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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A '''chromatic pair''' is a pair of [[mos scale]]s in some [[rank-2 temperament]] (either a full [[Harmonic limit|''p''-limit]] temperament or a [[subgroup temperament]]) that are analogous to the familiar [[5L 2s|diatonic]] and [[chromatic]] scales of standard tuning. The smaller scale is an '''albitonic scale''' (from Latin ''albus'', "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is a '''chromatic scale''', analogous to the chromatic scale of standard tuning. Other related scales can be associated to chromatic pairs, namely a '''haplotonic scale''' (from Greek ''haplóos'', "single, simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:guest|guest]] and made on <tt>2011-06-05 13:17:46 UTC</tt>.<br>
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| : The original revision id was <tt>234370796</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[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.
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| =Terrain=
| | In the sections below, the pair temperaments are listed in order of increasing [[Tp tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full ''p''-limit groups. |
| Subgroup: 2.9/5.9/7
| |
| Commas: 250047/250000
| |
| Sval name: 6&21
| |
| Related temperament: [[Minortonic family#Domain|domain]]
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|
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|
| POTE generator: ~10/9 = 182.462
| | == Terrain == |
| | {{See also| Subgroup temperaments #Terrain }} |
|
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|
| Map: [<3 0 -4|, <0 1 2|]
| | [[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]] |
| EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
| |
| Error: 0.0443 cents
| |
|
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|
| 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.
| | Scales: |
| | * [[Terrain9]] – 9-tone albitonic scale |
| | * [[Terrain15]] – 15-tone chromatic scale |
|
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|
| [[terrain9|Nine note albitonic scale]] | | ; Music |
| [[terrain15|Fifteen note chromatic scale]] | | * ''5 5 1 mode of 33 equal'' (2013) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/ blog] | [https://www.youtube.com/watch?v=2gYdUOPHXSQ YouTube] | [https://web.archive.org/web/20201127015117/http://micro.soonlabel.com/33edo/20130827_551of33.mp3 play] |
|
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|
| =Bridgetown= | | == Petrtri == |
| Subgroup: 2.3.11/5.13/5 | | {{See also| Subgroup temperaments #Petrtri }} |
| Commas: 352/351, 676/675
| |
| Sval name: 5&24
| |
| Related temperament: [[The Archipelago|barabados]]
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|
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|
| POTE generator: ~15/13 = 248.285
| | [[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]] |
|
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|
| Map: [<1 0 -6 -1|, <0 2 9 3|]
| | Scales: |
| EDOs: 5, 9, 14, 19, 24, 29
| | * [[Petrtri5]] – 5-tone haplotonic scale |
| Error: 0.8996 cents
| | * [[Petrtri8]] – 8-tone albitonic scale |
| | * [[Petrtri13]] – 13-tone chromatic scale |
|
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|
| [[bridgetown9|Nine note albitonic scale]] | | == Barton == |
| [[bridgetown14|Fourteen note chromatic scale]]
| | {{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}} |
| | {{See also| The Jacobins #Barton }} |
|
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|
| =Cata=
| | Scales: |
| Subgroup: 2.3.5.13
| | * [[Barton5]] – 5-tone haplotonic scale |
| Commas: 325/324, 625/624
| | * [[Barton7]] – 7-tone albitonic scale |
| Sval name: 15&19
| | * [[Barton9]] – 9-tone mega-albitonic scale |
| Related temperament: [[Kleismic family|catakleismic]]
| | * [[Barton11]] – 11-tone chromatic scale |
| | * [[Barton13]] – 13-tone mega-chromatic scale |
|
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|
| POTE generator: ~6/5 = 317.076
| | == Tridec == |
| | {{See also| Subgroup temperaments #Tridec }} |
|
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|
| Map: [<1 0 1 0|, <0 6 5 14|]
| | [[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]] |
| EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246
| |
| Error: 0.9355 cents
| |
|
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|
| [[cata7|Seven note albitonic scale]] | | Scales: |
| [[cata11|Eleven note mega albitonic scale]]
| | * [[Tridec8]] – 8-tone albitonic scale |
| [[cata15|Fifteen note chromatic scale]] | | * [[Tridec13]] – 13-tone chromatic scale |
| [[cata19|Nineteen note mega chromatic scale]]
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| =Tridec= | | == Nestoria == |
| Subgroup: 2.7/5.11/5.13/5
| | {{See also| Schismatic family #Nestoria (2.3.5.19)}} |
| Commas: 847/845, 1001/1000
| |
| Sval name: 5&8
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|
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|
| POTE generator: ~13/10 = 454.461
| | [[File:nestoria_171edo.png|right|alt=nestoria_171edo.png|Nestoria in 171edo]] |
|
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|
| Map: [<1 2 0 1|, <0 -4 3 1|]
| | Scales: |
| EDOs: 5, 8, 21, 29, 37, 66, 169, 235
| | * [[Nestoria7]] – 7-tone albitonic scale |
| Error: 1.057
| | * [[Nestoria12]] – 12-tone chromatic scale |
| | * [[Nestoria17]] – 17-tone mega chromatic scale |
|
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|
| [[Tridec8|Eight note albitonic scale]]
| | == Orgone == |
| [[Tridec13|Thirteen note chromatic scale]]
| | {{Main| Orgone }} |
| | {{See also| Orgonia #Orgone }} |
|
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|
| =Pepperoni=
| | [[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]] |
| 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.
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|
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|
| POTE generator: ~3/2 = 704.052
| | Scales: |
| | * [[Orgone7]] – 7-tone albitonic scale |
| | * [[Orgone11]] – 11-tone chromatic scale |
| | * [[Orgone15]] – 15-tone mega-chromatic scale |
|
| |
|
| Map: [<1 0 7 12|, <0 1 -4 -7|]
| | == Marveltwintri == |
| EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271
| | {{See also| Subgroup temperaments #Marveltwintri }} |
| Error: 1.298 cents
| |
|
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|
| [[pepperoni7|Seven note albitonic scale]] | | [[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]] |
| [[pepperoni12|Twelve note chromatic scale]]
| |
|
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|
| =Nestoria=
| | Scales: |
| Subgroup: 2.3.5.19
| | * [[Marveltwintri7]] – 7-tone albitonic scale |
| Commas: 361/360, 513/512
| | * [[Marveltwintri11]] – 11-tone chromatic scale |
| Sval name: 12&29
| | * [[Marveltwintri15]] – 15-tone mega-chromatic scale |
| Related temperament: [[Schismatic family|schismatic]]
| |
|
| |
|
| POTE generator: ~3/2 = 701.746
| | == Cata == |
| | {{Main| Kleismic }} |
| | {{See also| Kleismic family #Cata }} |
|
| |
|
| Map: [<1 0 15 9|, <0 1 -8 -3|]
| | [[File:cata_246edo.jpg|right|alt=cata_246edo.jpg|Cata in 246edo]] |
| EDOs: 7, 12, 17, 29, 41, 53, 118, 171
| |
| Error: 1.819 cents
| |
|
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|
| [[nestoria7|Seven note albitonic scale]] | | Scales: |
| [[nestoria12|Twelve note chromatic scale]] | | * [[Cata7]] – 7-tone albitonic scale |
| | * [[Cata11]] – 11-tone mega-albitonic scale |
| | * [[Cata15]] – 15-tone chromatic scale |
| | * [[Cata19]] – 19-tone mega-chromatic scale |
|
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|
| ==Photia== | | == Bridgetown == |
| Subgroup: 2.3.5.17.19 | | {{See also| Subgroup temperaments #Bridgetown }} |
| Commas: 171/170, 256/255, 324/323
| |
| Sval name: 12&41
| |
| Related temperament: [[Schismatic family|schismatic]]
| |
|
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|
| POTE generator: ~3/2 = 701.470
| | [[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]] |
|
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|
| Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|]
| | Scales: |
| EDOs: 7, 12, 17, 29, 41, 53, 65
| | * [[Bridgetown9]] – 9-tone albitonic scale |
| Error: 3.457 cents
| | * [[Bridgetown14]] – 14-tone chromatic scale |
|
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|
| [[photia7|Seven note albitonic scale]] | | ; Music |
| [[photia12|Twelve note chromatic scale]] | | * [https://web.archive.org/web/20201127014201/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3 ''Paint in the Water 29''] (archived 2020) by [[Igliashon Jones]] |
| | * ''Route 14 in Bridgetown'' (2011) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201127012744/http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 play] – in Bridgetown[14] for flute, bassoons, and contra-bassoon |
|
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|
| =Huntington= | | == Haumea == |
| Subgroup: 2.5.7.13 | | {{See also| Subgroup temperaments #Haumea }} |
| Commas: 640/637, 10985/10976
| |
| Sval name: 10&27
| |
|
| |
|
| POTE generator: ~16/13 = 357.002
| | Scales: |
| | * [[Haumea5]] – 5-tone haplotonic scale |
| | * [[Haumea9]] – 9-tone albitonic scale |
| | * [[Haumea14]] – 14-tone chromatic scale |
| | * [[Haumea19]] – 19-tone mega-chromatic scale |
|
| |
|
| Map: [<1 5 4 4|, <0 -9 -4 -1|]
| | == Neutral == |
| EDOs: 7, 10, 17, 27, 37, 84, 121, 400
| | {{See also| Rastmic clan #Neutral }} |
| Error: 2.1001 cents
| |
|
| |
|
| [[huntington7|Seven note haplotonic scale]] | | [[File:neutral_380edo.png|right|alt=neutral_380edo.png|Neutral in 380edo]] |
| [[huntington10|Ten note albitonic scale]]
| |
| [[huntington17|Seventeen note chromatic scale]]
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|
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|
| =Roulette=
| | Scales: |
| Subgroup: 2.5.7.11.13
| | * [[Neutral7]] – 7-tone albitonic scale |
| Commas: 176/175, 1375/1372, 640/637
| | * [[Neutral10]] – 10-tone chromatic scale |
| Sval name: 6&25
| | * [[Neutral17]] – 17-tone mega-chromatic scale |
| Related temperament: [[Wuerschmidt family|Hemiwuerschmidt]]
| |
|
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|
| POTE generator: ~28/25 = 194.594
| | ; Music |
| | * [https://soundcloud.com/jdfreivald/mo-happy-happy ''Mo - Happy - Happy''] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by [[Jake Freivald]] in Neutral[7], 24edo tuning |
|
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|
| Map: [<1 0 -3 -7 13|, <0 2 5 9 -8|]
| | == Slendric == |
| EDOs: 6, 7, 13, 19, 25, 31, 37
| | {{Main| Slendric }} |
| Error: 2.555 cents
| | :''See also: [[Gamelismic clan #Slendric]] and [[No-fives subgroup temperaments #Slendric]]'' |
|
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|
| [[roulette6|Six note haplotonic scale]] | | [[File:slendric_190edo.jpg|right|alt=slendric_190edo.jpg|Slendric in 190edo]] |
| [[roulette7|Seven note albitonic scale]]
| |
| [[roulette13|Thirteen note chromatic scale]]
| |
| [[roulette19|Nineteen note mega chromatic scale]]
| |
|
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|
| =Garibaldi=
| | Scales: |
| Group: 2.3.5.7
| | * [[Slendric5]] – 5-tone haplotonic scale |
| Commas: 225/224, 3125/3087
| | * [[Slendric6]] – 6-tone haplotonic scale |
| Val name: 12&29
| | * [[Slendric11]] – 11-tone albitonic scale |
| | * [[Slendric16]] – 16-tone chromatic scale |
|
| |
|
| POTE generator: ~3/2 = 702.085
| | == Huntington == |
| | {{See also| No-threes subgroup temperaments #Huntington }} |
|
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|
| Map: [<1 0 15 25|, <0 1 -8 -14|]
| | [[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]] |
| EDOs: 7, 12, 17, 29, 41, 53, 94
| |
| Error: 2.834
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|
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|
| [[garibaldi12|Twelve note albitonic scale]] | | Scales: |
| [[garibaldi17|Seventeen note chromatic scale]] | | * [[Huntington7]] – 7-tone haplotonic scale |
| | * [[Huntington10]] – 10-tone albitonic scale |
| | * [[Huntington17]] – 17-tone chromatic scale |
|
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|
| =Baldy= | | == Tobago == |
| Subgroup: 2.9.5.7.13 | | {{See also| Subgroup temperaments #Tobago }} |
| Commas: 225/224, 325/324, 640/637
| |
| Sval name: 6&35
| |
| Related temperament: [[Schismatic family|Garibaldi]]
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|
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|
| POTE generator: ~9/8 = 204.090
| | Scales: |
| | * [[Tobago6]] – 6-tone haplotonic scale |
| | * [[Tobago10]] – 10-tone albitonic scale |
| | * [[Tobago14]] – 14-tone chromatic scale |
| | * [[Tobago24]] – 24-tone quatertone scale |
|
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|
| Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|]
| | == Pepperoni == |
| EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
| | {{See also| Parapyth }} |
| Error: 2.617 cents
| | {{See also| Subgroup temperaments #Pepperoni }} |
|
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|
| [[baldy6|Six note haplotonic scale]] | | [[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]] |
| [[baldy11|Eleven note albitonic scale]]
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| [[baldy17|Seventeen note chromatic scale]]
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|
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|
| =Bossier=
| | Scales: |
| Subgroup: 2.7.11.13
| | * [[Pepperoni7]] – 7-tone albitonic scale |
| Commas: 1573/1569, 15488/15379
| | * [[Pepperoni12]] – 12-tone chromatic scale |
| Sval name: 3&17
| |
|
| |
|
| POTE generator: ~14/11 = 421.309
| | == Wizz == |
| | {{See also| No-threes subgroup temperaments #Wizz }} |
|
| |
|
| Map: [<1 0 1 3|, <0 8 7 2|]
| | Scales: |
| EDOs: 17, 20, 37, 57, 94, 225
| | * [[Wizz6]] – 6-tone haplotonic scale |
| Error: 2.665 cents
| | * [[Wizz10]] – 10-tone albitonic scale |
| | * [[Wizz16]] – 16-tone chromatic scale |
|
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|
| [[bossier8|Eight note albitonic scale]]
| | == Bossier == |
| [[bossier11|Eleven note chromatic scale]]
| | {{See also| No-threes subgroup temperaments #Bossier }} |
| [[bossier14|Fourteen note mega chromatic scale]]
| |
|
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|
| =Radon=
| | [[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]] |
| Subgroup: 2.3.7.11
| |
| Commas: 896/891, 1029/1024
| |
| Sval name: 5&36
| |
| Related temperament: [[Gamelismic clan|Rodan]]
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|
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|
| POTE generator: ~8/7 = 234.381
| | Scales: |
| | * [[Bossier8]] – 8-tone albitonic scale |
| | * [[Bossier11]] – 11-tone chromatic scale |
| | * [[Bossier14]] – 14-tone mega-chromatic scale |
|
| |
|
| Map: [<1 1 3 6|, <0 3 -1 -13|]
| | == Penta a.k.a. mechanism == |
| EDOs: 5, 36, 41, 87, 128
| | {{See also| Subgroup temperaments #Penta a.k.a. mechanism }} |
| Error: 2.925 cents
| |
|
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|
| [[radon5|Five note haplotonic scale]] | | Scales: |
| [[radon11|Eleven note albitonic scale]] | | * [[Penta5]] – 5-tone haplotonic scale |
| [[radon16|Sixteen note chromatic scale]] | | * [[Penta8]] – 8-tone albitonic scale |
| | * [[Penta11]] – 11-tone chromatic scale |
| | * [[Penta19]] – 19-tone mega-chromatic scale |
|
| |
|
| =Myna= | | == Bluebirds == |
| Group: 2.3.5.7
| | {{See also| No-threes subgroup temperaments #Bluebirds }} |
| Commas: 126/125, 1728/1715
| |
| Val name: 4&27
| |
|
| |
|
| POTE generator: ~6/5 = 310.146
| | Scales: |
| | * [[Bluebirds6]] – 6-tone haplotonic scale |
| | * [[Bluebirds7]] – 7-tone albitonic scale |
| | * [[Bluebirds13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 9 9 8|, <0 -10 -9 -7|]
| | == Marveltri == |
| EDOs: 4, 27, 31, 58, 89
| | {{See also| Subgroup temperaments #Marveltri }} |
| Error: 3.310 cents
| |
|
| |
|
| [[myna7|Seven note albitonic scale]] | | Scales: |
| [[myna11|Eleven note chromatic scale]] | | * [[Marveltri7]] – 7-tone albitonic scale |
| [[myna15|Fifteen note mega chromatic scale]] | | * [[Marveltri10]] – 10-tone chromatic scale |
| | * [[Marveltri13]] – 13-tone mega-chromatic scale |
|
| |
|
| =Silver= | | == Edson == |
| Subgroup: 2.5.7.13.17 | | {{See also| Subgroup temperaments #Edson }} |
| Commas: 170/169, 640/637, 5525/5488
| |
| Sval name: 10&27
| |
|
| |
|
| POTE generator: ~13/8 = 842.711
| | Scales: |
| | * [[Edson5]] – 5-tone haplotonic scale |
| | * [[Edson7]] – 7-tone albitonic scale |
| | * [[Edson12]] – 12-tone chromatic scale |
| | * [[Edson17]] – 17-tone mega-chromatic scale |
|
| |
|
| Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|]
| | == Photia == |
| EDOs: 7, 10, 17, 27, 37, 47, 84, 131
| | {{See also| Schismatic family #Photia (2.3.5.17) }} |
| Error: 3.437
| |
|
| |
|
| [[silver7|Seven note haplotonic scale]] | | [[File:photia_65edo.png|right|alt=photia_65edo.png|Photia in 65edo]] |
| [[silver10|Ten note albitonic scale]]
| |
| [[silver17|Seventeen note chromatic scale]]
| |
|
| |
|
| =Meantone=
| | Scales: |
| Group: 2.3.5.7
| | * [[Photia7]] – 7-tone albitonic scale |
| Commas: 81/80, 126/125
| | * [[Photia12]] – 12-tone chromatic scale |
| Val name: 12&19
| |
|
| |
|
| POTE generator: 696.495
| | == Shoe a.k.a. llywelyn == |
| | {{See also| Llywelynsmic clan #Llywelyn a.k.a. shoe }} |
|
| |
|
| Map: [<1 0 -4 -13|, <0 1 4 10|]
| | [[File:shoe_37edo.jpg|right|alt=shoe_37edo.jpg|Shoe in 37edo]] |
| EDOs: 5, 7, 12, 19, 31, 81, 112, 143
| |
| Error: 3.585
| |
|
| |
|
| [[meantone5|Five note haplotonic scale]] | | Scales: |
| [[meantone7|Seven note albitonic scale]] | | * [[Shoe5]] – 5-tone mini-haplotonic scale |
| [[meantone12|Twelve note chromatic scale]] | | * [[Shoe6]] – 6-tone haplotonic scale |
| | * [[Shoe11]] – 11-tone albitonic scale |
| | * [[Shoe16]] – 16-tone chromatic scale |
|
| |
|
| =Indium= | | == Roulette == |
| Subgroup: 2.5/3.7/3.11/3
| | {{See also | Hemimean clan #Roulette }} |
| Commas: 3025/3024, 3125/3087
| |
| Sval name: 8&33
| |
|
| |
|
| POTE generator: ~12/11 = 147.159
| | [[File:roulette_37edo.jpg|right|alt=roulette_37edo.jpg|Roulette in 37edo]] |
|
| |
|
| Map: [<1 0 0 2|, <0 6 10 -1|]
| | Scales: |
| EDOs: 33, 41, 49, 57, 106, 204, 253
| | * [[Roulette6]] – 6-tone haplotonic scale |
| Error: 3.968 cents
| | * [[Roulette7]] – 7-tone albitonic scale |
| | * [[Roulette13]] – 13-tone chromatic scale |
| | * [[Roulette19]] – 19-tone mega-chromatic scale |
|
| |
|
| [[indium8|Eight note albitonic scale]]
| | == Silver == |
| [[indium17|Seventeen note chromatic scale]]
| | {{See also | No-threes subgroup temperaments #Silver }} |
|
| |
|
| =Magic=
| | [[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]] |
| Group: 2.3.5.7.11
| |
| Commas: 100/99, 225/224, 245/243
| |
| Val name: 19&22
| |
|
| |
|
| POTE generator: ~5/4 = 380.696
| | Scales: |
| | * [[Silver7]] – 7-tone haplotonic scale |
| | * [[Silver10]] – 10-tone albitonic scale |
| | * [[Silver17]] – 17-tone chromatic scale |
|
| |
|
| Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]
| | == Baldy == |
| EDOs: 19, 22, 41, 104, 145
| | {{See also| Subgroup temperaments #Baldy }} |
| Error: 4.489
| |
|
| |
|
| [[magic7|Seven note haplotonic scale]] | | [[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]] |
| [[magic10|Ten note albitonic scale]]
| |
| [[magic13|Thirteen note chromatic scale]]
| |
| [[magic16|Sixteen note mega chromatic scale]]
| |
|
| |
|
| =Hemif=
| | Scales |
| Subgroup: 2.3.7.11.13
| | * [[Baldy6]] – 6-tone haplotonic scale |
| Commas: 144/143, 243/242, 364/363
| | * [[Baldy11]] – 11-tone albitonic scale |
| Related temperament: [[Breedsmic temperaments|Hemififths]]
| | * [[Baldy17]] – 17-tone chromatic scale |
|
| |
|
| POTE generator: ~11/9 = 351.691
| |
|
| |
|
| Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]
| | == Guanyintet == |
| EDOs: 7, 10, 17, 24, 41, 58
| | {{See also | Subgroup temperaments #Guanyintet }} |
| Error: 4.867 cents
| |
|
| |
|
| [[hemif7|Seven note haplotonic scale]] | | Scales: |
| [[hemif10|Ten note albitonic scale]] | | * [[Guanyintet5]] – 5-tone haplotonic scale |
| [[hemif17|Seventeen note chromatic scale]] | | * [[Guanyintet9]] – 9-tone albitonic scale |
| | * [[Guanyintet13]] – 13-tone chromatic scale |
|
| |
|
| =Skwares= | | == Radon == |
| Subgroup: 2.3.7.11
| | {{See also| Gamelismic clan #Radon }} |
| Commas: 99/98, 243/242
| |
| Related temperament: [[Meantone family|squares]]
| |
|
| |
|
| POTE generator: ~9/7 = 425.244
| | [[File:radon_128edo.jpg|right|alt=radon_128edo.jpg|Radon in 128edo]] |
|
| |
|
| Map: [<1 3 6 7|, <0 -4 -9 -10|]
| | * [[Radon5]] – 5-tone haplotonic scale |
| EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206
| | * [[Radon11]] – 11-tone albitonic scale |
| Error: 4.942 cents
| | * [[Radon16]] – 16-tone chromatic scale |
|
| |
|
| [[skwares8|Eight note albitonic scale]]
| | == Gariberttet == |
| [[skwares11|Eleven note mega albitonic scale]]
| | {{See also | Subgroup temperaments #Gariberttet }} |
| [[skwares14|Fourteen note chromatic scale]]
| |
|
| |
|
| =Sensi=
| | Scales: |
| Group: 2.3.5.7
| | * [[Gariberttet5]] – 5-tone haplotonic scale |
| Commas: 126/126, 245/243
| | * [[Gariberttet9]] – 9-tone albitonic scale |
| Val name: 19&27
| | * [[Gariberttet13]] – 13-tone chromatic scale |
|
| |
|
| POTE generator: ~9/7 = 443.383
| | == Namo == |
| | {{See also| Rastmic clan #Namo }} |
|
| |
|
| Map: [<1 6 8 11|, <0 -7 -9 -13|]
| | Scales: |
| EDOs: 5, 8, 11, 19, 27, 46
| | * [[Namo7]] – 7-tone haplotonic scale |
| Error: 5.019
| | * [[Namo10]] – 10-tone albitonic scale |
| | * [[Namo17]] – 17-tone chromatic scale |
|
| |
|
| [[sensi5|Five note haplotonic scale]]
| | == Sentry == |
| [[sensi8|Eight note albitonic scale]]
| | {{See also | Subgroup temperaments #Sentry }} |
| [[sensi11|Eleven note mega albitonic scale]]
| |
| [[sensi19|Nineteen note chromatic scale]]
| |
|
| |
|
| =Greeley=
| | Scales: |
| Subgroup: 2.5/3.7/3.11/3
| | * [[Sentry5]] – 5-tone haplotonic scale |
| Commas: 121/120, 126/125
| | * [[Sentry8]] – 8-tone albitonic scale |
| | * [[Sentry11]] – 11-tone chromatic scale |
|
| |
|
| POTE generator: ~11/10 = 156.055
| | == Hemif == |
| | {{See also| No-fives subgroup temperaments #Hemif }} |
|
| |
|
| Map: [<1 1 2 2|, <0 -2 -6 -1|]
| | [[File:hemif_58edo.jpg|right|alt=hemif_58edo.jpg|Hemif in 58edo]] |
| EDOs: 8, 15, 23, 77, 100
| |
| Error: 5.404 cents
| |
|
| |
|
| [[greeley8|Eight note albitonic scale]] | | Scales: |
| [[greeley15|Fifteen note chromatic scale]] | | * [[Hemif7]] – 7-tone haplotonic scale |
| | * [[Hemif10]] – 10-tone albitonic scale |
| | * [[Hemif17]] – 17-tone chromatic scale |
|
| |
|
| =Semidim= | | == Garibaldi == |
| Subgroup: 2.5/3.7/3.11/3.13/3
| | {{Main| Garibaldi temperament }} |
| Commas: 121/120, 169/168, 275/273
| | {{See also| Schismatic family #Garibaldi }} |
| Sval name: 8&29
| |
|
| |
|
| POTE generator: ~13/10 = 453.190
| | [[File:garibaldi_94edo.png|right|alt=garibaldi_94edo.png|Garibaldi in 94edo]] |
|
| |
|
| Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]
| | Scales: |
| EDOs: 5, 8, 13, 21, 29, 37, 45
| | * [[Garibaldi12]] – 12-tone albitonic scale |
| Error: 5.433 cents
| | * [[Garibaldi17]] – 17-tone chromatic scale |
|
| |
|
| [[semidim8|Eight note albitonic scale]]
| | == Mabilic == |
| [[semidim13|Thirteen note chromatic scale]]
| | {{See also| No-threes subgroup temperaments #Mabilic }} |
|
| |
|
| =Orwell=
| | [[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]] |
| Group: 2.3.5.7.11
| |
| Commas: 99/98, 121/120, 176/175
| |
| Val name: 9&22
| |
|
| |
|
| POTE generator: ~7/6 = 271.426
| | Scales: |
| | * [[Mabilic7]] – 7-tone haplotonic scale |
| | * [[Mabilic9]] – 9-tone albitonic scale |
| | * [[Mabilic16]] – 16-tone chromatic scale |
|
| |
|
| Map: [<1 0 3 1 3|, <0 7 -3 8 2|]
| | == Indium == |
| EDOs: 9, 22, 31, 53, 84
| | {{See also | Subgroup temperaments #Indium }} |
| Error: 5.584
| |
|
| |
|
| [[orwell5|Five note haplotonic scale]] | | [[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]] |
| [[orwell9|Nine note albitonic scale]]
| |
| [[orwell13|Thirteen note chromatic scale]]
| |
|
| |
|
| =Mohaha=
| | Scales: |
| Subgroup: 2.3.5.11
| | * [[Indium8]] – 8-tone albitonic scale |
| Commas: 81/80, 121/120
| | * [[Indium17]] – 17-tone chromatic scale |
| Related temperament: [[Meantone family|mohajira]]
| |
|
| |
|
| POTE generator: ~11/9 = 348.094
| | ; Music |
| | * ''The Cry of Indium'' (2011) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/the-cry-of-indium/ blog] | [https://web.archive.org/web/20201127012551/http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3 play] – in Indium[17] |
|
| |
|
| Map: [<1 1 0 2|, <0 2 8 5|]
| | == Starlingtet == |
| EDOs: 7, 10, 17, 24, 31, 131
| | {{See also | Subgroup temperaments #Starlingtet }} |
| Error: 6.733 cents
| |
|
| |
|
| [[mohaha7|Seven note albitonic scale]] | | Scales: |
| [[mohaha10|Ten note chromatic scale]] | | * [[Starlingtet4]] – 4-tone haplotonic scale |
| | * [[Starlingtet7]] – 7-tone albitonic scale |
| | * [[Starlingtet11]] – 11-tone chromatic scale |
|
| |
|
| ==Mohoho== | | == Lovecraft == |
| Subgroup: 2.3.5.11.13
| | {{See also | No-threes subgroup temperaments #Lovecraft }} |
| Commas: 66/65, 81/80, 121/120
| |
|
| |
|
| POTE generator: ~11/9 = 348.916
| | [[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]] |
|
| |
|
| Map: [<1 1 0 2 4|, <0 2 8 5 -1|]
| | Scales: |
| EDOs: 7, 10, 17, 24, 31, 55
| | * [[Lovecraft5]] – 5-tone haplotonic scale |
| Error: 9.556 cents
| | * [[Lovecraft9]] – 9-tone albitonic scale |
| | * [[Lovecraft13]] – 13-tone chromatic scale |
|
| |
|
| =Tutone= | | == Blackbirds == |
| Subgroup: 2.9.5.7.11
| | {{See also | No-threes subgroup temperaments #Blackbirds }} |
| Commas: 81/80, 99/98, 126/125
| |
| Related temperament: [[Meantone family|meantone]]
| |
|
| |
|
| POTE generator: ~9/8 = 193.937
| | Scales: |
| | * [[Blackbirds8]] – 8-tone albitonic scale |
| | * [[Blackbirds12]] – 12-tone chromatic scale |
| | * [[Blackbirds16]] – 16-tone mega-chromatic scale |
|
| |
|
| Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]
| | == Laz == |
| EDOs: 6, 7, 13, 19, 25, 31, 99
| | {{See also | Subgroup temperaments #Laz }} |
| Error: 7.047 cents
| |
|
| |
|
| [[tutone6|Six note haplotonic scale]] | | Scales: |
| [[tutone7|Seven note albitonic scale]] | | * [[Laz5]] – 5-tone haplotonic scale |
| [[tutone13|Thirteen note chromatic scale]] | | * [[Laz9]] – 9-tone albitonic scale |
| | * [[Laz13]] – 13-tone chromatic scale |
|
| |
|
| ==Leantone== | | == Myna == |
| Subgroup: 2.9.5.7.11
| | {{Main| Myna }} |
| Commas: 45/44, 56/55, 81/80
| | {{See also| Starling temperaments #Myna }} |
| Related temperament: [[Meantone family|flattone]]
| |
|
| |
|
| POTE generator: ~9/8 = 192.500
| | [[File:myna_89edo.jpg|right|alt=myna_89edo.jpg|Myna in 89edo]] |
|
| |
|
| Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
| | Scales: |
| EDOs: 6, 7, 13, 19, 25, 31, 56, 81
| | * [[Myna7]] – 7-tone haplotonic scale |
| Error: 20.338 cents
| | * [[Myna11]] – 11-tone albitonic scale |
| | * [[Myna15]] – 15-tone chromatic scale |
|
| |
|
| [[leantone6|Six note haplotonic scale]]
| | == Greeley == |
| [[leantone7|Seven note albitonic scale]]
| | {{See also| Subgroup temperaments #Greeley }} |
| [[leantone13|Thirteen note chromatic scale]]
| |
|
| |
|
| =Score=
| | [[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]] |
| Subgroup: 2.7.11.13
| |
| Commas: 343/338, 847/832
| |
|
| |
|
| POTE generator: ~11/8 = 540.099
| | Scales: |
| | * [[Greeley8]] – 8-tone albitonic scale |
| | * [[Greeley15]] – 15-tone chromatic scale |
|
| |
|
| Map: [<1 1 3 1|, <0 4 1 6|]
| | ; Music |
| EDOs: 5, 7, 9, 11, 20
| | * ''A Greeley Steals Halloween'' by [[Chris Vaisvil]] (2011) – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201201174756/http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 play] – in Greeley[15] |
| Error: 8.052 cents
| |
|
| |
|
| [[score5|Five note haplotonic scale]]
| | == Ammon == |
| [[score7|Seven note albitonic scale]]
| | {{See also| Subgroup temperaments #Ammon }} |
| [[score9|Nine note mega albitonic scale]]
| |
| [[score11|Eleven note chromatic scale]]
| |
|
| |
|
| =Supra=
| | [[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]] |
| Subgroup: 2.3.7.11
| |
| Commas: 64/63, 99/98
| |
| Related temperament: [[Archytas clan|superpyth]]
| |
|
| |
|
| POTE generator: ~3/2 = 707.192
| | Scales: |
| | * [[Ammon8]] – 8-tone albitonic scale |
| | * [[Ammon13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 6 13|, <0 1 -2 -6|]
| | == Mothwelltri == |
| EDOs: 5, 7, 12, 17, 22, 39, 56
| | {{See also| Subgroup temperaments #Mothwelltri }} |
| Error: 9.795 cents
| |
|
| |
|
| [[supra7|Seven note albitonic scale]] | | Scales: |
| [[supra12|Twelve note chromatic scale]] | | * [[Mothwelltri5]] – 5-tone haplotonic scale |
| | * [[Mothwelltri9]] – 9-tone albitonic scale |
| | * [[Mothwelltri13]] – 13-tone chromatic scale |
|
| |
|
| ==Supraphon== | | == Sulis == |
| Subgroup: 2.3.7.11.13 | | {{See also| Subgroup temperaments #Sulis }} |
| Commas: 64/63, 78/77, 99/98
| |
|
| |
|
| POTE generator: ~3/2 = 706.137
| | Scales: |
| | * [[Sulis7]] – 7-tone haplotonic scale |
| | * [[Sulis10]] – 10-tone albitonic scale |
| | * [[Sulis13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]
| | == Skwares == |
| EDOs: 5, 7, 12, 17
| | {{Main| Squares }} |
| Error: 10.534 cents
| | {{See also| No-fives subgroup temperaments #Skwares }} |
|
| |
|
| ==Machine==
| | [[File:skwares_206edo.png|right|alt=skwares_206edo.png|Skwares in 206edo]] |
| Subgroup: 2.9.7.11
| |
| Commas: 64/63, 99/98
| |
|
| |
|
| POTE generator: ~9/8 = 214.384
| | Scales: |
| | * [[Skwares8]] – 8-tone albitonic scale |
| | * [[Skwares11]] – 11-tone mega-albitonic scale |
| | * [[Skwares14]] – 14-tone chromatic scale |
|
| |
|
| Map: [<1 0 6 13|, <0 1 -1 -3|]
| | == Orwell == |
| EDOs: 5, 6, 11, 17, 28
| | {{Main| Orwell }} |
| Error: 10.100 cents
| | {{See also| Semicomma family #Orwell }} |
|
| |
|
| [[machine5|Five note haplotonic scale]] | | [[File:orwell_84edo.png|right|alt=orwell_84edo.png|Orwell in 84edo]] |
| [[machine6|Six note albitonic scale]]
| |
| [[machine11|Eleven note chromatic scale]]
| |
|
| |
|
| =Deutone=
| | Scales: |
| Subgroup: 2.9.5.7.13
| | * [[Orwell5]] – 5-tone haplotonic scale |
| Commas: 65/64, 81/80, 91/90
| | * [[Orwell9]] – 9-tone albitonic scale |
| Related temperament: [[Meantone family|meanpop]]
| | * [[Orwell13]] – 13-tone chromatic scale |
|
| |
|
| POTE generator: ~9/8 = 191.059
| | == Magicaltet == |
| | {{See also| Subgroup temperaments #Magicaltet }} |
|
| |
|
| Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|]
| | Scales: |
| EDOs: 6, 7, 13, 19, 25, 44, 69
| | * [[Magicaltet7]] – 7-tone albitonic scale |
| Error: 12.145 cents
| | * [[Magicaltet11]] – 11-tone chromatic scale |
| | * [[Magicaltet15]] – 15-tone mega-chromatic scale |
|
| |
|
| [[deutone6|Six note haplotonic scale]]
| | == Magic == |
| [[deutone7|seven note albitonic scale]]
| | {{Main| Magic }} |
| [[deutone13|Thirteen note chromatic scale]]
| | {{See also| Magic family #Magic }} |
|
| |
|
| =Augment=
| | [[File:magic_145edo.jpg|right|alt=magic_145edo.jpg|Magic in 145edo]] |
| Subgroup: 2.5.7.11
| |
| Commas: 56/55, 128/125
| |
| Related temperament: [[Augmented family|augmented]]
| |
|
| |
|
| POTE generator: ~8/7 = 228.275
| | Scales: |
| | * [[Magic7]] – 7-tone haplotonic scale |
| | * [[Magic10]] – 10-tone albitonic scale |
| | * [[Magic13]] – 13-tone chromatic scale |
| | * [[Magic16]] – 16-tone mega-chromatic scale |
|
| |
|
| Map: [<3 7 0 2|, <0 0 1 1|]
| | == Kiribati == |
| EDOs: 3, 6, 9, 15, 21
| | {{See also| Subgroup temperaments #Kiribati }} |
| Error: 12.830 cents
| |
|
| |
|
| [[augment6|Six note haplotonic scale]] | | Scales: |
| [[augment9|Nine note albitonic scale]] | | * [[Kiribati13]] – 13-tone chromatic scale |
| [[augment12|Twelve note chromatic scale]]</pre></div>
| | * [[Kiribati14]] – 14-tone chromatic scale |
| <h4>Original HTML content:</h4>
| | |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Chromatic pairs</title></head><body><!-- ws:start:WikiTextTocRule:68:&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:68 --><!-- ws:start:WikiTextTocRule:69: --><a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --> | <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --> | <a href="#Sensi">Sensi</a><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --> | <a href="#Deutone">Deutone</a><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: -->
| | == Score == |
| <!-- ws:end:WikiTextTocRule:103 -->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 />
| | {{See also|No-threes subgroup temperaments #Score }} |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h1>
| | [[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]] |
| Subgroup: 2.9/5.9/7<br />
| | |
| Commas: 250047/250000<br />
| | Scales: |
| Sval name: 6&amp;21<br />
| | * [[Score5]] – 5-tone haplotonic scale |
| Related temperament: <a class="wiki_link" href="/Minortonic%20family#Domain">domain</a><br />
| | * [[Score7]] – 7-tone albitonic scale |
| <br />
| | * [[Score9]] – 9-tone mega-albitonic scale |
| POTE generator: ~10/9 = 182.462<br />
| | * [[Score11]] – 11-tone chromatic scale |
| <br />
| | |
| Map: [&lt;3 0 -4|, &lt;0 1 2|]<br />
| | == Sensi == |
| EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558<br />
| | {{Main| Sensi }} |
| Error: 0.0443 cents<br />
| | {{See also| Sensipent family #Sensi }} |
| <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 />
| | [[File:sensi_46edo.jpg|right|alt=sensi_46edo.jpg|Sensi in 46edo]] |
| <br />
| | |
| <a class="wiki_link" href="/terrain9">Nine note albitonic scale</a><br />
| | Scales: |
| <a class="wiki_link" href="/terrain15">Fifteen note chromatic scale</a><br />
| | * [[Sensi5]] – 5-tone haplotonic scale |
| <br />
| | * [[Sensi8]] – 8-tone albitonic scale |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:2 -->Bridgetown</h1>
| | * [[Sensi11]] – 11-tone mega-albitonic scale |
| Subgroup: 2.3.11/5.13/5<br />
| | * [[Sensi19]] – 19-tone chromatic scale |
| Commas: 352/351, 676/675<br />
| | |
| Sval name: 5&amp;24<br />
| | === Sensation === |
| Related temperament: <a class="wiki_link" href="/The%20Archipelago">barabados</a><br />
| | {{Main| Sensi }} |
| <br />
| | {{See also| Sensipent family #Sensi }} |
| POTE generator: ~15/13 = 248.285<br />
| | |
| <br />
| | Scales: |
| Map: [&lt;1 0 -6 -1|, &lt;0 2 9 3|]<br />
| | * [[Sensi5]] – 5-tone haplotonic scale |
| EDOs: 5, 9, 14, 19, 24, 29<br />
| | * [[Sensi8]] – 8-tone albitonic scale |
| Error: 0.8996 cents<br />
| | * [[Sensi11]] – 11-tone mega-albitonic scale |
| <br />
| | * [[Sensi19]] – 19-tone chromatic scale |
| <a class="wiki_link" href="/bridgetown9">Nine note albitonic scale</a><br />
| | |
| <a class="wiki_link" href="/bridgetown14">Fourteen note chromatic scale</a><br />
| | == Meantone == |
| <br />
| | {{Main| Meantone }} |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:4 -->Cata</h1>
| | {{See also| Meantone family #Meantone }} |
| Subgroup: 2.3.5.13<br />
| | |
| Commas: 325/324, 625/624<br />
| | [[File:meantone_31edo.jpg|right|alt=meantone_31edo.jpg|Meantone in 31edo]] |
| Sval name: 15&amp;19<br />
| | |
| Related temperament: <a class="wiki_link" href="/Kleismic%20family">catakleismic</a><br />
| | Scales: |
| <br />
| | * [[Meantone5]] – 5-tone haplotonic scale |
| POTE generator: ~6/5 = 317.076<br />
| | * [[Meantone7]] – 7-tone albitonic scale |
| <br />
| | * [[Meantone12]] – 12-tone chromatic scale |
| Map: [&lt;1 0 1 0|, &lt;0 6 5 14|]<br />
| | |
| EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246<br />
| | == Mohaha == |
| Error: 0.9355 cents<br />
| | {{See also| Rastmic clan #Mohaha }} |
| <br />
| | |
| <a class="wiki_link" href="/cata7">Seven note albitonic scale</a><br />
| | [[File:mohaha_131edo.png|right|alt=mohaha_131edo.png|Mohaha in 131edo]] |
| <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 />
| | Scales: |
| <a class="wiki_link" href="/cata19">Nineteen note mega chromatic scale</a><br />
| | * [[Mohaha7]] – 7-tone albitonic scale |
| <br />
| | * [[Mohaha10]] – 10-tone chromatic scale |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Tridec"></a><!-- ws:end:WikiTextHeadingRule:6 -->Tridec</h1>
| | |
| Subgroup: 2.7/5.11/5.13/5<br />
| | Music: |
| Commas: 847/845, 1001/1000<br />
| | ; [[Billy Stiltner]] |
| Sval name: 5&amp;8<br />
| | * [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 ''Mohaha10ping2'']{{dead link}} |
| <br />
| | |
| POTE generator: ~13/10 = 454.461<br />
| | === Mohoho === |
| <br />
| | {{See also| Rastmic clan #Mohoho }} |
| Map: [&lt;1 2 0 1|, &lt;0 -4 3 1|]<br />
| | |
| EDOs: 5, 8, 21, 29, 37, 66, 169, 235<br />
| | == Joan == |
| Error: 1.057<br />
| | {{See also| Subgroup temperaments #Joan }} |
| <br />
| | |
| <a class="wiki_link" href="/Tridec8">Eight note albitonic scale</a><br />
| | Scales: |
| <a class="wiki_link" href="/Tridec13">Thirteen note chromatic scale</a><br />
| | * [[Joan5]] – 5-tone haplotonic scale |
| <br />
| | * [[Joan7]] – 7-tone albitonic scale |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:8 -->Pepperoni</h1>
| | * [[Joan9]] – 9-tone mega-albitonic scale |
| Subgroup: 2.3.11/7.13/7<br />
| | * [[Joan11]] – 11-tone chromatic scale |
| Commas: 352/351, 364/363<br />
| | |
| Sval name: 5&amp;12<br />
| | == Tutone == |
| 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 />
| | {{See also| Hemimean clan #Tutone }} |
| <br />
| | |
| POTE generator: ~3/2 = 704.052<br />
| | [[File:tutone_99edo.png|right|alt=tutone_99edo.png|Tutone in 99edo]] |
| <br />
| | |
| Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]<br />
| | Scales: |
| EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br />
| | * [[Tutone6]] – 6-tone haplotonic scale |
| Error: 1.298 cents<br />
| | * [[Tutone7]] – 7-tone albitonic scale |
| <br />
| | * [[Tutone13]] – 13-tone chromatic scale |
| <a class="wiki_link" href="/pepperoni7">Seven note albitonic scale</a><br />
| | |
| <a class="wiki_link" href="/pepperoni12">Twelve note chromatic scale</a><br />
| | == Stacks == |
| <br />
| | {{See also|Subgroup temperaments #Stacks (a.k.a. 2magic) }} |
| <!-- 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 />
| | Scales: |
| Commas: 361/360, 513/512<br />
| | * [[Stacks5]] – 5-tone haplotonic scale |
| Sval name: 12&amp;29<br />
| | * [[Stacks8]] – 8-tone albitonic scale |
| Related temperament: <a class="wiki_link" href="/Schismatic%20family">schismatic</a><br />
| | * [[Stacks11]] – 11-tone chromatic scale |
| <br />
| | * [[Stacks19]] – 19-tone mega-chromatic scale |
| POTE generator: ~3/2 = 701.746<br />
| | |
| <br />
| | == Bleu == |
| Map: [&lt;1 0 15 9|, &lt;0 1 -8 -3|]<br />
| | {{See also| No-fives subgroup temperaments #Bleu }} |
| EDOs: 7, 12, 17, 29, 41, 53, 118, 171<br />
| | |
| Error: 1.819 cents<br />
| | Scales: |
| <br />
| | * [[Bleu8]] – 8-tone haplotonic scale |
| <a class="wiki_link" href="/nestoria7">Seven note albitonic scale</a><br />
| | * [[Bleu9]] – 9-tone albitonic scale |
| <a class="wiki_link" href="/nestoria12">Twelve note chromatic scale</a><br />
| | * [[Bleu17]] – 17-tone chromatic scale |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Nestoria-Photia"></a><!-- ws:end:WikiTextHeadingRule:12 -->Photia</h2>
| | == Sephiroth == |
| Subgroup: 2.3.5.17.19<br />
| | {{See also| No-threes subgroup temperaments #Sephiroth }} |
| Commas: 171/170, 256/255, 324/323<br />
| | |
| Sval name: 12&amp;41<br />
| | Scales: |
| Related temperament: <a class="wiki_link" href="/Schismatic%20family">schismatic</a><br />
| | * [[Sephiroth7]] – 7-tone haplotonic scale |
| <br />
| | * [[Sephiroth10]] – 10-tone albitonic scale |
| POTE generator: ~3/2 = 701.470<br />
| | * [[Sephiroth13]] – 13-tone chromatic scale |
| <br />
| | * [[Sephiroth16]] – 16-tone mega-chromatic scale |
| Map: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]<br />
| | |
| EDOs: 7, 12, 17, 29, 41, 53, 65<br />
| | == Archy == |
| Error: 3.457 cents<br />
| | {{Main| Superpyth }} |
| <br />
| | {{See also| Archytas clan #Archy }} |
| <a class="wiki_link" href="/photia7">Seven note albitonic scale</a><br />
| | |
| <a class="wiki_link" href="/photia12">Twelve note chromatic scale</a><br />
| | Scales: |
| <br />
| | * [[Archy5]] – 5-tone haplotonic scale |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:14 -->Huntington</h1>
| | * [[Archy7]] – 7-tone albitonic scale |
| Subgroup: 2.5.7.13<br />
| | * [[Archy12]] – 12-tone chromatic scale |
| Commas: 640/637, 10985/10976<br />
| | |
| Sval name: 10&amp;27<br />
| | === Supra === |
| <br />
| | {{Main| Superpyth }} |
| POTE generator: ~16/13 = 357.002<br />
| | {{See also| Archytas clan #Supra }} |
| <br />
| | |
| Map: [&lt;1 5 4 4|, &lt;0 -9 -4 -1|]<br />
| | [[File:supra_56edo.png|right|alt=supra_56edo.png|Supra in 56edo]] |
| EDOs: 7, 10, 17, 27, 37, 84, 121, 400<br />
| | |
| Error: 2.1001 cents<br />
| | Scales: |
| <br />
| | * [[Supra7]] – 7-tone [[albitonic scale]] |
| <a class="wiki_link" href="/huntington7">Seven note haplotonic scale</a><br />
| | * [[Supra12]] – 12-tone [[chromatic scale]] |
| <a class="wiki_link" href="/huntington10">Ten note albitonic scale</a><br />
| | |
| <a class="wiki_link" href="/huntington17">Seventeen note chromatic scale</a><br />
| | === Supraphon === |
| <br />
| | {{Main| Superpyth }} |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:16 -->Roulette</h1>
| | {{See also| Archytas clan #Supraphon }} |
| Subgroup: 2.5.7.11.13<br />
| | |
| Commas: 176/175, 1375/1372, 640/637<br />
| | == Suhajira == |
| Sval name: 6&amp;25<br />
| | {{See also| Archytas clan #Suhajira }} |
| Related temperament: <a class="wiki_link" href="/Wuerschmidt%20family">Hemiwuerschmidt</a><br />
| | |
| <br />
| | Scales: |
| POTE generator: ~28/25 = 194.594<br />
| | * [[Suhajira7]] – 7-tone haplotonic scale |
| <br />
| | * [[Suhajira10]] – 10-tone albitonic scale |
| Map: [&lt;1 0 -3 -7 13|, &lt;0 2 5 9 -8|]<br />
| | * [[Suhajira17]] – 17-tone chromatic scale |
| EDOs: 6, 7, 13, 19, 25, 31, 37<br />
| | |
| Error: 2.555 cents<br />
| | == Machine == |
| <br />
| | {{See also| Subgroup temperaments #Machine}} |
| <a class="wiki_link" href="/roulette6">Six note haplotonic scale</a><br />
| | |
| <a class="wiki_link" href="/roulette7">Seven note albitonic scale</a><br />
| | [[File:machine_28edo.png|right|alt=machine_28edo.png|Machine in 28edo]] |
| <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 />
| | Scales: |
| <br />
| | * [[Machine5]] – 5-tone haplotonic scale |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:18 -->Garibaldi</h1>
| | * [[Machine6]] – 6-tone albitonic scale |
| Group: 2.3.5.7<br />
| | * [[Machine11]] – 11-tone chromatic scale |
| Commas: 225/224, 3125/3087<br />
| | |
| Val name: 12&amp;29<br />
| | == Deutone == |
| <br />
| | {{See also| Hemimean clan #Deutone }} |
| POTE generator: ~3/2 = 702.085<br />
| | |
| <br />
| | [[File:deutone_44edo.png|right|alt=deutone_44edo.png|Deutone in 44edo]] |
| Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]<br />
| | |
| EDOs: 7, 12, 17, 29, 41, 53, 94<br />
| | Scales: |
| Error: 2.834<br />
| | * [[Deutone6]] – 6-tone haplotonic scale |
| <br />
| | * [[Deutone7]] – 7-tone albitonic scale |
| <a class="wiki_link" href="/garibaldi12">Twelve note albitonic scale</a><br />
| | * [[Deutone13]] – 13-tone chromatic scale |
| <a class="wiki_link" href="/garibaldi17">Seventeen note chromatic scale</a><br />
| | |
| <br />
| | == Negra == |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:20 -->Baldy</h1>
| | {{Main| Negri }} |
| Subgroup: 2.9.5.7.13<br />
| | {{See also| Marvel temperaments #Negri }} |
| Commas: 225/224, 325/324, 640/637<br />
| | |
| Sval name: 6&amp;35<br />
| | == Porkypine == |
| Related temperament: <a class="wiki_link" href="/Schismatic%20family">Garibaldi</a><br />
| | {{Main| Porcupine }} |
| <br />
| | {{See also| Porcupine family #Porcupine }} |
| POTE generator: ~9/8 = 204.090<br />
| | |
| <br />
| | Scales: |
| Map: [&lt;1 0 15 25 -28|, &lt;0 1 -4 -7 10|]<br />
| | * [[Porkypine7]] – 7-tone haplotonic scale |
| EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147<br />
| | * [[Porkypine8]] – 8-tone albitonic scale |
| Error: 2.617 cents<br />
| | * [[Porkypine15]] – 15-tone chromatic scale |
| <br />
| | |
| <a class="wiki_link" href="/baldy6">Six note haplotonic scale</a><br />
| | == Skateboard == |
| <a class="wiki_link" href="/baldy11">Eleven note albitonic scale</a><br />
| | {{See also| Subgroup temperaments #Skateboard }} |
| <a class="wiki_link" href="/baldy17">Seventeen note chromatic scale</a><br />
| | |
| <br />
| | Scales: |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:22 -->Bossier</h1>
| | * [[Skateboard7]] – 7-tone haplotonic scale |
| Subgroup: 2.7.11.13<br />
| | * [[Skateboard11]] – 11-tone albitonic scale |
| Commas: 1573/1569, 15488/15379<br />
| | * [[Skateboard15]] – 15-tone chromatic scale |
| Sval name: 3&amp;17<br />
| | |
| <br />
| | == Augment == |
| POTE generator: ~14/11 = 421.309<br />
| | {{See also| No-threes subgroup temperaments #Augment }} |
| <br />
| | |
| Map: [&lt;1 0 1 3|, &lt;0 8 7 2|]<br />
| | [[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]] |
| EDOs: 17, 20, 37, 57, 94, 225<br />
| | |
| Error: 2.665 cents<br />
| | Scales: |
| <br />
| | * [[Augment6]] – 6-tone haplotonic scale |
| <a class="wiki_link" href="/bossier8">Eight note albitonic scale</a><br />
| | * [[Augment9]] – 9-tone albitonic scale |
| <a class="wiki_link" href="/bossier11">Eleven note chromatic scale</a><br />
| | * [[Augment12]] – 12-tone chromatic scale |
| <a class="wiki_link" href="/bossier14">Fourteen note mega chromatic scale</a><br />
| | |
| <br />
| | == Semaphore == |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:24 -->Radon</h1>
| | {{Main| Semaphore and godzilla }} |
| Subgroup: 2.3.7.11<br />
| | {{See also| Semaphoresmic clan #Semaphore }} |
| Commas: 896/891, 1029/1024<br />
| | |
| Sval name: 5&amp;36<br />
| | [[File:semaphore_24edo.png|right|alt=semaphore_24edo.png|Semaphore in 24edo]] |
| Related temperament: <a class="wiki_link" href="/Gamelismic%20clan">Rodan</a><br />
| | |
| <br />
| | Scales: |
| POTE generator: ~8/7 = 234.381<br />
| | * [[Semaphore5]] – 5-tone haplotonic scale |
| <br />
| | * [[Semaphore9]] – 9-tone albitonic scale |
| Map: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]<br />
| | * [[Semaphore14]] – 14-tone chromatic scale |
| EDOs: 5, 36, 41, 87, 128<br />
| | |
| Error: 2.925 cents<br />
| | == Kryptonite == |
| <br />
| | {{See also| Subgroup temperaments #Kryptonite }} |
| <a class="wiki_link" href="/radon5">Five note haplotonic scale</a><br />
| | |
| <a class="wiki_link" href="/radon11">Eleven note albitonic scale</a><br />
| | Scales: |
| <a class="wiki_link" href="/radon16">Sixteen note chromatic scale</a><br />
| | * [[Kryptonite9]] – 9-tone albitonic scale |
| <br />
| | * [[Kryptonite10]] – 10-tone albitonic scale |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule:26 -->Myna</h1>
| | * [[Kryptonite19]] – 19-tone mega-chromatic scale |
| Group: 2.3.5.7<br />
| | |
| Commas: 126/125, 1728/1715<br />
| | == Oregon == |
| Val name: 4&amp;27<br />
| | {{See also| Orgonia #Oregon }} |
| <br />
| | |
| POTE generator: ~6/5 = 310.146<br />
| | Scales: |
| <br />
| | * [[Oregon7]] – 7-tone haplotonic scale |
| Map: [&lt;1 9 9 8|, &lt;0 -10 -9 -7|]<br />
| | * [[Oregon11]] – 11-tone albitonic scale |
| EDOs: 4, 27, 31, 58, 89<br />
| | * [[Oregon15]] – 15-tone chromatic scale |
| Error: 3.310 cents<br />
| | |
| <br />
| | == Antikythera == |
| <a class="wiki_link" href="/myna7">Seven note albitonic scale</a><br />
| | {{See also| Jubilismic clan #Antikythera }} |
| <a class="wiki_link" href="/myna11">Eleven note chromatic scale</a><br />
| | |
| <a class="wiki_link" href="/myna15">Fifteen note mega chromatic scale</a><br />
| | [[File:antikythera_28edo.png|right|alt=antikythera_28edo.png|Antikythera in 28edo]] |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:28 -->Silver</h1>
| | Scales: |
| Subgroup: 2.5.7.13.17<br />
| | * [[Antikythera6]] – 6-tone haplotonic scale |
| Commas: 170/169, 640/637, 5525/5488<br />
| | * [[Antikythera10]] – 10-tone albitonic scale |
| Sval name: 10&amp;27<br />
| | * [[Antikythera16]] – 16-tone chromatic scale |
| <br />
| | |
| POTE generator: ~13/8 = 842.711<br />
| | == Glacial == |
| <br />
| | {{See also| Subgroup temperaments #Glacial }} |
| Map: [&lt;1 5 4 4 2|, &lt;0 -9 -4 -1 7|]<br />
| | |
| EDOs: 7, 10, 17, 27, 37, 47, 84, 131<br />
| | Scales: |
| Error: 3.437<br />
| | * [[Glacial6]] – 6-tone haplotonic scale |
| <br />
| | * [[Glacial7]] – 7-tone albitonic scale |
| <a class="wiki_link" href="/silver7">Seven note haplotonic scale</a><br />
| | * [[Glacial13]] – 13-tone chromatic scale |
| <a class="wiki_link" href="/silver10">Ten note albitonic scale</a><br />
| | |
| <a class="wiki_link" href="/silver17">Seventeen note chromatic scale</a><br />
| | == Leantone == |
| <br />
| | {{See also| Hemimean clan #Leantone }} |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Meantone"></a><!-- ws:end:WikiTextHeadingRule:30 -->Meantone</h1>
| | |
| Group: 2.3.5.7<br />
| | [[File:leantone_81edo.png|right|alt=leantone_81edo.png|Leantone in 81edo]] |
| Commas: 81/80, 126/125<br />
| | |
| Val name: 12&amp;19<br />
| | Scales: |
| <br />
| | * [[Leantone6]] – 6-tone haplotonic scale |
| POTE generator: 696.495<br />
| | * [[Leantone7]] – 7-tone albitonic scale |
| <br />
| | * [[Leantone13]] – 13-tone chromatic scale |
| Map: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]<br />
| | |
| EDOs: 5, 7, 12, 19, 31, 81, 112, 143<br />
| | == Notes == |
| Error: 3.585<br />
| | |
| <br />
| | [[Category:Lists of scales]] |
| <a class="wiki_link" href="/meantone5">Five note haplotonic scale</a><br />
| | [[Category:Tempered scales| ]] |
| <a class="wiki_link" href="/meantone7">Seven note albitonic scale</a><br />
| | [[Category:Listen]] |
| <a class="wiki_link" href="/meantone12">Twelve note chromatic scale</a><br />
| | [[Category:Rank 2]] |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule:32 -->Indium</h1>
| | {{todo|cleanup}} |
| 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:34:&lt;h1&gt; --><h1 id="toc17"><a name="Magic"></a><!-- ws:end:WikiTextHeadingRule:34 -->Magic</h1>
| |
| Group: 2.3.5.7.11<br />
| |
| Commas: 100/99, 225/224, 245/243<br />
| |
| Val name: 19&amp;22<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:36:&lt;h1&gt; --><h1 id="toc18"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:36 -->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:38:&lt;h1&gt; --><h1 id="toc19"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:38 -->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:40:&lt;h1&gt; --><h1 id="toc20"><a name="Sensi"></a><!-- ws:end:WikiTextHeadingRule:40 -->Sensi</h1>
| |
| Group: 2.3.5.7<br />
| |
| Commas: 126/126, 245/243<br />
| |
| Val name: 19&amp;27<br />
| |
| <br />
| |
| POTE generator: ~9/7 = 443.383<br />
| |
| <br />
| |
| Map: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]<br />
| |
| EDOs: 5, 8, 11, 19, 27, 46<br />
| |
| Error: 5.019<br />
| |
| <br />
| |
| <a class="wiki_link" href="/sensi5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="/sensi8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="/sensi11">Eleven note mega albitonic scale</a><br />
| |
| <a class="wiki_link" href="/sensi19">Nineteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:42 -->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:44:&lt;h1&gt; --><h1 id="toc22"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:44 -->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:46:&lt;h1&gt; --><h1 id="toc23"><a name="Orwell"></a><!-- ws:end:WikiTextHeadingRule:46 -->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="/orwell5">Five note haplotonic scale</a><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:48:&lt;h1&gt; --><h1 id="toc24"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:48 -->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:50:&lt;h2&gt; --><h2 id="toc25"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:50 -->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:52:&lt;h1&gt; --><h1 id="toc26"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:52 -->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:54:&lt;h2&gt; --><h2 id="toc27"><a name="Tutone-Leantone"></a><!-- ws:end:WikiTextHeadingRule:54 -->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:56:&lt;h1&gt; --><h1 id="toc28"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:56 -->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:58:&lt;h1&gt; --><h1 id="toc29"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:58 -->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:60:&lt;h2&gt; --><h2 id="toc30"><a name="Supra-Supraphon"></a><!-- ws:end:WikiTextHeadingRule:60 -->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:62:&lt;h2&gt; --><h2 id="toc31"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:62 -->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:64:&lt;h1&gt; --><h1 id="toc32"><a name="Deutone"></a><!-- ws:end:WikiTextHeadingRule:64 -->Deutone</h1>
| |
| Subgroup: 2.9.5.7.13<br />
| |
| Commas: 65/64, 81/80, 91/90<br />
| |
| Related temperament: <a class="wiki_link" href="/Meantone%20family">meanpop</a><br />
| |
| <br />
| |
| POTE generator: ~9/8 = 191.059<br />
| |
| <br />
| |
| Map: [&lt;1 0 -4 -13 10|, &lt;0 1 2 5 -2|]<br />
| |
| EDOs: 6, 7, 13, 19, 25, 44, 69<br />
| |
| Error: 12.145 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="/deutone6">Six note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="/deutone7">seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="/deutone13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:66 -->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 = 228.275<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></pre></div>
| |