Unidec/Chords: Difference between revisions

<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 [[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 = [&lt;2 5 8 5 6|, &lt;0 -6 -11 2 3|]. From this we may derive a val v = uni[1] + uni[2] = &lt;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=

=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=

<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 unidec&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="/Gamelismic%20clan#Unidec"&gt;unidec temperament&lt;/a&gt;. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 werckismicmic, and by 385/384 keenanismic. &lt;br /&gt;

&lt;table class="wiki_table"&gt;