Chromatic pairs: Difference between revisions

Revision as of 13:35, 11 March 2011

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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". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5].

==Terrain==
Subgroup: 2.9/5.9/7
Commas: 250047/250000

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: 0.0859 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: 0.611 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: 1.512 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: 0.735 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: 0.8489 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: 1.036 cents

[[huntington7|Seven note haplotonic scale]]
[[huntington10|Ten note albitonic scale]]
[[huntington17|Seventeen note 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: 1.363 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: 1.469 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: 1.756

[[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: 1.781 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: 2.155 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

==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]]

==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]]

==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

[[score5|Five note haplotonic scale]]
[[score7|Seven note albitonic scale]]
[[score9|Nine note mega albitonic scale]]
[[score11|Eleven 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].<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h2>
Subgroup: 2.9/5.9/7<br />
Commas: 250047/250000<br />
<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: 0.0859 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;h2&gt; --><h2 id="toc1"><a name="x-Nestoria"></a><!-- ws:end:WikiTextHeadingRule:2 -->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 />
Error: 0.611 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;h3&gt; --><h3 id="toc2"><a name="x-Nestoria-Photia"></a><!-- ws:end:WikiTextHeadingRule:4 -->Photia</h3>
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: 1.512 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;h2&gt; --><h2 id="toc3"><a name="x-Cata"></a><!-- ws:end:WikiTextHeadingRule:6 -->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 />
Error: 0.735 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;h2&gt; --><h2 id="toc4"><a name="x-Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:8 -->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 />
Error: 0.8489 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;h2&gt; --><h2 id="toc5"><a name="x-Huntington"></a><!-- ws:end:WikiTextHeadingRule:10 -->Huntington</h2>
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: 1.036 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;h2&gt; --><h2 id="toc6"><a name="x-Roulette"></a><!-- ws:end:WikiTextHeadingRule:12 -->Roulette</h2>
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: 1.363 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:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Baldy"></a><!-- ws:end:WikiTextHeadingRule:14 -->Baldy</h2>
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: 1.469 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:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Hemif"></a><!-- ws:end:WikiTextHeadingRule:16 -->Hemif</h2>
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: 1.756<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:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-Radon"></a><!-- ws:end:WikiTextHeadingRule:18 -->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 />
Error: 1.781 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:20:&lt;h2&gt; --><h2 id="toc10"><a name="x-Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:20 -->Pepperoni</h2>
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: 2.155 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:22:&lt;h2&gt; --><h2 id="toc11"><a name="x-Skwares"></a><!-- ws:end:WikiTextHeadingRule:22 -->Skwares</h2>
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:24:&lt;h2&gt; --><h2 id="toc12"><a name="x-Tutone"></a><!-- ws:end:WikiTextHeadingRule:24 -->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 />
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:26:&lt;h3&gt; --><h3 id="toc13"><a name="x-Tutone-Leantone"></a><!-- ws:end:WikiTextHeadingRule:26 -->Leantone</h3>
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:28:&lt;h2&gt; --><h2 id="toc14"><a name="x-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:28 -->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 />
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:30:&lt;h3&gt; --><h3 id="toc15"><a name="x-Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:30 -->Mohoho</h3>
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:32:&lt;h2&gt; --><h2 id="toc16"><a name="x-Supra"></a><!-- ws:end:WikiTextHeadingRule:32 -->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 />
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:34:&lt;h2&gt; --><h2 id="toc17"><a name="x-Augment"></a><!-- ws:end:WikiTextHeadingRule:34 -->Augment</h2>
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:36:&lt;h2&gt; --><h2 id="toc18"><a name="x-Greeley"></a><!-- ws:end:WikiTextHeadingRule:36 -->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 />
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><br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="x-Score"></a><!-- ws:end:WikiTextHeadingRule:38 -->Score</h2>
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 />
<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></body></html>

Chromatic pairs: Difference between revisions

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