445 || 1-11/7-7/5-7/4-11/10-11/9 || thrush || 28 ||
|| 4 || 0-104-208-413-1033-1445 || 1-4/3-16/9-10/9-14/9-11/9 || otonal || 28 ||
|| 5 || 0-208-413-620-1033-1445 || 1-16/9-10/9-7/5-14/9-11/9 || thrush || 28 ||
|| 6 || 0-413-620-827-1033-1445 || 1-10/9-7/5-7/4-14/9-11/9 || thrush || 28 ||
|| 7 || 0-414-827-1032-1239-1445 || 1-11/7-7/4-11/10-11/8-11/9 || thrush || 28 ||
|| 8 || 0-414-1032-1239-1343-1445 || 1-11/7-11/10-11/8-11/6-11/9 || utonal || 28 ||

Original HTML content:

<html><head><title>Chords of diaschismic</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit [[Diaschismic+family#Diaschismic|diaschismic temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 441/440 are labeled werckismic, by 176/175 valinorsmic, by 896/891 pentacircle, and by 126/125 starling. Those requiring tempering by any two of 126/125, 176/175 or 441/440 are labeled thrush, and by both 896/891 and 441/440 pele.<br />
<br />
The normal mapping for diaschismic is dia = [&lt;2 0 11 31 45|, &lt;0 1 -2 -8 -12|]. From this we may derive a val v = dia[1] - 100 dia[2] = &lt;2 -100 211 831 1245| which we may use to sort and normalize the chords of diaschismic. 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 />
Diaschsmic has MOS of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><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>0-104-208<br />
</td>
        <td>1-4/3-16/9<br />
</td>
        <td>ambitonal<br />
</td>
        <td>4<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-104-311<br />
</td>
        <td>1-4/3-5/3<br />
</td>
        <td>otonal<br />
</td>
        <td>6<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-207-311<br />
</td>
        <td>1-5/4-5/3<br />
</td>
        <td>utonal<br />
</td>
        <td>6<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-104-413<br />
</td>
        <td>1-4/3-10/9<br />
</td>
        <td>otonal<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-207-413<br />
</td>
        <td>1-5/4-10/9<br />
</td>
        <td>utonal<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-208-413<br />
</td>
        <td>1-16/9-10/9<br />
</td>
        <td>otonal<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-311-413<br />
</td>
        <td>1-5/3-10/9<br />
</td>
        <td>utonal<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-207-414<br />
</td>
        <td>1-5/4-11/7<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-208-414<br />
</td>
        <td>1-16/9-11/7<br />
</td>
        <td>pentacircle<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-207-620<br />
</td>
        <td>1-5/4-7/5<br />
</td>
        <td>starling<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-208-620<br />
</td>
        <td>1-16/9-7/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-311-620<br />
</td>
        <td>1-5/3-7/5<br />
</td>
        <td>starling<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-413-620<br />
</td>
        <td>1-10/9-7/5<br />
</td>
        <td>starling<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-414-620<br />
</td>
        <td>1-11/7-7/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-207-827<br />
</td>
        <td>1-5/4-7/4<br />
</td>
        <td>otonal<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-413-827<br />
</td>
        <td>1-10/9-7/4<br />
</td>
        <td>werckismic<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-414-827<br />
</td>
        <td>1-11/7-7/4<br />
</td>
        <td>werckismic<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-620-827<br />
</td>
        <td>1-7/5-7/4<br />
</td>
        <td>utonal<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-104-929<br />
</td>
        <td>1-4/3-7/6<br />
</td>
        <td>otonal<br />
</td>
        <td>18<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-311-929<br />
</td>
        <td>1-5/3-7/6<br />
</td>
        <td>otonal<br />
</td>
        <td>18<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-620-929<br />
</td>
        <td>1-7/5-7/6<br />
</td>
        <td>utonal<br />
</td>
        <td>18<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-827-929<br />
</td>
        <td>1-7/4-7/6<br />
</td>
        <td>utonal<br />
</td>
        <td>18<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-207-1032<br />
</td>
        <td>1-5/4-11/10<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-414-1032<br />
</td>
        <td>1-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-620-1032<br />
</td>
        <td>1-7/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-827-1032<br />
</td>
        <td>1-7/4-11/10<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-104-1033<br />
</td>
        <td>1-4/3-14/9<br />
</td>
        <td>otonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-208-1033<br />
</td>
        <td>1-16/9-14/9<br />
</td>
        <td>otonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-413-1033<br />
</td>
        <td>1-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-620-1033<br />
</td>
        <td>1-7/5-14/9<br />
</td>
        <td>utonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-827-1033<br />
</td>
        <td>1-7/4-14/9<br />
</td>
        <td>utonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-929-1033<br />
</td>
        <td>1-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-207-1239<br />
</td>
        <td>1-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-208-1239<br />
</td>
        <td>1-16/9-11/8<br />
</td>
        <td>pentacircle<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-414-1239<br />
</td>
        <td>1-11/7-11/8<br />
</td>
        <td>utonal<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-827-1239<br />
</td>
        <td>1-7/4-11/8<br />
</td>
        <td>otonal<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-1032-1239<br />
</td>
        <td>1-11/10-11/8<br />
</td>
        <td>utonal<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-1033-1239<br />
</td>
        <td>1-14/9-11/8<br />
</td>
        <td>pentacircle<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-104-1343<br />
</td>
        <td>1-4/3-11/6<br />
</td>
        <td>otonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-311-1343<br />
</td>
        <td>1-5/3-11/6<br />
</td>
        <td>otonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-414-1343<br />
</td>
        <td>1-11/7-11/6<br />
</td>
        <td>utonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-929-1343<br />
</td>
        <td>1-7/6-11/6<br />
</td>
        <td>otonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-1032-1343<br />
</td>
        <td>1-11/10-11/6<br />
</td>
        <td>utonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-1239-1343<br />
</td>
        <td>1-11/8-11/6<br />
</td>
        <td>utonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-104-1445<br />
</td>
        <td>1-4/3-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-208-1445<br />
</td>
        <td>1-16/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-413-1445<br />
</td>
        <td>1-10/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-414-1445<br />
</td>
        <td>1-11/7-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-620-1445<br />
</td>
        <td>1-7/5-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-827-1445<br />
</td>
        <td>1-7/4-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-1032-1445<br />
</td>
        <td>1-11/10-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-1033-1445<br />
</td>
        <td>1-14/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-1239-1445<br />
</td>
        <td>1-11/8-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-1343-1445<br />
</td>
        <td>1-11/6-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><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>0-104-208-413<br />
</td>
        <td>1-4/3-16/9-10/9<br />
</td>
        <td>otonal<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-104-311-413<br />
</td>
        <td>1-4/3-5/3-10/9<br />
</td>
        <td>ambitonal<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-207-311-413<br />
</td>
        <td>1-5/4-5/3-10/9<br />
</td>
        <td>utonal<br />
</td>
        <td>8<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-207-311-620<br />
</td>
        <td>1-5/4-5/3-7/5<br />
</td>
        <td>starling<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-207-413-620<br />
</td>
        <td>1-5/4-10/9-7/5<br />
</td>
        <td>starling<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-208-413-620<br />
</td>
        <td>1-16/9-10/9-7/5<br />
</td>
        <td>thrush<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-311-413-620<br />
</td>
        <td>1-5/3-10/9-7/5<br />
</td>
        <td>starling<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-207-414-620<br />
</td>
        <td>1-5/4-11/7-7/5<br />
</td>
        <td>thrush<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-208-414-620<br />
</td>
        <td>1-16/9-11/7-7/5<br />
</td>
        <td>pele<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-207-413-827<br />
</td>
        <td>1-5/4-10/9-7/4<br />
</td>
        <td>werckismic<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-207-414-827<br />
</td>
        <td>1-5/4-11/7-7/4<br />
</td>
        <td>thrush<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-207-620-827<br />
</td>
        <td>1-5/4-7/5-7/4<br />
</td>
        <td>starling<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-413-620-827<br />
</td>
        <td>1-10/9-7/5-7/4<br />
</td>
        <td>thrush<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-414-620-827<br />
</td>
        <td>1-11/7-7/5-7/4<br />
</td>
        <td>werckismic<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-104-311-929<br />
</td>
        <td>1-4/3-5/3-7/6<br />
</td>
        <td>otonal<br />
</td>
        <td>18<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-311-620-929<br />
</td>
        <td>1-5/3-7/5-7/6<br />
</td>
        <td>starling<br />
</td>
        <td>18<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-620-827-929<br />
</td>
        <td>1-7/5-7/4-7/6<br />
</td>
        <td>utonal<br />
</td>
        <td>18<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-207-414-1032<br />
</td>
        <td>1-5/4-11/7-11/10<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-207-620-1032<br />
</td>
        <td>1-5/4-7/5-11/10<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-414-620-1032<br />
</td>
        <td>1-11/7-7/5-11/10<br />
</td>
        <td>werckismic<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-207-827-1032<br />
</td>
        <td>1-5/4-7/4-11/10<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-414-827-1032<br />
</td>
        <td>1-11/7-7/4-11/10<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-620-827-1032<br />
</td>
        <td>1-7/5-7/4-11/10<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-104-208-1033<br />
</td>
        <td>1-4/3-16/9-14/9<br />
</td>
        <td>otonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-104-413-1033<br />
</td>
        <td>1-4/3-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-208-413-1033<br />
</td>
        <td>1-16/9-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-208-620-1033<br />
</td>
        <td>1-16/9-7/5-14/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-413-620-1033<br />
</td>
        <td>1-10/9-7/5-14/9<br />
</td>
        <td>starling<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-413-827-1033<br />
</td>
        <td>1-10/9-7/4-14/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-620-827-1033<br />
</td>
        <td>1-7/5-7/4-14/9<br />
</td>
        <td>utonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-104-929-1033<br />
</td>
        <td>1-4/3-7/6-14/9<br />
</td>
        <td>ambitonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-620-929-1033<br />
</td>
        <td>1-7/5-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-827-929-1033<br />
</td>
        <td>1-7/4-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-207-414-1239<br />
</td>
        <td>1-5/4-11/7-11/8<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-208-414-1239<br />
</td>
        <td>1-16/9-11/7-11/8<br />
</td>
        <td>pentacircle<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-207-827-1239<br />
</td>
        <td>1-5/4-7/4-11/8<br />
</td>
        <td>otonal<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-414-827-1239<br />
</td>
        <td>1-11/7-7/4-11/8<br />
</td>
        <td>werckismic<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-207-1032-1239<br />
</td>
        <td>1-5/4-11/10-11/8<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-414-1032-1239<br />
</td>
        <td>1-11/7-11/10-11/8<br />
</td>
        <td>utonal<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-827-1032-1239<br />
</td>
        <td>1-7/4-11/10-11/8<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-208-1033-1239<br />
</td>
        <td>1-16/9-14/9-11/8<br />
</td>
        <td>pentacircle<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-827-1033-1239<br />
</td>
        <td>1-7/4-14/9-11/8<br />
</td>
        <td>pentacircle<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-104-311-1343<br />
</td>
        <td>1-4/3-5/3-11/6<br />
</td>
        <td>otonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-104-929-1343<br />
</td>
        <td>1-4/3-7/6-11/6<br />
</td>
        <td>otonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-311-929-1343<br />
</td>
        <td>1-5/3-7/6-11/6<br />
</td>
        <td>otonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-414-1032-1343<br />
</td>
        <td>1-11/7-11/10-11/6<br />
</td>
        <td>utonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-414-1239-1343<br />
</td>
        <td>1-11/7-11/8-11/6<br />
</td>
        <td>utonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-1032-1239-1343<br />
</td>
        <td>1-11/10-11/8-11/6<br />
</td>
        <td>utonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-104-208-1445<br />
</td>
        <td>1-4/3-16/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-104-413-1445<br />
</td>
        <td>1-4/3-10/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-208-413-1445<br />
</td>
        <td>1-16/9-10/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-208-414-1445<br />
</td>
        <td>1-16/9-11/7-11/9<br />
</td>
        <td>pentacircle<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-208-620-1445<br />
</td>
        <td>1-16/9-7/5-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-413-620-1445<br />
</td>
        <td>1-10/9-7/5-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-414-620-1445<br />
</td>
        <td>1-11/7-7/5-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-413-827-1445<br />
</td>
        <td>1-10/9-7/4-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-414-827-1445<br />
</td>
        <td>1-11/7-7/4-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-620-827-1445<br />
</td>
        <td>1-7/5-7/4-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-414-1032-1445<br />
</td>
        <td>1-11/7-11/10-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-620-1032-1445<br />
</td>
        <td>1-7/5-11/10-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-827-1032-1445<br />
</td>
        <td>1-7/4-11/10-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-104-1033-1445<br />
</td>
        <td>1-4/3-14/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-208-1033-1445<br />
</td>
        <td>1-16/9-14/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-413-1033-1445<br />
</td>
        <td>1-10/9-14/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-620-1033-1445<br />
</td>
        <td>1-7/5-14/9-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>0-827-1033-1445<br />
</td>
        <td>1-7/4-14/9-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>0-208-1239-1445<br />
</td>
        <td>1-16/9-11/8-11/9<br />
</td>
        <td>pentacircle<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>0-414-1239-1445<br />
</td>
        <td>1-11/7-11/8-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>0-827-1239-1445<br />
</td>
        <td>1-7/4-11/8-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>0-1032-1239-1445<br />
</td>
        <td>1-11/10-11/8-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>0-1033-1239-1445<br />
</td>
        <td>1-14/9-11/8-11/9<br />
</td>
        <td>pentacircle<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>0-104-1343-1445<br />
</td>
        <td>1-4/3-11/6-11/9<br />
</td>
        <td>ambitonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>0-414-1343-1445<br />
</td>
        <td>1-11/7-11/6-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>74<br />
</td>
        <td>0-1032-1343-1445<br />
</td>
        <td>1-11/10-11/6-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>0-1239-1343-1445<br />
</td>
        <td>1-11/8-11/6-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><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>0-207-311-413-620<br />
</td>
        <td>1-5/4-5/3-10/9-7/5<br />
</td>
        <td>starling<br />
</td>
        <td>12<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-207-413-620-827<br />
</td>
        <td>1-5/4-10/9-7/5-7/4<br />
</td>
        <td>thrush<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-207-414-620-827<br />
</td>
        <td>1-5/4-11/7-7/5-7/4<br />
</td>
        <td>thrush<br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-207-414-620-1032<br />
</td>
        <td>1-5/4-11/7-7/5-11/10<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-207-414-827-1032<br />
</td>
        <td>1-5/4-11/7-7/4-11/10<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-207-620-827-1032<br />
</td>
        <td>1-5/4-7/5-7/4-11/10<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-414-620-827-1032<br />
</td>
        <td>1-11/7-7/5-7/4-11/10<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-104-208-413-1033<br />
</td>
        <td>1-4/3-16/9-10/9-14/9<br />
</td>
        <td>otonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-208-413-620-1033<br />
</td>
        <td>1-16/9-10/9-7/5-14/9<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-413-620-827-1033<br />
</td>
        <td>1-10/9-7/5-7/4-14/9<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-620-827-929-1033<br />
</td>
        <td>1-7/5-7/4-7/6-14/9<br />
</td>
        <td>utonal<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-207-414-827-1239<br />
</td>
        <td>1-5/4-11/7-7/4-11/8<br />
</td>
        <td>thrush<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-207-414-1032-1239<br />
</td>
        <td>1-5/4-11/7-11/10-11/8<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-207-827-1032-1239<br />
</td>
        <td>1-5/4-7/4-11/10-11/8<br />
</td>
        <td>valinorsmic<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-414-827-1032-1239<br />
</td>
        <td>1-11/7-7/4-11/10-11/8<br />
</td>
        <td>thrush<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-104-311-929-1343<br />
</td>
        <td>1-4/3-5/3-7/6-11/6<br />
</td>
        <td>otonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-414-1032-1239-1343<br />
</td>
        <td>1-11/7-11/10-11/8-11/6<br />
</td>
        <td>utonal<br />
</td>
        <td>26<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-104-208-413-1445<br />
</td>
        <td>1-4/3-16/9-10/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-208-413-620-1445<br />
</td>
        <td>1-16/9-10/9-7/5-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-208-414-620-1445<br />
</td>
        <td>1-16/9-11/7-7/5-11/9<br />
</td>
        <td>pele<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-413-620-827-1445<br />
</td>
        <td>1-10/9-7/5-7/4-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-414-620-827-1445<br />
</td>
        <td>1-11/7-7/5-7/4-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-414-620-1032-1445<br />
</td>
        <td>1-11/7-7/5-11/10-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-414-827-1032-1445<br />
</td>
        <td>1-11/7-7/4-11/10-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-620-827-1032-1445<br />
</td>
        <td>1-7/5-7/4-11/10-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-104-208-1033-1445<br />
</td>
        <td>1-4/3-16/9-14/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-104-413-1033-1445<br />
</td>
        <td>1-4/3-10/9-14/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-208-413-1033-1445<br />
</td>
        <td>1-16/9-10/9-14/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-208-620-1033-1445<br />
</td>
        <td>1-16/9-7/5-14/9-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-413-620-1033-1445<br />
</td>
        <td>1-10/9-7/5-14/9-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-413-827-1033-1445<br />
</td>
        <td>1-10/9-7/4-14/9-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-620-827-1033-1445<br />
</td>
        <td>1-7/5-7/4-14/9-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-208-414-1239-1445<br />
</td>
        <td>1-16/9-11/7-11/8-11/9<br />
</td>
        <td>pentacircle<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-414-827-1239-1445<br />
</td>
        <td>1-11/7-7/4-11/8-11/9<br />
</td>
        <td>werckismic<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-414-1032-1239-1445<br />
</td>
        <td>1-11/7-11/10-11/8-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-827-1032-1239-1445<br />
</td>
        <td>1-7/4-11/10-11/8-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-208-1033-1239-1445<br />
</td>
        <td>1-16/9-14/9-11/8-11/9<br />
</td>
        <td>pentacircle<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-827-1033-1239-1445<br />
</td>
        <td>1-7/4-14/9-11/8-11/9<br />
</td>
        <td>pele<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-414-1032-1343-1445<br />
</td>
        <td>1-11/7-11/10-11/6-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-414-1239-1343-1445<br />
</td>
        <td>1-11/7-11/8-11/6-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-1032-1239-1343-1445<br />
</td>
        <td>1-11/10-11/8-11/6-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><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>0-207-414-620-827-1032<br />
</td>
        <td>1-5/4-11/7-7/5-7/4-11/10<br />
</td>
        <td>thrush<br />
</td>
        <td>20<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-207-414-827-1032-1239<br />
</td>
        <td>1-5/4-11/7-7/4-11/10-11/8<br />
</td>
        <td>thrush<br />
</td>
        <td>24<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-414-620-827-1032-1445<br />
</td>
        <td>1-11/7-7/5-7/4-11/10-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-104-208-413-1033-1445<br />
</td>
        <td>1-4/3-16/9-10/9-14/9-11/9<br />
</td>
        <td>otonal<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-208-413-620-1033-1445<br />
</td>
        <td>1-16/9-10/9-7/5-14/9-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-413-620-827-1033-1445<br />
</td>
        <td>1-10/9-7/5-7/4-14/9-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-414-827-1032-1239-1445<br />
</td>
        <td>1-11/7-7/4-11/10-11/8-11/9<br />
</td>
        <td>thrush<br />
</td>
        <td>28<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-414-1032-1239-1343-1445<br />
</td>
        <td>1-11/7-11/10-11/8-11/6-11/9<br />
</td>
        <td>utonal<br />
</td>
        <td>28<br />
</td>
    </tr>
</table>

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