Chromatic pairs: Difference between revisions

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-09 20:47:51 UTC</tt>.<br>

: The original revision id was <tt>351884336</tt>.<br>

=Starlingtet=  

Group: 2.5/3.7/3

Comma: 126/125

Svalname: 4&amp;15

[[Gencom]]: [2 6/5; 126/125]

Map: [&lt;1 0 -1|, &lt;0 1 3|]

[[xenharmonic/starlingtet4|Four note haplotonic scale]]

[[xenharmonic/starlingtet7|Seven note albitonic scale]]

[[xenharmonic/starlingtet11|Eleven note chromatic scale]]

Subgroup: 2.5/3.7/3.13/11

Commas: 275/273, 847/845

[[Lp tuning|POL2 generator]]: ~13/11 = 293.679

[[Gencom]]: [2 13/11; 275/273 847/845]

Gencom map: [&lt;1 0 0 0 0 0|, &lt;0 -8/3 1/3 7/3 -1/2 1/2|]

Map: [&lt;1 0 0 0|, &lt;0 3 5 1|]

[[xenharmonic/gariberttet5|Five note haplotonic scale]]

[[xenharmonic/gariberttet9|Nine note albitonic scale]]

[[xenharmonic/gariberttet13|Thirteen note chromatic scale]]

=Indium=  

Subgroup: 2.5/3.7/3.11/3

=Hemif=  

Subgroup: 2.3.7.11.13

Commas: 144/143, 243/242, 364/363

Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]]

[[Lp tuning|POL2 generator]]: ~11/9 = 351.691

[[Gencom]]: [2 11/9; 144/143 243/242 364/363]

Gencom map: [&lt;1 1 0 -1 2 4|, &lt;0 2 0 13 5 -1|]

Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]

EDOs: 7, 10, 17, 24, 41, 58

[[Lp tuning#L2 tuning|L2 error]]: 1.756 cents

[[image:hemif_58edo.jpg]]

[[xenharmonic/hemif7|Seven note haplotonic scale]]

[[xenharmonic/hemif10|Ten note albitonic scale]]

[[xenharmonic/hemif17|Seventeen note chromatic scale]]

=Myna=  

Group: 2.3.5.7

Commas: 126/125, 1728/1715

Val name: 4&amp;27

[[Lp tuning|POL2 generator]]: ~6/5 = 310.146

[[Gencom]]: [2 6/5; 126/125 1728/1715]

Map: [&lt;1 9 9 8|, &lt;0 -10 -9 -7|]

[[image:myna_89edo.jpg]]

[[xenharmonic/myna7|Seven note haplotonic scale]]

[[xenharmonic/myna11|Eleven note albitonic scale]]

[[xenharmonic/myna15|Fifteen note chromatic scale]]

=Skwares=  

=Magic=  

Group: 2.3.5.7.11

Commas: 100/99, 225/224, 245/243

Val name: 19&amp;22

[[Lp tuning|POL2 generator]]: ~5/4 = 380.696

[[Gencom]]: [2 5/4; 100/99 225/224 245/243]

Gencom map: [&lt;1 0 2 -1 6|, &lt;0 5 1 12 -8|]

Map: [&lt;1 0 2 -1 6|, &lt;0 5 1 12 -8|]

EDOs: 19, 22, 41, 104, 145

[[Lp tuning#L2 tuning|L2 error]]: 2.741 cents

[[image:xenharmonic/magic_145edo.jpg]]

[[xenharmonic/magic7|Seven note haplotonic scale]]

[[xenharmonic/magic10|Ten note albitonic scale]]

[[xenharmonic/magic13|Thirteen note chromatic scale]]

[[xenharmonic/magic16|Sixteen note mega chromatic scale]]

==Music==  

&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3|Chromatic piece in magic 16]]////&lt;/span&gt; [[@http://www.chrisvaisvil.com/|Chris Vaisvil]]

=Meantone=

Group: 2.3.5.7

Commas: 81/80, 126/125

Val name: 12&amp;19

[[Lp tuning|POL2 generator]]: ~3/2 = 696.495

[[Gencom]]: [2 3/2; 81/80 126/125]

Gencom map: [&lt;1 1 0 -3|, &lt;0 1 4 10|]

Map: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]

[[Lp tuning#L2 tuning|L2 error]]: 2.763 cents

[[image:meantone_31edo.jpg]]

[[xenharmonic/meantone7|Seven note albitonic scale]]

[[xenharmonic/meantone12|Twelve note chromatic scale]]

Commas: 126/125, 245/243

[[Lp tuning|POL2 generator]]: ~9/7 = 443.383

Gencom map: [&lt;1 -1 -1 -2|, &lt;0 7 9 13|]

[[Lp tuning#L2 tuning|L2 error]]: 2.647 cents

[[image:xenharmonic/sensi_46edo.jpg]]

[[xenharmonic/sensi11|Eleven note mega albitonic scale]]

[[xenharmonic/sensi19|Nineteen note chromatic scale]]

Subgroup: 2.5/3.7/3.11/3

[[Gencom]]: [2 11/10; 121/120 126/125]

Gencom map: &lt;1 -5/4 -1/4 3/4 3/4|, &lt;0 9/4 1/4 -15/4 5/4|]

Map: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]

EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd

[[Lp tuning#L2 tuning|L2 error]]: 2.313 cents

[[image:greeley_100edo.png]]

[[xenharmonic/greeley8|Eight note albitonic scale]]

[[xenharmonic/greeley15|Fifteen note chromatic scale]]

==Music==  

&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3|A Greeley Steals Halloween]]////&lt;/span&gt;&lt;/span&gt; by [[@http://chrisvaisvil.com/?p=1485|Chris Vaisvil]] in Greeley 15

Subgroup: 2.5/3.7/3.11/3.13/3

[[Lp tuning|POL2 generator]]: ~13/10 = 453.242

Gencom map: [&lt;1 -3 0 2 0 1|, &lt;0 24/5 -6/5 -26/5 9/5 -1/5|]

Map: [&lt;1 3 5 3 4|, &lt;0 -6 -10 -3 -5|]

[[Lp tuning#L2 tuning|L2 error]]: 2.577 cents

[[image:semidim_770edo.png]]

[[xenharmonic/semidim8|Eight note albitonic scale]]

[[xenharmonic/semidim13|Thirteen note chromatic scale]]

Group: 2.3.5.7.11

Commas: 99/98, 121/120, 176/175

Val name: 9&amp;22

[[Lp tuning|POL2 generator]]: ~7/6 = 271.426

[[Gencom]]: [2 7/6; 99/98 121/120 176/175]

Gencom map: [&lt;1 0 3 1 3|, &lt;0 7 -3 8 2|]

Map: [&lt;1 0 3 1 3|, &lt;0 7 -3 8 2|]

EDOs: 9, 22, 31, 53, 84e

[[Lp tuning#L2 tuning|L2 error]]: 2.574 cents

[[image:xenharmonic/orwell_84edo.png]]

[[xenharmonic/orwell5|Five note haplotonic scale]]

[[xenharmonic/orwell9|Nine note albitonic scale]]

[[xenharmonic/orwell13|Thirteen note chromatic scale]]

Group: 2.5/3.7.11

Commas: 100/99, 385/384

Related temperaments: 4&amp;7&amp;15, magic

[[Lp tuning|POL2 generator]]: ~6/5 = 322.659

[[Gencom]]: [2 6/5; 100/99 385/384]

Gencom map: [&lt;1 -1/2 1/2 2 4|, &lt;0 1/2 -1/2 3 -2|]

[[Lp tuning#L2 tuning|L2 error]]: 2.696 cents

[[xenharmonic/magicaltet7|Seven note albitonic scale]]

[[xenharmonic/magicaltet11|Eleven note chromatic scale]]

[[xenharmonic/magicaltet15|Fifteen note mega scale]]

Group: 2.5/3.9/7

Commas: 245/243

Svalname: 3&amp;5

[[Lp tuning|POL2 generator]]: ~9/7 = 440.902

[[Gencom]]: [2 9/7; 245/243]

Gencom map: [&lt;1 0 0 0|, &lt;0 0 2 -1|]

Map: [&lt;1 0 0|, &lt;0 2 1|]

EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc

[[Lp tuning#L2 tuning|L2 error]]: 1.421 cents

[[xenharmonic/sentry5|Five note haplotonic scale]]

[[xenharmonic/sentry8|Eight note albitonic scale]]

[[xenharmonic/sentry11|Eleven note note chromatic scale]]

Group: 2.7/3.11

Comma: 99/98

Svalname: 1&amp;4

[[Lp tuning|POL2 generator]]: ~7/6 = 273.174

[[Gencom]]: [2 7/6; 99/98]

Gencom map: [&lt;1 -1/2 0 1/2 3|, &lt;0 -1/2 0 1/2 2|]

Map: [&lt;1 0 1|, &lt;0 1 2|]

[[Lp tuning#L2 tuning|L2 error]]: 2.380 cents

[[xenharmonic/mothwelltri9|Nine note albitonic scale]]

[[xenharmonic/mothwelltri13|Thirteen note chromatic scale]]

Group: 2.11.13

Commas: 1352/1331

[[Lp tuning|POL2 generator]]: ~13/11 = 279.318

Gencom map: [&lt;1 0 0 0 3 3|, &lt;0 0 0 0 2 3|]

[[Lp tuning#L2 tuning|L2 error]]: 2.070 cents

[[image:lovecraft_116edo.png]]

[[xenharmonic/lovecraft9|Nine note albitonic scale]]

[[xenharmonic/lovecraft13|Thirteen note chromatic scale]]

=Bleu=  

Group: 2.3.7.11.13

Commas: 78/77, 99/98, 144/143

[[Lp tuning|POL2 generator]]: ~13/12 = 139.990

[[Gencom]]: [2 13/12; 78/77 99/98 144/143]

Gencom map: [&lt;1 1 0 2 3 3|, &lt;0 5 0 7 4 6|]

Map: [&lt;1 1 2 3 3|, &lt;0 5 7 4 6|]

EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]]

[[Lp tuning#L2 tuning|L2 error]]: 4.292 cents

[[image:blue_60edo.png]]

[[xenharmonic/bleu8|bleu8]] - Eight note [[xenharmonic/haplotonic scale|haplotonic scale]]

[[xenharmonic/bleu17|bleu17]] - Seventeen note [[xenharmonic/chromatic scale|chromatic scale]]

Subgroup: 2.3.5.11

Commas: 81/80, 121/120

Related temperament: [[xenharmonic/Meantone family|mohajira]]

[[Lp tuning|POL2 generator]]: ~11/9 = 348.094

[[Gencom]]: [2 11/9; 81/80 121/120]

Gencom map: [&lt;1 1 0 0 2|, &lt;[0 2 8 0 5|]

Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]

EDOs: 24, 31, 69d, 100d, 131bd

[[Lp tuning#L2 tuning|L2 error]]: 3.113 cents

[[image:mohaha_131edo.png]]

[[xenharmonic/mohaha7|Seven note albitonic scale]]

[[xenharmonic/mohaha10|Ten note chromatic scale]]

////[[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]]//// by [[Billy Stiltner]]

Commas: 66/65, 81/80, 121/120

[[Lp tuning|POL2 generator]]: ~11/9 = 348.916

[[Gencom]]: [2 11/9; 66/65 81/80 121/120]

Gencom map: [&lt;1 1 0 0 2 4|, &lt;0 2 8 0 5 -1|]

[[Lp tuning#L2 tuning|L2 error]]: 4.829 cents

Subgroup: 2.9.15.7.11.13

Commas: 100/99, 105/104, 144/143, 196/195

Svalname: 11&amp;30

[[Lp tuning|POL2 generator]]: ~9/7 = 439.146

[[Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195]

Gencom map: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|]

Map: [&lt;1 0 2 -1 6 -2|, &lt;0 5 3 6 -4 9|]

[[Lp tuning#L2 tuning|L2 error]]: 3.772 cents

[[xenharmonic/stacks11|Eleven note note chromatic scale]]

[[xenharmonic/stacks19|Nineteen note note mega chromatic scale]]

Related temperament: [[xenharmonic/Meantone family|meantone]]

[[Lp tuning|POL2 generator]]: ~9/8 = 193.937

Gencom map: [&lt;1 3/2 2 2 2|, &lt;0 1/2 2 5 9|]

[[Lp tuning#L2 tuning|L2 error]]: 3.218 cents

[[xenharmonic/tutone6|Six note haplotonic scale]]

[[xenharmonic/tutone7|Seven note albitonic scale]]

[[xenharmonic/tutone13|Thirteen note chromatic scale]]

[[image:tutone_99edo.png]]

Related temperament: [[meanenneadecal]]

[[Lp tuning|POL2 generator]]: ~9/8 = 192.500

Gencom map: [&lt;1 3/2 2 2 3|, &lt;0 1/2 2 5 3|]

[[Lp tuning#L2 tuning|L2 error]]: 8.680 cents

[[image:leantone_81edo.png]]

[[xenharmonic/leantone13|Thirteen note chromatic scale]]

Subgroup: 2.7.11.13

[[Lp tuning|POL2 generator]]: ~11/8 = 540.099

Gencom map: [&lt;1 0 0 1 3 1|, &lt;0 0 0 4 1 6|]

 

 

 

=Supra=  

Subgroup: 2.3.7.11

[[Lp tuning|POL2 generator]]: ~3/2 = 707.192

[[Gencom]]: [2 3/2; 64/63 99/98]

Gencom map: [&lt;1 1 0 4 7|, &lt;0 1 0 -2 -6|]

Map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]

EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c

[[image:supra_56edo.png]]

[[xenharmonic/supra7|Seven note albitonic scale]]

[[xenharmonic/supra12|Twelve note chromatic scale]]

==Supraphon==  

Subgroup: 2.3.7.11.13

Commas: 64/63, 78/77, 99/98

[[Lp tuning|POL2 generator]]: ~3/2 = 706.137

[[Gencom]]: [2 3/2; 64/63 78/77 99/98]

Gencom map: [&lt;1 1 0 4 7 9|, &lt;0 1 0 -2 -6 -9|]

Map: [&lt;1 0 6 13 18|, &lt;0 1 -2 -6 -9|]

EDOs: 5, 7, 12, 17

[[Lp tuning#L2 tuning|L2 error]]: 5.132 cents

Subgroup: 2.9.7.11

[[Lp tuning|POL2 generator]]: ~9/8 = 214.384

[[Gencom]]: [2 9/8; 64/63 99/98]

Gencom map: [&lt;1 3/2 0 3 4|, &lt;0 1/2 0 -1 -3|]

[[Lp tuning#L2 tuning|L2 error]]: 4.421 cents

[[image:machine_28edo.png]]

[[xenharmonic/machine5|Five note haplotonic scale]]

[[xenharmonic/machine6|Six note albitonic scale]]

[[xenharmonic/machine11|Eleven note chromatic scale]]

Related temperament: [[xenharmonic/pajara|pajara]]

[[Lp tuning|POL2 generator]]: ~8/7 = 214.095

Gencom map: [&lt;2 3 5 6|, &lt;0 1/2 -1 -1|]

[[Lp tuning#L2 tuning|L2 error]]: 5.145 cents

[[image:antikythera_28edo.png]]

[[xenharmonic/antikythera6|Six note haplotonic scale]]

[[xenharmonic/antikythera10|Ten note albitonic scale]]

[[xenharmonic/antikythera16|Sixteen note chromatic scale]]

Related temperament: [[xenharmonic/Meantone family|meanpop]]

[[Lp tuning|POL2 generator]]: ~9/8 = 191.059

 

[[Gencom]]: [2 9/8; 65/64 81/80 91/90]

Gencom map: [&lt;1 3/2 2 2 0 4|, &lt;0 1/2 2 5 0 -2|]

Map: [&lt;1 0 -4 -13 10|, &lt;0 1 2 5 -2|]

EDOs: 6, 7, 13, 19, 25e, 44de

[[Lp tuning#L2 tuning|L2 error]]: 4.906 cents

[[image:deutone_44edo.png]]

[[xenharmonic/deutone6|Six note haplotonic scale]]

[[xenharmonic/deutone7|seven note albitonic scale]]

[[xenharmonic/deutone13|Thirteen note chromatic scale]]

Subgroup: 2.3.7

Comma: 49/48

[[Lp tuning|POL2 generator]]: ~7/6 = 250.385

[[Gencom]]: [2 7/6; 49/48]

Gencom map: [&lt;1 2 0 3}, &lt;0 -2 0 -1|]

 

Map: [&lt;1 0 2|, &lt;0 2 1|]

EDOs: 5, 9, 14, 19, 24, 67c, 91c

[[Lp tuning#L2 tuning|L2 error]]: 5.046 cents

 

[[image:semaphore_24edo.png]]

 

 

Subgroup: 2.5.7.11

Commas: 56/55, 128/125

Related temperament: [[xenharmonic/Augmented family|augmented]]

 

[[Lp tuning|POL2 generator]]: ~8/7 = 228.275

 

Gencom map: [&lt;3 0 7 9 11|, &lt;0 0 0 -1 -1|]

 

Map: [&lt;3 7 0 2|, &lt;0 0 1 1|]

[[Lp tuning#L2 tuning|L2 error]]: 5.415 cents

 

[[image:augment_21edo.png]]

 

<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;&lt;!-- ws:start:WikiTextTocRule:123:&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:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt;&lt;a href="#Definitions"&gt;Definitions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextTocRule:125: --&gt; | &lt;a href="#Terrain"&gt;Terrain&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:125 --&gt;&lt;!-- ws:start:WikiTextTocRule:126: --&gt; | &lt;a href="#Petrtri"&gt;Petrtri&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:126 --&gt;&lt;!-- ws:start:WikiTextTocRule:127: --&gt; | &lt;a href="#Tridec"&gt;Tridec&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:127 --&gt;&lt;!-- ws:start:WikiTextTocRule:128: --&gt; | &lt;a href="#Orgone"&gt;Orgone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt; | &lt;a href="#Nestoria"&gt;Nestoria&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&gt; | &lt;a href="#Marveltwintri"&gt;Marveltwintri&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:130 --&gt;&lt;!-- ws:start:WikiTextTocRule:131: --&gt; | &lt;a href="#Cata"&gt;Cata&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:131 --&gt;&lt;!-- ws:start:WikiTextTocRule:132: --&gt; | &lt;a href="#Bridgetown"&gt;Bridgetown&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:132 --&gt;&lt;!-- ws:start:WikiTextTocRule:133: --&gt;&lt;!-- ws:end:WikiTextTocRule:133 --&gt;&lt;!-- ws:start:WikiTextTocRule:134: --&gt; | &lt;a href="#Slendric"&gt;Slendric&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:134 --&gt;&lt;!-- ws:start:WikiTextTocRule:135: --&gt;&lt;!-- ws:end:WikiTextTocRule:135 --&gt;&lt;!-- ws:start:WikiTextTocRule:136: --&gt; | &lt;a href="#Neutraltet"&gt;Neutraltet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:136 --&gt;&lt;!-- ws:start:WikiTextTocRule:137: --&gt; | &lt;a href="#Huntington"&gt;Huntington&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:137 --&gt;&lt;!-- ws:start:WikiTextTocRule:138: --&gt; | &lt;a href="#Pepperoni"&gt;Pepperoni&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:138 --&gt;&lt;!-- ws:start:WikiTextTocRule:139: --&gt; | &lt;a href="#Penta"&gt;Penta&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:139 --&gt;&lt;!-- ws:start:WikiTextTocRule:140: --&gt; | &lt;a href="#Marveltri"&gt;Marveltri&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:140 --&gt;&lt;!-- ws:start:WikiTextTocRule:141: --&gt; | &lt;a href="#Bossier"&gt;Bossier&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:141 --&gt;&lt;!-- ws:start:WikiTextTocRule:142: --&gt; | &lt;a href="#Shoe"&gt;Shoe&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:142 --&gt;&lt;!-- ws:start:WikiTextTocRule:143: --&gt; | &lt;a href="#Guanyintet"&gt;Guanyintet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:143 --&gt;&lt;!-- ws:start:WikiTextTocRule:144: --&gt; | &lt;a href="#Roulette"&gt;Roulette&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:144 --&gt;&lt;!-- ws:start:WikiTextTocRule:145: --&gt; | &lt;a href="#Garibaldi"&gt;Garibaldi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:145 --&gt;&lt;!-- ws:start:WikiTextTocRule:146: --&gt; | &lt;a href="#Radon"&gt;Radon&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:146 --&gt;&lt;!-- ws:start:WikiTextTocRule:147: --&gt; | &lt;a href="#Baldy"&gt;Baldy&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:147 --&gt;&lt;!-- ws:start:WikiTextTocRule:148: --&gt; | &lt;a href="#Photia"&gt;Photia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:148 --&gt;&lt;!-- ws:start:WikiTextTocRule:149: --&gt; | &lt;a href="#Mabila"&gt;Mabila&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:149 --&gt;&lt;!-- ws:start:WikiTextTocRule:150: --&gt; | &lt;a href="#Silver"&gt;Silver&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:150 --&gt;&lt;!-- ws:start:WikiTextTocRule:151: --&gt; | &lt;a href="#Starlingtet"&gt;Starlingtet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:151 --&gt;&lt;!-- ws:start:WikiTextTocRule:152: --&gt; | &lt;a href="#Gariberttet"&gt;Gariberttet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:152 --&gt;&lt;!-- ws:start:WikiTextTocRule:153: --&gt; | &lt;a href="#Indium"&gt;Indium&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:153 --&gt;&lt;!-- ws:start:WikiTextTocRule:154: --&gt;&lt;!-- ws:end:WikiTextTocRule:154 --&gt;&lt;!-- ws:start:WikiTextTocRule:155: --&gt; | &lt;a href="#Hemif"&gt;Hemif&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:155 --&gt;&lt;!-- ws:start:WikiTextTocRule:156: --&gt; | &lt;a href="#Myna"&gt;Myna&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:156 --&gt;&lt;!-- ws:start:WikiTextTocRule:157: --&gt; | &lt;a href="#Skwares"&gt;Skwares&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:157 --&gt;&lt;!-- ws:start:WikiTextTocRule:158: --&gt; | &lt;a href="#Magic"&gt;Magic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:158 --&gt;&lt;!-- ws:start:WikiTextTocRule:159: --&gt;&lt;!-- ws:end:WikiTextTocRule:159 --&gt;&lt;!-- ws:start:WikiTextTocRule:160: --&gt; | &lt;a href="#Meantone"&gt;Meantone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:160 --&gt;&lt;!-- ws:start:WikiTextTocRule:161: --&gt; | &lt;a href="#Sensi"&gt;Sensi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:161 --&gt;&lt;!-- ws:start:WikiTextTocRule:162: --&gt; | &lt;a href="#Greeley"&gt;Greeley&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:162 --&gt;&lt;!-- ws:start:WikiTextTocRule:163: --&gt;&lt;!-- ws:end:WikiTextTocRule:163 --&gt;&lt;!-- ws:start:WikiTextTocRule:164: --&gt; | &lt;a href="#Semidim"&gt;Semidim&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:164 --&gt;&lt;!-- ws:start:WikiTextTocRule:165: --&gt; | &lt;a href="#Orwell"&gt;Orwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:165 --&gt;&lt;!-- ws:start:WikiTextTocRule:166: --&gt; | &lt;a href="#Magicaltet"&gt;Magicaltet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:166 --&gt;&lt;!-- ws:start:WikiTextTocRule:167: --&gt; | &lt;a href="#Sentry"&gt;Sentry&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&gt; | &lt;a href="#Mothwelltri"&gt;Mothwelltri&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt; | &lt;a href="#Lovecraft"&gt;Lovecraft&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:169 --&gt;&lt;!-- ws:start:WikiTextTocRule:170: --&gt; | &lt;a href="#Bleu"&gt;Bleu&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:170 --&gt;&lt;!-- ws:start:WikiTextTocRule:171: --&gt; | &lt;a href="#Mohaha"&gt;Mohaha&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:171 --&gt;&lt;!-- ws:start:WikiTextTocRule:172: --&gt;&lt;!-- ws:end:WikiTextTocRule:172 --&gt;&lt;!-- ws:start:WikiTextTocRule:173: --&gt;&lt;!-- ws:end:WikiTextTocRule:173 --&gt;&lt;!-- ws:start:WikiTextTocRule:174: --&gt; | &lt;a href="#Stacks"&gt;Stacks&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:174 --&gt;&lt;!-- ws:start:WikiTextTocRule:175: --&gt; | &lt;a href="#Tutone"&gt;Tutone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:175 --&gt;&lt;!-- ws:start:WikiTextTocRule:176: --&gt; | &lt;a href="#Leantone"&gt;Leantone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:176 --&gt;&lt;!-- ws:start:WikiTextTocRule:177: --&gt; | &lt;a href="#Score"&gt;Score&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:177 --&gt;&lt;!-- ws:start:WikiTextTocRule:178: --&gt; | &lt;a href="#Supra"&gt;Supra&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:178 --&gt;&lt;!-- ws:start:WikiTextTocRule:179: --&gt;&lt;!-- ws:end:WikiTextTocRule:179 --&gt;&lt;!-- ws:start:WikiTextTocRule:180: --&gt;&lt;!-- ws:end:WikiTextTocRule:180 --&gt;&lt;!-- ws:start:WikiTextTocRule:181: --&gt; | &lt;a href="#Antikythera"&gt;Antikythera&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:181 --&gt;&lt;!-- ws:start:WikiTextTocRule:182: --&gt; | &lt;a href="#Deutone"&gt;Deutone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:182 --&gt;&lt;!-- ws:start:WikiTextTocRule:183: --&gt; | &lt;a href="#Semaphore"&gt;Semaphore&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:183 --&gt;&lt;!-- ws:start:WikiTextTocRule:184: --&gt; | &lt;a href="#Augment"&gt;Augment&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:184 --&gt;&lt;!-- ws:start:WikiTextTocRule:185: --&gt;

&lt;!-- ws:end:WikiTextTocRule:185 --&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/11052942?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;11052942&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://mediaplayer.yahoo.com/js"&gt;

&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;br /&gt;

&lt;hr /&gt;

By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; in some rank two temperament (which may often be a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 &lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 error&lt;/a&gt;, which is an appropriate error measure for subgroups as well as full p-limit groups.&lt;br /&gt;

&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [63/50 10/9; 250047/250000]&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:55:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Starlingtet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:55 --&gt;Starlingtet&lt;/h1&gt;

  Group: 2.5/3.7/3&lt;br /&gt;

Comma: 126/125&lt;br /&gt;

Svalname: 4&amp;amp;15&lt;br /&gt;

&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~6/5 = 311.154&lt;br /&gt;

&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 6/5; 126/125]&lt;br /&gt;

Gencom map: [&amp;lt;1 -1 0 1|, &amp;lt;0 4/3 1/3 -5/3|]&lt;br /&gt;

Map: [&amp;lt;1 0 -1|, &amp;lt;0 1 3|]&lt;br /&gt;

EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b&lt;br /&gt;

&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 1.680 cents&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet4"&gt;Four note haplotonic scale&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet11"&gt;Eleven note chromatic scale&lt;/a&gt;&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:57:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc28"&gt;&lt;a name="Gariberttet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:57 --&gt;Gariberttet&lt;/h1&gt;

Subgroup: 2.5/3.7/3.13/11&lt;br /&gt;

Commas: 275/273, 847/845&lt;br /&gt;

Svalname: 4&amp;amp;29&lt;br /&gt;

&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~13/11 = 293.679&lt;br /&gt;

&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 13/11; 275/273 847/845]&lt;br /&gt;

Gencom map: [&amp;lt;1 0 0 0 0 0|, &amp;lt;0 -8/3 1/3 7/3 -1/2 1/2|]&lt;br /&gt;

&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 1.694 cents&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet5"&gt;Five note haplotonic scale&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet9"&gt;Nine note albitonic scale&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:59:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Indium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:59 --&gt;Indium&lt;/h1&gt;

  Subgroup: 2.5/3.7/3.11/3&lt;br /&gt;

Commas: 3025/3024, 3125/3087&lt;br /&gt;

Sval name: 8&amp;amp;33&lt;br /&gt;

&lt;!-- ws:start:WikiTextLocalImageRule:208:&amp;lt;img src=&amp;quot;/file/view/indium_253edo.png/284867050/indium_253edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/indium_253edo.png/284867050/indium_253edo.png" alt="indium_253edo.png" title="indium_253edo.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:208 --&gt;&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:61:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Indium-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:61 --&gt;Music&lt;/h2&gt;

&lt;!-- ws:start:WikiTextHeadingRule:63:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="Hemif"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:63 --&gt;Hemif&lt;/h1&gt;

  Subgroup: 2.3.7.11.13&lt;br /&gt;

Commas: 144/143, 243/242, 364/363&lt;br /&gt;

Related temperament: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments"&gt;Hemififths&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~11/9 = 351.691&lt;br /&gt;

&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 11/9; 144/143 243/242 364/363]&lt;br /&gt;

Gencom map: [&amp;lt;1 1 0 -1 2 4|, &amp;lt;0 2 0 13 5 -1|]&lt;br /&gt;

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;

&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 1.756 cents&lt;br /&gt;

&lt;!-- ws:start:WikiTextLocalImageRule:209:&amp;lt;img src=&amp;quot;/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg" alt="hemif_58edo.jpg" title="hemif_58edo.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:209 --&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif7"&gt;Seven note haplotonic scale&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif10"&gt;Ten note albitonic scale&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:65:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="Myna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:65 --&gt;Myna&lt;/h1&gt;

  Group: 2.3.5.7&lt;br /&gt;

Commas: 126/125, 1728/1715&lt;br /&gt;

Val name: 4&amp;amp;27&lt;br /&gt;

&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~6/5 = 310.146&lt;br /&gt;

&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 6/5; 126/125 1728/1715]&lt;br /&gt;

Gencom map: [&amp;lt;1 -1 0 1|,&amp;lt;0 10 9 7|]&lt;br /&gt;

Map: [&amp;lt;1 9 9 8|, &amp;lt;0 -10 -9 -7|]&lt;br /&gt;

EDOs: 4, 27, 31, 58, 89, 236c, 325cd&lt;br /&gt;

&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 1.903 cents&lt;br /&gt;