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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>2011-12-07 15:12:20 UTC</tt>.<br>
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| : The original revision id was <tt>283411932</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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| [[media type="custom" key="11052942"]] | |
| ----
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| =Definitions=
| | 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. |
| By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/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 [[xenharmonic/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= | | == Terrain == |
| Subgroup: 2.9/5.9/7 | | {{See also| Subgroup temperaments #Terrain }} |
| Commas: 250047/250000
| |
| Sval name: 6&21
| |
| Related temperament: [[xenharmonic/Minortonic family#Domain|domain]]
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|
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|
| [[xenharmonic/POTE generator|POTE generator]]: ~10/9 = 182.462 | | [[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]] |
|
| |
|
| Map: [<3 0 -4|, <0 1 2|]
| | Scales: |
| EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
| | * [[Terrain9]] – 9-tone albitonic scale |
| Error: 0.0443 cents
| | * [[Terrain15]] – 15-tone chromatic scale |
|
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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.
| | ; Music |
| | * ''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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| [[xenharmonic/terrain9|Nine note albitonic scale]]
| | == Petrtri == |
| [[xenharmonic/terrain15|Fifteen note chromatic scale]]
| | {{See also| Subgroup temperaments #Petrtri }} |
|
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|
| =Orgone=
| | [[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]] |
| Subgroup: 2.7.11
| |
| Commas: 65536/65219
| |
| Svals: 4&7
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|
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|
| POTE generator: ~77/64 = 323.372
| | Scales: |
| | * [[Petrtri5]] – 5-tone haplotonic scale |
| | * [[Petrtri8]] – 8-tone albitonic scale |
| | * [[Petrtri13]] – 13-tone chromatic scale |
|
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|
| Map: [<1 2 4|, <0 3, -2|]
| | == Barton == |
| EDOs: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308
| | {{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}} |
| Error: 0.7313
| | {{See also| The Jacobins #Barton }} |
|
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|
| [[image:orgone_308edo.jpg]] | | Scales: |
| | * [[Barton5]] – 5-tone haplotonic scale |
| | * [[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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|
| [[xenharmonic/orgone7|Seven note albitonic scale]]
| | == Tridec == |
| [[xenharmonic/orgone11|Eleven note chromatic scale]]
| | {{See also| Subgroup temperaments #Tridec }} |
| [[xenharmonic/orgone15|Fifteen note mega chromatic scale]]
| |
|
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|
| =Bridgetown=
| | [[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]] |
| Subgroup: 2.3.11/5.13/5
| |
| Commas: 352/351, 676/675
| |
| Sval name: 5&24
| |
| Related temperament: [[xenharmonic/The Archipelago|barabados]]
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|
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|
| POTE generator: ~15/13 = 248.285
| | Scales: |
| | * [[Tridec8]] – 8-tone albitonic scale |
| | * [[Tridec13]] – 13-tone chromatic scale |
|
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|
| Map: [<1 0 -6 -1|, <0 2 9 3|]
| | == Nestoria == |
| EDOs: 5, 9, 14, 19, 24, 29
| | {{See also| Schismatic family #Nestoria (2.3.5.19)}} |
| Error: 0.8996 cents
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| [[xenharmonic/bridgetown9|Nine note albitonic scale]] | | [[File:nestoria_171edo.png|right|alt=nestoria_171edo.png|Nestoria in 171edo]] |
| [[xenharmonic/bridgetown14|Fourteen note chromatic scale]]
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| ==Music==
| | Scales: |
| [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3|Paint in the Water 29]] by [[xenharmonic/Igliashon Jones|Igliashon Jones]] | | * [[Nestoria7]] – 7-tone albitonic scale |
| [[http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3|Route 14 in Bridgetown]] by [[xenharmonic/Chris Vaisvil|Chris Vaisvil]] | | * [[Nestoria12]] – 12-tone chromatic scale |
| | * [[Nestoria17]] – 17-tone mega chromatic scale |
|
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|
| =Cata= | | == Orgone == |
| Subgroup: 2.3.5.13
| | {{Main| Orgone }} |
| Commas: 325/324, 625/624
| | {{See also| Orgonia #Orgone }} |
| Sval name: 15&19
| |
| Related temperament: [[xenharmonic/Kleismic family|catakleismic]]
| |
|
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|
| POTE generator: ~6/5 = 317.076
| | [[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]] |
|
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|
| Map: [<1 0 1 0|, <0 6 5 14|]
| | Scales: |
| EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd
| | * [[Orgone7]] – 7-tone albitonic scale |
| Error: 0.9355 cents
| | * [[Orgone11]] – 11-tone chromatic scale |
| | * [[Orgone15]] – 15-tone mega-chromatic scale |
|
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| [[image:xenharmonic/cata_246edo2.jpg]]
| | == Marveltwintri == |
| [[xenharmonic/cata7|Seven note albitonic scale]]
| | {{See also| Subgroup temperaments #Marveltwintri }} |
| [[xenharmonic/cata11|Eleven note mega albitonic scale]]
| |
| [[xenharmonic/cata15|Fifteen note chromatic scale]]
| |
| [[xenharmonic/cata19|Nineteen note mega chromatic scale]]
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|
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|
| =Neutraltri=
| | [[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]] |
| Subgroup: 2.3.11
| |
| Commas: 243/242
| |
| Svalname: 7&17
| |
|
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|
| POTE generator: ~11/9 = 350.525
| | Scales: |
| | * [[Marveltwintri7]] – 7-tone albitonic scale |
| | * [[Marveltwintri11]] – 11-tone chromatic scale |
| | * [[Marveltwintri15]] – 15-tone mega-chromatic scale |
|
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|
| Map: [<1 1 2|, <0 2 5|]
| | == Cata == |
| EDOs: 7, 17, 24, 65, 89, 202, 291, 380
| | {{Main| Kleismic }} |
| Error: 1.007
| | {{See also| Kleismic family #Cata }} |
|
| |
|
| [[xenharmonic/neutraltri7|Seven note albitonic scale]] | | [[File:cata_246edo.jpg|right|alt=cata_246edo.jpg|Cata in 246edo]] |
| [[xenharmonic/neutraltri10|Ten note chromatic scale]]
| |
| [[xenharmonic/neutraltri17|Seventeen note mega chromatic scale]]
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|
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|
| =Tridec=
| | Scales: |
| Subgroup: 2.7/5.11/5.13/5
| | * [[Cata7]] – 7-tone albitonic scale |
| Commas: 847/845, 1001/1000
| | * [[Cata11]] – 11-tone mega-albitonic scale |
| Sval name: 5&8
| | * [[Cata15]] – 15-tone chromatic scale |
| | * [[Cata19]] – 19-tone mega-chromatic scale |
|
| |
|
| POTE generator: ~13/10 = 454.461
| | == Bridgetown == |
| | {{See also| Subgroup temperaments #Bridgetown }} |
|
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|
| Map: [<1 2 0 1|, <0 -4 3 1|]
| | [[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]] |
| EDOs: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c
| |
| Error: 1.057
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|
| [[xenharmonic/Tridec8|Eight note albitonic scale]] | | Scales: |
| [[xenharmonic/Tridec13|Thirteen note chromatic scale]] | | * [[Bridgetown9]] – 9-tone albitonic scale |
| | * [[Bridgetown14]] – 14-tone chromatic scale |
|
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|
| =Pepperoni=
| | ; Music |
| Subgroup: 2.3.11/7.13/7
| | * [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]] |
| Commas: 352/351, 364/363
| | * ''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 |
| Sval name: 5&12
| |
| Related temperament: The [[xenharmonic/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
| | == Haumea == |
| | {{See also| Subgroup temperaments #Haumea }} |
|
| |
|
| Map: [<1 0 7 12|, <0 1 -4 -7|]
| | Scales: |
| EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271
| | * [[Haumea5]] – 5-tone haplotonic scale |
| Error: 1.298 cents
| | * [[Haumea9]] – 9-tone albitonic scale |
| | * [[Haumea14]] – 14-tone chromatic scale |
| | * [[Haumea19]] – 19-tone mega-chromatic scale |
|
| |
|
| [[xenharmonic/pepperoni7|Seven note albitonic scale]]
| | == Neutral == |
| [[xenharmonic/pepperoni12|Twelve note chromatic scale]]
| | {{See also| Rastmic clan #Neutral }} |
|
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|
| =Slendric=
| | [[File:neutral_380edo.png|right|alt=neutral_380edo.png|Neutral in 380edo]] |
| Subgroup: 2.3.7
| |
| Comma: 1029/1024
| |
| Sval name: 5&21
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|
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|
| POTE generator: ~8/7 = 233.688
| | Scales: |
| | * [[Neutral7]] – 7-tone albitonic scale |
| | * [[Neutral10]] – 10-tone chromatic scale |
| | * [[Neutral17]] – 17-tone mega-chromatic scale |
|
| |
|
| Map: [<1 1 3|, <0 3 -1|]
| | ; Music |
| EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190
| | * [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 |
| Error: 1.109 cents
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| [[image:xenharmonic/slendric_190edo.jpg]] | | == Slendric == |
| | {{Main| Slendric }} |
| | :''See also: [[Gamelismic clan #Slendric]] and [[No-fives subgroup temperaments #Slendric]]'' |
|
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|
| [[xenharmonic/slendric5|Five note haplotonic scale]] | | [[File:slendric_190edo.jpg|right|alt=slendric_190edo.jpg|Slendric in 190edo]] |
| [[xenharmonic/slendric6|Six note haplotonic scale]]
| |
| [[xenharmonic/slendric11|Eleven note albitonic scale]]
| |
| [[xenharmonic/slendric16|Sixteen note chromatic scale]]
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| ==Music==
| | Scales: |
| [[http://micro.soonlabel.com/tuning-survey/daily20111026-the-11th-slendric-fanfare.mp3|The 11th Slendric Fanfare]] | | * [[Slendric5]] – 5-tone haplotonic scale |
| [[http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3|16 Slendric Virgins]] | | * [[Slendric6]] – 6-tone haplotonic scale |
| by [[xenharmonic/Chris Vaisvil|Chris Vaisvil]]
| | * [[Slendric11]] – 11-tone albitonic scale |
| | * [[Slendric16]] – 16-tone chromatic scale |
|
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| =Marveltwintri= | | == Huntington == |
| Subgroup: 2.5/3.13/9
| | {{See also| No-threes subgroup temperaments #Huntington }} |
|
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|
| POTE generator: ~6/5 =
| | [[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]] |
|
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| =Nestoria=
| | Scales: |
| Subgroup: 2.3.5.19
| | * [[Huntington7]] – 7-tone haplotonic scale |
| Commas: 361/360, 513/512
| | * [[Huntington10]] – 10-tone albitonic scale |
| Sval name: 12&29
| | * [[Huntington17]] – 17-tone chromatic scale |
| Related temperament: [[xenharmonic/Schismatic family|schismatic]]
| |
|
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|
| POTE generator: ~3/2 = 701.746
| | == Tobago == |
| | {{See also| Subgroup temperaments #Tobago }} |
|
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|
| Map: [<1 0 15 9|, <0 1 -8 -3|]
| | Scales: |
| EDOs: 7, 12, 17, 29, 41, 53, 118, 171
| | * [[Tobago6]] – 6-tone haplotonic scale |
| Error: 1.819 cents
| | * [[Tobago10]] – 10-tone albitonic scale |
| | * [[Tobago14]] – 14-tone chromatic scale |
| | * [[Tobago24]] – 24-tone quatertone scale |
|
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|
| [[xenharmonic/nestoria7|Seven note albitonic scale]]
| | == Pepperoni == |
| [[xenharmonic/nestoria12|Twelve note chromatic scale]]
| | {{See also| Parapyth }} |
| | {{See also| Subgroup temperaments #Pepperoni }} |
|
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|
| =Marveltri=
| | [[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]] |
| Subgroup: 2.5.9/7
| |
| Comma: 225/224
| |
| Sval name: 3&13
| |
| Related temperaments: marvel, 22&47, magic
| |
|
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|
| POTE generator: ~5/4 = 382.618
| | Scales: |
| | * [[Pepperoni7]] – 7-tone albitonic scale |
| | * [[Pepperoni12]] – 12-tone chromatic scale |
|
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|
| Map: [<1 0 5|, <0 1 -2|]
| | == Wizz == |
| EDOs: 12, 13, 16, 19, 22, 47, 69
| | {{See also| No-threes subgroup temperaments #Wizz }} |
| Error: 2.043 cents
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|
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|
| [[xenharmonic/marveltri7|Seven note albitonic scale]] | | Scales: |
| [[xenharmonic/marveltri10|Ten note chromatic scale]] | | * [[Wizz6]] – 6-tone haplotonic scale |
| [[xenharmonic/marveltri13|Thirteen note mega chromatic scale]] | | * [[Wizz10]] – 10-tone albitonic scale |
| | * [[Wizz16]] – 16-tone chromatic scale |
|
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| =Guanyintet= | | == Bossier == |
| Subgroup: 2.5.7/3.11/3
| | {{See also| No-threes subgroup temperaments #Bossier }} |
| Commas: 176/175, 540/539
| |
| Svalname: 4&9
| |
| Related temperaments: guanyin, orwell
| |
|
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|
| POTE generator: ~7/6 = 269.619
| | [[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]] |
|
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|
| Map: [<1 0 2 -2|, <0 3 -1 5|]
| | Scales: |
| EDOs: 9, 31, 40, 49, 89, 227bc, 316bcd
| | * [[Bossier8]] – 8-tone albitonic scale |
| Error: 2.533 cents
| | * [[Bossier11]] – 11-tone chromatic scale |
| | * [[Bossier14]] – 14-tone mega-chromatic scale |
|
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|
| [[xenharmonic/guanyintet5|Five note haplotonic scale]]
| | == Penta a.k.a. mechanism == |
| [[xenharmonic/guanyintet9|Nine note albitonic scale]]
| | {{See also| Subgroup temperaments #Penta a.k.a. mechanism }} |
| [[xenharmonic/guanyintet13|Thirteen note chromatic scale]]
| |
|
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|
| =Photia=
| | Scales: |
| Subgroup: 2.3.5.17.19
| | * [[Penta5]] – 5-tone haplotonic scale |
| Commas: 171/170, 256/255, 324/323
| | * [[Penta8]] – 8-tone albitonic scale |
| Sval name: 12&41
| | * [[Penta11]] – 11-tone chromatic scale |
| Related temperament: [[xenharmonic/Schismatic family|schismatic]]
| | * [[Penta19]] – 19-tone mega-chromatic scale |
|
| |
|
| POTE generator: ~3/2 = 701.470
| | == Bluebirds == |
| | {{See also| No-threes subgroup temperaments #Bluebirds }} |
|
| |
|
| Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|]
| | Scales: |
| EDOs: 7, 12, 17, 29, 41, 53, 65
| | * [[Bluebirds6]] – 6-tone haplotonic scale |
| Error: 3.457 cents
| | * [[Bluebirds7]] – 7-tone albitonic scale |
| | * [[Bluebirds13]] – 13-tone chromatic scale |
|
| |
|
| [[xenharmonic/photia7|Seven note albitonic scale]]
| | == Marveltri == |
| [[xenharmonic/photia12|Twelve note chromatic scale]]
| | {{See also| Subgroup temperaments #Marveltri }} |
|
| |
|
| =Huntington=
| | Scales: |
| Subgroup: 2.5.7.13
| | * [[Marveltri7]] – 7-tone albitonic scale |
| Commas: 640/637, 10985/10976
| | * [[Marveltri10]] – 10-tone chromatic scale |
| Sval name: 10&27
| | * [[Marveltri13]] – 13-tone mega-chromatic scale |
|
| |
|
| POTE generator: ~16/13 = 357.002
| | == Edson == |
| | {{See also| Subgroup temperaments #Edson }} |
|
| |
|
| Map: [<1 5 4 4|, <0 -9 -4 -1|]
| | Scales: |
| EDOs: 7, 10, 17, 27, 37, 84, 121, 400
| | * [[Edson5]] – 5-tone haplotonic scale |
| Error: 2.1001 cents
| | * [[Edson7]] – 7-tone albitonic scale |
| | * [[Edson12]] – 12-tone chromatic scale |
| | * [[Edson17]] – 17-tone mega-chromatic scale |
|
| |
|
| [[image:huntington_400edo.jpg]]
| | == Photia == |
| | {{See also| Schismatic family #Photia (2.3.5.17) }} |
|
| |
|
| [[xenharmonic/huntington7|Seven note haplotonic scale]] | | [[File:photia_65edo.png|right|alt=photia_65edo.png|Photia in 65edo]] |
| [[xenharmonic/huntington10|Ten note albitonic scale]]
| |
| [[xenharmonic/huntington17|Seventeen note chromatic scale]]
| |
|
| |
|
| =Shoe=
| | Scales: |
| Subgroup: 2.5.7.11.13
| | * [[Photia7]] – 7-tone albitonic scale |
| Commas: 176/175, 640/637, 847/845
| | * [[Photia12]] – 12-tone chromatic scale |
| Sval name: 16&21
| |
|
| |
|
| POTE generator: ~8/7 = 227.108
| | == Shoe a.k.a. llywelyn == |
| | {{See also| Llywelynsmic clan #Llywelyn a.k.a. shoe }} |
|
| |
|
| Map: [<1 1 3 1 2|, <0 7 -1 13 9|]
| | [[File:shoe_37edo.jpg|right|alt=shoe_37edo.jpg|Shoe in 37edo]] |
| EDOs: 16, 21, 37
| |
| Error: 2.488
| |
|
| |
|
| [[image:xenharmonic/shoe_37edo.jpg]] | | Scales: |
| | * [[Shoe5]] – 5-tone mini-haplotonic scale |
| | * [[Shoe6]] – 6-tone haplotonic scale |
| | * [[Shoe11]] – 11-tone albitonic scale |
| | * [[Shoe16]] – 16-tone chromatic scale |
|
| |
|
| [[xenharmonic/shoe5|shoe5]] - five note mini [[xenharmonic/haplotonic scale|haplotonic scale]]
| | == Roulette == |
| [[xenharmonic/shoe6|shoe6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]]
| | {{See also | Hemimean clan #Roulette }} |
| [[xenharmonic/shoe11|shoe11]] - eleven note note [[xenharmonic/albitonic scale|albitonic scale]]
| |
| [[xenharmonic/shoe16|shoe16]] - sixteen note [[xenharmonic/chromatic scale|chromatic scale]]
| |
|
| |
|
| =Roulette=
| | [[File:roulette_37edo.jpg|right|alt=roulette_37edo.jpg|Roulette in 37edo]] |
| Subgroup: 2.5.7.11.13
| |
| Commas: 176/175, 1375/1372, 640/637
| |
| Sval name: 6&25
| |
| Related temperament: [[xenharmonic/Wuerschmidt family|Hemiwuerschmidt]]
| |
|
| |
|
| POTE generator: ~28/25 = 194.594
| | Scales: |
| | * [[Roulette6]] – 6-tone haplotonic scale |
| | * [[Roulette7]] – 7-tone albitonic scale |
| | * [[Roulette13]] – 13-tone chromatic scale |
| | * [[Roulette19]] – 19-tone mega-chromatic scale |
|
| |
|
| Map: [<1 0 -3 -7 13|, <0 2 5 9 -8|]
| | == Silver == |
| EDOs: 6, 7, 13, 19, 25, 31, 37
| | {{See also | No-threes subgroup temperaments #Silver }} |
| Error: 2.555 cents
| |
|
| |
|
| [[image:xenharmonic/roulette_37edo.jpg]] | | [[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]] |
|
| |
|
| [[xenharmonic/roulette6|roulette6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] | | Scales: |
| [[xenharmonic/roulette7|roulette7]] - seven note [[xenharmonic/albitonic scale|albitonic scale]] | | * [[Silver7]] – 7-tone haplotonic scale |
| [[xenharmonic/roulette13|roulette13]] - thirteen note [[xenharmonic/chromatic scale|chromatic scale]] | | * [[Silver10]] – 10-tone albitonic scale |
| [[xenharmonic/roulette19|roulette19]] - nineteen note [[xenharmonic/mega chromatic scale|mega chromatic scale]]
| | * [[Silver17]] – 17-tone chromatic scale |
|
| |
|
| =Garibaldi= | | == Baldy == |
| Group: 2.3.5.7
| | {{See also| Subgroup temperaments #Baldy }} |
| Commas: 225/224, 3125/3087
| |
| Val name: 12&29
| |
|
| |
|
| POTE generator: ~3/2 = 702.085
| | [[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]] |
|
| |
|
| Map: [<1 0 15 25|, <0 1 -8 -14|]
| | Scales |
| EDOs: 7, 12, 17, 29, 41, 53, 94
| | * [[Baldy6]] – 6-tone haplotonic scale |
| Error: 2.834
| | * [[Baldy11]] – 11-tone albitonic scale |
| | * [[Baldy17]] – 17-tone chromatic scale |
|
| |
|
| [[xenharmonic/garibaldi12|Twelve note albitonic scale]]
| |
| [[xenharmonic/garibaldi17|Seventeen note chromatic scale]]
| |
|
| |
|
| =Baldy= | | == Guanyintet == |
| Subgroup: 2.9.5.7.13 | | {{See also | Subgroup temperaments #Guanyintet }} |
| Commas: 225/224, 325/324, 640/637
| |
| Sval name: 6&35
| |
| Related temperament: [[xenharmonic/Schismatic family|Garibaldi]]
| |
|
| |
|
| POTE generator: ~9/8 = 204.090
| | Scales: |
| | * [[Guanyintet5]] – 5-tone haplotonic scale |
| | * [[Guanyintet9]] – 9-tone albitonic scale |
| | * [[Guanyintet13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|]
| | == Radon == |
| EDOs: 6, 11, 17, 23, 29, 35, 41, [[xenharmonic/47edo|47]], 100, [[xenharmonic/147edo|147]]
| | {{See also| Gamelismic clan #Radon }} |
| Error: 2.617 cents
| |
|
| |
|
| [[image:baldy_147edo.jpg]] | | [[File:radon_128edo.jpg|right|alt=radon_128edo.jpg|Radon in 128edo]] |
|
| |
|
| [[xenharmonic/baldy6|baldy6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] | | * [[Radon5]] – 5-tone haplotonic scale |
| [[xenharmonic/baldy11|baldy11]] - eleven note [[xenharmonic/albitonic scale|albitonic scale]] | | * [[Radon11]] – 11-tone albitonic scale |
| [[xenharmonic/baldy17|baldy17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] | | * [[Radon16]] – 16-tone chromatic scale |
|
| |
|
| =Bossier= | | == Gariberttet == |
| Subgroup: 2.7.11.13 | | {{See also | Subgroup temperaments #Gariberttet }} |
| Commas: 1573/1569, 15488/15379
| |
| Sval name: 3&17
| |
|
| |
|
| POTE generator: ~14/11 = 421.309
| | Scales: |
| | * [[Gariberttet5]] – 5-tone haplotonic scale |
| | * [[Gariberttet9]] – 9-tone albitonic scale |
| | * [[Gariberttet13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 1 3|, <0 8 7 2|]
| | == Namo == |
| EDOs: 17, 20, 37, 57, 94, 225
| | {{See also| Rastmic clan #Namo }} |
| Error: 2.665 cents
| |
|
| |
|
| [[image:bossier_225edo.jpg]] | | Scales: |
| | * [[Namo7]] – 7-tone haplotonic scale |
| | * [[Namo10]] – 10-tone albitonic scale |
| | * [[Namo17]] – 17-tone chromatic scale |
|
| |
|
| [[xenharmonic/bossier8|Eight note albitonic scale]]
| | == Sentry == |
| [[xenharmonic/bossier11|Eleven note chromatic scale]]
| | {{See also | Subgroup temperaments #Sentry }} |
| [[xenharmonic/bossier14|Fourteen note mega chromatic scale]]
| |
|
| |
|
| =Radon=
| | Scales: |
| Subgroup: 2.3.7.11
| | * [[Sentry5]] – 5-tone haplotonic scale |
| Commas: 896/891, 1029/1024
| | * [[Sentry8]] – 8-tone albitonic scale |
| Sval name: 5&36
| | * [[Sentry11]] – 11-tone chromatic scale |
| Related temperament: [[xenharmonic/Gamelismic clan|Rodan]]
| |
|
| |
|
| POTE generator: ~8/7 = 234.381
| | == Hemif == |
| | {{See also| No-fives subgroup temperaments #Hemif }} |
|
| |
|
| Map: [<1 1 3 6|, <0 3 -1 -13|]
| | [[File:hemif_58edo.jpg|right|alt=hemif_58edo.jpg|Hemif in 58edo]] |
| EDOs: 5, 36, 41, 87, 128
| |
| Error: 2.925 cents
| |
|
| |
|
| [[image:radon_128edo.jpg]] | | Scales: |
| | * [[Hemif7]] – 7-tone haplotonic scale |
| | * [[Hemif10]] – 10-tone albitonic scale |
| | * [[Hemif17]] – 17-tone chromatic scale |
|
| |
|
| [[xenharmonic/radon5|Five note haplotonic scale]]
| | == Garibaldi == |
| [[xenharmonic/radon11|Eleven note albitonic scale]]
| | {{Main| Garibaldi temperament }} |
| [[xenharmonic/radon16|Sixteen note chromatic scale]]
| | {{See also| Schismatic family #Garibaldi }} |
|
| |
|
| =Myna=
| | [[File:garibaldi_94edo.png|right|alt=garibaldi_94edo.png|Garibaldi in 94edo]] |
| Group: 2.3.5.7
| |
| Commas: 126/125, 1728/1715
| |
| Val name: 4&27
| |
|
| |
|
| POTE generator: ~6/5 = 310.146
| | Scales: |
| | * [[Garibaldi12]] – 12-tone albitonic scale |
| | * [[Garibaldi17]] – 17-tone chromatic scale |
|
| |
|
| Map: [<1 9 9 8|, <0 -10 -9 -7|]
| | == Mabilic == |
| EDOs: 4, 27, 31, 58, 89
| | {{See also| No-threes subgroup temperaments #Mabilic }} |
| Error: 3.310 cents
| |
|
| |
|
| [[image:myna_89edo.jpg]] | | [[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]] |
|
| |
|
| [[xenharmonic/myna7|Seven note haplotonic scale]] | | Scales: |
| [[xenharmonic/myna11|Eleven note albitonic scale]] | | * [[Mabilic7]] – 7-tone haplotonic scale |
| [[xenharmonic/myna15|Fifteen note chromatic scale]] | | * [[Mabilic9]] – 9-tone albitonic scale |
| | * [[Mabilic16]] – 16-tone chromatic scale |
|
| |
|
| =Silver= | | == Indium == |
| Subgroup: 2.5.7.13.17 | | {{See also | Subgroup temperaments #Indium }} |
| Commas: 170/169, 640/637, 5525/5488
| |
| Sval name: 10&27
| |
|
| |
|
| POTE generator: ~13/8 = 842.711
| | [[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]] |
|
| |
|
| Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|]
| | Scales: |
| EDOs: 7, 10, 17, 27, 37, [[xenharmonic/47edo|47]], 84, 131, [[xenharmonic/487edo|487]]
| | * [[Indium8]] – 8-tone albitonic scale |
| Error: 3.437
| | * [[Indium17]] – 17-tone chromatic scale |
|
| |
|
| [[image:silver_487edo.jpg]] | | ; 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] |
|
| |
|
| [[xenharmonic/silver7|silver7]] -seven note [[xenharmonic/haplotonic scale|haplotonic scale]]
| | == Starlingtet == |
| [[xenharmonic/silver10|silver10]] - ten note [[xenharmonic/albitonic scale|albitonic scale]]
| | {{See also | Subgroup temperaments #Starlingtet }} |
| [[xenharmonic/silver17|silver17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]]
| |
|
| |
|
| =Mabila=
| | Scales: |
| Subgroup: 2.5.7
| | * [[Starlingtet4]] – 4-tone haplotonic scale |
| Comma: 1071875/1048576
| | * [[Starlingtet7]] – 7-tone albitonic scale |
| Sval name: 7&9
| | * [[Starlingtet11]] – 11-tone chromatic scale |
|
| |
|
| POTE generator: ~175/128 = 527.236
| | == Lovecraft == |
| | {{See also | No-threes subgroup temperaments #Lovecraft }} |
|
| |
|
| Map: [<1 1 5|, <0 3 -5|]
| | [[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]] |
| EDOs: 7, 9, 16, 25, 41, 66
| |
| Error: 3.560
| |
|
| |
|
| [[image:mabila_66edo.jpg]] | | Scales: |
| | * [[Lovecraft5]] – 5-tone haplotonic scale |
| | * [[Lovecraft9]] – 9-tone albitonic scale |
| | * [[Lovecraft13]] – 13-tone chromatic scale |
|
| |
|
| [[xenharmonic/mabila7|Seven note haplotonic scale]]
| | == Blackbirds == |
| [[xenharmonic/mabila9|Nine note albitonic scale]]
| | {{See also | No-threes subgroup temperaments #Blackbirds }} |
| [[xenharmonic/mabila16|Sixteen note chromatic scale]]
| |
|
| |
|
| =Meantone=
| | Scales: |
| Group: 2.3.5.7
| | * [[Blackbirds8]] – 8-tone albitonic scale |
| Commas: 81/80, 126/125
| | * [[Blackbirds12]] – 12-tone chromatic scale |
| Val name: 12&19
| | * [[Blackbirds16]] – 16-tone mega-chromatic scale |
|
| |
|
| POTE generator: 696.495
| | == Laz == |
| | {{See also | Subgroup temperaments #Laz }} |
|
| |
|
| Map: [<1 0 -4 -13|, <0 1 4 10|]
| | Scales: |
| EDOs: 5, 7, 12, 19, 31, 81, 112, 143
| | * [[Laz5]] – 5-tone haplotonic scale |
| Error: 3.585
| | * [[Laz9]] – 9-tone albitonic scale |
| | * [[Laz13]] – 13-tone chromatic scale |
|
| |
|
| [[image:meantone_31edo.jpg]]
| | == Myna == |
| | {{Main| Myna }} |
| | {{See also| Starling temperaments #Myna }} |
|
| |
|
| [[xenharmonic/meantone5|Five note haplotonic scale]] | | [[File:myna_89edo.jpg|right|alt=myna_89edo.jpg|Myna in 89edo]] |
| [[xenharmonic/meantone7|Seven note albitonic scale]]
| |
| [[xenharmonic/meantone12|Twelve note chromatic scale]]
| |
|
| |
|
| =Starlingtet=
| | Scales: |
| Group: 2.5/3.7/3
| | * [[Myna7]] – 7-tone haplotonic scale |
| Comma: 126/125
| | * [[Myna11]] – 11-tone albitonic scale |
| Svalname: 4&15
| | * [[Myna15]] – 15-tone chromatic scale |
| Related temperaments: starling; becomes myna
| |
| POTE generator: ~6/5 = 311.213
| |
|
| |
|
| Map: [<1 0 -1|, <0 1 3|]
| | == Greeley == |
| EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b
| | {{See also| Subgroup temperaments #Greeley }} |
| Error: 311.213
| |
|
| |
|
| [[xenharmonic/starlingtet4|Four note haplotonic scale]] | | [[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]] |
| [[xenharmonic/starlingtet7|Seven note albitonic scale]]
| |
| [[xenharmonic/starlingtet11|Eleven note chromatic scale]]
| |
|
| |
|
| =Indium=
| | Scales: |
| Subgroup: 2.5/3.7/3.11/3
| | * [[Greeley8]] – 8-tone albitonic scale |
| Commas: 3025/3024, 3125/3087
| | * [[Greeley15]] – 15-tone chromatic scale |
| Sval name: 8&33
| |
|
| |
|
| POTE generator: ~12/11 = 147.159
| | ; Music |
| | * ''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] |
|
| |
|
| Map: [<1 0 0 2|, <0 6 10 -1|]
| | == Ammon == |
| EDOs: 33, 41, 49, 57, 106, 204, 253
| | {{See also| Subgroup temperaments #Ammon }} |
| Error: 3.968 cents
| |
|
| |
|
| [[xenharmonic/indium8|Eight note albitonic scale]] | | [[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]] |
| [[xenharmonic/indium17|Seventeen note chromatic scale]]
| |
|
| |
|
| Music
| | Scales: |
| [[http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3|The Cry of Indium]] (in Indium 17) by [[@http://www.chrisvaisvil.com/|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=1532|details]] | | * [[Ammon8]] – 8-tone albitonic scale |
| | * [[Ammon13]] – 13-tone chromatic scale |
|
| |
|
| =Magic= | | == Mothwelltri == |
| Group: 2.3.5.7.11
| | {{See also| Subgroup temperaments #Mothwelltri }} |
| Commas: 100/99, 225/224, 245/243
| |
| Val name: 19&22
| |
|
| |
|
| POTE generator: ~5/4 = 380.696
| | Scales: |
| | * [[Mothwelltri5]] – 5-tone haplotonic scale |
| | * [[Mothwelltri9]] – 9-tone albitonic scale |
| | * [[Mothwelltri13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]
| | == Sulis == |
| EDOs: 19, 22, 41, 104, 145
| | {{See also| Subgroup temperaments #Sulis }} |
| Error: 4.489
| |
|
| |
|
| [[image:xenharmonic/magic_145edo.jpg]] | | Scales: |
| | * [[Sulis7]] – 7-tone haplotonic scale |
| | * [[Sulis10]] – 10-tone albitonic scale |
| | * [[Sulis13]] – 13-tone chromatic scale |
|
| |
|
| [[xenharmonic/magic7|Seven note haplotonic scale]]
| | == Skwares == |
| [[xenharmonic/magic10|Ten note albitonic scale]]
| | {{Main| Squares }} |
| [[xenharmonic/magic13|Thirteen note chromatic scale]]
| | {{See also| No-fives subgroup temperaments #Skwares }} |
| [[xenharmonic/magic16|Sixteen note mega chromatic scale]]
| |
|
| |
|
| =Hemif=
| | [[File:skwares_206edo.png|right|alt=skwares_206edo.png|Skwares in 206edo]] |
| Subgroup: 2.3.7.11.13
| |
| Commas: 144/143, 243/242, 364/363
| |
| Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]]
| |
|
| |
|
| POTE generator: ~11/9 = 351.691
| | Scales: |
| | * [[Skwares8]] – 8-tone albitonic scale |
| | * [[Skwares11]] – 11-tone mega-albitonic scale |
| | * [[Skwares14]] – 14-tone chromatic scale |
|
| |
|
| Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]
| | == Orwell == |
| EDOs: 7, 10, 17, 24, 41, 58
| | {{Main| Orwell }} |
| Error: 4.867 cents
| | {{See also| Semicomma family #Orwell }} |
|
| |
|
| [[image:hemif_58edo.jpg]] | | [[File:orwell_84edo.png|right|alt=orwell_84edo.png|Orwell in 84edo]] |
|
| |
|
| [[xenharmonic/hemif7|Seven note haplotonic scale]] | | Scales: |
| [[xenharmonic/hemif10|Ten note albitonic scale]] | | * [[Orwell5]] – 5-tone haplotonic scale |
| [[xenharmonic/hemif17|Seventeen note chromatic scale]] | | * [[Orwell9]] – 9-tone albitonic scale |
| | * [[Orwell13]] – 13-tone chromatic scale |
|
| |
|
| =Skwares= | | == Magicaltet == |
| Subgroup: 2.3.7.11 | | {{See also| Subgroup temperaments #Magicaltet }} |
| Commas: 99/98, 243/242
| |
| Related temperament: [[xenharmonic/Meantone family|squares]]
| |
|
| |
|
| POTE generator: ~9/7 = 425.244
| | Scales: |
| | * [[Magicaltet7]] – 7-tone albitonic scale |
| | * [[Magicaltet11]] – 11-tone chromatic scale |
| | * [[Magicaltet15]] – 15-tone mega-chromatic scale |
|
| |
|
| Map: [<1 3 6 7|, <0 -4 -9 -10|]
| | == Magic == |
| EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206
| | {{Main| Magic }} |
| Error: 4.942 cents
| | {{See also| Magic family #Magic }} |
|
| |
|
| [[xenharmonic/skwares8|Eight note albitonic scale]] | | [[File:magic_145edo.jpg|right|alt=magic_145edo.jpg|Magic in 145edo]] |
| [[xenharmonic/skwares11|Eleven note mega albitonic scale]]
| |
| [[xenharmonic/skwares14|Fourteen note chromatic scale]]
| |
|
| |
|
| =Sensi=
| | Scales: |
| Group: 2.3.5.7
| | * [[Magic7]] – 7-tone haplotonic scale |
| Commas: 126/126, 245/243
| | * [[Magic10]] – 10-tone albitonic scale |
| Val name: 19&27
| | * [[Magic13]] – 13-tone chromatic scale |
| | * [[Magic16]] – 16-tone mega-chromatic scale |
|
| |
|
| POTE generator: ~9/7 = 443.383
| | == Kiribati == |
| | {{See also| Subgroup temperaments #Kiribati }} |
|
| |
|
| Map: [<1 6 8 11|, <0 -7 -9 -13|]
| | Scales: |
| EDOs: 5, 8, 11, 19, 27, 46
| | * [[Kiribati13]] – 13-tone chromatic scale |
| Error: 5.019
| | * [[Kiribati14]] – 14-tone chromatic scale |
|
| |
|
| [[image:xenharmonic/sensi_46edo.jpg]]
| | == Score == |
| | {{See also|No-threes subgroup temperaments #Score }} |
|
| |
|
| [[xenharmonic/sensi5|Five note haplotonic scale]] | | [[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]] |
| [[xenharmonic/sensi8|Eight note albitonic scale]]
| |
| [[xenharmonic/sensi11|Eleven note mega albitonic scale]]
| |
| [[xenharmonic/sensi19|Nineteen note chromatic scale]]
| |
|
| |
|
| =Greeley=
| | Scales: |
| Subgroup: 2.5/3.7/3.11/3
| | * [[Score5]] – 5-tone haplotonic scale |
| Commas: 121/120, 126/125
| | * [[Score7]] – 7-tone albitonic scale |
| | * [[Score9]] – 9-tone mega-albitonic scale |
| | * [[Score11]] – 11-tone chromatic scale |
|
| |
|
| POTE generator: ~11/10 = 156.055
| | == Sensi == |
| | {{Main| Sensi }} |
| | {{See also| Sensipent family #Sensi }} |
|
| |
|
| Map: [<1 1 2 2|, <0 -2 -6 -1|]
| | [[File:sensi_46edo.jpg|right|alt=sensi_46edo.jpg|Sensi in 46edo]] |
| EDOs: 8, 15, 23, 77, 100
| |
| Error: 5.404 cents
| |
|
| |
|
| [[xenharmonic/greeley8|Eight note albitonic scale]] | | Scales: |
| [[xenharmonic/greeley15|Fifteen note chromatic scale]] | | * [[Sensi5]] – 5-tone haplotonic scale |
| | * [[Sensi8]] – 8-tone albitonic scale |
| | * [[Sensi11]] – 11-tone mega-albitonic scale |
| | * [[Sensi19]] – 19-tone chromatic scale |
|
| |
|
| ==Music== | | === Sensation === |
| [[http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3|A Greeley Steals Halloween]] by [[@http://chrisvaisvil.com/?p=1485|Chris Vaisvil]] in Greeley 15
| | {{Main| Sensi }} |
| | {{See also| Sensipent family #Sensi }} |
|
| |
|
| =Semidim=
| | Scales: |
| Subgroup: 2.5/3.7/3.11/3.13/3
| | * [[Sensi5]] – 5-tone haplotonic scale |
| Commas: 121/120, 169/168, 275/273
| | * [[Sensi8]] – 8-tone albitonic scale |
| Sval name: 8&29
| | * [[Sensi11]] – 11-tone mega-albitonic scale |
| | * [[Sensi19]] – 19-tone chromatic scale |
|
| |
|
| POTE generator: ~13/10 = 453.190
| | == Meantone == |
| | {{Main| Meantone }} |
| | {{See also| Meantone family #Meantone }} |
|
| |
|
| Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]
| | [[File:meantone_31edo.jpg|right|alt=meantone_31edo.jpg|Meantone in 31edo]] |
| EDOs: 5, 8, 13, 21, 29, 37, 45
| |
| Error: 5.433 cents
| |
|
| |
|
| [[xenharmonic/semidim8|Eight note albitonic scale]] | | Scales: |
| [[xenharmonic/semidim13|Thirteen note chromatic scale]] | | * [[Meantone5]] – 5-tone haplotonic scale |
| | * [[Meantone7]] – 7-tone albitonic scale |
| | * [[Meantone12]] – 12-tone chromatic scale |
|
| |
|
| =Orwell= | | == Mohaha == |
| Group: 2.3.5.7.11
| | {{See also| Rastmic clan #Mohaha }} |
| Commas: 99/98, 121/120, 176/175
| |
| Val name: 9&22
| |
|
| |
|
| POTE generator: ~7/6 = 271.426
| | [[File:mohaha_131edo.png|right|alt=mohaha_131edo.png|Mohaha in 131edo]] |
|
| |
|
| Map: [<1 0 3 1 3|, <0 7 -3 8 2|]
| | Scales: |
| EDOs: 9, 22, 31, 53, 84
| | * [[Mohaha7]] – 7-tone albitonic scale |
| Error: 5.584
| | * [[Mohaha10]] – 10-tone chromatic scale |
|
| |
|
| [[image:xenharmonic/orwell_84edo.png]] | | Music: |
| | ; [[Billy Stiltner]] |
| | * [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 ''Mohaha10ping2'']{{dead link}} |
|
| |
|
| [[xenharmonic/orwell5|Five note haplotonic scale]]
| | === Mohoho === |
| [[xenharmonic/orwell9|Nine note albitonic scale]]
| | {{See also| Rastmic clan #Mohoho }} |
| [[xenharmonic/orwell13|Thirteen note chromatic scale]]
| |
|
| |
|
| =Magicaltet= | | == Joan == |
| Group: 2.5/3.7.11
| | {{See also| Subgroup temperaments #Joan }} |
| Commas: 100/99, 385/384
| |
| Related temperaments: 4&7&15, magic
| |
|
| |
|
| POTE generator: ~6/5 = 319.424
| | Scales: |
| | * [[Joan5]] – 5-tone haplotonic scale |
| | * [[Joan7]] – 7-tone albitonic scale |
| | * [[Joan9]] – 9-tone mega-albitonic scale |
| | * [[Joan11]] – 11-tone chromatic scale |
|
| |
|
| Map: [<1 0 5 2|, <0 1 -3 2|]
| | == Tutone == |
| EDOs: 11, 15, 79cd, 94cd, 109cd, 124cd, 139cd
| | {{See also| Hemimean clan #Tutone }} |
| Error: 5.720
| |
|
| |
|
| [[xenharmonic/magicaltet7|Seven note albitonic scale]] | | [[File:tutone_99edo.png|right|alt=tutone_99edo.png|Tutone in 99edo]] |
| [[xenharmonic/magicaltet11|Eleven note chromatic scale]]
| |
| [[xenharmonic/magicaltet15|Fifteen note mega scale]]
| |
|
| |
|
| =Mothwelltri=
| | Scales: |
| Group: 2.7/3.11
| | * [[Tutone6]] – 6-tone haplotonic scale |
| Comma: 99/98
| | * [[Tutone7]] – 7-tone albitonic scale |
| Svalname: 1&4
| | * [[Tutone13]] – 13-tone chromatic scale |
| Related temperament: Orwell
| |
|
| |
|
| POTE generator:~7/6 = 268.508
| | == Stacks == |
| | {{See also|Subgroup temperaments #Stacks (a.k.a. 2magic) }} |
|
| |
|
| Map: [<1 0 1|, <0 1 2|]
| | Scales: |
| EDOs: 9, 40, 49c, 58c, 67c, 76c
| | * [[Stacks5]] – 5-tone haplotonic scale |
| Error: 6.119 cents
| | * [[Stacks8]] – 8-tone albitonic scale |
| | * [[Stacks11]] – 11-tone chromatic scale |
| | * [[Stacks19]] – 19-tone mega-chromatic scale |
|
| |
|
| [[xenharmonic/mothwelltri5|Five note haplotonic scale]]
| | == Bleu == |
| [[xenharmonic/mothwelltri9|Nine note albitonic scale]]
| | {{See also| No-fives subgroup temperaments #Bleu }} |
| [[xenharmonic/mothwelltri13|Thirteen note chromatic scale]]
| |
|
| |
|
| =Lovecraft=
| | Scales: |
| Group: 2.11.13
| | * [[Bleu8]] – 8-tone haplotonic scale |
| | * [[Bleu9]] – 9-tone albitonic scale |
| | * [[Bleu17]] – 17-tone chromatic scale |
|
| |
|
| POTE generator: ~13/11 = 279.318
| | == Sephiroth == |
| | {{See also| No-threes subgroup temperaments #Sephiroth }} |
|
| |
|
| Map: [<1 1 0|, <0 2 3|]
| | Scales: |
| EDOS: 13, 30, 43, 73, 116b
| | * [[Sephiroth7]] – 7-tone haplotonic scale |
| Error: 6.026
| | * [[Sephiroth10]] – 10-tone albitonic scale |
| | * [[Sephiroth13]] – 13-tone chromatic scale |
| | * [[Sephiroth16]] – 16-tone mega-chromatic scale |
|
| |
|
| [[xenharmonic/lovecraft5|Five note haplotonic scale]]
| | == Archy == |
| [[xenharmonic/lovecraft9|Nine note albitonic scale]]
| | {{Main| Superpyth }} |
| [[xenharmonic/lovecraft13|Thirteen note chromatic scale]]
| | {{See also| Archytas clan #Archy }} |
|
| |
|
| =Bleu=
| | Scales: |
| Group: 2.3.7.11.13
| | * [[Archy5]] – 5-tone haplotonic scale |
| Commas: 78/77, 99/98, 144/143
| | * [[Archy7]] – 7-tone albitonic scale |
| Sval name: 9&17
| | * [[Archy12]] – 12-tone chromatic scale |
|
| |
|
| POTE generator: ~13/12 = 139.990
| | === Supra === |
| | {{Main| Superpyth }} |
| | {{See also| Archytas clan #Supra }} |
|
| |
|
| Map: [<1 1 2 3 3|, <0 5 7 4 6|]
| | [[File:supra_56edo.png|right|alt=supra_56edo.png|Supra in 56edo]] |
| EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]]
| |
| Error: 6.361
| |
|
| |
|
| [[xenharmonic/bleu8|bleu8]] - Eight note [[xenharmonic/haplotonic scale|haplotonic scale]]
| | Scales: |
| [[xenharmonic/bleu9|bleu9]] - Nine note [[xenharmonic/albitonic scale|albitonic scale]] | | * [[Supra7]] – 7-tone [[albitonic scale]] |
| [[xenharmonic/bleu17|bleu17]] - Seventeen note [[xenharmonic/chromatic scale|chromatic scale]] | | * [[Supra12]] – 12-tone [[chromatic scale]] |
|
| |
|
| =Mohaha= | | === Supraphon === |
| Subgroup: 2.3.5.11
| | {{Main| Superpyth }} |
| Commas: 81/80, 121/120
| | {{See also| Archytas clan #Supraphon }} |
| Related temperament: [[xenharmonic/Meantone family|mohajira]]
| |
|
| |
|
| POTE generator: ~11/9 = 348.094
| | == Suhajira == |
| | {{See also| Archytas clan #Suhajira }} |
|
| |
|
| Map: [<1 1 0 2|, <0 2 8 5|]
| | Scales: |
| EDOs: 24, 31, 69d, 100d, 131bd
| | * [[Suhajira7]] – 7-tone haplotonic scale |
| Error: 6.733 cents
| | * [[Suhajira10]] – 10-tone albitonic scale |
| | * [[Suhajira17]] – 17-tone chromatic scale |
|
| |
|
| [[xenharmonic/mohaha7|Seven note albitonic scale]]
| | == Machine == |
| [[xenharmonic/mohaha10|Ten note chromatic scale]]
| | {{See also| Subgroup temperaments #Machine}} |
|
| |
|
| ==Mohoho==
| | [[File:machine_28edo.png|right|alt=machine_28edo.png|Machine in 28edo]] |
| Subgroup: 2.3.5.11.13
| |
| Commas: 66/65, 81/80, 121/120
| |
|
| |
|
| POTE generator: ~11/9 = 348.916
| | Scales: |
| | * [[Machine5]] – 5-tone haplotonic scale |
| | * [[Machine6]] – 6-tone albitonic scale |
| | * [[Machine11]] – 11-tone chromatic scale |
|
| |
|
| Map: [<1 1 0 2 4|, <0 2 8 5 -1|]
| | == Deutone == |
| EDOs: 17c, 24, 31, 55, 86de, 141cde
| | {{See also| Hemimean clan #Deutone }} |
| Error: 9.556 cents
| |
|
| |
|
| =Tutone=
| | [[File:deutone_44edo.png|right|alt=deutone_44edo.png|Deutone in 44edo]] |
| Subgroup: 2.9.5.7.11
| |
| Commas: 81/80, 99/98, 126/125
| |
| Related temperament: [[xenharmonic/Meantone family|meantone]]
| |
|
| |
|
| POTE generator: ~9/8 = 193.937
| | Scales: |
| | * [[Deutone6]] – 6-tone haplotonic scale |
| | * [[Deutone7]] – 7-tone albitonic scale |
| | * [[Deutone13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]
| | == Negra == |
| EDOs: 25, 31, 68b, 99b
| | {{Main| Negri }} |
| Error: 7.047 cents
| | {{See also| Marvel temperaments #Negri }} |
|
| |
|
| [[xenharmonic/tutone6|Six note haplotonic scale]]
| | == Porkypine == |
| [[xenharmonic/tutone7|Seven note albitonic scale]]
| | {{Main| Porcupine }} |
| [[xenharmonic/tutone13|Thirteen note chromatic scale]]
| | {{See also| Porcupine family #Porcupine }} |
|
| |
|
| =Leantone=
| | Scales: |
| Subgroup: 2.9.5.7.11
| | * [[Porkypine7]] – 7-tone haplotonic scale |
| Commas: 45/44, 56/55, 81/80
| | * [[Porkypine8]] – 8-tone albitonic scale |
| Related temperament: [[meanenneadecal]]
| | * [[Porkypine15]] – 15-tone chromatic scale |
|
| |
|
| POTE generator: ~9/8 = 192.500
| | == Skateboard == |
| | {{See also| Subgroup temperaments #Skateboard }} |
|
| |
|
| Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
| | Scales: |
| EDOs: 6, 7, 13, 19, 25, 31, 56, 81
| | * [[Skateboard7]] – 7-tone haplotonic scale |
| Error: 20.338 cents
| | * [[Skateboard11]] – 11-tone albitonic scale |
| | * [[Skateboard15]] – 15-tone chromatic scale |
|
| |
|
| [[xenharmonic/leantone6|Six note haplotonic scale]]
| | == Augment == |
| [[xenharmonic/leantone7|Seven note albitonic scale]]
| | {{See also| No-threes subgroup temperaments #Augment }} |
| [[xenharmonic/leantone13|Thirteen note chromatic scale]]
| |
|
| |
|
| =Score=
| | [[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]] |
| Subgroup: 2.7.11.13
| |
| Commas: 343/338, 847/832
| |
|
| |
|
| POTE generator: ~11/8 = 540.099
| | Scales: |
| | * [[Augment6]] – 6-tone haplotonic scale |
| | * [[Augment9]] – 9-tone albitonic scale |
| | * [[Augment12]] – 12-tone chromatic scale |
|
| |
|
| Map: [<1 1 3 1|, <0 4 1 6|]
| | == Semaphore == |
| EDOs: 5, 7, 9, 11, 20
| | {{Main| Semaphore and godzilla }} |
| Error: 8.052 cents
| | {{See also| Semaphoresmic clan #Semaphore }} |
|
| |
|
| [[image:xenharmonic/score_20edo.jpg]] | | [[File:semaphore_24edo.png|right|alt=semaphore_24edo.png|Semaphore in 24edo]] |
|
| |
|
| [[xenharmonic/score5|Five note haplotonic scale]] | | Scales: |
| [[xenharmonic/score7|Seven note albitonic scale]] | | * [[Semaphore5]] – 5-tone haplotonic scale |
| [[xenharmonic/score9|Nine note mega albitonic scale]] | | * [[Semaphore9]] – 9-tone albitonic scale |
| [[xenharmonic/score11|Eleven note chromatic scale]]
| | * [[Semaphore14]] – 14-tone chromatic scale |
|
| |
|
| =Supra= | | == Kryptonite == |
| Subgroup: 2.3.7.11 | | {{See also| Subgroup temperaments #Kryptonite }} |
| Commas: 64/63, 99/98
| |
| Related temperament: [[xenharmonic/suprapyth|suprapyth]]
| |
|
| |
|
| POTE generator: ~3/2 = 707.192
| | Scales: |
| | * [[Kryptonite9]] – 9-tone albitonic scale |
| | * [[Kryptonite10]] – 10-tone albitonic scale |
| | * [[Kryptonite19]] – 19-tone mega-chromatic scale |
|
| |
|
| Map: [<1 0 6 13|, <0 1 -2 -6|]
| | == Oregon == |
| EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c
| | {{See also| Orgonia #Oregon }} |
| Error: 9.795 cents
| |
|
| |
|
| [[xenharmonic/supra7|Seven note albitonic scale]] | | Scales: |
| [[xenharmonic/supra12|Twelve note chromatic scale]] | | * [[Oregon7]] – 7-tone haplotonic scale |
| | * [[Oregon11]] – 11-tone albitonic scale |
| | * [[Oregon15]] – 15-tone chromatic scale |
|
| |
|
| ==Supraphon== | | == Antikythera == |
| Subgroup: 2.3.7.11.13
| | {{See also| Jubilismic clan #Antikythera }} |
| Commas: 64/63, 78/77, 99/98
| |
|
| |
|
| POTE generator: ~3/2 = 706.137
| | [[File:antikythera_28edo.png|right|alt=antikythera_28edo.png|Antikythera in 28edo]] |
|
| |
|
| Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]
| | Scales: |
| EDOs: 5, 7, 12, 17
| | * [[Antikythera6]] – 6-tone haplotonic scale |
| Error: 10.534 cents
| | * [[Antikythera10]] – 10-tone albitonic scale |
| | * [[Antikythera16]] – 16-tone chromatic scale |
|
| |
|
| ==Machine== | | == Glacial == |
| Subgroup: 2.9.7.11 | | {{See also| Subgroup temperaments #Glacial }} |
| Commas: 64/63, 99/98
| |
|
| |
|
| POTE generator: ~9/8 = 214.384
| | Scales: |
| | * [[Glacial6]] – 6-tone haplotonic scale |
| | * [[Glacial7]] – 7-tone albitonic scale |
| | * [[Glacial13]] – 13-tone chromatic scale |
|
| |
|
| Map: [<1 0 6 13|, <0 1 -1 -3|]
| | == Leantone == |
| EDOs: 5, 6, 11, 17, 28
| | {{See also| Hemimean clan #Leantone }} |
| Error: 10.100 cents
| |
|
| |
|
| [[xenharmonic/machine5|Five note haplotonic scale]] | | [[File:leantone_81edo.png|right|alt=leantone_81edo.png|Leantone in 81edo]] |
| [[xenharmonic/machine6|Six note albitonic scale]]
| |
| [[xenharmonic/machine11|Eleven note chromatic scale]]
| |
|
| |
|
| =Antikythera=
| | Scales: |
| Subgroup: 2.9.5.7
| | * [[Leantone6]] – 6-tone haplotonic scale |
| Commas: 50/49, 64/63
| | * [[Leantone7]] – 7-tone albitonic scale |
| Related temperament: [[xenharmonic/pajara|pajara]]
| | * [[Leantone13]] – 13-tone chromatic scale |
|
| |
|
| POTE generator: ~8/7 = 214.095
| | == Notes == |
|
| |
|
| Map: [<2 0 11 12|, <0 1 -1 -1|]
| | [[Category:Lists of scales]] |
| EDOS: 4, 6, 10, 16, 22, 28
| | [[Category:Tempered scales| ]] |
| Error: 11.508 cents
| | [[Category:Listen]] |
| | [[Category:Rank 2]] |
|
| |
|
| [[xenharmonic/antikythera6|Six note haplotonic scale]]
| | {{todo|cleanup}} |
| [[xenharmonic/antikythera10|Ten note albitonic scale]]
| |
| [[xenharmonic/antikythera16|Sixteen note chromatic scale]]
| |
| | |
| =Deutone=
| |
| Subgroup: 2.9.5.7.13
| |
| Commas: 65/64, 81/80, 91/90
| |
| Related temperament: [[xenharmonic/Meantone family|meanpop]]
| |
| | |
| POTE generator: ~9/8 = 191.059
| |
| | |
| Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|]
| |
| EDOs: 6, 7, 13, 19, 25, 44, 69
| |
| Error: 12.145 cents
| |
| | |
| [[xenharmonic/deutone6|Six note haplotonic scale]]
| |
| [[xenharmonic/deutone7|seven note albitonic scale]]
| |
| [[xenharmonic/deutone13|Thirteen note chromatic scale]]
| |
| | |
| =Semiphore=
| |
| Subgroup: 2.3.7
| |
| Comma: 49/48
| |
| | |
| POTE generator: ~7/6 = 250.385
| |
| | |
| Map: [<1 0 2|, <0 2 1|]
| |
| EDOs: 5, 9, 14, 19, 24
| |
| Error: 12.428
| |
| | |
| [[xenharmonic/semiphore5|Five note haplotonic scale]]
| |
| [[xenharmonic/semiphore9|Nine note albitonic scale]]
| |
| [[xenharmonic/semiphore14|Fourteen note chromatic scale]]
| |
| | |
| =Augment=
| |
| Subgroup: 2.5.7.11
| |
| Commas: 56/55, 128/125
| |
| Related temperament: [[xenharmonic/Augmented family|augmented]]
| |
| | |
| POTE generator: ~8/7 = 228.275
| |
| | |
| Map: [<3 7 0 2|, <0 0 1 1|]
| |
| EDOs: 3, 6, 9, 15, 21
| |
| Error: 12.830 cents
| |
| | |
| [[xenharmonic/augment6|Six note haplotonic scale]]
| |
| [[xenharmonic/augment9|Nine note albitonic scale]]
| |
| [[xenharmonic/augment12|Twelve note chromatic scale]]</pre></div>
| |
| <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:107:&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:107 --><!-- ws:start:WikiTextTocRule:108: --><a href="#Definitions">Definitions</a><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --> | <a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --> | <a href="#Orgone">Orgone</a><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --> | <a href="#Neutraltri">Neutraltri</a><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --> | <a href="#Slendric">Slendric</a><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --> | <a href="#Marveltwintri">Marveltwintri</a><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --> | <a href="#Marveltri">Marveltri</a><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --> | <a href="#Guanyintet">Guanyintet</a><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --> | <a href="#Photia">Photia</a><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --> | <a href="#Shoe">Shoe</a><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --> | <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --> | <a href="#Mabila">Mabila</a><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --> | <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --> | <a href="#Starlingtet">Starlingtet</a><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --> | <a href="#Sensi">Sensi</a><!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --> | <a href="#Magicaltet">Magicaltet</a><!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --> | <a href="#Mothwelltri">Mothwelltri</a><!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --> | <a href="#Lovecraft">Lovecraft</a><!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --> | <a href="#Bleu">Bleu</a><!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --> | <a href="#Leantone">Leantone</a><!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --> | <a href="#Antikythera">Antikythera</a><!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --> | <a href="#Deutone">Deutone</a><!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --> | <a href="#Semiphore">Semiphore</a><!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: -->
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| <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/11052942?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;11052942&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js">
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| </script><!-- ws:end:WikiTextMediaRule:0 --><br />
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| <hr />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Definitions"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definitions</h1>
| |
| By a <em>chromatic pair</em> is meant a pair of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> in some rank two temperament (which may often be a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/Target%20tunings">tuning target</a> the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:3 -->Terrain</h1>
| |
| Subgroup: 2.9/5.9/7<br />
| |
| Commas: 250047/250000<br />
| |
| Sval name: 6&amp;21<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Minortonic%20family#Domain">domain</a><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/POTE%20generator">POTE generator</a>: ~10/9 = 182.462<br />
| |
| <br />
| |
| Map: [&lt;3 0 -4|, &lt;0 1 2|]<br />
| |
| EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558<br />
| |
| Error: 0.0443 cents<br />
| |
| <br />
| |
| Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic.<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain9">Nine note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain15">Fifteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Orgone"></a><!-- ws:end:WikiTextHeadingRule:5 -->Orgone</h1>
| |
| Subgroup: 2.7.11<br />
| |
| Commas: 65536/65219<br />
| |
| Svals: 4&amp;7<br />
| |
| <br />
| |
| POTE generator: ~77/64 = 323.372<br />
| |
| <br />
| |
| Map: [&lt;1 2 4|, &lt;0 3, -2|]<br />
| |
| EDOs: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308<br />
| |
| Error: 0.7313<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:163:&lt;img src=&quot;/file/view/orgone_308edo.jpg/270849182/orgone_308edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/orgone_308edo.jpg/270849182/orgone_308edo.jpg" alt="orgone_308edo.jpg" title="orgone_308edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:163 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orgone7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orgone11">Eleven note chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orgone15">Fifteen note mega chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:7 -->Bridgetown</h1>
| |
| Subgroup: 2.3.11/5.13/5<br />
| |
| Commas: 352/351, 676/675<br />
| |
| Sval name: 5&amp;24<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Archipelago">barabados</a><br />
| |
| <br />
| |
| POTE generator: ~15/13 = 248.285<br />
| |
| <br />
| |
| Map: [&lt;1 0 -6 -1|, &lt;0 2 9 3|]<br />
| |
| EDOs: 5, 9, 14, 19, 24, 29<br />
| |
| Error: 0.8996 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown9">Nine note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown14">Fourteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="Bridgetown-Music"></a><!-- ws:end:WikiTextHeadingRule:9 -->Music</h2>
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3" rel="nofollow">Paint in the Water 29</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Igliashon%20Jones">Igliashon Jones</a><br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3" rel="nofollow">Route 14 in Bridgetown</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chris%20Vaisvil">Chris Vaisvil</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc5"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:11 -->Cata</h1>
| |
| Subgroup: 2.3.5.13<br />
| |
| Commas: 325/324, 625/624<br />
| |
| Sval name: 15&amp;19<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kleismic%20family">catakleismic</a><br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.076<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 0|, &lt;0 6 5 14|]<br />
| |
| EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd<br />
| |
| Error: 0.9355 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:164:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/cata_246edo2.jpg/270809448/cata_246edo2.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/cata_246edo2.jpg/270809448/cata_246edo2.jpg" alt="cata_246edo2.jpg" title="cata_246edo2.jpg" /><!-- ws:end:WikiTextLocalImageRule:164 --><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cata7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cata11">Eleven note mega albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cata15">Fifteen note chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cata19">Nineteen note mega chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="Neutraltri"></a><!-- ws:end:WikiTextHeadingRule:13 -->Neutraltri</h1>
| |
| Subgroup: 2.3.11<br />
| |
| Commas: 243/242<br />
| |
| Svalname: 7&amp;17<br />
| |
| <br />
| |
| POTE generator: ~11/9 = 350.525<br />
| |
| <br />
| |
| Map: [&lt;1 1 2|, &lt;0 2 5|]<br />
| |
| EDOs: 7, 17, 24, 65, 89, 202, 291, 380<br />
| |
| Error: 1.007<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltri7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltri10">Ten note chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltri17">Seventeen note mega chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc7"><a name="Tridec"></a><!-- ws:end:WikiTextHeadingRule:15 -->Tridec</h1>
| |
| Subgroup: 2.7/5.11/5.13/5<br />
| |
| Commas: 847/845, 1001/1000<br />
| |
| Sval name: 5&amp;8<br />
| |
| <br />
| |
| POTE generator: ~13/10 = 454.461<br />
| |
| <br />
| |
| Map: [&lt;1 2 0 1|, &lt;0 -4 3 1|]<br />
| |
| EDOs: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c<br />
| |
| Error: 1.057<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tridec8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tridec13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:17 -->Pepperoni</h1>
| |
| Subgroup: 2.3.11/7.13/7<br />
| |
| Commas: 352/351, 364/363<br />
| |
| Sval name: 5&amp;12<br />
| |
| Related temperament: The <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Peppermint-24">Pepper fifth</a>, which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 704.052<br />
| |
| <br />
| |
| Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]<br />
| |
| EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br />
| |
| Error: 1.298 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/pepperoni7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/pepperoni12">Twelve note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc9"><a name="Slendric"></a><!-- ws:end:WikiTextHeadingRule:19 -->Slendric</h1>
| |
| Subgroup: 2.3.7<br />
| |
| Comma: 1029/1024<br />
| |
| Sval name: 5&amp;21<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 233.688<br />
| |
| <br />
| |
| Map: [&lt;1 1 3|, &lt;0 3 -1|]<br />
| |
| EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190<br />
| |
| Error: 1.109 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:165:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/slendric_190edo.jpg/270813524/slendric_190edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/slendric_190edo.jpg/270813524/slendric_190edo.jpg" alt="slendric_190edo.jpg" title="slendric_190edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:165 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/slendric5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/slendric6">Six note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/slendric11">Eleven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/slendric16">Sixteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:21:&lt;h2&gt; --><h2 id="toc10"><a name="Slendric-Music"></a><!-- ws:end:WikiTextHeadingRule:21 -->Music</h2>
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-the-11th-slendric-fanfare.mp3" rel="nofollow">The 11th Slendric Fanfare</a><br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3" rel="nofollow">16 Slendric Virgins</a><br />
| |
| by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chris%20Vaisvil">Chris Vaisvil</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:23:&lt;h1&gt; --><h1 id="toc11"><a name="Marveltwintri"></a><!-- ws:end:WikiTextHeadingRule:23 -->Marveltwintri</h1>
| |
| Subgroup: 2.5/3.13/9<br />
| |
| <br />
| |
| POTE generator: ~6/5 = <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:25:&lt;h1&gt; --><h1 id="toc12"><a name="Nestoria"></a><!-- ws:end:WikiTextHeadingRule:25 -->Nestoria</h1>
| |
| Subgroup: 2.3.5.19<br />
| |
| Commas: 361/360, 513/512<br />
| |
| Sval name: 12&amp;29<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">schismatic</a><br />
| |
| <br />
| |
| POTE generator: ~3/2 = 701.746<br />
| |
| <br />
| |
| Map: [&lt;1 0 15 9|, &lt;0 1 -8 -3|]<br />
| |
| EDOs: 7, 12, 17, 29, 41, 53, 118, 171<br />
| |
| Error: 1.819 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nestoria7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nestoria12">Twelve note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:27:&lt;h1&gt; --><h1 id="toc13"><a name="Marveltri"></a><!-- ws:end:WikiTextHeadingRule:27 -->Marveltri</h1>
| |
| Subgroup: 2.5.9/7<br />
| |
| Comma: 225/224<br />
| |
| Sval name: 3&amp;13<br />
| |
| Related temperaments: marvel, 22&amp;47, magic<br />
| |
| <br />
| |
| POTE generator: ~5/4 = 382.618<br />
| |
| <br />
| |
| Map: [&lt;1 0 5|, &lt;0 1 -2|]<br />
| |
| EDOs: 12, 13, 16, 19, 22, 47, 69<br />
| |
| Error: 2.043 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltri7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltri10">Ten note chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltri13">Thirteen note mega chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:29:&lt;h1&gt; --><h1 id="toc14"><a name="Guanyintet"></a><!-- ws:end:WikiTextHeadingRule:29 -->Guanyintet</h1>
| |
| Subgroup: 2.5.7/3.11/3<br />
| |
| Commas: 176/175, 540/539<br />
| |
| Svalname: 4&amp;9<br />
| |
| Related temperaments: guanyin, orwell<br />
| |
| <br />
| |
| POTE generator: ~7/6 = 269.619<br />
| |
| <br />
| |
| Map: [&lt;1 0 2 -2|, &lt;0 3 -1 5|]<br />
| |
| EDOs: 9, 31, 40, 49, 89, 227bc, 316bcd<br />
| |
| Error: 2.533 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/guanyintet5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/guanyintet9">Nine note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/guanyintet13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:31:&lt;h1&gt; --><h1 id="toc15"><a name="Photia"></a><!-- ws:end:WikiTextHeadingRule:31 -->Photia</h1>
| |
| Subgroup: 2.3.5.17.19<br />
| |
| Commas: 171/170, 256/255, 324/323<br />
| |
| Sval name: 12&amp;41<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">schismatic</a><br />
| |
| <br />
| |
| POTE generator: ~3/2 = 701.470<br />
| |
| <br />
| |
| Map: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]<br />
| |
| EDOs: 7, 12, 17, 29, 41, 53, 65<br />
| |
| Error: 3.457 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/photia7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/photia12">Twelve note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:33:&lt;h1&gt; --><h1 id="toc16"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:33 -->Huntington</h1>
| |
| Subgroup: 2.5.7.13<br />
| |
| Commas: 640/637, 10985/10976<br />
| |
| Sval name: 10&amp;27<br />
| |
| <br />
| |
| POTE generator: ~16/13 = 357.002<br />
| |
| <br />
| |
| Map: [&lt;1 5 4 4|, &lt;0 -9 -4 -1|]<br />
| |
| EDOs: 7, 10, 17, 27, 37, 84, 121, 400<br />
| |
| Error: 2.1001 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:166:&lt;img src=&quot;/file/view/huntington_400edo.jpg/271195682/huntington_400edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/huntington_400edo.jpg/271195682/huntington_400edo.jpg" alt="huntington_400edo.jpg" title="huntington_400edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:166 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/huntington7">Seven note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/huntington10">Ten note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/huntington17">Seventeen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:35:&lt;h1&gt; --><h1 id="toc17"><a name="Shoe"></a><!-- ws:end:WikiTextHeadingRule:35 -->Shoe</h1>
| |
| Subgroup: 2.5.7.11.13<br />
| |
| Commas: 176/175, 640/637, 847/845<br />
| |
| Sval name: 16&amp;21<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 227.108<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 1 2|, &lt;0 7 -1 13 9|]<br />
| |
| EDOs: 16, 21, 37<br />
| |
| Error: 2.488<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:167:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/shoe_37edo.jpg/270828948/shoe_37edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/shoe_37edo.jpg/270828948/shoe_37edo.jpg" alt="shoe_37edo.jpg" title="shoe_37edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:167 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/shoe5">shoe5</a> - five note mini <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/shoe6">shoe6</a> - six note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/shoe11">shoe11</a> - eleven note note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/shoe16">shoe16</a> - sixteen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:37:&lt;h1&gt; --><h1 id="toc18"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:37 -->Roulette</h1>
| |
| Subgroup: 2.5.7.11.13<br />
| |
| Commas: 176/175, 1375/1372, 640/637<br />
| |
| Sval name: 6&amp;25<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Wuerschmidt%20family">Hemiwuerschmidt</a><br />
| |
| <br />
| |
| POTE generator: ~28/25 = 194.594<br />
| |
| <br />
| |
| Map: [&lt;1 0 -3 -7 13|, &lt;0 2 5 9 -8|]<br />
| |
| EDOs: 6, 7, 13, 19, 25, 31, 37<br />
| |
| Error: 2.555 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:168:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/roulette_37edo.jpg/270817184/roulette_37edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/roulette_37edo.jpg/270817184/roulette_37edo.jpg" alt="roulette_37edo.jpg" title="roulette_37edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:168 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette6">roulette6</a> - six note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette7">roulette7</a> - seven note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette13">roulette13</a> - thirteen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette19">roulette19</a> - nineteen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mega%20chromatic%20scale">mega chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:39:&lt;h1&gt; --><h1 id="toc19"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:39 -->Garibaldi</h1>
| |
| Group: 2.3.5.7<br />
| |
| Commas: 225/224, 3125/3087<br />
| |
| Val name: 12&amp;29<br />
| |
| <br />
| |
| POTE generator: ~3/2 = 702.085<br />
| |
| <br />
| |
| Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]<br />
| |
| EDOs: 7, 12, 17, 29, 41, 53, 94<br />
| |
| Error: 2.834<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/garibaldi12">Twelve note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/garibaldi17">Seventeen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:41:&lt;h1&gt; --><h1 id="toc20"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:41 -->Baldy</h1>
| |
| Subgroup: 2.9.5.7.13<br />
| |
| Commas: 225/224, 325/324, 640/637<br />
| |
| Sval name: 6&amp;35<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">Garibaldi</a><br />
| |
| <br />
| |
| POTE generator: ~9/8 = 204.090<br />
| |
| <br />
| |
| Map: [&lt;1 0 15 25 -28|, &lt;0 1 -4 -7 10|]<br />
| |
| EDOs: 6, 11, 17, 23, 29, 35, 41, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 100, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/147edo">147</a><br />
| |
| Error: 2.617 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:169:&lt;img src=&quot;/file/view/baldy_147edo.jpg/271199372/baldy_147edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/baldy_147edo.jpg/271199372/baldy_147edo.jpg" alt="baldy_147edo.jpg" title="baldy_147edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:169 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/baldy6">baldy6</a> - six note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/baldy11">baldy11</a> - eleven note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/baldy17">baldy17</a> - seventeen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:43:&lt;h1&gt; --><h1 id="toc21"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:43 -->Bossier</h1>
| |
| Subgroup: 2.7.11.13<br />
| |
| Commas: 1573/1569, 15488/15379<br />
| |
| Sval name: 3&amp;17<br />
| |
| <br />
| |
| POTE generator: ~14/11 = 421.309<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 3|, &lt;0 8 7 2|]<br />
| |
| EDOs: 17, 20, 37, 57, 94, 225<br />
| |
| Error: 2.665 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:170:&lt;img src=&quot;/file/view/bossier_225edo.jpg/271202010/bossier_225edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/bossier_225edo.jpg/271202010/bossier_225edo.jpg" alt="bossier_225edo.jpg" title="bossier_225edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:170 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier11">Eleven note chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier14">Fourteen note mega chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:45:&lt;h1&gt; --><h1 id="toc22"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:45 -->Radon</h1>
| |
| Subgroup: 2.3.7.11<br />
| |
| Commas: 896/891, 1029/1024<br />
| |
| Sval name: 5&amp;36<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gamelismic%20clan">Rodan</a><br />
| |
| <br />
| |
| POTE generator: ~8/7 = 234.381<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]<br />
| |
| EDOs: 5, 36, 41, 87, 128<br />
| |
| Error: 2.925 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:171:&lt;img src=&quot;/file/view/radon_128edo.jpg/271207646/radon_128edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/radon_128edo.jpg/271207646/radon_128edo.jpg" alt="radon_128edo.jpg" title="radon_128edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:171 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/radon5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/radon11">Eleven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/radon16">Sixteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:47:&lt;h1&gt; --><h1 id="toc23"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule:47 -->Myna</h1>
| |
| Group: 2.3.5.7<br />
| |
| Commas: 126/125, 1728/1715<br />
| |
| Val name: 4&amp;27<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 310.146<br />
| |
| <br />
| |
| Map: [&lt;1 9 9 8|, &lt;0 -10 -9 -7|]<br />
| |
| EDOs: 4, 27, 31, 58, 89<br />
| |
| Error: 3.310 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:172:&lt;img src=&quot;/file/view/myna_89edo.jpg/271260474/myna_89edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/myna_89edo.jpg/271260474/myna_89edo.jpg" alt="myna_89edo.jpg" title="myna_89edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:172 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/myna7">Seven note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/myna11">Eleven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/myna15">Fifteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:49:&lt;h1&gt; --><h1 id="toc24"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:49 -->Silver</h1>
| |
| Subgroup: 2.5.7.13.17<br />
| |
| Commas: 170/169, 640/637, 5525/5488<br />
| |
| Sval name: 10&amp;27<br />
| |
| <br />
| |
| POTE generator: ~13/8 = 842.711<br />
| |
| <br />
| |
| Map: [&lt;1 5 4 4 2|, &lt;0 -9 -4 -1 7|]<br />
| |
| EDOs: 7, 10, 17, 27, 37, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 84, 131, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/487edo">487</a><br />
| |
| Error: 3.437<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:173:&lt;img src=&quot;/file/view/silver_487edo.jpg/271264440/silver_487edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/silver_487edo.jpg/271264440/silver_487edo.jpg" alt="silver_487edo.jpg" title="silver_487edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:173 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/silver7">silver7</a> -seven note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/silver10">silver10</a> - ten note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/silver17">silver17</a> - seventeen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:51:&lt;h1&gt; --><h1 id="toc25"><a name="Mabila"></a><!-- ws:end:WikiTextHeadingRule:51 -->Mabila</h1>
| |
| Subgroup: 2.5.7<br />
| |
| Comma: 1071875/1048576<br />
| |
| Sval name: 7&amp;9<br />
| |
| <br />
| |
| POTE generator: ~175/128 = 527.236<br />
| |
| <br />
| |
| Map: [&lt;1 1 5|, &lt;0 3 -5|]<br />
| |
| EDOs: 7, 9, 16, 25, 41, 66<br />
| |
| Error: 3.560<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:174:&lt;img src=&quot;/file/view/mabila_66edo.jpg/271267504/mabila_66edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/mabila_66edo.jpg/271267504/mabila_66edo.jpg" alt="mabila_66edo.jpg" title="mabila_66edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:174 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mabila7">Seven note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mabila9">Nine note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mabila16">Sixteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:53:&lt;h1&gt; --><h1 id="toc26"><a name="Meantone"></a><!-- ws:end:WikiTextHeadingRule:53 -->Meantone</h1>
| |
| Group: 2.3.5.7<br />
| |
| Commas: 81/80, 126/125<br />
| |
| Val name: 12&amp;19<br />
| |
| <br />
| |
| POTE generator: 696.495<br />
| |
| <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 />
| |
| <!-- ws:start:WikiTextLocalImageRule:175:&lt;img src=&quot;/file/view/meantone_31edo.jpg/272175716/meantone_31edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/meantone_31edo.jpg/272175716/meantone_31edo.jpg" alt="meantone_31edo.jpg" title="meantone_31edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:175 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone12">Twelve note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:55:&lt;h1&gt; --><h1 id="toc27"><a name="Starlingtet"></a><!-- ws:end:WikiTextHeadingRule:55 -->Starlingtet</h1>
| |
| Group: 2.5/3.7/3<br />
| |
| Comma: 126/125<br />
| |
| Svalname: 4&amp;15<br />
| |
| Related temperaments: starling; becomes myna<br />
| |
| POTE generator: ~6/5 = 311.213<br />
| |
| <br />
| |
| Map: [&lt;1 0 -1|, &lt;0 1 3|]<br />
| |
| EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b<br />
| |
| Error: 311.213<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet4">Four note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet11">Eleven note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:57:&lt;h1&gt; --><h1 id="toc28"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule:57 -->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="http://xenharmonic.wikispaces.com/indium8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/indium17">Seventeen note chromatic scale</a><br />
| |
| <br />
| |
| Music<br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3" rel="nofollow">The Cry of Indium</a> (in Indium 17) by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1532" rel="nofollow" target="_blank">details</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:59:&lt;h1&gt; --><h1 id="toc29"><a name="Magic"></a><!-- ws:end:WikiTextHeadingRule:59 -->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 />
| |
| <!-- ws:start:WikiTextLocalImageRule:176:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/magic_145edo.jpg/270820174/magic_145edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/magic_145edo.jpg/270820174/magic_145edo.jpg" alt="magic_145edo.jpg" title="magic_145edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:176 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magic7">Seven note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magic10">Ten note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magic13">Thirteen note chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magic16">Sixteen note mega chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:61:&lt;h1&gt; --><h1 id="toc30"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:61 -->Hemif</h1>
| |
| Subgroup: 2.3.7.11.13<br />
| |
| Commas: 144/143, 243/242, 364/363<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 />
| |
| <!-- ws:start:WikiTextLocalImageRule:177:&lt;img src=&quot;/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg" alt="hemif_58edo.jpg" title="hemif_58edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:177 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif7">Seven note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif10">Ten note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif17">Seventeen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:63:&lt;h1&gt; --><h1 id="toc31"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:63 -->Skwares</h1>
| |
| Subgroup: 2.3.7.11<br />
| |
| Commas: 99/98, 243/242<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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="http://xenharmonic.wikispaces.com/skwares8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/skwares11">Eleven note mega albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/skwares14">Fourteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:65:&lt;h1&gt; --><h1 id="toc32"><a name="Sensi"></a><!-- ws:end:WikiTextHeadingRule:65 -->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 />
| |
| <!-- ws:start:WikiTextLocalImageRule:178:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/sensi_46edo.jpg/270823804/sensi_46edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/sensi_46edo.jpg/270823804/sensi_46edo.jpg" alt="sensi_46edo.jpg" title="sensi_46edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:178 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi11">Eleven note mega albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi19">Nineteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:67:&lt;h1&gt; --><h1 id="toc33"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:67 -->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="http://xenharmonic.wikispaces.com/greeley8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/greeley15">Fifteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:69:&lt;h2&gt; --><h2 id="toc34"><a name="Greeley-Music"></a><!-- ws:end:WikiTextHeadingRule:69 -->Music</h2>
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3" rel="nofollow">A Greeley Steals Halloween</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1485" rel="nofollow" target="_blank">Chris Vaisvil</a> in Greeley 15<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:71:&lt;h1&gt; --><h1 id="toc35"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:71 -->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="http://xenharmonic.wikispaces.com/semidim8">Eight note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semidim13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:73:&lt;h1&gt; --><h1 id="toc36"><a name="Orwell"></a><!-- ws:end:WikiTextHeadingRule:73 -->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 />
| |
| <!-- ws:start:WikiTextLocalImageRule:179:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/orwell_84edo.png/279497768/orwell_84edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/orwell_84edo.png/279497768/orwell_84edo.png" alt="orwell_84edo.png" title="orwell_84edo.png" /><!-- ws:end:WikiTextLocalImageRule:179 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orwell5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orwell9">Nine note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orwell13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:75:&lt;h1&gt; --><h1 id="toc37"><a name="Magicaltet"></a><!-- ws:end:WikiTextHeadingRule:75 -->Magicaltet</h1>
| |
| Group: 2.5/3.7.11<br />
| |
| Commas: 100/99, 385/384<br />
| |
| Related temperaments: 4&amp;7&amp;15, magic<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 319.424<br />
| |
| <br />
| |
| Map: [&lt;1 0 5 2|, &lt;0 1 -3 2|]<br />
| |
| EDOs: 11, 15, 79cd, 94cd, 109cd, 124cd, 139cd<br />
| |
| Error: 5.720<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magicaltet7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magicaltet11">Eleven note chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magicaltet15">Fifteen note mega scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:77:&lt;h1&gt; --><h1 id="toc38"><a name="Mothwelltri"></a><!-- ws:end:WikiTextHeadingRule:77 -->Mothwelltri</h1>
| |
| Group: 2.7/3.11<br />
| |
| Comma: 99/98<br />
| |
| Svalname: 1&amp;4<br />
| |
| Related temperament: Orwell<br />
| |
| <br />
| |
| POTE generator:~7/6 = 268.508<br />
| |
| <br />
| |
| Map: [&lt;1 0 1|, &lt;0 1 2|]<br />
| |
| EDOs: 9, 40, 49c, 58c, 67c, 76c<br />
| |
| Error: 6.119 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mothwelltri5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mothwelltri9">Nine note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mothwelltri13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:79:&lt;h1&gt; --><h1 id="toc39"><a name="Lovecraft"></a><!-- ws:end:WikiTextHeadingRule:79 -->Lovecraft</h1>
| |
| Group: 2.11.13<br />
| |
| <br />
| |
| POTE generator: ~13/11 = 279.318<br />
| |
| <br />
| |
| Map: [&lt;1 1 0|, &lt;0 2 3|]<br />
| |
| EDOS: 13, 30, 43, 73, 116b<br />
| |
| Error: 6.026<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lovecraft5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lovecraft9">Nine note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lovecraft13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:81:&lt;h1&gt; --><h1 id="toc40"><a name="Bleu"></a><!-- ws:end:WikiTextHeadingRule:81 -->Bleu</h1>
| |
| Group: 2.3.7.11.13<br />
| |
| Commas: 78/77, 99/98, 144/143<br />
| |
| Sval name: 9&amp;17<br />
| |
| <br />
| |
| POTE generator: ~13/12 = 139.990<br />
| |
| <br />
| |
| Map: [&lt;1 1 2 3 3|, &lt;0 5 7 4 6|]<br />
| |
| EDOs: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/43edo">43</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/60edo">60c</a><br />
| |
| Error: 6.361<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu8">bleu8</a> - Eight note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu9">bleu9</a> - Nine note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu17">bleu17</a> - Seventeen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:83:&lt;h1&gt; --><h1 id="toc41"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:83 -->Mohaha</h1>
| |
| Subgroup: 2.3.5.11<br />
| |
| Commas: 81/80, 121/120<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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: 24, 31, 69d, 100d, 131bd<br />
| |
| Error: 6.733 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mohaha7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mohaha10">Ten note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:85:&lt;h2&gt; --><h2 id="toc42"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:85 -->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: 17c, 24, 31, 55, 86de, 141cde<br />
| |
| Error: 9.556 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:87:&lt;h1&gt; --><h1 id="toc43"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:87 -->Tutone</h1>
| |
| Subgroup: 2.9.5.7.11<br />
| |
| Commas: 81/80, 99/98, 126/125<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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: 25, 31, 68b, 99b<br />
| |
| Error: 7.047 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone6">Six note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:89:&lt;h1&gt; --><h1 id="toc44"><a name="Leantone"></a><!-- ws:end:WikiTextHeadingRule:89 -->Leantone</h1>
| |
| Subgroup: 2.9.5.7.11<br />
| |
| Commas: 45/44, 56/55, 81/80<br />
| |
| Related temperament: <a class="wiki_link" href="/meanenneadecal">meanenneadecal</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="http://xenharmonic.wikispaces.com/leantone6">Six note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/leantone7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/leantone13">Thirteen note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:91:&lt;h1&gt; --><h1 id="toc45"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:91 -->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 />
| |
| <!-- ws:start:WikiTextLocalImageRule:180:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/score_20edo.jpg/270826026/score_20edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/score_20edo.jpg/270826026/score_20edo.jpg" alt="score_20edo.jpg" title="score_20edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:180 --><br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/score5">Five note haplotonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/score7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/score9">Nine note mega albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/score11">Eleven note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:93:&lt;h1&gt; --><h1 id="toc46"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:93 -->Supra</h1>
| |
| Subgroup: 2.3.7.11<br />
| |
| Commas: 64/63, 99/98<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/suprapyth">suprapyth</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, 34c, 39c, 56c<br />
| |
| Error: 9.795 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/supra7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/supra12">Twelve note chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:95:&lt;h2&gt; --><h2 id="toc47"><a name="Supra-Supraphon"></a><!-- ws:end:WikiTextHeadingRule:95 -->Supraphon</h2>
| |
| Subgroup: 2.3.7.11.13<br />
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| Commas: 64/63, 78/77, 99/98<br />
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| <br />
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| POTE generator: ~3/2 = 706.137<br />
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| <br />
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| Map: [&lt;1 0 6 13 18|, &lt;0 1 -2 -6 -9|]<br />
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| EDOs: 5, 7, 12, 17<br />
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| Error: 10.534 cents<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:97:&lt;h2&gt; --><h2 id="toc48"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:97 -->Machine</h2>
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| Subgroup: 2.9.7.11<br />
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| Commas: 64/63, 99/98<br />
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| <br />
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| POTE generator: ~9/8 = 214.384<br />
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| <br />
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| Map: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]<br />
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| EDOs: 5, 6, 11, 17, 28<br />
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| Error: 10.100 cents<br />
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| <br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine5">Five note haplotonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine6">Six note albitonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine11">Eleven note chromatic scale</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:99:&lt;h1&gt; --><h1 id="toc49"><a name="Antikythera"></a><!-- ws:end:WikiTextHeadingRule:99 -->Antikythera</h1>
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| Subgroup: 2.9.5.7<br />
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| Commas: 50/49, 64/63<br />
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| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/pajara">pajara</a><br />
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| <br />
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| POTE generator: ~8/7 = 214.095<br />
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| <br />
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| Map: [&lt;2 0 11 12|, &lt;0 1 -1 -1|]<br />
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| EDOS: 4, 6, 10, 16, 22, 28<br />
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| Error: 11.508 cents<br />
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| <br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/antikythera6">Six note haplotonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/antikythera10">Ten note albitonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/antikythera16">Sixteen note chromatic scale</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:101:&lt;h1&gt; --><h1 id="toc50"><a name="Deutone"></a><!-- ws:end:WikiTextHeadingRule:101 -->Deutone</h1>
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| Subgroup: 2.9.5.7.13<br />
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| Commas: 65/64, 81/80, 91/90<br />
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| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">meanpop</a><br />
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| <br />
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| POTE generator: ~9/8 = 191.059<br />
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| <br />
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| Map: [&lt;1 0 -4 -13 10|, &lt;0 1 2 5 -2|]<br />
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| EDOs: 6, 7, 13, 19, 25, 44, 69<br />
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| Error: 12.145 cents<br />
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| <br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/deutone6">Six note haplotonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/deutone7">seven note albitonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/deutone13">Thirteen note chromatic scale</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:103:&lt;h1&gt; --><h1 id="toc51"><a name="Semiphore"></a><!-- ws:end:WikiTextHeadingRule:103 -->Semiphore</h1>
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| Subgroup: 2.3.7<br />
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| Comma: 49/48<br />
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| <br />
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| POTE generator: ~7/6 = 250.385<br />
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| <br />
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| Map: [&lt;1 0 2|, &lt;0 2 1|]<br />
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| EDOs: 5, 9, 14, 19, 24<br />
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| Error: 12.428<br />
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| <br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semiphore5">Five note haplotonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semiphore9">Nine note albitonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semiphore14">Fourteen note chromatic scale</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:105:&lt;h1&gt; --><h1 id="toc52"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:105 -->Augment</h1>
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| Subgroup: 2.5.7.11<br />
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| Commas: 56/55, 128/125<br />
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| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Augmented%20family">augmented</a><br />
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| <br />
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| POTE generator: ~8/7 = 228.275<br />
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| <br />
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| Map: [&lt;3 7 0 2|, &lt;0 0 1 1|]<br />
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| EDOs: 3, 6, 9, 15, 21<br />
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| Error: 12.830 cents<br />
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| <br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment6">Six note haplotonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment9">Nine note albitonic scale</a><br />
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| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment12">Twelve note chromatic scale</a></body></html></pre></div>
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