Chromatic pairs: Difference between revisions

Revision as of 16:11, 18 March 2011

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By a //chromatic pair// is meant a pair of MOS in some rank two temperament (which may often be a [[Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with [[Target tunings|tuning target]] the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.

[[toc|flat]]

=Terrain=
Subgroup: 2.9/5.9/7
Commas: 250047/250000
Related temperament: [[Minortonic family#Domain|domain]]
POTE generator: ~10/9 = 182.462

Map: [<3 0 -4|, <0 1 2|]
EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
Error: 0.0443 cents

Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic.

[[terrain9|Nine note albitonic scale]]
[[terrain15|Fifteen note chromatic scale]]

=Nestoria=
Subgroup: 2.3.5.19
Commas: 361/360, 513/512
Related temperament: [[Schismatic family|schismatic]]

POTE generator: ~3/2 = 701.746

Map: [<1 0 15 9], <0 1 -8 -3|]
EDOs: 7, 12, 17, 29, 41, 53, 118, 171
Error: 1.819 cents

[[nestoria7|Seven note albitonic scale]]
[[nestoria12|Twelve note chromatic scale]]

==Photia==
Subgroup 2.3.5.17.19
Commas: 171/170, 256/255, 324/323
Related temperament: [[Schismatic family|schismatic]]

POTE generator: ~3/2 = 701.470

Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|]
EDOs: 7, 12, 17, 29, 41, 53, 65
Error: 3.457 cents

[[photia7|Seven note albitonic scale]]
[[photia12|Twelve note chromatic scale]]

=Cata=
Subgroup: 2.3.5.13
Commas: 325/324, 625/624
Related temperament: [[Kleismic family|catakleismic]]

POTE generator: ~6/5 = 317.076

Map: [<1 0 1 0|, <0 6 5 14|]
EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246
Error: 0.9355 cents

[[cata7|Seven note albitonic scale]]
[[cata11|Eleven note mega albitonic scale]]
[[cata15|Fifteen note chromatic scale]]
[[cata19|Nineteen note mega chromatic scale]]

=Bridgetown=
Subgroup: 2.3.11/5.13/5
Commas: 352/351, 676/675
Related temperament: [[The Archipelago|barabdos]]

POTE generator: ~15/13 = 248.285

Map: [<1 0 -6 -1|, <0 2 9 3|]
EDOs: 5, 9, 14, 19, 24, 29
Error: 0.8996 cents

[[bridgetown9|Nine note albitonic scale]]
[[bridgetown14|Fourteen note chromatic scale]]

=Huntington=
Subgroup: 2.5.7.13
Commas: 640/637, 10985/10976

POTE generator: ~16/13 = 357.002

Map: [<1 5 4 4|, <0 -9 -4 -1|]
EDOs: 7, 10, 17, 27, 37, 84, 121, 400
Error: 2.1001 cents

[[huntington7|Seven note haplotonic scale]]
[[huntington10|Ten note albitonic scale]]
[[huntington17|Seventeen note chromatic scale]]

=Bossier=
Subgroup: 2.7.11.13
Commas: 1573/1569, 15488/15379

POTE generator: ~14/11 = 421.309

Map: [<1 0 1 3|, <0 8 7 2|]
EDOs: 17, 20, 37, 57, 94, 225
Error: 2.665 cents

[[bossier8|Eight note albitonic scale]]
[[bossier11|Eleven note chromatic scale]]
[[bossier14|Fourteen note mega chromatic scale]]

=Roulette=
Subgroup: 2.5.7.11.13
Commas: 176/175, 1375/1372, 640/637
Related temperament: [[Wuerschmidt family|Hemiwuerschmidt]]

POTE generator: ~28/25 = 194.594

Map: [<1 0 -3 -7 -13|, <0 2 5 9 -8|]
EDOs: 6, 7, 13, 19, 25, 31, 37
Error: 2.555 cents

[[roulette6|Six note haplotonic scale]]
[[roulette7|Seven note albitonic scale]]
[[roulette13|Thirteen note chromatic scale]]
[[roulette19|Nineteen note mega chromatic scale]]

=Baldy=
Subgroup: 2.9.5.7.13
Commas: 225/224, 325/325, 640/637
Related temperament: [[Schismatic family|Garibaldi]]

POTE generator: ~9/8 = 204.090

Map: [<1 0 15 25 -8|, <0 1 -4 -7 10|]
EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
Error: 2.617 cents

[[baldy6|Six note haplotonic scale]]
[[baldy11|Eleven note albitonic scale]]
[[baldy17|Seventeen note chromatic scale]]

=Hemif=
Subgroup: 2.3.7.11.13
Commas: 144/143, 243/242, 364/363
Related temperament: [[Breedsmic temperaments|Hemififths]]

POTE generator: ~11/9 = 351.691

Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]
EDOs: 7, 10, 17, 24, 41, 58
Error: 4.867 cents

[[hemif7|Seven note haplotonic scale]]
[[hemif10|Ten note albitonic scale]]
[[hemif17|Seventeen note chromatic scale]]

=Radon=
Subgroup: 2.3.7.11
Commas: 896/891, 1029/1024
Related temperament: [[Gamelismic clan|Rodan]]

POTE generator: ~8/7 = 234.381

Map: [<1 1 3 6|, <0 3 -1 -13|]
EDOs: 5, 36, 41, 87, 128
Error: 2.925 cents

[[radon5|Five note haplotonic scale]]
[[radon11|Eleven note albitonic scale]]
[[radon16|Sixteen note chromatic scale]]

=Pepperoni=
Subgroup: 2.3.11/7.13/7
Commas: 352/351, 364/363
Related temperament: [[Margo Schulter]]'s [[Pepper temperament|pepper temperament]]

POTE generator: ~3/2 = 704.052

Map: [<1 0 7 12|, <0 1 -4 -7|]
EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271
Error: 1.298 cents

[[pepperoni7|Seven note albitonic scale]]
[[pepperoni12|Twelve note chromatic scale]]

=Skwares=
Subgroup: 2.3.7.11
Commas: 99/98, 243/242
Related temperament: [[Meantone family|squares]]

POTE generator: ~9/7 = 425.244

Map: [<1 3 6 7|, <0 -4 -9 -10|]
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206
Error: 3.009 cents

[[skwares8|Eight note albitonic scale]]
[[skwares11|Eleven note mega albitonic scale]]
[[skwares14|Fourteen note chromatic scale]]

=Tutone=
Subgroup: 2.9.5.7.11
Commas: 81/80, 99/98, 126/125
Related temperament: [[Meantone family|meantone]]

POTE generator: ~9/8 = 193.937

Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]
EDOs: 6, 7, 13, 19, 25, 31, 99
Error: 3.218 cents

[[tutone6|Six note haplotonic scale]]
[[tutone7|Seven note albitonic scale]]
[[tutone13|Thirteen note chromatic scale]]

==Leantone==
Subgroup: 2.9.5.7.11
Commas: 45/44, 56/55, 81/80
Related temperament: [[Meantone family|flattone]]

POTE generator: ~9/8 = 192.500

Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
EDOs: 6, 7, 13, 19, 25, 31, 56, 81
Error: 8.680 cents

[[leantone6|Six note haplotonic scale]]
[[leantone7|Seven note albitonic scale]]
[[leantone13|Thirteen note chromatic scale]]

=Mohaha=
Subgroup: 2.3.5.11
Commas: 81/80, 121/120
Related temperament: [[Meantone family|mohajira]]

POTE generator: ~11/9 = 348.094

Map: [<1 1 0 2|, <0 2 8 5|]
EDOs: 7, 10, 17, 24, 31, 131
Error: 3.813 cents

[[mohaha7|Seven note albitonic scale]]
[[mohaha10|Ten note chromatic scale]]

==Mohoho==
Subgroup: 2.3.5.11.13
Commas: 66/65, 81/80, 121/120

POTE generator: ~11/9 = 348.916

Map: [<1 1 0 2 4|, <0 2 8 5 -1|]
EDOs: 7, 10, 17, 24, 31, 55
Error: 4.829 cents

=Score=
Subgroup: 2.7.11.13
Commas: 343/338, 847/832

POTE generator: ~11/8 = 540.099

Map: [<1 1 3 1|, <0 4 1 6|]
EDOs: 5, 7, 9, 11, 20
Error: 3.846 cents

[[score5|Five note haplotonic scale]]
[[score7|Seven note albitonic scale]]
[[score9|Nine note mega albitonic scale]]
[[score11|Eleven note chromatic scale]]

=Supra=
Subgroup: 2.3.7.11
Commas: 64/63, 99/98
Related temperament: [[Archytas clan|superpyth]]

POTE generator: ~3/2 = 707.192

Map: [<1 0 6 13|, <0 1 -2 -6|]
EDOs: 5, 7, 12, 17, 22, 39, 56
Error: 5.414 cents

[[supra7|Seven note albitonic scale]]
[[supra12|Twelve note chromatic scale]]

==Supraphon==
Subgroup: 2.3.7.11.13
Commas: 64/63, 78/77, 99/98

POTE generator: ~3/2 = 706.137

Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]
EDOs: 5, 7, 12, 17
Error: 5.132 cents

==Machine==
Subgroup: 2.9.7.11
Commas: 64/63, 99/98

POTE generator: ~9/8 = 214.384

Map: [<1 0 6 13|, <0 1 -1 -3|]
EDOs: 5, 6, 11, 17, 28
Error: 5.414 cents

[[machine5|Five note haplotonic scale]]
[[machine6|Six note albitonic scale]]
[[machine11|Eleven note chromatic scale]]

=Augment=
Subgroup: 2.5.7.11
Commas: 56/55, 128/125
Related temperament: [[Augmented family|augmented]]

POTE generator: ~8/7

Map: [<3 7 0 2|, <0 0 1 1|]
EDOs: 3, 6, 9, 15, 21
Error: 6.632 cents

[[augment6|Six note haplotonic scale]]
[[augment9|Nine note albitonic scale]]
[[augment12|Twelve note chromatic scale]]

=Greeley=
Subgroup: 2.5/3.7/3.11/3
Commas: 121/120, 126/125

POTE generator: ~11/10 = 156.055

Map: [<1 1 2 2|, <0 -2 -6 -1|]
EDOs: 8, 15, 23, 77, 100
Error: 7.555 cents

[[greeley8|Eight note albitonic scale]]
[[greeley15|Fifteen note chromatic scale]]

Original HTML content:

<html><head><title>Chromatic pairs</title></head><body>By a <em>chromatic pair</em> is meant a pair of MOS in some rank two temperament (which may often be a <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup temperament</a>) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called &quot;albitonic&quot; from the Latin word for &quot;white&quot;. Also included at times are &quot;haplotonic&quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with <a class="wiki_link" href="/Target%20tunings">tuning target</a> the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.<br />
<br />
<!-- ws:start:WikiTextTocRule:46:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: -->
<!-- ws:end:WikiTextTocRule:70 --><br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h1>
Subgroup: 2.9/5.9/7<br />
Commas: 250047/250000<br />
Related temperament: <a class="wiki_link" href="/Minortonic%20family#Domain">domain</a><br />
POTE generator: ~10/9 = 182.462<br />
<br />
Map: [&lt;3 0 -4|, &lt;0 1 2|]<br />
EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558<br />
Error: 0.0443 cents<br />
<br />
Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic.<br />
<br />
<a class="wiki_link" href="/terrain9">Nine note albitonic scale</a><br />
<a class="wiki_link" href="/terrain15">Fifteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Nestoria"></a><!-- ws:end:WikiTextHeadingRule:2 -->Nestoria</h1>
Subgroup: 2.3.5.19<br />
Commas: 361/360, 513/512<br />
Related temperament: <a class="wiki_link" href="/Schismatic%20family">schismatic</a><br />
<br />
POTE generator: ~3/2 = 701.746<br />
<br />
Map: [&lt;1 0 15 9], &lt;0 1 -8 -3|]<br />
EDOs: 7, 12, 17, 29, 41, 53, 118, 171<br />
Error: 1.819 cents<br />
<br />
<a class="wiki_link" href="/nestoria7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/nestoria12">Twelve note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Nestoria-Photia"></a><!-- ws:end:WikiTextHeadingRule:4 -->Photia</h2>
Subgroup 2.3.5.17.19<br />
Commas: 171/170, 256/255, 324/323<br />
Related temperament: <a class="wiki_link" href="/Schismatic%20family">schismatic</a><br />
<br />
POTE generator: ~3/2 = 701.470<br />
<br />
Map: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]<br />
EDOs: 7, 12, 17, 29, 41, 53, 65<br />
Error: 3.457 cents<br />
<br />
<a class="wiki_link" href="/photia7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/photia12">Twelve note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:6 -->Cata</h1>
Subgroup: 2.3.5.13<br />
Commas: 325/324, 625/624<br />
Related temperament: <a class="wiki_link" href="/Kleismic%20family">catakleismic</a><br />
<br />
POTE generator: ~6/5 = 317.076<br />
<br />
Map: [&lt;1 0 1 0|, &lt;0 6 5 14|]<br />
EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246<br />
Error: 0.9355 cents<br />
<br />
<a class="wiki_link" href="/cata7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/cata11">Eleven note mega albitonic scale</a><br />
<a class="wiki_link" href="/cata15">Fifteen note chromatic scale</a><br />
<a class="wiki_link" href="/cata19">Nineteen note mega chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:8 -->Bridgetown</h1>
Subgroup: 2.3.11/5.13/5<br />
Commas: 352/351, 676/675<br />
Related temperament: <a class="wiki_link" href="/The%20Archipelago">barabdos</a><br />
<br />
POTE generator: ~15/13 = 248.285<br />
<br />
Map: [&lt;1 0 -6 -1|, &lt;0 2 9 3|]<br />
EDOs: 5, 9, 14, 19, 24, 29<br />
Error: 0.8996 cents<br />
<br />
<a class="wiki_link" href="/bridgetown9">Nine note albitonic scale</a><br />
<a class="wiki_link" href="/bridgetown14">Fourteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:10 -->Huntington</h1>
Subgroup: 2.5.7.13<br />
Commas: 640/637, 10985/10976<br />
<br />
POTE generator: ~16/13 = 357.002<br />
<br />
Map: [&lt;1 5 4 4|, &lt;0 -9 -4 -1|]<br />
EDOs: 7, 10, 17, 27, 37, 84, 121, 400<br />
Error: 2.1001 cents<br />
<br />
<a class="wiki_link" href="/huntington7">Seven note haplotonic scale</a><br />
<a class="wiki_link" href="/huntington10">Ten note albitonic scale</a><br />
<a class="wiki_link" href="/huntington17">Seventeen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:12 -->Bossier</h1>
Subgroup: 2.7.11.13<br />
Commas: 1573/1569, 15488/15379<br />
<br />
POTE generator: ~14/11 = 421.309<br />
<br />
Map: [&lt;1 0 1 3|, &lt;0 8 7 2|]<br />
EDOs: 17, 20, 37, 57, 94, 225<br />
Error: 2.665 cents<br />
<br />
<a class="wiki_link" href="/bossier8">Eight note albitonic scale</a><br />
<a class="wiki_link" href="/bossier11">Eleven note chromatic scale</a><br />
<a class="wiki_link" href="/bossier14">Fourteen note mega chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:14 -->Roulette</h1>
Subgroup: 2.5.7.11.13<br />
Commas: 176/175, 1375/1372, 640/637<br />
Related temperament: <a class="wiki_link" href="/Wuerschmidt%20family">Hemiwuerschmidt</a><br />
<br />
POTE generator: ~28/25 = 194.594<br />
<br />
Map: [&lt;1 0 -3 -7 -13|, &lt;0 2 5 9 -8|]<br />
EDOs: 6, 7, 13, 19, 25, 31, 37<br />
Error: 2.555 cents<br />
<br />
<a class="wiki_link" href="/roulette6">Six note haplotonic scale</a><br />
<a class="wiki_link" href="/roulette7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/roulette13">Thirteen note chromatic scale</a><br />
<a class="wiki_link" href="/roulette19">Nineteen note mega chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:16 -->Baldy</h1>
Subgroup: 2.9.5.7.13<br />
Commas: 225/224, 325/325, 640/637<br />
Related temperament: <a class="wiki_link" href="/Schismatic%20family">Garibaldi</a><br />
<br />
POTE generator: ~9/8 = 204.090<br />
<br />
Map: [&lt;1 0 15 25 -8|, &lt;0 1 -4 -7 10|]<br />
EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147<br />
Error: 2.617 cents<br />
<br />
<a class="wiki_link" href="/baldy6">Six note haplotonic scale</a><br />
<a class="wiki_link" href="/baldy11">Eleven note albitonic scale</a><br />
<a class="wiki_link" href="/baldy17">Seventeen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hemif</h1>
Subgroup: 2.3.7.11.13<br />
Commas: 144/143, 243/242, 364/363<br />
Related temperament: <a class="wiki_link" href="/Breedsmic%20temperaments">Hemififths</a><br />
<br />
POTE generator: ~11/9 = 351.691<br />
<br />
Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]<br />
EDOs: 7, 10, 17, 24, 41, 58<br />
Error: 4.867 cents<br />
<br />
<a class="wiki_link" href="/hemif7">Seven note haplotonic scale</a><br />
<a class="wiki_link" href="/hemif10">Ten note albitonic scale</a><br />
<a class="wiki_link" href="/hemif17">Seventeen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:20 -->Radon</h1>
Subgroup: 2.3.7.11<br />
Commas: 896/891, 1029/1024<br />
Related temperament: <a class="wiki_link" href="/Gamelismic%20clan">Rodan</a><br />
<br />
POTE generator: ~8/7 = 234.381<br />
<br />
Map: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]<br />
EDOs: 5, 36, 41, 87, 128<br />
Error: 2.925 cents<br />
<br />
<a class="wiki_link" href="/radon5">Five note haplotonic scale</a><br />
<a class="wiki_link" href="/radon11">Eleven note albitonic scale</a><br />
<a class="wiki_link" href="/radon16">Sixteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:22 -->Pepperoni</h1>
Subgroup: 2.3.11/7.13/7<br />
Commas: 352/351, 364/363<br />
Related temperament: <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>'s <a class="wiki_link" href="/Pepper%20temperament">pepper temperament</a><br />
<br />
POTE generator: ~3/2 = 704.052<br />
<br />
Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]<br />
EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br />
Error: 1.298 cents<br />
<br />
<a class="wiki_link" href="/pepperoni7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/pepperoni12">Twelve note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:24 -->Skwares</h1>
Subgroup: 2.3.7.11<br />
Commas: 99/98, 243/242<br />
Related temperament: <a class="wiki_link" href="/Meantone%20family">squares</a><br />
<br />
POTE generator: ~9/7 = 425.244<br />
<br />
Map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]<br />
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206<br />
Error: 3.009 cents<br />
<br />
<a class="wiki_link" href="/skwares8">Eight note albitonic scale</a><br />
<a class="wiki_link" href="/skwares11">Eleven note mega albitonic scale</a><br />
<a class="wiki_link" href="/skwares14">Fourteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:26 -->Tutone</h1>
Subgroup: 2.9.5.7.11<br />
Commas: 81/80, 99/98, 126/125<br />
Related temperament: <a class="wiki_link" href="/Meantone%20family">meantone</a><br />
<br />
POTE generator: ~9/8 = 193.937<br />
<br />
Map: [&lt;1 0 -4 -13 -25|, &lt;0 1 2 5 9|]<br />
EDOs: 6, 7, 13, 19, 25, 31, 99<br />
Error: 3.218 cents<br />
<br />
<a class="wiki_link" href="/tutone6">Six note haplotonic scale</a><br />
<a class="wiki_link" href="/tutone7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/tutone13">Thirteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Tutone-Leantone"></a><!-- ws:end:WikiTextHeadingRule:28 -->Leantone</h2>
Subgroup: 2.9.5.7.11<br />
Commas: 45/44, 56/55, 81/80<br />
Related temperament: <a class="wiki_link" href="/Meantone%20family">flattone</a><br />
<br />
POTE generator: ~9/8 = 192.500<br />
<br />
Map: [&lt;1 0 -4 -13 -6|, &lt;0 1 2 5 3|]<br />
EDOs: 6, 7, 13, 19, 25, 31, 56, 81<br />
Error: 8.680 cents<br />
<br />
<a class="wiki_link" href="/leantone6">Six note haplotonic scale</a><br />
<a class="wiki_link" href="/leantone7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/leantone13">Thirteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:30 -->Mohaha</h1>
Subgroup: 2.3.5.11<br />
Commas: 81/80, 121/120<br />
Related temperament: <a class="wiki_link" href="/Meantone%20family">mohajira</a><br />
<br />
POTE generator: ~11/9 = 348.094<br />
<br />
Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]<br />
EDOs: 7, 10, 17, 24, 31, 131<br />
Error: 3.813 cents<br />
<br />
<a class="wiki_link" href="/mohaha7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/mohaha10">Ten note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:32 -->Mohoho</h2>
Subgroup: 2.3.5.11.13<br />
Commas: 66/65, 81/80, 121/120<br />
<br />
POTE generator: ~11/9 = 348.916<br />
<br />
Map: [&lt;1 1 0 2 4|, &lt;0 2 8 5 -1|]<br />
EDOs: 7, 10, 17, 24, 31, 55<br />
Error: 4.829 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:34 -->Score</h1>
Subgroup: 2.7.11.13<br />
Commas: 343/338, 847/832<br />
<br />
POTE generator: ~11/8 = 540.099<br />
<br />
Map: [&lt;1 1 3 1|, &lt;0 4 1 6|]<br />
EDOs: 5, 7, 9, 11, 20<br />
Error: 3.846 cents<br />
<br />
<a class="wiki_link" href="/score5">Five note haplotonic scale</a><br />
<a class="wiki_link" href="/score7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/score9">Nine note mega albitonic scale</a><br />
<a class="wiki_link" href="/score11">Eleven note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:36 -->Supra</h1>
Subgroup: 2.3.7.11<br />
Commas: 64/63, 99/98<br />
Related temperament: <a class="wiki_link" href="/Archytas%20clan">superpyth</a><br />
<br />
POTE generator: ~3/2 = 707.192<br />
<br />
Map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]<br />
EDOs: 5, 7, 12, 17, 22, 39, 56<br />
Error: 5.414 cents<br />
<br />
<a class="wiki_link" href="/supra7">Seven note albitonic scale</a><br />
<a class="wiki_link" href="/supra12">Twelve note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Supra-Supraphon"></a><!-- ws:end:WikiTextHeadingRule:38 -->Supraphon</h2>
Subgroup: 2.3.7.11.13<br />
Commas: 64/63, 78/77, 99/98<br />
<br />
POTE generator: ~3/2 = 706.137<br />
<br />
Map: [&lt;1 0 6 13 18|, &lt;0 1 -2 -6 -9|]<br />
EDOs: 5, 7, 12, 17<br />
Error: 5.132 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:40 -->Machine</h2>
Subgroup: 2.9.7.11<br />
Commas: 64/63, 99/98<br />
<br />
POTE generator: ~9/8 = 214.384<br />
<br />
Map: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]<br />
EDOs: 5, 6, 11, 17, 28<br />
Error: 5.414 cents<br />
<br />
<a class="wiki_link" href="/machine5">Five note haplotonic scale</a><br />
<a class="wiki_link" href="/machine6">Six note albitonic scale</a><br />
<a class="wiki_link" href="/machine11">Eleven note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:42 -->Augment</h1>
Subgroup: 2.5.7.11<br />
Commas: 56/55, 128/125<br />
Related temperament: <a class="wiki_link" href="/Augmented%20family">augmented</a><br />
<br />
POTE generator: ~8/7<br />
<br />
Map: [&lt;3 7 0 2|, &lt;0 0 1 1|]<br />
EDOs: 3, 6, 9, 15, 21<br />
Error: 6.632 cents<br />
<br />
<a class="wiki_link" href="/augment6">Six note haplotonic scale</a><br />
<a class="wiki_link" href="/augment9">Nine note albitonic scale</a><br />
<a class="wiki_link" href="/augment12">Twelve note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:44 -->Greeley</h1>
Subgroup: 2.5/3.7/3.11/3<br />
Commas: 121/120, 126/125<br />
<br />
POTE generator: ~11/10 = 156.055<br />
<br />
Map: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]<br />
EDOs: 8, 15, 23, 77, 100<br />
Error: 7.555 cents<br />
<br />
<a class="wiki_link" href="/greeley8">Eight note albitonic scale</a><br />
<a class="wiki_link" href="/greeley15">Fifteen note chromatic scale</a></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>2011-03-18 12:46:58 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-18 16:11:50 UTC</tt>.<br>
-: The original revision id was <tt>211803830</tt>.<br>
+: The original revision id was <tt>211872328</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">By a //chromatic pair// is meant a pair of MOS in some rank two temperament (which may often be a [[Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it. Even so, note that many of these temperaments are quite accurate.
+<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">By a //chromatic pair// is meant a pair of MOS in some rank two temperament (which may often be a [[Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with [[Target tunings|tuning target]] the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.
 [[toc|flat]]
@@ Line 18: / Line 18: @@
 Map: [&lt;3 0 -4|, &lt;0 1 2|]
 EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
-Error: 0.0859 cents
+Error: 0.0443 cents
 Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic.
@@ Line 34: / Line 34: @@
 Map: [&lt;1 0 15 9], &lt;0 1 -8 -3|]
 EDOs: 7, 12, 17, 29, 41, 53, 118, 171
-Error: 0.611 cents
+Error: 1.819 cents
 [[nestoria7|Seven note albitonic scale]]
@@ Line 48: / Line 48: @@
 Map: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]
 EDOs: 7, 12, 17, 29, 41, 53, 65
-Error: 1.512 cents
+Error: 3.457 cents
 [[photia7|Seven note albitonic scale]]
@@ Line 62: / Line 62: @@
 Map: [&lt;1 0 1 0|, &lt;0 6 5 14|]
 EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246
-Error: 0.735 cents
+Error: 0.9355 cents
 [[cata7|Seven note albitonic scale]]
@@ Line 78: / Line 78: @@
 Map: [&lt;1 0 -6 -1|, &lt;0 2 9 3|]
 EDOs: 5, 9, 14, 19, 24, 29
-Error: 0.8489 cents
+Error: 0.8996 cents
 [[bridgetown9|Nine note albitonic scale]]
@@ Line 91: / Line 91: @@
 Map: [&lt;1 5 4 4|, &lt;0 -9 -4 -1|]
 EDOs: 7, 10, 17, 27, 37, 84, 121, 400
-Error: 1.036 cents
+Error: 2.1001 cents
 [[huntington7|Seven note haplotonic scale]]
@@ Line 105: / Line 105: @@
 Map: [&lt;1 0 1 3|, &lt;0 8 7 2|]
 EDOs: 17, 20, 37, 57, 94, 225
-Error: 1.213 cents
+Error: 2.665 cents
 [[bossier8|Eight note albitonic scale]]
@@ Line 120: / Line 120: @@
 Map: [&lt;1 0 -3 -7 -13|, &lt;0 2 5 9 -8|]
 EDOs: 6, 7, 13, 19, 25, 31, 37
-Error: 1.363 cents
+Error: 2.555 cents
 [[roulette6|Six note haplotonic scale]]
@@ Line 136: / Line 136: @@
 Map: [&lt;1 0 15 25 -8|, &lt;0 1 -4 -7 10|]
 EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
-Error: 1.469 cents
+Error: 2.617 cents
 [[baldy6|Six note haplotonic scale]]
@@ Line 151: / Line 151: @@
 Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]
 EDOs: 7, 10, 17, 24, 41, 58
-Error: 1.756
+Error: 4.867 cents
 [[hemif7|Seven note haplotonic scale]]
@@ Line 166: / Line 166: @@
 Map: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]
 EDOs: 5, 36, 41, 87, 128
-Error: 1.781 cents
+Error: 2.925 cents
 [[radon5|Five note haplotonic scale]]
@@ Line 181: / Line 181: @@
 Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]
 EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271
-Error: 2.155 cents
+Error: 1.298 cents
 [[pepperoni7|Seven note albitonic scale]]
@@ Line 337: / Line 337: @@
 </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;Chromatic pairs&lt;/title&gt;&lt;/head&gt;&lt;body&gt;By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of MOS in some rank two temperament (which may often be a &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup temperament&lt;/a&gt;) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called &amp;quot;albitonic&amp;quot; from the Latin word for &amp;quot;white&amp;quot;. Also included at times are &amp;quot;haplotonic&amp;quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it. Even so, note that many of these temperaments are quite accurate.&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;Chromatic pairs&lt;/title&gt;&lt;/head&gt;&lt;body&gt;By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of MOS in some rank two temperament (which may often be a &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup temperament&lt;/a&gt;) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called &amp;quot;albitonic&amp;quot; from the Latin word for &amp;quot;white&amp;quot;. Also included at times are &amp;quot;haplotonic&amp;quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with &lt;a class="wiki_link" href="/Target%20tunings"&gt;tuning target&lt;/a&gt; the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextTocRule:46:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;a href="#Terrain"&gt;Terrain&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Nestoria"&gt;Nestoria&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Cata"&gt;Cata&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt; | &lt;a href="#Bridgetown"&gt;Bridgetown&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Huntington"&gt;Huntington&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Bossier"&gt;Bossier&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#Roulette"&gt;Roulette&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt; | &lt;a href="#Baldy"&gt;Baldy&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Hemif"&gt;Hemif&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt; | &lt;a href="#Radon"&gt;Radon&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Pepperoni"&gt;Pepperoni&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Skwares"&gt;Skwares&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Tutone"&gt;Tutone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Mohaha"&gt;Mohaha&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Score"&gt;Score&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Supra"&gt;Supra&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Augment"&gt;Augment&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt; | &lt;a href="#Greeley"&gt;Greeley&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;
@@ Line 349: / Line 349: @@
 Map: [&amp;lt;3 0 -4|, &amp;lt;0 1 2|]&lt;br /&gt;
 EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558&lt;br /&gt;
-Error: 0.0859 cents&lt;br /&gt;
+Error: 0.0443 cents&lt;br /&gt;
 &lt;br /&gt;
 Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic.&lt;br /&gt;
@@ Line 365: / Line 365: @@
 Map: [&amp;lt;1 0 15 9], &amp;lt;0 1 -8 -3|]&lt;br /&gt;
 EDOs: 7, 12, 17, 29, 41, 53, 118, 171&lt;br /&gt;
-Error: 0.611 cents&lt;br /&gt;
+Error: 1.819 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/nestoria7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 379: / Line 379: @@
 Map: [&amp;lt;1 0 15 -7 9|, &amp;lt;0 1 -8 7 -3|]&lt;br /&gt;
 EDOs: 7, 12, 17, 29, 41, 53, 65&lt;br /&gt;
-Error: 1.512 cents&lt;br /&gt;
+Error: 3.457 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/photia7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 393: / Line 393: @@
 Map: [&amp;lt;1 0 1 0|, &amp;lt;0 6 5 14|]&lt;br /&gt;
 EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246&lt;br /&gt;
-Error: 0.735 cents&lt;br /&gt;
+Error: 0.9355 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/cata7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 409: / Line 409: @@
 Map: [&amp;lt;1 0 -6 -1|, &amp;lt;0 2 9 3|]&lt;br /&gt;
 EDOs: 5, 9, 14, 19, 24, 29&lt;br /&gt;
-Error: 0.8489 cents&lt;br /&gt;
+Error: 0.8996 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/bridgetown9"&gt;Nine note albitonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 422: / Line 422: @@
 Map: [&amp;lt;1 5 4 4|, &amp;lt;0 -9 -4 -1|]&lt;br /&gt;
 EDOs: 7, 10, 17, 27, 37, 84, 121, 400&lt;br /&gt;
-Error: 1.036 cents&lt;br /&gt;
+Error: 2.1001 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/huntington7"&gt;Seven note haplotonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 436: / Line 436: @@
 Map: [&amp;lt;1 0 1 3|, &amp;lt;0 8 7 2|]&lt;br /&gt;
 EDOs: 17, 20, 37, 57, 94, 225&lt;br /&gt;
-Error: 1.213 cents&lt;br /&gt;
+Error: 2.665 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/bossier8"&gt;Eight note albitonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 451: / Line 451: @@
 Map: [&amp;lt;1 0 -3 -7 -13|, &amp;lt;0 2 5 9 -8|]&lt;br /&gt;
 EDOs: 6, 7, 13, 19, 25, 31, 37&lt;br /&gt;
-Error: 1.363 cents&lt;br /&gt;
+Error: 2.555 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/roulette6"&gt;Six note haplotonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 467: / Line 467: @@
 Map: [&amp;lt;1 0 15 25 -8|, &amp;lt;0 1 -4 -7 10|]&lt;br /&gt;
 EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147&lt;br /&gt;
-Error: 1.469 cents&lt;br /&gt;
+Error: 2.617 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/baldy6"&gt;Six note haplotonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 482: / Line 482: @@
 Map: [&amp;lt;1 1 -1 2 4|, &amp;lt;0 2 13 5 -1|]&lt;br /&gt;
 EDOs: 7, 10, 17, 24, 41, 58&lt;br /&gt;
-Error: 1.756&lt;br /&gt;
+Error: 4.867 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/hemif7"&gt;Seven note haplotonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 497: / Line 497: @@
 Map: [&amp;lt;1 1 3 6|, &amp;lt;0 3 -1 -13|]&lt;br /&gt;
 EDOs: 5, 36, 41, 87, 128&lt;br /&gt;
-Error: 1.781 cents&lt;br /&gt;
+Error: 2.925 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/radon5"&gt;Five note haplotonic scale&lt;/a&gt;&lt;br /&gt;
@@ Line 512: / Line 512: @@
 Map: [&amp;lt;1 0 7 12|, &amp;lt;0 1 -4 -7|]&lt;br /&gt;
 EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271&lt;br /&gt;
-Error: 2.155 cents&lt;br /&gt;
+Error: 1.298 cents&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/pepperoni7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;

Chromatic pairs: Difference between revisions

Revision as of 16:11, 18 March 2011

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