Chromatic pairs

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This revision was by author genewardsmith and made on 2011-03-07 11:59:21 UTC.

The original revision id was 208071398.

The revision comment was:

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Original Wikitext content:

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".

==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

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

==Pepperoni==
Subgroup: 2.3.11/7.13/7
Commas: 352/351, 364/363

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
Related temperament: [[Margo Schulter]]'s [[Pepper temperament|pepper temperament]]

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

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

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

==Skwares==
Subgroup: 2.3.7.11
Commas: 99/98, 243/242

==Hemif==
Subgroup: 2.3.7.11
Commas: 243/242, 896/891

==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

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

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

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

[[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

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

[[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

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;.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Greeley"></a><!-- ws:end:WikiTextHeadingRule:0 -->Greeley</h2>
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 />
<br />
<a class="wiki_link" href="/greeley8">Eight note albitonic scale</a><br />
<a class="wiki_link" href="/greeley15">Fifteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pepperoni</h2>
Subgroup: 2.3.11/7.13/7<br />
Commas: 352/351, 364/363<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 />
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 />
<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:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:4 -->Bridgetown</h2>
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 />
<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:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Radon"></a><!-- ws:end:WikiTextHeadingRule:6 -->Radon</h2>
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 />
<br />
<a class="wiki_link" href="/radon5">Five note pentacircle 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:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Skwares"></a><!-- ws:end:WikiTextHeadingRule:8 -->Skwares</h2>
Subgroup: 2.3.7.11<br />
Commas: 99/98, 243/242<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Hemif"></a><!-- ws:end:WikiTextHeadingRule:10 -->Hemif</h2>
Subgroup: 2.3.7.11<br />
Commas: 243/242, 896/891<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Supra"></a><!-- ws:end:WikiTextHeadingRule:12 -->Supra</h2>
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 />
<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:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:14 -->Mohaha</h2>
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 />
<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:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Cata"></a><!-- ws:end:WikiTextHeadingRule:16 -->Cata</h2>
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 />
<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:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-Nestoria"></a><!-- ws:end:WikiTextHeadingRule:18 -->Nestoria</h2>
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 />
<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:20:&lt;h2&gt; --><h2 id="toc10"><a name="x-Photia"></a><!-- ws:end:WikiTextHeadingRule:20 -->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 />
<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:22:&lt;h2&gt; --><h2 id="toc11"><a name="x-Tutone"></a><!-- ws:end:WikiTextHeadingRule:22 -->Tutone</h2>
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 />
<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:24:&lt;h2&gt; --><h2 id="toc12"><a name="x-Leantone"></a><!-- ws:end:WikiTextHeadingRule:24 -->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</body></html>