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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:genewardsmith|genewardsmith]] and made on <tt>2011-04-24 13:45:51 UTC</tt>.<br>
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| : The original revision id was <tt>222523768</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]]
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| | 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. |
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| By a //chromatic pair// is meant a pair of MOS in some rank two temperament (which may often be a [[Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with [[Target tunings|tuning target]] the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.
| | == Terrain == |
| | {{See also| Subgroup temperaments #Terrain }} |
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|
| =Terrain=
| | [[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]] |
| Subgroup: 2.9/5.9/7
| |
| Commas: 250047/250000
| |
| Sval name: 6&21
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| Related temperament: [[Minortonic family#Domain|domain]]
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| POTE generator: ~10/9 = 182.462
| | Scales: |
| | * [[Terrain9]] – 9-tone albitonic scale |
| | * [[Terrain15]] – 15-tone chromatic scale |
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|
| Map: [<3 0 -4|, <0 1 2|]
| | ; Music |
| EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
| | * ''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] |
| 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.
| | == Petrtri == |
| | {{See also| Subgroup temperaments #Petrtri }} |
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| [[terrain9|Nine note albitonic scale]] | | [[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]] |
| [[terrain15|Fifteen note chromatic scale]]
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|
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|
| =Bridgetown=
| | Scales: |
| Subgroup: 2.3.11/5.13/5
| | * [[Petrtri5]] – 5-tone haplotonic scale |
| Commas: 352/351, 676/675
| | * [[Petrtri8]] – 8-tone albitonic scale |
| Sval name: 5&24
| | * [[Petrtri13]] – 13-tone chromatic scale |
| Related temperament: [[The Archipelago|barabdos]]
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| POTE generator: ~15/13 = 248.285
| | == Barton == |
| | {{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}} |
| | {{See also| The Jacobins #Barton }} |
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|
| Map: [<1 0 -6 -1|, <0 2 9 3|]
| | Scales: |
| EDOs: 5, 9, 14, 19, 24, 29
| | * [[Barton5]] – 5-tone haplotonic scale |
| Error: 0.8996 cents
| | * [[Barton7]] – 7-tone albitonic scale |
| | * [[Barton9]] – 9-tone mega-albitonic scale |
| | * [[Barton11]] – 11-tone chromatic scale |
| | * [[Barton13]] – 13-tone mega-chromatic scale |
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| [[bridgetown9|Nine note albitonic scale]]
| | == Tridec == |
| [[bridgetown14|Fourteen note chromatic scale]]
| | {{See also| Subgroup temperaments #Tridec }} |
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| =Cata=
| | [[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]] |
| Subgroup: 2.3.5.13
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| Commas: 325/324, 625/624
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| Sval name: 15&19
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| Related temperament: [[Kleismic family|catakleismic]]
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| POTE generator: ~6/5 = 317.076
| | Scales: |
| | * [[Tridec8]] – 8-tone albitonic scale |
| | * [[Tridec13]] – 13-tone chromatic scale |
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| Map: [<1 0 1 0|, <0 6 5 14|]
| | == Nestoria == |
| EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246
| | {{See also| Schismatic family #Nestoria (2.3.5.19)}} |
| Error: 0.9355 cents
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| [[cata7|Seven note albitonic scale]] | | [[File:nestoria_171edo.png|right|alt=nestoria_171edo.png|Nestoria in 171edo]] |
| [[cata11|Eleven note mega albitonic scale]]
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| [[cata15|Fifteen note chromatic scale]]
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| [[cata19|Nineteen note mega chromatic scale]]
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| =Tridec=
| | Scales: |
| Subgroups: 2.7/5.11/5.13/5
| | * [[Nestoria7]] – 7-tone albitonic scale |
| Commas: 847/845, 1001/1000
| | * [[Nestoria12]] – 12-tone chromatic scale |
| Sval name: 5&8
| | * [[Nestoria17]] – 17-tone mega chromatic scale |
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| POTE generator: ~13/10 = 454.461
| | == Orgone == |
| | {{Main| Orgone }} |
| | {{See also| Orgonia #Orgone }} |
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|
| Map: [<1 2 0 1|, <0 -4 3 1|]
| | [[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]] |
| EDOs: 5, 8, 21, 29, 37, 66, 169, 235
| |
| Error: 1.057
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| [[Tridec8|Eight note albitonic scale]] | | Scales: |
| [[Tridec13|Thirteen note chromatic scale]] | | * [[Orgone7]] – 7-tone albitonic scale |
| | * [[Orgone11]] – 11-tone chromatic scale |
| | * [[Orgone15]] – 15-tone mega-chromatic scale |
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| =Pepperoni= | | == Marveltwintri == |
| Subgroup: 2.3.11/7.13/7 | | {{See also| Subgroup temperaments #Marveltwintri }} |
| 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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| POTE generator: ~3/2 = 704.052
| | [[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]] |
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|
| Map: [<1 0 7 12|, <0 1 -4 -7|]
| | Scales: |
| EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271
| | * [[Marveltwintri7]] – 7-tone albitonic scale |
| Error: 1.298 cents
| | * [[Marveltwintri11]] – 11-tone chromatic scale |
| | * [[Marveltwintri15]] – 15-tone mega-chromatic scale |
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| [[pepperoni7|Seven note albitonic scale]]
| | == Cata == |
| [[pepperoni12|Twelve note chromatic scale]]
| | {{Main| Kleismic }} |
| | {{See also| Kleismic family #Cata }} |
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| =Nestoria=
| | [[File:cata_246edo.jpg|right|alt=cata_246edo.jpg|Cata in 246edo]] |
| Subgroup: 2.3.5.19
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| Commas: 361/360, 513/512
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| Sval name: 12&29
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| Related temperament: [[Schismatic family|schismatic]]
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|
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|
| POTE generator: ~3/2 = 701.746
| | Scales: |
| | * [[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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| Map: [<1 0 15 9], <0 1 -8 -3|]
| | == Bridgetown == |
| EDOs: 7, 12, 17, 29, 41, 53, 118, 171
| | {{See also| Subgroup temperaments #Bridgetown }} |
| Error: 1.819 cents
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| [[nestoria7|Seven note albitonic scale]] | | [[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]] |
| [[nestoria12|Twelve note chromatic scale]]
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| ==Photia==
| | Scales: |
| Subgroup 2.3.5.17.19
| | * [[Bridgetown9]] – 9-tone albitonic scale |
| Commas: 171/170, 256/255, 324/323
| | * [[Bridgetown14]] – 14-tone chromatic scale |
| Sval name: 12&41
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| Related temperament: [[Schismatic family|schismatic]]
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| POTE generator: ~3/2 = 701.470
| | ; Music |
| | * [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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| Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|]
| | == Haumea == |
| EDOs: 7, 12, 17, 29, 41, 53, 65
| | {{See also| Subgroup temperaments #Haumea }} |
| Error: 3.457 cents
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|
| [[photia7|Seven note albitonic scale]] | | Scales: |
| [[photia12|Twelve note chromatic scale]] | | * [[Haumea5]] – 5-tone haplotonic scale |
| | * [[Haumea9]] – 9-tone albitonic scale |
| | * [[Haumea14]] – 14-tone chromatic scale |
| | * [[Haumea19]] – 19-tone mega-chromatic scale |
|
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| =Huntington= | | == Neutral == |
| Subgroup: 2.5.7.13
| | {{See also| Rastmic clan #Neutral }} |
| Commas: 640/637, 10985/10976
| |
| Sval name: 10&27
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|
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|
| POTE generator: ~16/13 = 357.002
| | [[File:neutral_380edo.png|right|alt=neutral_380edo.png|Neutral in 380edo]] |
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|
| Map: [<1 5 4 4|, <0 -9 -4 -1|]
| | Scales: |
| EDOs: 7, 10, 17, 27, 37, 84, 121, 400
| | * [[Neutral7]] – 7-tone albitonic scale |
| Error: 2.1001 cents
| | * [[Neutral10]] – 10-tone chromatic scale |
| | * [[Neutral17]] – 17-tone mega-chromatic scale |
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| [[huntington7|Seven note haplotonic scale]] | | ; Music |
| [[huntington10|Ten note albitonic scale]] | | * [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 |
| [[huntington17|Seventeen note chromatic scale]] | |
|
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| =Roulette= | | == Slendric == |
| Subgroup: 2.5.7.11.13
| | {{Main| Slendric }} |
| Commas: 176/175, 1375/1372, 640/637
| | :''See also: [[Gamelismic clan #Slendric]] and [[No-fives subgroup temperaments #Slendric]]'' |
| Sval name: 6&25
| |
| Related temperament: [[Wuerschmidt family|Hemiwuerschmidt]]
| |
|
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|
| POTE generator: ~28/25 = 194.594
| | [[File:slendric_190edo.jpg|right|alt=slendric_190edo.jpg|Slendric in 190edo]] |
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|
| Map: [<1 0 -3 -7 -13|, <0 2 5 9 -8|]
| | Scales: |
| EDOs: 6, 7, 13, 19, 25, 31, 37
| | * [[Slendric5]] – 5-tone haplotonic scale |
| Error: 2.555 cents
| | * [[Slendric6]] – 6-tone haplotonic scale |
| | * [[Slendric11]] – 11-tone albitonic scale |
| | * [[Slendric16]] – 16-tone chromatic scale |
|
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| [[roulette6|Six note haplotonic scale]]
| | == Huntington == |
| [[roulette7|Seven note albitonic scale]]
| | {{See also| No-threes subgroup temperaments #Huntington }} |
| [[roulette13|Thirteen note chromatic scale]]
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| [[roulette19|Nineteen note mega chromatic scale]]
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|
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|
| =Garibaldi=
| | [[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]] |
| Group: 2.3.5.7
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| Commas: 225/224, 3125/3087
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| Val name: 12&29
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|
| POTE generator: ~3/2 = 702.085
| | Scales: |
| | * [[Huntington7]] – 7-tone haplotonic scale |
| | * [[Huntington10]] – 10-tone albitonic scale |
| | * [[Huntington17]] – 17-tone chromatic scale |
|
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| Map: [<1 0 15 25|, <0 1 -8 -14|]
| | == Tobago == |
| EDOs: 7, 12, 17, 29, 41, 53, 94
| | {{See also| Subgroup temperaments #Tobago }} |
| Error: 2.834
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| [[garibaldi12|Twelve note albitonic scale]] | | Scales: |
| [[garibaldi17|Seventeen note chromatic scale]] | | * [[Tobago6]] – 6-tone haplotonic scale |
| | * [[Tobago10]] – 10-tone albitonic scale |
| | * [[Tobago14]] – 14-tone chromatic scale |
| | * [[Tobago24]] – 24-tone quatertone scale |
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| =Baldy= | | == Pepperoni == |
| Subgroup: 2.9.5.7.13
| | {{See also| Parapyth }} |
| Commas: 225/224, 325/324, 640/637
| | {{See also| Subgroup temperaments #Pepperoni }} |
| Sval name: 6&35
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| Related temperament: [[Schismatic family|Garibaldi]]
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| POTE generator: ~9/8 = 204.090
| | [[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]] |
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| Map: [<1 0 15 25 -8|, <0 1 -4 -7 10|]
| | Scales: |
| EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
| | * [[Pepperoni7]] – 7-tone albitonic scale |
| Error: 2.617 cents
| | * [[Pepperoni12]] – 12-tone chromatic scale |
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| [[baldy6|Six note haplotonic scale]]
| | == Wizz == |
| [[baldy11|Eleven note albitonic scale]]
| | {{See also| No-threes subgroup temperaments #Wizz }} |
| [[baldy17|Seventeen note chromatic scale]]
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|
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| =Bossier=
| | Scales: |
| Subgroup: 2.7.11.13
| | * [[Wizz6]] – 6-tone haplotonic scale |
| Commas: 1573/1569, 15488/15379
| | * [[Wizz10]] – 10-tone albitonic scale |
| Sval name: 3&17
| | * [[Wizz16]] – 16-tone chromatic scale |
|
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| POTE generator: ~14/11 = 421.309
| | == Bossier == |
| | {{See also| No-threes subgroup temperaments #Bossier }} |
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| Map: [<1 0 1 3|, <0 8 7 2|]
| | [[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]] |
| EDOs: 17, 20, 37, 57, 94, 225
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| Error: 2.665 cents
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| [[bossier8|Eight note albitonic scale]] | | Scales: |
| [[bossier11|Eleven note chromatic scale]] | | * [[Bossier8]] – 8-tone albitonic scale |
| [[bossier14|Fourteen note mega chromatic scale]] | | * [[Bossier11]] – 11-tone chromatic scale |
| | * [[Bossier14]] – 14-tone mega-chromatic scale |
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| =Radon= | | == Penta a.k.a. mechanism == |
| Subgroup: 2.3.7.11 | | {{See also| Subgroup temperaments #Penta a.k.a. mechanism }} |
| 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: |
| | * [[Penta5]] – 5-tone haplotonic scale |
| | * [[Penta8]] – 8-tone albitonic scale |
| | * [[Penta11]] – 11-tone chromatic scale |
| | * [[Penta19]] – 19-tone mega-chromatic scale |
|
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|
| Map: [<1 1 3 6|, <0 3 -1 -13|]
| | == Bluebirds == |
| EDOs: 5, 36, 41, 87, 128
| | {{See also| No-threes subgroup temperaments #Bluebirds }} |
| Error: 2.925 cents
| |
|
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| [[radon5|Five note haplotonic scale]] | | Scales: |
| [[radon11|Eleven note albitonic scale]] | | * [[Bluebirds6]] – 6-tone haplotonic scale |
| [[radon16|Sixteen note chromatic scale]] | | * [[Bluebirds7]] – 7-tone albitonic scale |
| | * [[Bluebirds13]] – 13-tone chromatic scale |
|
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| =Myna= | | == Marveltri == |
| Group: 2.3.5.7
| | {{See also| Subgroup temperaments #Marveltri }} |
| Commas: 126/125, 1728/1715
| |
| Val name: 4&27
| |
|
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|
| POTE generator: ~6/5 = 310.146
| | Scales: |
| | * [[Marveltri7]] – 7-tone albitonic scale |
| | * [[Marveltri10]] – 10-tone chromatic scale |
| | * [[Marveltri13]] – 13-tone mega-chromatic scale |
|
| |
|
| Map: [<1 9 9 8|, <0 -10 -9 -7|]
| | == Edson == |
| EDOs: 4, 27, 31, 58, 89
| | {{See also| Subgroup temperaments #Edson }} |
| Error: 3.310 cents
| |
|
| |
|
| [[myna7|Seven note albitonic scale]] | | Scales: |
| [[myna11|Eleven note chromatic scale]] | | * [[Edson5]] – 5-tone haplotonic scale |
| [[myna15|Fifteen note mega chromatic scale]] | | * [[Edson7]] – 7-tone albitonic scale |
| | * [[Edson12]] – 12-tone chromatic scale |
| | * [[Edson17]] – 17-tone mega-chromatic scale |
|
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| =Silver= | | == Photia == |
| Subgroup: 2.5.7.13.17
| | {{See also| Schismatic family #Photia (2.3.5.17) }} |
| Commas: 170/169, 640/637, 5525/5488
| |
| Sval name: 10&27
| |
|
| |
|
| POTE generator: ~13/8 = 842.711
| | [[File:photia_65edo.png|right|alt=photia_65edo.png|Photia in 65edo]] |
|
| |
|
| Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|]
| | Scales: |
| EDOs: 7, 10, 17, 27, 37, 47, 84, 131
| | * [[Photia7]] – 7-tone albitonic scale |
| Error: 3.437
| | * [[Photia12]] – 12-tone chromatic scale |
|
| |
|
| [[silver7|Seven note haplotonic scale]]
| | == Shoe a.k.a. llywelyn == |
| [[silver10|Ten note albitonic scale]]
| | {{See also| Llywelynsmic clan #Llywelyn a.k.a. shoe }} |
| [[silver17|Seventeen note chromatic scale]]
| |
|
| |
|
| =Meantone=
| | [[File:shoe_37edo.jpg|right|alt=shoe_37edo.jpg|Shoe in 37edo]] |
| Group: 2.3.5.7
| |
| Commas: 81/80, 126/125
| |
| Val name: 12&19
| |
|
| |
|
| POTE generator: 696.495
| | Scales: |
| | * [[Shoe5]] – 5-tone mini-haplotonic scale |
| | * [[Shoe6]] – 6-tone haplotonic scale |
| | * [[Shoe11]] – 11-tone albitonic scale |
| | * [[Shoe16]] – 16-tone chromatic scale |
|
| |
|
| Map: [<1 0 -4 -13|, <0 1 4 10|]
| | == Roulette == |
| EDOs: 5, 7, 12, 19, 31, 81, 112, 143
| | {{See also | Hemimean clan #Roulette }} |
| Error: 3.585
| |
|
| |
|
| [[meantone5|Five note haplotonic scale]] | | [[File:roulette_37edo.jpg|right|alt=roulette_37edo.jpg|Roulette in 37edo]] |
| [[meantone7|Seven note albitonic scale]]
| |
| [[meantone12|Twelve note chromatic scale]]
| |
|
| |
|
| =Indium=
| | Scales: |
| Subgroup: 2.5/3.7/3.11/3
| | * [[Roulette6]] – 6-tone haplotonic scale |
| Commas: 3025/3024, 3125/3087
| | * [[Roulette7]] – 7-tone albitonic scale |
| Sval name: 8&33
| | * [[Roulette13]] – 13-tone chromatic scale |
| | * [[Roulette19]] – 19-tone mega-chromatic scale |
|
| |
|
| POTE generator: ~12/11 = 147.159
| | == Silver == |
| | {{See also | No-threes subgroup temperaments #Silver }} |
|
| |
|
| Map: [<1 0 0 2|, <0 6 10 -1|]
| | [[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]] |
| EDOs: 33, 41, 49, 57, 106, 204, 253
| |
| Error: 3.968 cents
| |
|
| |
|
| [[indium8|Eight note albitonic scale]] | | Scales: |
| [[indium17|Seventeen note chromatic scale]] | | * [[Silver7]] – 7-tone haplotonic scale |
| | * [[Silver10]] – 10-tone albitonic scale |
| | * [[Silver17]] – 17-tone chromatic scale |
|
| |
|
| =Magic= | | == Baldy == |
| Group: 2.3.5.7.11
| | {{See also| Subgroup temperaments #Baldy }} |
| Commas: 100/99, 225/224, 245/243
| |
| Val name: 19&22
| |
|
| |
|
| POTE generator: ~5/4 = 380.696
| | [[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]] |
|
| |
|
| Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]
| | Scales |
| EDOs: 19, 22, 41, 104, 145
| | * [[Baldy6]] – 6-tone haplotonic scale |
| Error: 4.489
| | * [[Baldy11]] – 11-tone albitonic scale |
| | * [[Baldy17]] – 17-tone chromatic scale |
|
| |
|
| [[magic7|Seven note haplotonic scale]]
| |
| [[magic10|Ten note albitonic scale]]
| |
| [[magic13|Thirteen note chromatic scale]]
| |
| [[magic16|Sixteen note mega chromatic scale]]
| |
|
| |
|
| =Hemif= | | == Guanyintet == |
| Subgroup: 2.3.7.11.13 | | {{See also | Subgroup temperaments #Guanyintet }} |
| Commas: 144/143, 243/242, 364/363
| |
| Related temperament: [[Breedsmic temperaments|Hemififths]]
| |
|
| |
|
| POTE generator: ~11/9 = 351.691
| | Scales: |
| | * [[Guanyintet5]] – 5-tone haplotonic scale |
| | * [[Guanyintet9]] – 9-tone albitonic scale |
| | * [[Guanyintet13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]
| | == Radon == |
| EDOs: 7, 10, 17, 24, 41, 58
| | {{See also| Gamelismic clan #Radon }} |
| Error: 4.867 cents
| |
|
| |
|
| [[hemif7|Seven note haplotonic scale]] | | [[File:radon_128edo.jpg|right|alt=radon_128edo.jpg|Radon in 128edo]] |
| [[hemif10|Ten note albitonic scale]]
| |
| [[hemif17|Seventeen note chromatic scale]]
| |
|
| |
|
| =Skwares=
| | * [[Radon5]] – 5-tone haplotonic scale |
| Subgroup: 2.3.7.11
| | * [[Radon11]] – 11-tone albitonic scale |
| Commas: 99/98, 243/242
| | * [[Radon16]] – 16-tone chromatic scale |
| Related temperament: [[Meantone family|squares]]
| |
|
| |
|
| POTE generator: ~9/7 = 425.244
| | == Gariberttet == |
| | {{See also | Subgroup temperaments #Gariberttet }} |
|
| |
|
| Map: [<1 3 6 7|, <0 -4 -9 -10|]
| | Scales: |
| EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206
| | * [[Gariberttet5]] – 5-tone haplotonic scale |
| Error: 4.942 cents
| | * [[Gariberttet9]] – 9-tone albitonic scale |
| | * [[Gariberttet13]] – 13-tone chromatic scale |
|
| |
|
| [[skwares8|Eight note albitonic scale]]
| | == Namo == |
| [[skwares11|Eleven note mega albitonic scale]]
| | {{See also| Rastmic clan #Namo }} |
| [[skwares14|Fourteen note chromatic scale]]
| |
|
| |
|
| =Sensi=
| | Scales: |
| Group: 2.3.5.7
| | * [[Namo7]] – 7-tone haplotonic scale |
| Commas: 126/126, 245/243
| | * [[Namo10]] – 10-tone albitonic scale |
| Val name: 19&27
| | * [[Namo17]] – 17-tone chromatic scale |
|
| |
|
| POTE generator: ~9/7 = 443.383
| | == Sentry == |
| | {{See also | Subgroup temperaments #Sentry }} |
|
| |
|
| Map: [<1 6 8 11|, <0 -7 -9 -13|]
| | Scales: |
| EDOs: 5, 8, 11, 19, 27, 46
| | * [[Sentry5]] – 5-tone haplotonic scale |
| Error: 5.019
| | * [[Sentry8]] – 8-tone albitonic scale |
| | * [[Sentry11]] – 11-tone chromatic scale |
|
| |
|
| [[sensi5|Five note haplotonic scale]]
| | == Hemif == |
| [[sensi8|Eight note albitonic scale]]
| | {{See also| No-fives subgroup temperaments #Hemif }} |
| [[sensi11|Eleven note mega albitonic scale]]
| |
| [[sensi19|Nineteen note chromatic scale]]
| |
|
| |
|
| =Greeley=
| | [[File:hemif_58edo.jpg|right|alt=hemif_58edo.jpg|Hemif in 58edo]] |
| Subgroup: 2.5/3.7/3.11/3
| |
| Commas: 121/120, 126/125
| |
|
| |
|
| POTE generator: ~11/10 = 156.055
| | Scales: |
| | * [[Hemif7]] – 7-tone haplotonic scale |
| | * [[Hemif10]] – 10-tone albitonic scale |
| | * [[Hemif17]] – 17-tone chromatic scale |
|
| |
|
| Map: [<1 1 2 2|, <0 -2 -6 -1|]
| | == Garibaldi == |
| EDOs: 8, 15, 23, 77, 100
| | {{Main| Garibaldi temperament }} |
| Error: 5.404 cents
| | {{See also| Schismatic family #Garibaldi }} |
|
| |
|
| [[greeley8|Eight note albitonic scale]] | | [[File:garibaldi_94edo.png|right|alt=garibaldi_94edo.png|Garibaldi in 94edo]] |
| [[greeley15|Fifteen note chromatic scale]]
| |
|
| |
|
| =Semidim=
| | Scales: |
| Subgroup: 2.5/3.7/3.11/3.13/3
| | * [[Garibaldi12]] – 12-tone albitonic scale |
| Commas: 121/120, 169/168, 275/273
| | * [[Garibaldi17]] – 17-tone chromatic scale |
| Sval name: 8&29
| |
|
| |
|
| POTE generator: ~13/10 = 453.190
| | == Mabilic == |
| | {{See also| No-threes subgroup temperaments #Mabilic }} |
|
| |
|
| Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]
| | [[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]] |
| EDOs: 5, 8, 13, 21, 29, 37, 45
| |
| Error: 5.433 cents
| |
|
| |
|
| [[semidim8|Eight note albitonic scale]] | | Scales: |
| [[semidim13|Thirteen note chromatic scale]] | | * [[Mabilic7]] – 7-tone haplotonic scale |
| | * [[Mabilic9]] – 9-tone albitonic scale |
| | * [[Mabilic16]] – 16-tone chromatic scale |
|
| |
|
| =Orwell= | | == Indium == |
| Group: 2.3.5.7.11
| | {{See also | Subgroup temperaments #Indium }} |
| Commas: 99/98, 121/120, 176/175
| |
| Val name: 9&22
| |
|
| |
|
| POTE generator: ~7/6 = 271.426
| | [[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]] |
|
| |
|
| Map: [<1 0 3 1 3|, <0 7 -3 8 2|]
| | Scales: |
| EDOs: 9, 22, 31, 53, 84
| | * [[Indium8]] – 8-tone albitonic scale |
| Error: 5.584
| | * [[Indium17]] – 17-tone chromatic scale |
|
| |
|
| [[orwell5|Five note haplotonic scale]] | | ; Music |
| [[orwell9|Nine note albitonic scale]] | | * ''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] |
| [[orwell13|Thirteen note chromatic scale]] | |
|
| |
|
| =Mohaha= | | == Starlingtet == |
| Subgroup: 2.3.5.11 | | {{See also | Subgroup temperaments #Starlingtet }} |
| Commas: 81/80, 121/120
| |
| Related temperament: [[Meantone family|mohajira]]
| |
|
| |
|
| POTE generator: ~11/9 = 348.094
| | Scales: |
| | * [[Starlingtet4]] – 4-tone haplotonic scale |
| | * [[Starlingtet7]] – 7-tone albitonic scale |
| | * [[Starlingtet11]] – 11-tone chromatic scale |
|
| |
|
| Map: [<1 1 0 2|, <0 2 8 5|]
| | == Lovecraft == |
| EDOs: 7, 10, 17, 24, 31, 131
| | {{See also | No-threes subgroup temperaments #Lovecraft }} |
| Error: 6.733 cents
| |
|
| |
|
| [[mohaha7|Seven note albitonic scale]] | | [[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]] |
| [[mohaha10|Ten note chromatic scale]]
| |
|
| |
|
| ==Mohoho==
| | Scales: |
| Subgroup: 2.3.5.11.13
| | * [[Lovecraft5]] – 5-tone haplotonic scale |
| Commas: 66/65, 81/80, 121/120
| | * [[Lovecraft9]] – 9-tone albitonic scale |
| | * [[Lovecraft13]] – 13-tone chromatic scale |
|
| |
|
| POTE generator: ~11/9 = 348.916
| | == Blackbirds == |
| | {{See also | No-threes subgroup temperaments #Blackbirds }} |
|
| |
|
| Map: [<1 1 0 2 4|, <0 2 8 5 -1|]
| | Scales: |
| EDOs: 7, 10, 17, 24, 31, 55
| | * [[Blackbirds8]] – 8-tone albitonic scale |
| Error: 9.556 cents
| | * [[Blackbirds12]] – 12-tone chromatic scale |
| | * [[Blackbirds16]] – 16-tone mega-chromatic scale |
|
| |
|
| =Tutone= | | == Laz == |
| Subgroup: 2.9.5.7.11 | | {{See also | Subgroup temperaments #Laz }} |
| Commas: 81/80, 99/98, 126/125
| |
| Related temperament: [[Meantone family|meantone]]
| |
|
| |
|
| POTE generator: ~9/8 = 193.937
| | Scales: |
| | * [[Laz5]] – 5-tone haplotonic scale |
| | * [[Laz9]] – 9-tone albitonic scale |
| | * [[Laz13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]
| | == Myna == |
| EDOs: 6, 7, 13, 19, 25, 31, 99
| | {{Main| Myna }} |
| Error: 7.047 cents
| | {{See also| Starling temperaments #Myna }} |
|
| |
|
| [[tutone6|Six note haplotonic scale]] | | [[File:myna_89edo.jpg|right|alt=myna_89edo.jpg|Myna in 89edo]] |
| [[tutone7|Seven note albitonic scale]]
| |
| [[tutone13|Thirteen note chromatic scale]]
| |
|
| |
|
| ==Leantone==
| | Scales: |
| Subgroup: 2.9.5.7.11
| | * [[Myna7]] – 7-tone haplotonic scale |
| Commas: 45/44, 56/55, 81/80
| | * [[Myna11]] – 11-tone albitonic scale |
| Related temperament: [[Meantone family|flattone]]
| | * [[Myna15]] – 15-tone chromatic scale |
|
| |
|
| POTE generator: ~9/8 = 192.500
| | == Greeley == |
| | {{See also| Subgroup temperaments #Greeley }} |
|
| |
|
| Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
| | [[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]] |
| EDOs: 6, 7, 13, 19, 25, 31, 56, 81
| |
| Error: 20.338 cents
| |
|
| |
|
| [[leantone6|Six note haplotonic scale]] | | Scales: |
| [[leantone7|Seven note albitonic scale]] | | * [[Greeley8]] – 8-tone albitonic scale |
| [[leantone13|Thirteen note chromatic scale]]
| | * [[Greeley15]] – 15-tone chromatic scale |
|
| |
|
| =Score=
| | ; Music |
| Subgroup: 2.7.11.13
| | * ''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] |
| Commas: 343/338, 847/832
| |
|
| |
|
| POTE generator: ~11/8 = 540.099
| | == Ammon == |
| | {{See also| Subgroup temperaments #Ammon }} |
|
| |
|
| Map: [<1 1 3 1|, <0 4 1 6|]
| | [[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]] |
| EDOs: 5, 7, 9, 11, 20
| |
| Error: 8.052 cents
| |
|
| |
|
| [[score5|Five note haplotonic scale]] | | Scales: |
| [[score7|Seven note albitonic scale]]
| | * [[Ammon8]] – 8-tone albitonic scale |
| [[score9|Nine note mega albitonic scale]] | | * [[Ammon13]] – 13-tone chromatic scale |
| [[score11|Eleven note chromatic scale]]
| |
|
| |
|
| =Supra= | | == Mothwelltri == |
| Subgroup: 2.3.7.11 | | {{See also| Subgroup temperaments #Mothwelltri }} |
| Commas: 64/63, 99/98
| |
| Related temperament: [[Archytas clan|superpyth]]
| |
|
| |
|
| POTE generator: ~3/2 = 707.192
| | Scales: |
| | * [[Mothwelltri5]] – 5-tone haplotonic scale |
| | * [[Mothwelltri9]] – 9-tone albitonic scale |
| | * [[Mothwelltri13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 6 13|, <0 1 -2 -6|]
| | == Sulis == |
| EDOs: 5, 7, 12, 17, 22, 39, 56
| | {{See also| Subgroup temperaments #Sulis }} |
| Error: 9.795 cents
| |
|
| |
|
| [[supra7|Seven note albitonic scale]] | | Scales: |
| [[supra12|Twelve note chromatic scale]] | | * [[Sulis7]] – 7-tone haplotonic scale |
| | * [[Sulis10]] – 10-tone albitonic scale |
| | * [[Sulis13]] – 13-tone chromatic scale |
|
| |
|
| ==Supraphon== | | == Skwares == |
| Subgroup: 2.3.7.11.13
| | {{Main| Squares }} |
| Commas: 64/63, 78/77, 99/98
| | {{See also| No-fives subgroup temperaments #Skwares }} |
|
| |
|
| POTE generator: ~3/2 = 706.137
| | [[File:skwares_206edo.png|right|alt=skwares_206edo.png|Skwares in 206edo]] |
|
| |
|
| Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]
| | Scales: |
| EDOs: 5, 7, 12, 17
| | * [[Skwares8]] – 8-tone albitonic scale |
| Error: 10.534 cents
| | * [[Skwares11]] – 11-tone mega-albitonic scale |
| | * [[Skwares14]] – 14-tone chromatic scale |
|
| |
|
| ==Machine== | | == Orwell == |
| Subgroup: 2.9.7.11
| | {{Main| Orwell }} |
| Commas: 64/63, 99/98
| | {{See also| Semicomma family #Orwell }} |
|
| |
|
| POTE generator: ~9/8 = 214.384
| | [[File:orwell_84edo.png|right|alt=orwell_84edo.png|Orwell in 84edo]] |
|
| |
|
| Map: [<1 0 6 13|, <0 1 -1 -3|]
| | Scales: |
| EDOs: 5, 6, 11, 17, 28
| | * [[Orwell5]] – 5-tone haplotonic scale |
| Error: 10.100 cents
| | * [[Orwell9]] – 9-tone albitonic scale |
| | * [[Orwell13]] – 13-tone chromatic scale |
|
| |
|
| [[machine5|Five note haplotonic scale]]
| | == Magicaltet == |
| [[machine6|Six note albitonic scale]]
| | {{See also| Subgroup temperaments #Magicaltet }} |
| [[machine11|Eleven note chromatic scale]]
| |
|
| |
|
| =Deutone=
| | Scales: |
| Subgroup: 2.9.5.7.13
| | * [[Magicaltet7]] – 7-tone albitonic scale |
| Commas: 81/80, 91/90, 126/125
| | * [[Magicaltet11]] – 11-tone chromatic scale |
| Related temperament: [[Meantone family|meanpop]]
| | * [[Magicaltet15]] – 15-tone mega-chromatic scale |
|
| |
|
| POTE generator: ~9/8 = 191.059
| | == Magic == |
| | {{Main| Magic }} |
| | {{See also| Magic family #Magic }} |
|
| |
|
| Map: [<1 0 -4 -13 10|, <0, 1 2 5 -2|]
| | [[File:magic_145edo.jpg|right|alt=magic_145edo.jpg|Magic in 145edo]] |
| EDOs: 6, 7, 13, 19, 25, 44, 69
| |
| Error: 12.145 cents
| |
|
| |
|
| [[deutone6|Six note haplotonic scale]] | | Scales: |
| [deutone7|seven note albitonic scale]] | | * [[Magic7]] – 7-tone haplotonic scale |
| [[deutone13|Thirteen note chromatic scale]] | | * [[Magic10]] – 10-tone albitonic scale |
| | * [[Magic13]] – 13-tone chromatic scale |
| | * [[Magic16]] – 16-tone mega-chromatic scale |
|
| |
|
| =Augment= | | == Kiribati == |
| Subgroup: 2.5.7.11 | | {{See also| Subgroup temperaments #Kiribati }} |
| Commas: 56/55, 128/125
| |
| Related temperament: [[Augmented family|augmented]]
| |
|
| |
|
| POTE generator: ~8/7 = 228.275
| | Scales: |
| | * [[Kiribati13]] – 13-tone chromatic scale |
| | * [[Kiribati14]] – 14-tone chromatic scale |
|
| |
|
| Map: [<3 7 0 2|, <0 0 1 1|]
| | == Score == |
| EDOs: 3, 6, 9, 15, 21
| | {{See also|No-threes subgroup temperaments #Score }} |
| Error: 12.830 cents
| |
|
| |
|
| [[augment6|Six note haplotonic scale]] | | [[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]] |
| [[augment9|Nine note albitonic scale]] | | |
| [[augment12|Twelve note chromatic scale]] | | Scales: |
| </pre></div>
| | * [[Score5]] – 5-tone haplotonic scale |
| <h4>Original HTML content:</h4>
| | * [[Score7]] – 7-tone albitonic scale |
| <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: -->
| | * [[Score9]] – 9-tone mega-albitonic scale |
| <!-- ws:end:WikiTextTocRule:103 --><br />
| | * [[Score11]] – 11-tone chromatic scale |
| <br />
| | |
| By a <em>chromatic pair</em> is meant a pair of MOS in some rank two temperament (which may often be a <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup temperament</a>) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called &quot;albitonic&quot; from the Latin word for &quot;white&quot;. Also included at times are &quot;haplotonic&quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with <a class="wiki_link" href="/Target%20tunings">tuning target</a> the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.<br />
| | == Sensi == |
| <br />
| | {{Main| Sensi }} |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h1>
| | {{See also| Sensipent family #Sensi }} |
| Subgroup: 2.9/5.9/7<br />
| | |
| Commas: 250047/250000<br />
| | [[File:sensi_46edo.jpg|right|alt=sensi_46edo.jpg|Sensi in 46edo]] |
| Sval name: 6&amp;21<br />
| | |
| Related temperament: <a class="wiki_link" href="/Minortonic%20family#Domain">domain</a><br />
| | Scales: |
| <br />
| | * [[Sensi5]] – 5-tone haplotonic scale |
| POTE generator: ~10/9 = 182.462<br />
| | * [[Sensi8]] – 8-tone albitonic scale |
| <br />
| | * [[Sensi11]] – 11-tone mega-albitonic scale |
| Map: [&lt;3 0 -4|, &lt;0 1 2|]<br />
| | * [[Sensi19]] – 19-tone chromatic scale |
| EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558<br />
| | |
| Error: 0.0443 cents<br />
| | === Sensation === |
| <br />
| | {{Main| Sensi }} |
| 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 />
| | {{See also| Sensipent family #Sensi }} |
| <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 />
| | == Meantone == |
| Related temperament: <a class="wiki_link" href="/The%20Archipelago">barabdos</a><br />
| | {{Main| Meantone }} |
| <br />
| | {{See also| Meantone family #Meantone }} |
| POTE generator: ~15/13 = 248.285<br />
| | |
| <br />
| | [[File:meantone_31edo.jpg|right|alt=meantone_31edo.jpg|Meantone in 31edo]] |
| Map: [&lt;1 0 -6 -1|, &lt;0 2 9 3|]<br />
| | |
| EDOs: 5, 9, 14, 19, 24, 29<br />
| | Scales: |
| Error: 0.8996 cents<br />
| | * [[Meantone5]] – 5-tone haplotonic scale |
| <br />
| | * [[Meantone7]] – 7-tone albitonic scale |
| <a class="wiki_link" href="/bridgetown9">Nine note albitonic scale</a><br />
| | * [[Meantone12]] – 12-tone chromatic scale |
| <a class="wiki_link" href="/bridgetown14">Fourteen note chromatic scale</a><br />
| | |
| <br />
| | == Mohaha == |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:4 -->Cata</h1>
| | {{See also| Rastmic clan #Mohaha }} |
| Subgroup: 2.3.5.13<br />
| | |
| Commas: 325/324, 625/624<br />
| | [[File:mohaha_131edo.png|right|alt=mohaha_131edo.png|Mohaha in 131edo]] |
| Sval name: 15&amp;19<br />
| | |
| Related temperament: <a class="wiki_link" href="/Kleismic%20family">catakleismic</a><br />
| | Scales: |
| <br />
| | * [[Mohaha7]] – 7-tone albitonic scale |
| POTE generator: ~6/5 = 317.076<br />
| | * [[Mohaha10]] – 10-tone chromatic scale |
| <br />
| | |
| Map: [&lt;1 0 1 0|, &lt;0 6 5 14|]<br />
| | Music: |
| EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246<br />
| | ; [[Billy Stiltner]] |
| Error: 0.9355 cents<br />
| | * [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 ''Mohaha10ping2'']{{dead link}} |
| <br />
| | |
| <a class="wiki_link" href="/cata7">Seven note albitonic scale</a><br />
| | === Mohoho === |
| <a class="wiki_link" href="/cata11">Eleven note mega albitonic scale</a><br />
| | {{See also| Rastmic clan #Mohoho }} |
| <a class="wiki_link" href="/cata15">Fifteen note chromatic scale</a><br />
| | |
| <a class="wiki_link" href="/cata19">Nineteen note mega chromatic scale</a><br />
| | == Joan == |
| <br />
| | {{See also| Subgroup temperaments #Joan }} |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Tridec"></a><!-- ws:end:WikiTextHeadingRule:6 -->Tridec</h1>
| | |
| Subgroups: 2.7/5.11/5.13/5<br />
| | Scales: |
| Commas: 847/845, 1001/1000<br />
| | * [[Joan5]] – 5-tone haplotonic scale |
| Sval name: 5&amp;8<br />
| | * [[Joan7]] – 7-tone albitonic scale |
| <br />
| | * [[Joan9]] – 9-tone mega-albitonic scale |
| POTE generator: ~13/10 = 454.461<br />
| | * [[Joan11]] – 11-tone chromatic scale |
| <br />
| | |
| Map: [&lt;1 2 0 1|, &lt;0 -4 3 1|]<br />
| | == Tutone == |
| EDOs: 5, 8, 21, 29, 37, 66, 169, 235<br />
| | {{See also| Hemimean clan #Tutone }} |
| Error: 1.057<br />
| | |
| <br />
| | [[File:tutone_99edo.png|right|alt=tutone_99edo.png|Tutone in 99edo]] |
| <a class="wiki_link" href="/Tridec8">Eight note albitonic scale</a><br />
| | |
| <a class="wiki_link" href="/Tridec13">Thirteen note chromatic scale</a><br />
| | Scales: |
| <br />
| | * [[Tutone6]] – 6-tone haplotonic scale |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:8 -->Pepperoni</h1>
| | * [[Tutone7]] – 7-tone albitonic scale |
| Subgroup: 2.3.11/7.13/7<br />
| | * [[Tutone13]] – 13-tone chromatic scale |
| Commas: 352/351, 364/363<br />
| | |
| Sval name: 5&amp;12<br />
| | == Stacks == |
| 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|Subgroup temperaments #Stacks (a.k.a. 2magic) }} |
| <br />
| | |
| POTE generator: ~3/2 = 704.052<br />
| | Scales: |
| <br />
| | * [[Stacks5]] – 5-tone haplotonic scale |
| Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]<br />
| | * [[Stacks8]] – 8-tone albitonic scale |
| EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br />
| | * [[Stacks11]] – 11-tone chromatic scale |
| Error: 1.298 cents<br />
| | * [[Stacks19]] – 19-tone mega-chromatic scale |
| <br />
| | |
| <a class="wiki_link" href="/pepperoni7">Seven note albitonic scale</a><br />
| | == Bleu == |
| <a class="wiki_link" href="/pepperoni12">Twelve note chromatic scale</a><br />
| | {{See also| No-fives subgroup temperaments #Bleu }} |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Nestoria"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nestoria</h1>
| | Scales: |
| Subgroup: 2.3.5.19<br />
| | * [[Bleu8]] – 8-tone haplotonic scale |
| Commas: 361/360, 513/512<br />
| | * [[Bleu9]] – 9-tone albitonic scale |
| Sval name: 12&amp;29<br />
| | * [[Bleu17]] – 17-tone chromatic scale |
| Related temperament: <a class="wiki_link" href="/Schismatic%20family">schismatic</a><br />
| | |
| <br />
| | == Sephiroth == |
| POTE generator: ~3/2 = 701.746<br />
| | {{See also| No-threes subgroup temperaments #Sephiroth }} |
| <br />
| | |
| Map: [&lt;1 0 15 9], &lt;0 1 -8 -3|]<br />
| | Scales: |
| EDOs: 7, 12, 17, 29, 41, 53, 118, 171<br />
| | * [[Sephiroth7]] – 7-tone haplotonic scale |
| Error: 1.819 cents<br />
| | * [[Sephiroth10]] – 10-tone albitonic scale |
| <br />
| | * [[Sephiroth13]] – 13-tone chromatic scale |
| <a class="wiki_link" href="/nestoria7">Seven note albitonic scale</a><br />
| | * [[Sephiroth16]] – 16-tone mega-chromatic scale |
| <a class="wiki_link" href="/nestoria12">Twelve note chromatic scale</a><br />
| | |
| <br />
| | == Archy == |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Nestoria-Photia"></a><!-- ws:end:WikiTextHeadingRule:12 -->Photia</h2>
| | {{Main| Superpyth }} |
| Subgroup 2.3.5.17.19<br />
| | {{See also| Archytas clan #Archy }} |
| 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 />
| | * [[Archy5]] – 5-tone haplotonic scale |
| <br />
| | * [[Archy7]] – 7-tone albitonic scale |
| POTE generator: ~3/2 = 701.470<br />
| | * [[Archy12]] – 12-tone chromatic scale |
| <br />
| | |
| Map: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]<br />
| | === Supra === |
| EDOs: 7, 12, 17, 29, 41, 53, 65<br />
| | {{Main| Superpyth }} |
| Error: 3.457 cents<br />
| | {{See also| Archytas clan #Supra }} |
| <br />
| | |
| <a class="wiki_link" href="/photia7">Seven note albitonic scale</a><br />
| | [[File:supra_56edo.png|right|alt=supra_56edo.png|Supra in 56edo]] |
| <a class="wiki_link" href="/photia12">Twelve note chromatic scale</a><br />
| | |
| <br />
| | Scales: |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:14 -->Huntington</h1>
| | * [[Supra7]] – 7-tone [[albitonic scale]] |
| Subgroup: 2.5.7.13<br />
| | * [[Supra12]] – 12-tone [[chromatic scale]] |
| Commas: 640/637, 10985/10976<br />
| | |
| Sval name: 10&amp;27<br />
| | === Supraphon === |
| <br />
| | {{Main| Superpyth }} |
| POTE generator: ~16/13 = 357.002<br />
| | {{See also| Archytas clan #Supraphon }} |
| <br />
| | |
| Map: [&lt;1 5 4 4|, &lt;0 -9 -4 -1|]<br />
| | == Suhajira == |
| EDOs: 7, 10, 17, 27, 37, 84, 121, 400<br />
| | {{See also| Archytas clan #Suhajira }} |
| Error: 2.1001 cents<br />
| | |
| <br />
| | Scales: |
| <a class="wiki_link" href="/huntington7">Seven note haplotonic scale</a><br />
| | * [[Suhajira7]] – 7-tone haplotonic scale |
| <a class="wiki_link" href="/huntington10">Ten note albitonic scale</a><br />
| | * [[Suhajira10]] – 10-tone albitonic scale |
| <a class="wiki_link" href="/huntington17">Seventeen note chromatic scale</a><br />
| | * [[Suhajira17]] – 17-tone chromatic scale |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:16 -->Roulette</h1>
| | == Machine == |
| Subgroup: 2.5.7.11.13<br />
| | {{See also| Subgroup temperaments #Machine}} |
| Commas: 176/175, 1375/1372, 640/637<br />
| | |
| Sval name: 6&amp;25<br />
| | [[File:machine_28edo.png|right|alt=machine_28edo.png|Machine in 28edo]] |
| Related temperament: <a class="wiki_link" href="/Wuerschmidt%20family">Hemiwuerschmidt</a><br />
| | |
| <br />
| | Scales: |
| POTE generator: ~28/25 = 194.594<br />
| | * [[Machine5]] – 5-tone haplotonic scale |
| <br />
| | * [[Machine6]] – 6-tone albitonic scale |
| Map: [&lt;1 0 -3 -7 -13|, &lt;0 2 5 9 -8|]<br />
| | * [[Machine11]] – 11-tone chromatic scale |
| EDOs: 6, 7, 13, 19, 25, 31, 37<br />
| | |
| Error: 2.555 cents<br />
| | == Deutone == |
| <br />
| | {{See also| Hemimean clan #Deutone }} |
| <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:deutone_44edo.png|right|alt=deutone_44edo.png|Deutone in 44edo]] |
| <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 />
| | * [[Deutone6]] – 6-tone haplotonic scale |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:18 -->Garibaldi</h1>
| | * [[Deutone7]] – 7-tone albitonic scale |
| Group: 2.3.5.7<br />
| | * [[Deutone13]] – 13-tone chromatic scale |
| Commas: 225/224, 3125/3087<br />
| | |
| Val name: 12&amp;29<br />
| | == Negra == |
| <br />
| | {{Main| Negri }} |
| POTE generator: ~3/2 = 702.085<br />
| | {{See also| Marvel temperaments #Negri }} |
| <br />
| | |
| Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]<br />
| | == Porkypine == |
| EDOs: 7, 12, 17, 29, 41, 53, 94<br />
| | {{Main| Porcupine }} |
| Error: 2.834<br />
| | {{See also| Porcupine family #Porcupine }} |
| <br />
| | |
| <a class="wiki_link" href="/garibaldi12">Twelve note albitonic scale</a><br />
| | Scales: |
| <a class="wiki_link" href="/garibaldi17">Seventeen note chromatic scale</a><br />
| | * [[Porkypine7]] – 7-tone haplotonic scale |
| <br />
| | * [[Porkypine8]] – 8-tone albitonic scale |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:20 -->Baldy</h1>
| | * [[Porkypine15]] – 15-tone chromatic scale |
| Subgroup: 2.9.5.7.13<br />
| | |
| Commas: 225/224, 325/324, 640/637<br />
| | == Skateboard == |
| Sval name: 6&amp;35<br />
| | {{See also| Subgroup temperaments #Skateboard }} |
| Related temperament: <a class="wiki_link" href="/Schismatic%20family">Garibaldi</a><br />
| | |
| <br />
| | Scales: |
| POTE generator: ~9/8 = 204.090<br />
| | * [[Skateboard7]] – 7-tone haplotonic scale |
| <br />
| | * [[Skateboard11]] – 11-tone albitonic scale |
| Map: [&lt;1 0 15 25 -8|, &lt;0 1 -4 -7 10|]<br />
| | * [[Skateboard15]] – 15-tone chromatic scale |
| EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147<br />
| | |
| Error: 2.617 cents<br />
| | == Augment == |
| <br />
| | {{See also| No-threes subgroup temperaments #Augment }} |
| <a class="wiki_link" href="/baldy6">Six note haplotonic scale</a><br />
| | |
| <a class="wiki_link" href="/baldy11">Eleven note albitonic scale</a><br />
| | [[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]] |
| <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>
| | * [[Augment6]] – 6-tone haplotonic scale |
| Subgroup: 2.7.11.13<br />
| | * [[Augment9]] – 9-tone albitonic scale |
| Commas: 1573/1569, 15488/15379<br />
| | * [[Augment12]] – 12-tone chromatic scale |
| Sval name: 3&amp;17<br />
| | |
| <br />
| | == Semaphore == |
| POTE generator: ~14/11 = 421.309<br />
| | {{Main| Semaphore and godzilla }} |
| <br />
| | {{See also| Semaphoresmic clan #Semaphore }} |
| Map: [&lt;1 0 1 3|, &lt;0 8 7 2|]<br />
| | |
| EDOs: 17, 20, 37, 57, 94, 225<br />
| | [[File:semaphore_24edo.png|right|alt=semaphore_24edo.png|Semaphore in 24edo]] |
| Error: 2.665 cents<br />
| | |
| <br />
| | Scales: |
| <a class="wiki_link" href="/bossier8">Eight note albitonic scale</a><br />
| | * [[Semaphore5]] – 5-tone haplotonic scale |
| <a class="wiki_link" href="/bossier11">Eleven note chromatic scale</a><br />
| | * [[Semaphore9]] – 9-tone albitonic scale |
| <a class="wiki_link" href="/bossier14">Fourteen note mega chromatic scale</a><br />
| | * [[Semaphore14]] – 14-tone chromatic scale |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:24 -->Radon</h1>
| | == Kryptonite == |
| Subgroup: 2.3.7.11<br />
| | {{See also| Subgroup temperaments #Kryptonite }} |
| Commas: 896/891, 1029/1024<br />
| | |
| Sval name: 5&amp;36<br />
| | Scales: |
| Related temperament: <a class="wiki_link" href="/Gamelismic%20clan">Rodan</a><br />
| | * [[Kryptonite9]] – 9-tone albitonic scale |
| <br />
| | * [[Kryptonite10]] – 10-tone albitonic scale |
| POTE generator: ~8/7 = 234.381<br />
| | * [[Kryptonite19]] – 19-tone mega-chromatic scale |
| <br />
| | |
| Map: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]<br />
| | == Oregon == |
| EDOs: 5, 36, 41, 87, 128<br />
| | {{See also| Orgonia #Oregon }} |
| Error: 2.925 cents<br />
| | |
| <br />
| | Scales: |
| <a class="wiki_link" href="/radon5">Five note haplotonic scale</a><br />
| | * [[Oregon7]] – 7-tone haplotonic scale |
| <a class="wiki_link" href="/radon11">Eleven note albitonic scale</a><br />
| | * [[Oregon11]] – 11-tone albitonic scale |
| <a class="wiki_link" href="/radon16">Sixteen note chromatic scale</a><br />
| | * [[Oregon15]] – 15-tone chromatic scale |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule:26 -->Myna</h1>
| | == Antikythera == |
| Group: 2.3.5.7<br />
| | {{See also| Jubilismic clan #Antikythera }} |
| Commas: 126/125, 1728/1715<br />
| | |
| Val name: 4&amp;27<br />
| | [[File:antikythera_28edo.png|right|alt=antikythera_28edo.png|Antikythera in 28edo]] |
| <br />
| | |
| POTE generator: ~6/5 = 310.146<br />
| | Scales: |
| <br />
| | * [[Antikythera6]] – 6-tone haplotonic scale |
| Map: [&lt;1 9 9 8|, &lt;0 -10 -9 -7|]<br />
| | * [[Antikythera10]] – 10-tone albitonic scale |
| EDOs: 4, 27, 31, 58, 89<br />
| | * [[Antikythera16]] – 16-tone chromatic scale |
| Error: 3.310 cents<br />
| | |
| <br />
| | == Glacial == |
| <a class="wiki_link" href="/myna7">Seven note albitonic scale</a><br />
| | {{See also| Subgroup temperaments #Glacial }} |
| <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 />
| | Scales: |
| <br />
| | * [[Glacial6]] – 6-tone haplotonic scale |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:28 -->Silver</h1>
| | * [[Glacial7]] – 7-tone albitonic scale |
| Subgroup: 2.5.7.13.17<br />
| | * [[Glacial13]] – 13-tone chromatic scale |
| Commas: 170/169, 640/637, 5525/5488<br />
| | |
| Sval name: 10&amp;27<br />
| | == Leantone == |
| <br />
| | {{See also| Hemimean clan #Leantone }} |
| POTE generator: ~13/8 = 842.711<br />
| | |
| <br />
| | [[File:leantone_81edo.png|right|alt=leantone_81edo.png|Leantone in 81edo]] |
| 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 />
| | * [[Leantone6]] – 6-tone haplotonic scale |
| <br />
| | * [[Leantone7]] – 7-tone albitonic scale |
| <a class="wiki_link" href="/silver7">Seven note haplotonic scale</a><br />
| | * [[Leantone13]] – 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 />
| | == Notes == |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Meantone"></a><!-- ws:end:WikiTextHeadingRule:30 -->Meantone</h1>
| | [[Category:Lists of scales]] |
| Group: 2.3.5.7<br />
| | [[Category:Tempered scales| ]] |
| Commas: 81/80, 126/125<br />
| | [[Category:Listen]] |
| Val name: 12&amp;19<br />
| | [[Category:Rank 2]] |
| <br />
| | |
| POTE generator: 696.495<br />
| | {{todo|cleanup}} |
| <br />
| |
| Map: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]<br />
| |
| EDOs: 5, 7, 12, 19, 31, 81, 112, 143<br />
| |
| Error: 3.585<br />
| |
| <br />
| |
| <a class="wiki_link" href="/meantone5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="/meantone7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="/meantone12">Twelve note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule:32 -->Indium</h1>
| |
| Subgroup: 2.5/3.7/3.11/3<br />
| |
| Commas: 3025/3024, 3125/3087<br />
| |
| Sval name: 8&amp;33<br />
| |
| <br />
| |
| POTE generator: ~12/11 = 147.159<br />
| |
| <br />
| |
| Map: [&lt;1 0 0 2|, &lt;0 6 10 -1|]<br />
| |
| EDOs: 33, 41, 49, 57, 106, 204, 253<br />
| |
| Error: 3.968 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="/indium8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="/indium17">Seventeen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule: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: 81/80, 91/90, 126/125<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 />
| |
| [deutone7|seven note albitonic scale]]<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>
| |