Chromatic pairs: Difference between revisions

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[[toc|flat]]


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.

=Terrain=
Subgroup: 2.9/5.9/7
Commas: 250047/250000
Sval name: 6&21
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]]

=Bridgetown=
Subgroup: 2.3.11/5.13/5
Commas: 352/351, 676/675
Sval name: 5&24
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]]

=Cata=
Subgroup: 2.3.5.13
Commas: 325/324, 625/624
Sval name: 15&19
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]]

=Tridec=
Subgroups: 2.7/5.11/5.13/5
Commas: 847/845, 1001/1000
Sval name: 5&8

POTE generator: ~13/10 = 454.461

Map: [<1 2 0 1|, <0 -4 3 1|]
EDOs: 5, 8, 21, 29, 37, 66, 169, 235
Error: 1.057

[[Tridec8|Eight note albitonic scale]]
[[Tridec13|Thirteen note chromatic scale]]

=Pepperoni=
Subgroup: 2.3.11/7.13/7
Commas: 352/351, 364/363
Sval name: 5&12
Related temperament: The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.

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]]

=Nestoria=
Subgroup: 2.3.5.19
Commas: 361/360, 513/512
Sval name: 12&29
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
Sval name: 12&41
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]]

=Huntington=
Subgroup: 2.5.7.13
Commas: 640/637, 10985/10976
Sval name: 10&27

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]]

=Roulette=
Subgroup: 2.5.7.11.13
Commas: 176/175, 1375/1372, 640/637
Sval name: 6&25
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, 325/324, 640/637
Sval name: 6&35
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]]

=Bossier=
Subgroup: 2.7.11.13
Commas: 1573/1569, 15488/15379
Sval name: 3&17

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]]

=Radon=
Subgroup: 2.3.7.11
Commas: 896/891, 1029/1024
Sval name: 5&36
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]]

=Silver=
Subgroup: 2.5.7.13.17
Commas: 170/169, 640/637, 5525/5488
Sval name: 10&27

POTE generator: ~13/8 = 842.711

Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|]
EDOs: 7, 10, 17, 27, 37, 47, 84, 131
Error: 3.437

[[silver7|Seven note haplotonic scale]]
[[silver10|Ten note albitonic scale]]
[[silver17|Seventeen note chromatic scale]]

=Indium=
Subgroup: 2.5/3.7/3.11/3
Commas: 3025/3024, 3125/3087
Sval name: 8&33

POTE generator: ~12/11 = 147.159

Map: [<1 0 0 2|, <0 6 10 -1|]
EDOs: 33, 41, 49, 57, 106, 204, 253
Error: 3.968 cents

[[indium8|Eight note albitonic scale]]
[[indium17|Seventeen note chromatic scale]]

=Magic=
Group: 2.3.5.7.11
Commas: 100/99, 225/224, 245/243

POTE generator: ~5/4 = 380.696

Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]
EDOs: 19, 22, 41, 104, 145
Error: 4.489

[[magic7|Seven note haplotonic scale]]
[[magic10|Ten note albitonic scale]]
[[magic13|Thirteen note chromatic scale]]
[[magic16|Sixteen note mega 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]]

=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: 4.942 cents

[[skwares8|Eight note albitonic scale]]
[[skwares11|Eleven note mega albitonic scale]]
[[skwares14|Fourteen 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: 5.404 cents

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

=Semidim=
Subgroup: 2.5/3.7/3.11/3.13/3
Commas: 121/120, 169/168, 275/273
Sval name: 8&29

POTE generator: ~13/10 = 453.190

Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]
EDOs: 5, 8, 13, 21, 29, 37, 45
Error: 5.433 cents

[[semidim8|Eight note albitonic scale]]
[[semidim13|Thirteen note chromatic scale]]

=Orwell=
Group: 2.3.5.7.11
Commas: 99/98, 121/120, 176/175
Val name: 9&22

POTE generator: ~7/6 = 271.426

Map: [<1 0 3 1 3|, <0 7 -3 8 2|]
EDOs: 9, 22, 31, 53, 84
Error: 5.584

[[orwell9|nine note albitonic scale]]
[[orwell13|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: 6.733 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: 9.556 cents

=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: 7.047 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: 20.338 cents

[[leantone6|Six note haplotonic scale]]
[[leantone7|Seven note albitonic scale]]
[[leantone13|Thirteen 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
Error: 8.052 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: 9.795 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: 10.534 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: 10.100 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: 12.830 cents

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

Original HTML content:

<html><head><title>Chromatic pairs</title></head><body><!-- ws:start:WikiTextTocRule:58:&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:58 --><!-- ws:start:WikiTextTocRule:59: --><a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: -->
<!-- ws:end:WikiTextTocRule:88 --><br />
<br />
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: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 />
Sval name: 6&amp;21<br />
Related temperament: <a class="wiki_link" href="/Minortonic%20family#Domain">domain</a><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: 0.0443 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="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:2 -->Bridgetown</h1>
Subgroup: 2.3.11/5.13/5<br />
Commas: 352/351, 676/675<br />
Sval name: 5&amp;24<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:4:&lt;h1&gt; --><h1 id="toc2"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:4 -->Cata</h1>
Subgroup: 2.3.5.13<br />
Commas: 325/324, 625/624<br />
Sval name: 15&amp;19<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:6:&lt;h1&gt; --><h1 id="toc3"><a name="Tridec"></a><!-- ws:end:WikiTextHeadingRule:6 -->Tridec</h1>
Subgroups: 2.7/5.11/5.13/5<br />
Commas: 847/845, 1001/1000<br />
Sval name: 5&amp;8<br />
<br />
POTE generator: ~13/10 = 454.461<br />
<br />
Map: [&lt;1 2 0 1|, &lt;0 -4 3 1|]<br />
EDOs: 5, 8, 21, 29, 37, 66, 169, 235<br />
Error: 1.057<br />
<br />
<a class="wiki_link" href="/Tridec8">Eight note albitonic scale</a><br />
<a class="wiki_link" href="/Tridec13">Thirteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:8 -->Pepperoni</h1>
Subgroup: 2.3.11/7.13/7<br />
Commas: 352/351, 364/363<br />
Sval name: 5&amp;12<br />
Related temperament: The <a class="wiki_link" href="/Peppermint-24">Pepper fifth</a>, which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.<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:10:&lt;h1&gt; --><h1 id="toc5"><a name="Nestoria"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nestoria</h1>
Subgroup: 2.3.5.19<br />
Commas: 361/360, 513/512<br />
Sval name: 12&amp;29<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:12:&lt;h2&gt; --><h2 id="toc6"><a name="Nestoria-Photia"></a><!-- ws:end:WikiTextHeadingRule:12 -->Photia</h2>
Subgroup 2.3.5.17.19<br />
Commas: 171/170, 256/255, 324/323<br />
Sval name: 12&amp;41<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:14:&lt;h1&gt; --><h1 id="toc7"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:14 -->Huntington</h1>
Subgroup: 2.5.7.13<br />
Commas: 640/637, 10985/10976<br />
Sval name: 10&amp;27<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:16:&lt;h1&gt; --><h1 id="toc8"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:16 -->Roulette</h1>
Subgroup: 2.5.7.11.13<br />
Commas: 176/175, 1375/1372, 640/637<br />
Sval name: 6&amp;25<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:18:&lt;h1&gt; --><h1 id="toc9"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:18 -->Baldy</h1>
Subgroup: 2.9.5.7.13<br />
Commas: 225/224, 325/324, 640/637<br />
Sval name: 6&amp;35<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:20:&lt;h1&gt; --><h1 id="toc10"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:20 -->Bossier</h1>
Subgroup: 2.7.11.13<br />
Commas: 1573/1569, 15488/15379<br />
Sval name: 3&amp;17<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:22:&lt;h1&gt; --><h1 id="toc11"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:22 -->Radon</h1>
Subgroup: 2.3.7.11<br />
Commas: 896/891, 1029/1024<br />
Sval name: 5&amp;36<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:24:&lt;h1&gt; --><h1 id="toc12"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:24 -->Silver</h1>
Subgroup: 2.5.7.13.17<br />
Commas: 170/169, 640/637, 5525/5488<br />
Sval name: 10&amp;27<br />
<br />
POTE generator: ~13/8 = 842.711<br />
<br />
Map: [&lt;1 5 4 4 2|, &lt;0 -9 -4 -1 7|]<br />
EDOs: 7, 10, 17, 27, 37, 47, 84, 131<br />
Error: 3.437<br />
<br />
<a class="wiki_link" href="/silver7">Seven note haplotonic scale</a><br />
<a class="wiki_link" href="/silver10">Ten note albitonic scale</a><br />
<a class="wiki_link" href="/silver17">Seventeen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule:26 -->Indium</h1>
Subgroup: 2.5/3.7/3.11/3<br />
Commas: 3025/3024, 3125/3087<br />
Sval name: 8&amp;33<br />
<br />
POTE generator: ~12/11 = 147.159<br />
<br />
Map: [&lt;1 0 0 2|, &lt;0 6 10 -1|]<br />
EDOs: 33, 41, 49, 57, 106, 204, 253<br />
Error: 3.968 cents<br />
<br />
<a class="wiki_link" href="/indium8">Eight note albitonic scale</a><br />
<a class="wiki_link" href="/indium17">Seventeen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Magic"></a><!-- ws:end:WikiTextHeadingRule:28 -->Magic</h1>
Group: 2.3.5.7.11<br />
Commas: 100/99, 225/224, 245/243<br />
<br />
POTE generator: ~5/4 = 380.696<br />
<br />
Map: [&lt;1 0 2 -1 6|, &lt;0 5 1 12 -8|]<br />
EDOs: 19, 22, 41, 104, 145<br />
Error: 4.489<br />
<br />
<a class="wiki_link" href="/magic7">Seven note haplotonic scale</a><br />
<a class="wiki_link" href="/magic10">Ten note albitonic scale</a><br />
<a class="wiki_link" href="/magic13">Thirteen note chromatic scale</a><br />
<a class="wiki_link" href="/magic16">Sixteen note mega chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:30 -->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:32:&lt;h1&gt; --><h1 id="toc16"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:32 -->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: 4.942 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:34:&lt;h1&gt; --><h1 id="toc17"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:34 -->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: 5.404 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:36:&lt;h1&gt; --><h1 id="toc18"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:36 -->Semidim</h1>
Subgroup: 2.5/3.7/3.11/3.13/3<br />
Commas: 121/120, 169/168, 275/273<br />
Sval name: 8&amp;29<br />
<br />
POTE generator: ~13/10 = 453.190<br />
<br />
Map: [&lt;1 3 5 3 4|, &lt;0 -6 -10 -3 -5|]<br />
EDOs: 5, 8, 13, 21, 29, 37, 45<br />
Error: 5.433 cents<br />
<br />
<a class="wiki_link" href="/semidim8">Eight note albitonic scale</a><br />
<a class="wiki_link" href="/semidim13">Thirteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Orwell"></a><!-- ws:end:WikiTextHeadingRule:38 -->Orwell</h1>
Group: 2.3.5.7.11<br />
Commas: 99/98, 121/120, 176/175<br />
Val name: 9&amp;22<br />
<br />
POTE generator: ~7/6 = 271.426<br />
<br />
Map: [&lt;1 0 3 1 3|, &lt;0 7 -3 8 2|]<br />
EDOs: 9, 22, 31, 53, 84<br />
Error: 5.584<br />
<br />
<a class="wiki_link" href="/orwell9">nine note albitonic scale</a><br />
<a class="wiki_link" href="/orwell13">Thirteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:40 -->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: 6.733 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:42:&lt;h2&gt; --><h2 id="toc21"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:42 -->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: 9.556 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:44 -->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: 7.047 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:46:&lt;h2&gt; --><h2 id="toc23"><a name="Tutone-Leantone"></a><!-- ws:end:WikiTextHeadingRule:46 -->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: 20.338 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:48:&lt;h1&gt; --><h1 id="toc24"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:48 -->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: 8.052 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:50:&lt;h1&gt; --><h1 id="toc25"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:50 -->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: 9.795 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:52:&lt;h2&gt; --><h2 id="toc26"><a name="Supra-Supraphon"></a><!-- ws:end:WikiTextHeadingRule:52 -->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: 10.534 cents<br />
<br />
<!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:54 -->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: 10.100 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:56:&lt;h1&gt; --><h1 id="toc28"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:56 -->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: 12.830 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></body></html>

Chromatic pairs: Difference between revisions

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