Diaschismic/Chords: Difference between revisions

Revision as of 15:23, 25 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 2011-12-25 15:23:12 UTC.

The original revision id was 288444762.

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 [[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 <a class="wiki_link" href="/Diaschismic%20family#Diaschismic">diaschismic temperament</a>. 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>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-12-25 15:19:36 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-25 15:23:12 UTC</tt>.<br>
-: The original revision id was <tt>288444650</tt>.<br>
+: The original revision id was <tt>288444762</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>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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.
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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 = [&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 "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.
@@ Line 203: / Line 203: @@
 </pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chords of diaschismic&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; 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.&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chords of diaschismic&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; of 11-limit &lt;a class="wiki_link" href="/Diaschismic%20family#Diaschismic"&gt;diaschismic temperament&lt;/a&gt;. 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.&lt;br /&gt;
 &lt;br /&gt;
 The normal mapping for diaschismic is dia = [&amp;lt;2 0 11 31 45|, &amp;lt;0 1 -2 -8 -12|]. From this we may derive a val v = dia[1] - 100 dia[2] = &amp;lt;2 -100 211 831 1245| which we may use to sort and normalize the chords of diaschismic. Under &amp;quot;Chord&amp;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.&lt;br /&gt;

Diaschismic/Chords: Difference between revisions

Revision as of 15:23, 25 December 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search