Unidec/Chords
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Original Wikitext content:
Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Gamelismic clan#Unidec|unidec temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 werckismicmic, and by 385/384 keenanismic. The normal mapping for unidec is uni = [<2 5 8 5 6|, <0 -6 -11 2 3|]. From this we may derive a val v = uni[1] + uni[2] = <2 -595 -1092 205 306| which we may use to sort and normalize the chords of harry. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column. Unidec has MOS of size 6, 20, 26, 46, and 72. Even the six-note MOS has some werckismic triads, and there are many more in the twenty note MOS, including many of the werckismic tetrad of complexity six and the keenanismic tetrad of complexity ten, which are likely to figure large in any composition in unidec. The essentially tempered chords of unidec either temper out 441/440 or 385/384; putting these together produces portent temperament, but there are no essentially portent chords. Adding the small ragisma, 4375/4374, to the commas of portent gives unidec, with very little additional tuning damage. Unidec is, in fact, quite an accurate temperament even compared to such things as miracle, but still has enough give in it to allow for some interesting essential tempering. =Triads= || Number || Chord || Transversal || Type || Complexity || || 1 || 0-100-201 || 1-10/9-7/4 || werckismic || 4 || || 2 || 0-101-201 || 1-11/7-7/4 || werckismic || 4 || || 3 || 0-101-300 || 1-11/7-11/8 || utonal || 6 || || 4 || 0-201-300 || 1-7/4-11/8 || otonal || 6 || || 5 || 0-201-499 || 1-7/4-6/5 || keenanismic || 10 || || 6 || 0-300-499 || 1-11/8-6/5 || keenanismic || 10 || || 7 || 0-100-599 || 1-10/9-4/3 || otonal || 12 || || 8 || 0-499-599 || 1-6/5-4/3 || utonal || 12 || || 9 || 0-201-798 || 1-7/4-7/6 || utonal || 16 || || 10 || 0-599-798 || 1-4/3-7/6 || otonal || 16 || || 11 || 0-101-899 || 1-11/7-11/6 || utonal || 18 || || 12 || 0-300-899 || 1-11/8-11/6 || utonal || 18 || || 13 || 0-599-899 || 1-4/3-11/6 || otonal || 18 || || 14 || 0-798-899 || 1-7/6-11/6 || otonal || 18 || || 15 || 0-201-1098 || 1-7/4-8/5 || keenanismic || 22 || || 16 || 0-300-1098 || 1-11/8-8/5 || keenanismic || 22 || || 17 || 0-499-1098 || 1-6/5-8/5 || otonal || 22 || || 18 || 0-599-1098 || 1-4/3-8/5 || utonal || 22 || || 19 || 0-798-1098 || 1-7/6-8/5 || keenanismic || 22 || || 20 || 0-899-1098 || 1-11/6-8/5 || keenanismic || 22 || || 21 || 0-100-1198 || 1-10/9-16/9 || otonal || 24 || || 22 || 0-599-1198 || 1-4/3-16/9 || ambitonal || 24 || || 23 || 0-1098-1198 || 1-8/5-16/9 || utonal || 24 || || 24 || 0-101-1297 || 1-11/7-7/5 || werckismic || 26 || || 25 || 0-201-1297 || 1-7/4-7/5 || utonal || 26 || || 26 || 0-499-1297 || 1-6/5-7/5 || otonal || 26 || || 27 || 0-798-1297 || 1-7/6-7/5 || utonal || 26 || || 28 || 0-1098-1297 || 1-8/5-7/5 || otonal || 26 || || 29 || 0-1198-1297 || 1-16/9-7/5 || werckismic || 26 || || 30 || 0-101-1396 || 1-11/7-11/10 || utonal || 28 || || 31 || 0-300-1396 || 1-11/8-11/10 || utonal || 28 || || 32 || 0-499-1396 || 1-6/5-11/10 || otonal || 28 || || 33 || 0-899-1396 || 1-11/6-11/10 || utonal || 28 || || 34 || 0-1098-1396 || 1-8/5-11/10 || otonal || 28 || || 35 || 0-1297-1396 || 1-7/5-11/10 || otonal || 28 || || 36 || 0-100-1397 || 1-10/9-14/9 || otonal || 28 || || 37 || 0-201-1397 || 1-7/4-14/9 || utonal || 28 || || 38 || 0-599-1397 || 1-4/3-14/9 || otonal || 28 || || 39 || 0-798-1397 || 1-7/6-14/9 || utonal || 28 || || 40 || 0-1198-1397 || 1-16/9-14/9 || otonal || 28 || || 41 || 0-1297-1397 || 1-7/5-14/9 || utonal || 28 || || 42 || 0-100-1496 || 1-10/9-11/9 || otonal || 30 || || 43 || 0-101-1496 || 1-11/7-11/9 || utonal || 30 || || 44 || 0-201-1496 || 1-7/4-11/9 || werckismic || 30 || || 45 || 0-300-1496 || 1-11/8-11/9 || utonal || 30 || || 46 || 0-599-1496 || 1-4/3-11/9 || otonal || 30 || || 47 || 0-899-1496 || 1-11/6-11/9 || utonal || 30 || || 48 || 0-1198-1496 || 1-16/9-11/9 || otonal || 30 || || 49 || 0-1297-1496 || 1-7/5-11/9 || werckismic || 30 || || 50 || 0-1396-1496 || 1-11/10-11/9 || utonal || 30 || || 51 || 0-1397-1496 || 1-14/9-11/9 || otonal || 30 || =Tetrads= || Number || Chord || Transversal || Type || Complexity || || 1 || 0-101-201-300 || 1-11/7-7/4-11/8 || werckismic || 6 || || 2 || 0-201-300-499 || 1-7/4-11/8-6/5 || keenanismic || 10 || || 3 || 0-101-300-899 || 1-11/7-11/8-11/6 || utonal || 18 || || 4 || 0-599-798-899 || 1-4/3-7/6-11/6 || otonal || 18 || || 5 || 0-201-300-1098 || 1-7/4-11/8-8/5 || keenanismic || 22 || || 6 || 0-201-499-1098 || 1-7/4-6/5-8/5 || keenanismic || 22 || || 7 || 0-300-499-1098 || 1-11/8-6/5-8/5 || keenanismic || 22 || || 8 || 0-499-599-1098 || 1-6/5-4/3-8/5 || ambitonal || 22 || || 9 || 0-201-798-1098 || 1-7/4-7/6-8/5 || keenanismic || 22 || || 10 || 0-599-798-1098 || 1-4/3-7/6-8/5 || keenanismic || 22 || || 11 || 0-300-899-1098 || 1-11/8-11/6-8/5 || keenanismic || 22 || || 12 || 0-599-899-1098 || 1-4/3-11/6-8/5 || keenanismic || 22 || || 13 || 0-798-899-1098 || 1-7/6-11/6-8/5 || keenanismic || 22 || || 14 || 0-100-599-1198 || 1-10/9-4/3-16/9 || otonal || 24 || || 15 || 0-599-1098-1198 || 1-4/3-8/5-16/9 || utonal || 24 || || 16 || 0-101-201-1297 || 1-11/7-7/4-7/5 || werckismic || 26 || || 17 || 0-201-499-1297 || 1-7/4-6/5-7/5 || keenanismic || 26 || || 18 || 0-201-798-1297 || 1-7/4-7/6-7/5 || utonal || 26 || || 19 || 0-201-1098-1297 || 1-7/4-8/5-7/5 || keenanismic || 26 || || 20 || 0-499-1098-1297 || 1-6/5-8/5-7/5 || otonal || 26 || || 21 || 0-798-1098-1297 || 1-7/6-8/5-7/5 || keenanismic || 26 || || 22 || 0-1098-1198-1297 || 1-8/5-16/9-7/5 || werckismic || 26 || || 23 || 0-101-300-1396 || 1-11/7-11/8-11/10 || utonal || 28 || || 24 || 0-300-499-1396 || 1-11/8-6/5-11/10 || keenanismic || 28 || || 25 || 0-101-899-1396 || 1-11/7-11/6-11/10 || utonal || 28 || || 26 || 0-300-899-1396 || 1-11/8-11/6-11/10 || utonal || 28 || || 27 || 0-300-1098-1396 || 1-11/8-8/5-11/10 || keenanismic || 28 || || 28 || 0-499-1098-1396 || 1-6/5-8/5-11/10 || otonal || 28 || || 29 || 0-899-1098-1396 || 1-11/6-8/5-11/10 || keenanismic || 28 || || 30 || 0-101-1297-1396 || 1-11/7-7/5-11/10 || werckismic || 28 || || 31 || 0-499-1297-1396 || 1-6/5-7/5-11/10 || otonal || 28 || || 32 || 0-1098-1297-1396 || 1-8/5-7/5-11/10 || otonal || 28 || || 33 || 0-100-201-1397 || 1-10/9-7/4-14/9 || werckismic || 28 || || 34 || 0-100-599-1397 || 1-10/9-4/3-14/9 || otonal || 28 || || 35 || 0-201-798-1397 || 1-7/4-7/6-14/9 || utonal || 28 || || 36 || 0-599-798-1397 || 1-4/3-7/6-14/9 || ambitonal || 28 || || 37 || 0-100-1198-1397 || 1-10/9-16/9-14/9 || otonal || 28 || || 38 || 0-599-1198-1397 || 1-4/3-16/9-14/9 || otonal || 28 || || 39 || 0-201-1297-1397 || 1-7/4-7/5-14/9 || utonal || 28 || || 40 || 0-798-1297-1397 || 1-7/6-7/5-14/9 || utonal || 28 || || 41 || 0-1198-1297-1397 || 1-16/9-7/5-14/9 || werckismic || 28 || || 42 || 0-100-201-1496 || 1-10/9-7/4-11/9 || werckismic || 30 || || 43 || 0-101-201-1496 || 1-11/7-7/4-11/9 || werckismic || 30 || || 44 || 0-101-300-1496 || 1-11/7-11/8-11/9 || utonal || 30 || || 45 || 0-201-300-1496 || 1-7/4-11/8-11/9 || werckismic || 30 || || 46 || 0-100-599-1496 || 1-10/9-4/3-11/9 || otonal || 30 || || 47 || 0-101-899-1496 || 1-11/7-11/6-11/9 || utonal || 30 || || 48 || 0-300-899-1496 || 1-11/8-11/6-11/9 || utonal || 30 || || 49 || 0-599-899-1496 || 1-4/3-11/6-11/9 || ambitonal || 30 || || 50 || 0-100-1198-1496 || 1-10/9-16/9-11/9 || otonal || 30 || || 51 || 0-599-1198-1496 || 1-4/3-16/9-11/9 || otonal || 30 || || 52 || 0-101-1297-1496 || 1-11/7-7/5-11/9 || werckismic || 30 || || 53 || 0-201-1297-1496 || 1-7/4-7/5-11/9 || werckismic || 30 || || 54 || 0-1198-1297-1496 || 1-16/9-7/5-11/9 || werckismic || 30 || || 55 || 0-101-1396-1496 || 1-11/7-11/10-11/9 || utonal || 30 || || 56 || 0-300-1396-1496 || 1-11/8-11/10-11/9 || utonal || 30 || || 57 || 0-899-1396-1496 || 1-11/6-11/10-11/9 || utonal || 30 || || 58 || 0-1297-1396-1496 || 1-7/5-11/10-11/9 || werckismic || 30 || || 59 || 0-100-1397-1496 || 1-10/9-14/9-11/9 || otonal || 30 || || 60 || 0-201-1397-1496 || 1-7/4-14/9-11/9 || werckismic || 30 || || 61 || 0-599-1397-1496 || 1-4/3-14/9-11/9 || otonal || 30 || || 62 || 0-1198-1397-1496 || 1-16/9-14/9-11/9 || otonal || 30 || || 63 || 0-1297-1397-1496 || 1-7/5-14/9-11/9 || werckismic || 30 || =Pentads= || Number || Chord || Transversal || Type || Complexity || || 1 || 0-201-300-499-1098 || 1-7/4-11/8-6/5-8/5 || keenanismic || 22 || || 2 || 0-599-798-899-1098 || 1-4/3-7/6-11/6-8/5 || keenanismic || 22 || || 3 || 0-201-499-1098-1297 || 1-7/4-6/5-8/5-7/5 || keenanismic || 26 || || 4 || 0-201-798-1098-1297 || 1-7/4-7/6-8/5-7/5 || keenanismic || 26 || || 5 || 0-101-300-899-1396 || 1-11/7-11/8-11/6-11/10 || utonal || 28 || || 6 || 0-300-499-1098-1396 || 1-11/8-6/5-8/5-11/10 || keenanismic || 28 || || 7 || 0-300-899-1098-1396 || 1-11/8-11/6-8/5-11/10 || keenanismic || 28 || || 8 || 0-499-1098-1297-1396 || 1-6/5-8/5-7/5-11/10 || otonal || 28 || || 9 || 0-100-599-1198-1397 || 1-10/9-4/3-16/9-14/9 || otonal || 28 || || 10 || 0-201-798-1297-1397 || 1-7/4-7/6-7/5-14/9 || utonal || 28 || || 11 || 0-101-201-300-1496 || 1-11/7-7/4-11/8-11/9 || werckismic || 30 || || 12 || 0-101-300-899-1496 || 1-11/7-11/8-11/6-11/9 || utonal || 30 || || 13 || 0-100-599-1198-1496 || 1-10/9-4/3-16/9-11/9 || otonal || 30 || || 14 || 0-101-201-1297-1496 || 1-11/7-7/4-7/5-11/9 || werckismic || 30 || || 15 || 0-101-300-1396-1496 || 1-11/7-11/8-11/10-11/9 || utonal || 30 || || 16 || 0-101-899-1396-1496 || 1-11/7-11/6-11/10-11/9 || utonal || 30 || || 17 || 0-300-899-1396-1496 || 1-11/8-11/6-11/10-11/9 || utonal || 30 || || 18 || 0-101-1297-1396-1496 || 1-11/7-7/5-11/10-11/9 || werckismic || 30 || || 19 || 0-100-201-1397-1496 || 1-10/9-7/4-14/9-11/9 || werckismic || 30 || || 20 || 0-100-599-1397-1496 || 1-10/9-4/3-14/9-11/9 || otonal || 30 || || 21 || 0-100-1198-1397-1496 || 1-10/9-16/9-14/9-11/9 || otonal || 30 || || 22 || 0-599-1198-1397-1496 || 1-4/3-16/9-14/9-11/9 || otonal || 30 || || 23 || 0-201-1297-1397-1496 || 1-7/4-7/5-14/9-11/9 || werckismic || 30 || || 24 || 0-1198-1297-1397-1496 || 1-16/9-7/5-14/9-11/9 || werckismic || 30 || =Hexads= || Number || Chord || Transversal || Type || Complexity || || 1 || 0-101-300-899-1396-1496 || 1-11/7-11/8-11/6-11/10-11/9 || utonal || 30 || || 2 || 0-100-599-1198-1397-1496 || 1-10/9-4/3-16/9-14/9-11/9 || otonal || 30 ||
Original HTML content:
<html><head><title>Chords of unidec</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="/Gamelismic%20clan#Unidec">unidec temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 werckismicmic, and by 385/384 keenanismic. <br />
<br />
The normal mapping for unidec is uni = [<2 5 8 5 6|, <0 -6 -11 2 3|]. From this we may derive a val v = uni[1] + uni[2] = <2 -595 -1092 205 306| which we may use to sort and normalize the chords of harry. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.<br />
<br />
Unidec has MOS of size 6, 20, 26, 46, and 72. Even the six-note MOS has some werckismic triads, and there are many more in the twenty note MOS, including many of the werckismic tetrad of complexity six and the keenanismic tetrad of complexity ten, which are likely to figure large in any composition in unidec. The essentially tempered chords of unidec either temper out 441/440 or 385/384; putting these together produces portent temperament, but there are no essentially portent chords. Adding the small ragisma, 4375/4374, to the commas of portent gives unidec, with very little additional tuning damage. Unidec is, in fact, quite an accurate temperament even compared to such things as miracle, but still has enough give in it to allow for some interesting essential tempering.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
<td>Complexity<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-100-201<br />
</td>
<td>1-10/9-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>4<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-101-201<br />
</td>
<td>1-11/7-7/4<br />
</td>
<td>werckismic<br />
</td>
<td>4<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-101-300<br />
</td>
<td>1-11/7-11/8<br />
</td>
<td>utonal<br />
</td>
<td>6<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-201-300<br />
</td>
<td>1-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
<td>6<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-201-499<br />
</td>
<td>1-7/4-6/5<br />
</td>
<td>keenanismic<br />
</td>
<td>10<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-300-499<br />
</td>
<td>1-11/8-6/5<br />
</td>
<td>keenanismic<br />
</td>
<td>10<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-100-599<br />
</td>
<td>1-10/9-4/3<br />
</td>
<td>otonal<br />
</td>
<td>12<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-499-599<br />
</td>
<td>1-6/5-4/3<br />
</td>
<td>utonal<br />
</td>
<td>12<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-201-798<br />
</td>
<td>1-7/4-7/6<br />
</td>
<td>utonal<br />
</td>
<td>16<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-599-798<br />
</td>
<td>1-4/3-7/6<br />
</td>
<td>otonal<br />
</td>
<td>16<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-101-899<br />
</td>
<td>1-11/7-11/6<br />
</td>
<td>utonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-300-899<br />
</td>
<td>1-11/8-11/6<br />
</td>
<td>utonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-599-899<br />
</td>
<td>1-4/3-11/6<br />
</td>
<td>otonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-798-899<br />
</td>
<td>1-7/6-11/6<br />
</td>
<td>otonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-201-1098<br />
</td>
<td>1-7/4-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-300-1098<br />
</td>
<td>1-11/8-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-499-1098<br />
</td>
<td>1-6/5-8/5<br />
</td>
<td>otonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-599-1098<br />
</td>
<td>1-4/3-8/5<br />
</td>
<td>utonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-798-1098<br />
</td>
<td>1-7/6-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-899-1098<br />
</td>
<td>1-11/6-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-100-1198<br />
</td>
<td>1-10/9-16/9<br />
</td>
<td>otonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-599-1198<br />
</td>
<td>1-4/3-16/9<br />
</td>
<td>ambitonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-1098-1198<br />
</td>
<td>1-8/5-16/9<br />
</td>
<td>utonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-101-1297<br />
</td>
<td>1-11/7-7/5<br />
</td>
<td>werckismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-201-1297<br />
</td>
<td>1-7/4-7/5<br />
</td>
<td>utonal<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-499-1297<br />
</td>
<td>1-6/5-7/5<br />
</td>
<td>otonal<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-798-1297<br />
</td>
<td>1-7/6-7/5<br />
</td>
<td>utonal<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-1098-1297<br />
</td>
<td>1-8/5-7/5<br />
</td>
<td>otonal<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-1198-1297<br />
</td>
<td>1-16/9-7/5<br />
</td>
<td>werckismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-101-1396<br />
</td>
<td>1-11/7-11/10<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-300-1396<br />
</td>
<td>1-11/8-11/10<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-499-1396<br />
</td>
<td>1-6/5-11/10<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-899-1396<br />
</td>
<td>1-11/6-11/10<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-1098-1396<br />
</td>
<td>1-8/5-11/10<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-1297-1396<br />
</td>
<td>1-7/5-11/10<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-100-1397<br />
</td>
<td>1-10/9-14/9<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-201-1397<br />
</td>
<td>1-7/4-14/9<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-599-1397<br />
</td>
<td>1-4/3-14/9<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-798-1397<br />
</td>
<td>1-7/6-14/9<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-1198-1397<br />
</td>
<td>1-16/9-14/9<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-1297-1397<br />
</td>
<td>1-7/5-14/9<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-100-1496<br />
</td>
<td>1-10/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-101-1496<br />
</td>
<td>1-11/7-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-201-1496<br />
</td>
<td>1-7/4-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-300-1496<br />
</td>
<td>1-11/8-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-599-1496<br />
</td>
<td>1-4/3-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-899-1496<br />
</td>
<td>1-11/6-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-1198-1496<br />
</td>
<td>1-16/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-1297-1496<br />
</td>
<td>1-7/5-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-1396-1496<br />
</td>
<td>1-11/10-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-1397-1496<br />
</td>
<td>1-14/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Tetrads"></a><!-- ws:end:WikiTextHeadingRule:2 -->Tetrads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
<td>Complexity<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-101-201-300<br />
</td>
<td>1-11/7-7/4-11/8<br />
</td>
<td>werckismic<br />
</td>
<td>6<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-201-300-499<br />
</td>
<td>1-7/4-11/8-6/5<br />
</td>
<td>keenanismic<br />
</td>
<td>10<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-101-300-899<br />
</td>
<td>1-11/7-11/8-11/6<br />
</td>
<td>utonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-599-798-899<br />
</td>
<td>1-4/3-7/6-11/6<br />
</td>
<td>otonal<br />
</td>
<td>18<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-201-300-1098<br />
</td>
<td>1-7/4-11/8-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-201-499-1098<br />
</td>
<td>1-7/4-6/5-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-300-499-1098<br />
</td>
<td>1-11/8-6/5-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-499-599-1098<br />
</td>
<td>1-6/5-4/3-8/5<br />
</td>
<td>ambitonal<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-201-798-1098<br />
</td>
<td>1-7/4-7/6-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-599-798-1098<br />
</td>
<td>1-4/3-7/6-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-300-899-1098<br />
</td>
<td>1-11/8-11/6-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-599-899-1098<br />
</td>
<td>1-4/3-11/6-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-798-899-1098<br />
</td>
<td>1-7/6-11/6-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-100-599-1198<br />
</td>
<td>1-10/9-4/3-16/9<br />
</td>
<td>otonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-599-1098-1198<br />
</td>
<td>1-4/3-8/5-16/9<br />
</td>
<td>utonal<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-101-201-1297<br />
</td>
<td>1-11/7-7/4-7/5<br />
</td>
<td>werckismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-201-499-1297<br />
</td>
<td>1-7/4-6/5-7/5<br />
</td>
<td>keenanismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-201-798-1297<br />
</td>
<td>1-7/4-7/6-7/5<br />
</td>
<td>utonal<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-201-1098-1297<br />
</td>
<td>1-7/4-8/5-7/5<br />
</td>
<td>keenanismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-499-1098-1297<br />
</td>
<td>1-6/5-8/5-7/5<br />
</td>
<td>otonal<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-798-1098-1297<br />
</td>
<td>1-7/6-8/5-7/5<br />
</td>
<td>keenanismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-1098-1198-1297<br />
</td>
<td>1-8/5-16/9-7/5<br />
</td>
<td>werckismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-101-300-1396<br />
</td>
<td>1-11/7-11/8-11/10<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-300-499-1396<br />
</td>
<td>1-11/8-6/5-11/10<br />
</td>
<td>keenanismic<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-101-899-1396<br />
</td>
<td>1-11/7-11/6-11/10<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-300-899-1396<br />
</td>
<td>1-11/8-11/6-11/10<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-300-1098-1396<br />
</td>
<td>1-11/8-8/5-11/10<br />
</td>
<td>keenanismic<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-499-1098-1396<br />
</td>
<td>1-6/5-8/5-11/10<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-899-1098-1396<br />
</td>
<td>1-11/6-8/5-11/10<br />
</td>
<td>keenanismic<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-101-1297-1396<br />
</td>
<td>1-11/7-7/5-11/10<br />
</td>
<td>werckismic<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-499-1297-1396<br />
</td>
<td>1-6/5-7/5-11/10<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-1098-1297-1396<br />
</td>
<td>1-8/5-7/5-11/10<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-100-201-1397<br />
</td>
<td>1-10/9-7/4-14/9<br />
</td>
<td>werckismic<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-100-599-1397<br />
</td>
<td>1-10/9-4/3-14/9<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-201-798-1397<br />
</td>
<td>1-7/4-7/6-14/9<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-599-798-1397<br />
</td>
<td>1-4/3-7/6-14/9<br />
</td>
<td>ambitonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-100-1198-1397<br />
</td>
<td>1-10/9-16/9-14/9<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-599-1198-1397<br />
</td>
<td>1-4/3-16/9-14/9<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-201-1297-1397<br />
</td>
<td>1-7/4-7/5-14/9<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-798-1297-1397<br />
</td>
<td>1-7/6-7/5-14/9<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-1198-1297-1397<br />
</td>
<td>1-16/9-7/5-14/9<br />
</td>
<td>werckismic<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-100-201-1496<br />
</td>
<td>1-10/9-7/4-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-101-201-1496<br />
</td>
<td>1-11/7-7/4-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-101-300-1496<br />
</td>
<td>1-11/7-11/8-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-201-300-1496<br />
</td>
<td>1-7/4-11/8-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-100-599-1496<br />
</td>
<td>1-10/9-4/3-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-101-899-1496<br />
</td>
<td>1-11/7-11/6-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-300-899-1496<br />
</td>
<td>1-11/8-11/6-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-599-899-1496<br />
</td>
<td>1-4/3-11/6-11/9<br />
</td>
<td>ambitonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-100-1198-1496<br />
</td>
<td>1-10/9-16/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-599-1198-1496<br />
</td>
<td>1-4/3-16/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-101-1297-1496<br />
</td>
<td>1-11/7-7/5-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-201-1297-1496<br />
</td>
<td>1-7/4-7/5-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-1198-1297-1496<br />
</td>
<td>1-16/9-7/5-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-101-1396-1496<br />
</td>
<td>1-11/7-11/10-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-300-1396-1496<br />
</td>
<td>1-11/8-11/10-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-899-1396-1496<br />
</td>
<td>1-11/6-11/10-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-1297-1396-1496<br />
</td>
<td>1-7/5-11/10-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-100-1397-1496<br />
</td>
<td>1-10/9-14/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-201-1397-1496<br />
</td>
<td>1-7/4-14/9-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-599-1397-1496<br />
</td>
<td>1-4/3-14/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-1198-1397-1496<br />
</td>
<td>1-16/9-14/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-1297-1397-1496<br />
</td>
<td>1-7/5-14/9-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Pentads"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pentads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
<td>Complexity<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-201-300-499-1098<br />
</td>
<td>1-7/4-11/8-6/5-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-599-798-899-1098<br />
</td>
<td>1-4/3-7/6-11/6-8/5<br />
</td>
<td>keenanismic<br />
</td>
<td>22<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-201-499-1098-1297<br />
</td>
<td>1-7/4-6/5-8/5-7/5<br />
</td>
<td>keenanismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-201-798-1098-1297<br />
</td>
<td>1-7/4-7/6-8/5-7/5<br />
</td>
<td>keenanismic<br />
</td>
<td>26<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-101-300-899-1396<br />
</td>
<td>1-11/7-11/8-11/6-11/10<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-300-499-1098-1396<br />
</td>
<td>1-11/8-6/5-8/5-11/10<br />
</td>
<td>keenanismic<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-300-899-1098-1396<br />
</td>
<td>1-11/8-11/6-8/5-11/10<br />
</td>
<td>keenanismic<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-499-1098-1297-1396<br />
</td>
<td>1-6/5-8/5-7/5-11/10<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-100-599-1198-1397<br />
</td>
<td>1-10/9-4/3-16/9-14/9<br />
</td>
<td>otonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-201-798-1297-1397<br />
</td>
<td>1-7/4-7/6-7/5-14/9<br />
</td>
<td>utonal<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-101-201-300-1496<br />
</td>
<td>1-11/7-7/4-11/8-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-101-300-899-1496<br />
</td>
<td>1-11/7-11/8-11/6-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-100-599-1198-1496<br />
</td>
<td>1-10/9-4/3-16/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-101-201-1297-1496<br />
</td>
<td>1-11/7-7/4-7/5-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-101-300-1396-1496<br />
</td>
<td>1-11/7-11/8-11/10-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-101-899-1396-1496<br />
</td>
<td>1-11/7-11/6-11/10-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-300-899-1396-1496<br />
</td>
<td>1-11/8-11/6-11/10-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-101-1297-1396-1496<br />
</td>
<td>1-11/7-7/5-11/10-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-100-201-1397-1496<br />
</td>
<td>1-10/9-7/4-14/9-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-100-599-1397-1496<br />
</td>
<td>1-10/9-4/3-14/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-100-1198-1397-1496<br />
</td>
<td>1-10/9-16/9-14/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-599-1198-1397-1496<br />
</td>
<td>1-4/3-16/9-14/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-201-1297-1397-1496<br />
</td>
<td>1-7/4-7/5-14/9-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-1198-1297-1397-1496<br />
</td>
<td>1-16/9-7/5-14/9-11/9<br />
</td>
<td>werckismic<br />
</td>
<td>30<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Hexads"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hexads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
<td>Complexity<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-101-300-899-1396-1496<br />
</td>
<td>1-11/7-11/8-11/6-11/10-11/9<br />
</td>
<td>utonal<br />
</td>
<td>30<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-100-599-1198-1397-1496<br />
</td>
<td>1-10/9-4/3-16/9-14/9-11/9<br />
</td>
<td>otonal<br />
</td>
<td>30<br />
</td>
</tr>
</table>
</body></html>