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Wikispaces>genewardsmith **Imported revision 318560556 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 318956300 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-10 00:00:19 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>318956300</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]] by [[http://soundcloud.com/cityoftheasleep/sad-like-winter-trees|Igliashon Jones]] | [[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]] by [[http://soundcloud.com/cityoftheasleep/sad-like-winter-trees|Igliashon Jones]] | ||
[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]] by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Taylor]] | |||
=Inflated= | =Inflated= | ||
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<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a> by <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/sad-like-winter-trees" rel="nofollow">Igliashon Jones</a><br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a> by <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/sad-like-winter-trees" rel="nofollow">Igliashon Jones</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Taylor</a><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Inflated"></a><!-- ws:end:WikiTextHeadingRule:14 -->Inflated</h1> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Inflated"></a><!-- ws:end:WikiTextHeadingRule:14 -->Inflated</h1> | ||
Revision as of 00:00, 10 April 2012
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 2012-04-10 00:00:19 UTC.
- The original revision id was 318956300.
- 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:
[[toc|flat]] The 5-limit parent comma for the **augmented family** is 128/125, the [[128_125|diesis]]. Its [[monzo]] is |7 0 -3>, and flipping that yields <<3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for [[5-limit]] augmented, though a sharper fifth might be preferred to go with the sharp third. =Seven limit children= The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones. =August= [[Comma]]s: 36/35, 128/125 [[POTE tuning|POTE generator]]: 696.011 [[Map]]: [<3 0 7 -1|, <0 1 0 2|] [[Wedgie]]: <<3 0 6 -7 1 14|| [[edo|EDOs]]: [[9edo|9]], [[12edo|12]], [[45edo|45cd]], [[57edo|57cd]], [[69edo|69cd]] [[Badness]]: 0.0265 ==11-limit== Commas: 36/35, 45/44, 56/55 POTE generator: ~3/2 = 692.514 Map: [<3 0 7 -1 1|, <0 1 0 2 2|] EDOs: 9, 12, [[21edo|21]], [[33edo|33e]], [[45edo|45cde]] Badness: 0.0202 ==13-limit== Commas: 27/26, 36/35, 45/44, 56/55 POTE generator: ~3/2 = 688.783 Map: [<3 0 7 -1 1 -3|, <0 1 0 2 2 3|] EDOs: 9, 12, [[21edo|21]], [[33edo|33ef]], [[54edo|54bcef]] Badness: 0.0184 ==Augustus== Commas: 26/25, 36/35, 45/44, 56/55 POTE generator: ~3/2 = 685.356 Map: [<3 0 7 -1 1 11|, <0 1 0 2 2 0|] EDOs: 9, 12, 21f Badness: 0.0222 =Augene= Commas: 64/63, 126/125 [[POTE tuning|POTE generator]]: 709.257 Map: [<3 0 7 18|, <0 1 0 -2|] Wedgie: <<3 0 -6 -7 -18 -14|| EDOs: [[12edo|12]], [[27edo|27]], [[39edo|39d]], [[66edo|66cd]] Badness: 0.0248 ==11-limit== Commas: 56/55, 64/63, 100/99 POTE generator: ~3/2 = 711.177 Map: [<3 0 7 18 20|, <0 1 0 -2 -2|] EDOs: 12, 15, 27e Badness: 0.0196 [[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]] by [[http://soundcloud.com/cityoftheasleep/sad-like-winter-trees|Igliashon Jones]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]] by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Taylor]] =Inflated= Commas: 28/27, 128/125 POTE generator: ~3/2 = 722.719 Map: [<3 0 7 -6|, <0 1 0 3|] Wedgie: <<3 0 9 -7 6 21|| EDOs: 15, 48bc, 63bc, 78bc Badness: 0.0547 ==11-limit== Commas: 28/27, 55/54, 128/125 POTE generator: ~3/2 = 722.663 Map: [<3 0 7 -6|, <0 1 0 3|] EDOs: 15, 48bce, 63bce, 78bce Badness: 0.0312 =Deflated= Commas: 21/20, 128/125 POTE generator: ~3/2 = 681.629 Map: [<3 0 7 13|, <0 1 0 -1|] Wedgie: <<3 0 -3 -7 -13 -7|| EDOs: 3, 9, 18bd, 21d, 30bd Badness: 0.0591 =Hexe= Commas: 50/49, 128/125 [[POTE tuning|POTE generator]]: 710.963 Map: [<6 0 14 17|, <0 1 0 0|] Wedgie: <<6 0 0 -14 -17 0|| EDOs: [[6edo|6]], [[12edo|12]], [[30edo|30d]], [[37edo|37d]], [[42edo|42d]], [[54edo|54cd]] Badness: 0.0577 =Hemiaug= Commas: 128/125, 245/243 [[POTE tuning|POTE generator]]: ~28/27 = 45.118 Map: [<3 1 7 -1|, <0 2 0 5|] Wedgie: <<6 0 15 -14 7 35|| EDOs: [[24edo|24]], [[27edo|27]], [[105edo|105bc]] Badness: 0.0705 ==11-limit== Commas: 56/55, 128/125, 245/243 POTE generator: ~28/27 = 45.788 EDOs: 24, 27e, 51ce, 78ce Badness: 0.0382 =Triforce= Commas: 49/48, 128/125 [[POTE tuning|POTE generator]]: ~7/6 = 247.049 Map: [<3 0 7 6|, <0 2 0 1|] Wedgie: <<6 0 3 -14 -12 7|| EDOs: 6, 9, [[15edo|15]], [[24edo|24]], [[39edo|39]], [[63edo|63cd]], [[102edo|102cd]] Badness: 0.0202 [[image:triforce9.jpg]] ==11-limit== Commas: 56/55, 77/75, 128/125 [[POTE tuning|POTE generator]]: ~7/6 = 247.068 Map: [<3 0 7 6 8|, <0 2 0 1 1|] EDOs: 6, 9, 15, 24, 39, [[63edo|63cd]], [[102edo|102cd]] Badness: 0.0262 ==13-limit== Commas: 49/48, 56/55, 66/65, 77/75 [[POTE tuning|POTE generator]]: ~7/6 = 248.313 Map: [<3 0 7 6 8 4|, <0 2 0 1 1 3|] EDOs: 6, 9, 15, 24, [[63edo|63cdf]], [[87edo|87cdf]] Badness: 0.0202 [[triphi|Triforce(9) with L:s = phi]] =Niner= Niner gives 9 as the complexity of an otonal tetrad, tying it with augene as a temperament supported by 27edo. Niner[18], therefore, has nine such tetrads. Commas: 128/125, 686/675 POTE generator: ~3/2 = 707.167 Map: [<9 0 21 11|, <0 1 0 1|] Wedgie: <<9 0 9 -21 -11 21|| EDOs: 9, 18, 27, 63c, 90c Badness: 0.0672
Original HTML content:
<html><head><title>Augmented family</title></head><body><!-- ws:start:WikiTextTocRule:34:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#August">August</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Augene">Augene</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Inflated">Inflated</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Deflated">Deflated</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#Hexe">Hexe</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Hemiaug">Hemiaug</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Triforce">Triforce</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Niner">Niner</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> <!-- ws:end:WikiTextTocRule:52 --><br /> The 5-limit parent comma for the <strong>augmented family</strong> is 128/125, the <a class="wiki_link" href="/128_125">diesis</a>. Its <a class="wiki_link" href="/monzo">monzo</a> is |7 0 -3>, and flipping that yields <<3 0 -7|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. Hence the period is 1/3 octave, and this is what is used for a major third. The <a class="wiki_link" href="/generator">generator</a> can be taken as a fifth or a semitone, and <a class="wiki_link" href="/12edo">12edo</a>, with its excellent fifth, is an obvious tuning for <a class="wiki_link" href="/5-limit">5-limit</a> augmented, though a sharper fifth might be preferred to go with the sharp third. <br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1> The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="August"></a><!-- ws:end:WikiTextHeadingRule:2 -->August</h1> <a class="wiki_link" href="/Comma">Comma</a>s: 36/35, 128/125<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.011<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<3 0 7 -1|, <0 1 0 2|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<3 0 6 -7 1 14||<br /> <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/45edo">45cd</a>, <a class="wiki_link" href="/57edo">57cd</a>, <a class="wiki_link" href="/69edo">69cd</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0265<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="August-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> Commas: 36/35, 45/44, 56/55<br /> <br /> POTE generator: ~3/2 = 692.514<br /> <br /> Map: [<3 0 7 -1 1|, <0 1 0 2 2|]<br /> EDOs: 9, 12, <a class="wiki_link" href="/21edo">21</a>, <a class="wiki_link" href="/33edo">33e</a>, <a class="wiki_link" href="/45edo">45cde</a><br /> Badness: 0.0202<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="August-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 27/26, 36/35, 45/44, 56/55<br /> <br /> POTE generator: ~3/2 = 688.783<br /> <br /> Map: [<3 0 7 -1 1 -3|, <0 1 0 2 2 3|]<br /> EDOs: 9, 12, <a class="wiki_link" href="/21edo">21</a>, <a class="wiki_link" href="/33edo">33ef</a>, <a class="wiki_link" href="/54edo">54bcef</a><br /> Badness: 0.0184<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="August-Augustus"></a><!-- ws:end:WikiTextHeadingRule:8 -->Augustus</h2> Commas: 26/25, 36/35, 45/44, 56/55<br /> <br /> POTE generator: ~3/2 = 685.356<br /> <br /> Map: [<3 0 7 -1 1 11|, <0 1 0 2 2 0|]<br /> EDOs: 9, 12, 21f<br /> Badness: 0.0222<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Augene"></a><!-- ws:end:WikiTextHeadingRule:10 -->Augene</h1> Commas: 64/63, 126/125<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 709.257<br /> <br /> Map: [<3 0 7 18|, <0 1 0 -2|]<br /> Wedgie: <<3 0 -6 -7 -18 -14||<br /> EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/39edo">39d</a>, <a class="wiki_link" href="/66edo">66cd</a><br /> Badness: 0.0248<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Augene-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> Commas: 56/55, 64/63, 100/99<br /> <br /> POTE generator: ~3/2 = 711.177<br /> <br /> Map: [<3 0 7 18 20|, <0 1 0 -2 -2|]<br /> EDOs: 12, 15, 27e<br /> Badness: 0.0196<br /> <br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a> by <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/sad-like-winter-trees" rel="nofollow">Igliashon Jones</a><br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Taylor</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Inflated"></a><!-- ws:end:WikiTextHeadingRule:14 -->Inflated</h1> Commas: 28/27, 128/125<br /> <br /> POTE generator: ~3/2 = 722.719<br /> <br /> Map: [<3 0 7 -6|, <0 1 0 3|]<br /> Wedgie: <<3 0 9 -7 6 21||<br /> EDOs: 15, 48bc, 63bc, 78bc<br /> Badness: 0.0547<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Inflated-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> Commas: 28/27, 55/54, 128/125<br /> <br /> POTE generator: ~3/2 = 722.663<br /> <br /> Map: [<3 0 7 -6|, <0 1 0 3|]<br /> EDOs: 15, 48bce, 63bce, 78bce<br /> Badness: 0.0312<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Deflated"></a><!-- ws:end:WikiTextHeadingRule:18 -->Deflated</h1> Commas: 21/20, 128/125<br /> <br /> POTE generator: ~3/2 = 681.629<br /> <br /> Map: [<3 0 7 13|, <0 1 0 -1|]<br /> Wedgie: <<3 0 -3 -7 -13 -7||<br /> EDOs: 3, 9, 18bd, 21d, 30bd<br /> Badness: 0.0591<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="Hexe"></a><!-- ws:end:WikiTextHeadingRule:20 -->Hexe</h1> Commas: 50/49, 128/125<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.963<br /> <br /> Map: [<6 0 14 17|, <0 1 0 0|]<br /> Wedgie: <<6 0 0 -14 -17 0||<br /> EDOs: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/30edo">30d</a>, <a class="wiki_link" href="/37edo">37d</a>, <a class="wiki_link" href="/42edo">42d</a>, <a class="wiki_link" href="/54edo">54cd</a><br /> Badness: 0.0577<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h1> --><h1 id="toc11"><a name="Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:22 -->Hemiaug</h1> Commas: 128/125, 245/243<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~28/27 = 45.118<br /> <br /> Map: [<3 1 7 -1|, <0 2 0 5|]<br /> Wedgie: <<6 0 15 -14 7 35||<br /> EDOs: <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/105edo">105bc</a><br /> Badness: 0.0705<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Hemiaug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> Commas: 56/55, 128/125, 245/243<br /> <br /> POTE generator: ~28/27 = 45.788<br /> <br /> EDOs: 24, 27e, 51ce, 78ce<br /> Badness: 0.0382<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h1> --><h1 id="toc13"><a name="Triforce"></a><!-- ws:end:WikiTextHeadingRule:26 -->Triforce</h1> Commas: 49/48, 128/125<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 247.049<br /> <br /> Map: [<3 0 7 6|, <0 2 0 1|]<br /> Wedgie: <<6 0 3 -14 -12 7||<br /> EDOs: 6, 9, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/39edo">39</a>, <a class="wiki_link" href="/63edo">63cd</a>, <a class="wiki_link" href="/102edo">102cd</a><br /> Badness: 0.0202<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:53:<img src="/file/view/triforce9.jpg/271381934/triforce9.jpg" alt="" title="" /> --><img src="/file/view/triforce9.jpg/271381934/triforce9.jpg" alt="triforce9.jpg" title="triforce9.jpg" /><!-- ws:end:WikiTextLocalImageRule:53 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h2> --><h2 id="toc14"><a name="Triforce-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h2> Commas: 56/55, 77/75, 128/125<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 247.068<br /> <br /> Map: [<3 0 7 6 8|, <0 2 0 1 1|]<br /> EDOs: 6, 9, 15, 24, 39, <a class="wiki_link" href="/63edo">63cd</a>, <a class="wiki_link" href="/102edo">102cd</a><br /> Badness: 0.0262<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h2> --><h2 id="toc15"><a name="Triforce-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h2> Commas: 49/48, 56/55, 66/65, 77/75<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 248.313<br /> <br /> Map: [<3 0 7 6 8 4|, <0 2 0 1 1 3|]<br /> EDOs: 6, 9, 15, 24, <a class="wiki_link" href="/63edo">63cdf</a>, <a class="wiki_link" href="/87edo">87cdf</a><br /> Badness: 0.0202<br /> <br /> <a class="wiki_link" href="/triphi">Triforce(9) with L:s = phi</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h1> --><h1 id="toc16"><a name="Niner"></a><!-- ws:end:WikiTextHeadingRule:32 -->Niner</h1> Niner gives 9 as the complexity of an otonal tetrad, tying it with augene as a temperament supported by 27edo. Niner[18], therefore, has nine such tetrads.<br /> <br /> Commas: 128/125, 686/675<br /> <br /> POTE generator: ~3/2 = 707.167<br /> <br /> Map: [<9 0 21 11|, <0 1 0 1|]<br /> Wedgie: <<9 0 9 -21 -11 21||<br /> EDOs: 9, 18, 27, 63c, 90c<br /> Badness: 0.0672</body></html>