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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | __FORCETOC__ |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | This page discusses some of the temperaments tempering out |-5 2 2 -1> =[[225/224| 225/224]], the [[Marvel_family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone_family|meantone]], [[Miracle|miracle]], [[Magic_family|magic]], [[pajara|pajara]], [[Orwell|orwell]], [[Kleismic_family|catakleismic]], [[Garibaldi_temperament|garibaldi]], [[Augmented_family|august]], [[Pythagorean_family|compton]], [[Dicot_family|sharp]], [[Escapade_family|escapade]] and [[Pelogic_family|mavila]]. |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-18 12:15:04 UTC</tt>.<br>
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| : The original revision id was <tt>602440728</tt>.<br>
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| : The revision comment was: <tt>removed tel links</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]]
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| This page discusses some of the temperaments tempering out |-5 2 2 -1> =[[225_224| 225/224]], the [[Marvel family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone family|meantone]], [[Miracle|miracle]], [[Magic family|magic]], [[Pajara|pajara]], [[Orwell|orwell]], [[Kleismic family|catakleismic]], [[Garibaldi temperament|garibaldi]], [[Augmented family|august]], [[Pythagorean family|compton]], [[Dicot family|sharp]], [[Escapade family|escapade]] and [[Pelogic family|mavila]]. | |
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| Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds. | | Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds. |
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| Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.) | | Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.) |
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| =Negri= | | =Negri= |
| [[Comma]]s: 49/48, 225/224 | | [[Comma|Comma]]s: 49/48, 225/224 |
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| [[POTE tuning|POTE temperament]]: ~15/14 = 125.608 | | [[POTE_tuning|POTE temperament]]: ~15/14 = 125.608 |
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| | [[Map|Map]]: [<1 2 2 3|, <0 -4 3 -2|] |
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| | [[wedgie|Wedgie]]: <<4 -3 2 -14 -8 13|| |
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| [[Map]]: [<1 2 2 3|, <0 -4 3 -2|]
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| [[Wedgie]]: <<4 -3 2 -14 -8 13||
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| EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]] | | EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]] |
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| ==11-limit== | | ==11-limit== |
| Commas: 45/44, 49/48, 56/55 | | Commas: 45/44, 49/48, 56/55 |
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| [[POTE tuning|POTE generator]]: ~15/14 = 126.474 | | [[POTE_tuning|POTE generator]]: ~15/14 = 126.474 |
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| Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|] | | Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|] |
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| EDOs: 9, 10, 19 | | EDOs: 9, 10, 19 |
| [[Badness]]: 0.0262
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| ==13-limit== | | [[Badness|Badness]]: 0.0262 |
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| | ==13-limit== |
| Commas: 45/44, 49/48, 56/55, 78/77 | | Commas: 45/44, 49/48, 56/55, 78/77 |
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| [[POTE tuning|POTE generator]]: ~14/13 = 126.431 | | [[POTE_tuning|POTE generator]]: ~14/13 = 126.431 |
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| Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|] | | Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|] |
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| EDOs: 9, 10, 19 | | EDOs: 9, 10, 19 |
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| =Negril= | | =Negril= |
| Commas: 49/48, 100/99, 225/224 | | Commas: 49/48, 100/99, 225/224 |
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| Map: [<1 2 2 3 2|, <0 -4 3 -2 14|] | | Map: [<1 2 2 3 2|, <0 -4 3 -2 14|] |
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| EDOs: 19, [[29edo|29]], [[48edo|48df]], [[77edo|77cdf]] | | EDOs: 19, [[29edo|29]], [[48edo|48df]], [[77edo|77cdf]] |
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| Badness: 0.0387 | | Badness: 0.0387 |
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| ==13-limit== | | ==13-limit== |
| Commas: 49/48, 65/64, 91/90, 875/858 | | Commas: 49/48, 65/64, 91/90, 875/858 |
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| Map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|] | | Map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|] |
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| EDOs: 9, 10, 19, 29, 48, 77 | | EDOs: 9, 10, 19, 29, 48, 77 |
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| Badness: 0.0244 | | Badness: 0.0244 |
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| =Negric= | | =Negric= |
| Commas: 33/32, 49/48, 77/75 | | Commas: 33/32, 49/48, 77/75 |
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| Map: [<1 2 2 3 3|, <0 -4 3 -2 4|] | | Map: [<1 2 2 3 3|, <0 -4 3 -2 4|] |
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| EDOs: 9, 19, [[85edo|85]] | | EDOs: 9, 19, [[85edo|85]] |
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| Badness: 0.0306 | | Badness: 0.0306 |
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| ==13-limit== | | ==13-limit== |
| Commas: 33/32, 49/48, 65/64, 91/90 | | Commas: 33/32, 49/48, 65/64, 91/90 |
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| Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|] | | Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|] |
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| EDOs: 9, 19, 85 | | EDOs: 9, 19, 85 |
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| Badness: 0.0202 | | Badness: 0.0202 |
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| =Negroni= | | =Negroni= |
| Commas: 49/48, 55/54, 225/224 | | Commas: 49/48, 55/54, 225/224 |
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| Map: [<1 2 2 3 5|, <0 -4 3 -2 -15|] | | Map: [<1 2 2 3 5|, <0 -4 3 -2 -15|] |
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| EDOs: 10, 19e, 29, 77cde | | EDOs: 10, 19e, 29, 77cde |
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| Badness: 0.0353 | | Badness: 0.0353 |
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| ==13-limit== | | ==13-limit== |
| Commas: 49/48, 55/54, 65/64, 91/90 | | Commas: 49/48, 55/54, 65/64, 91/90 |
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| Map: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|] | | Map: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|] |
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| EDOs: 10, 19e, 29, 77cdef | | EDOs: 10, 19e, 29, 77cdef |
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| Badness: 0.0216 | | Badness: 0.0216 |
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| =Wizard= | | =Wizard= |
| Comma: 2197265625/2147483648 | | Comma: 2197265625/2147483648 |
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| Map: [<2 1 5|, <0 6 -1|] | | Map: [<2 1 5|, <0 6 -1|] |
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| EDOs: 22, 50, 72, 166, 238c, 310c, 548bc | | EDOs: 22, 50, 72, 166, 238c, 310c, 548bc |
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| Badness: 0.3864 | | Badness: 0.3864 |
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| ==7-limit== | | ==7-limit== |
| Commas: 225/224, 118098/117649 | | Commas: 225/224, 118098/117649 |
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| [[POTE tuning|POTE temperament]]: 383.256 | | [[POTE_tuning|POTE temperament]]: 383.256 |
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| Map: [<2 1 5 2|, <0 6 -1 10|] | | Map: [<2 1 5 2|, <0 6 -1 10|] |
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| Wedgie: <<12 -2 20 -31 -2 52|| | | Wedgie: <<12 -2 20 -31 -2 52|| |
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| EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238c]], [[310edo|310c]], [[382edo|382c]] | | EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238c]], [[310edo|310c]], [[382edo|382c]] |
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| Badness: 0.0408 | | Badness: 0.0408 |
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| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 385/384, 4000/3993 | | Commas: 225/224, 385/384, 4000/3993 |
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| [[POTE tuning|POTE temperament]]: 383.232 | | [[POTE_tuning|POTE temperament]]: 383.232 |
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| Map: [<2 1 5 2 8|, <0 6 -1 10 -3|] | | Map: [<2 1 5 2 8|, <0 6 -1 10 -3|] |
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| EDOs: 22, 50, 72, 94, [[166edo|166]], [[238edo|238c]], [[310edo|310c]] | | EDOs: 22, 50, 72, 94, [[166edo|166]], [[238edo|238c]], [[310edo|310c]] |
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| Badness: 0.0185 | | Badness: 0.0185 |
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| ==Lizard== | | ==Lizard== |
| Commas: 225/224, 351/350, 364/363, 385/384 | | Commas: 225/224, 351/350, 364/363, 385/384 |
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| [[POTE tuning|POTE temperament]]: 383.389 | | [[POTE_tuning|POTE temperament]]: 383.389 |
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| Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|] | | Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|] |
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| EDOs: 22, 50, 72, 122, 194df | | EDOs: 22, 50, 72, 122, 194df |
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| Badness: 0.0218 | | Badness: 0.0218 |
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| ===17-limit=== | | ===17-limit=== |
| Commas: 221/220, 273/272, 289/288, 351/350, 375/374 | | Commas: 221/220, 273/272, 289/288, 351/350, 375/374 |
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| [[POTE tuning|POTE temperament]]: 383.381 | | [[POTE_tuning|POTE temperament]]: 383.381 |
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| Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|] | | Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|] |
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| EDOs: 22, 50, 72, 122g, 194dfg | | EDOs: 22, 50, 72, 122g, 194dfg |
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| Badness: 0.0145 | | Badness: 0.0145 |
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| ===19-limit=== | | ===19-limit=== |
| Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342 | | Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342 |
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| [[POTE tuning|POTE generator]]: ~5/4 = 383.477 | | [[POTE_tuning|POTE generator]]: ~5/4 = 383.477 |
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| Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|] | | Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|] |
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| EDOs: 22h, 50, 72, [[122edo|122g]], [[194edo|194dfg]] | | EDOs: 22h, 50, 72, [[122edo|122g]], [[194edo|194dfg]] |
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| Badness: 0.0157 | | Badness: 0.0157 |
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| ==Gizzard== | | ==Gizzard== |
| Commas: 225/224, 385/384, 325/324, 1573/1568 | | Commas: 225/224, 385/384, 325/324, 1573/1568 |
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| Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|] | | Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|] |
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| EDOs: [[22edo|22]], [[26edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238cf]] | | EDOs: [[22edo|22]], [[26edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238cf]] |
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| Badness: 0.0203 | | Badness: 0.0203 |
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| ===17-limit=== | | ===17-limit=== |
| Commas: 225/224, 289/288, 325/324, 375/374, 385/384 | | Commas: 225/224, 289/288, 325/324, 375/374, 385/384 |
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| Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|] | | Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|] |
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| EDOs: 22f, 72, 94, [[166edo|166g]], [[238edo|238cfg]] | | EDOs: 22f, 72, 94, [[166edo|166g]], [[238edo|238cfg]] |
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| Badness: 0.0136 | | Badness: 0.0136 |
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| ===19-limit=== | | ===19-limit=== |
| Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399 | | Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399 |
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| Map: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|] | | Map: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|] |
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| EDOs: 22f, 72, 94, 166g | | EDOs: 22f, 72, 94, 166g |
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| Badness: 0.0148 | | Badness: 0.0148 |
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| ==Mage== | | ==Mage== |
| Commas: 99/98, 176/175, 1331/1296 | | Commas: 99/98, 176/175, 1331/1296 |
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| Map: [<2 1 5 2 4|, <0 6 -1 10 8|] | | Map: [<2 1 5 2 4|, <0 6 -1 10 8|] |
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| EDOs: 22, 72e, 94e | | EDOs: 22, 72e, 94e |
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| Badness: 0.0578 | | Badness: 0.0578 |
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| =Triton= | | =Triton= |
| Commas: 225/224, 1029/1000 | | Commas: 225/224, 1029/1000 |
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| [[POTE tuning|POTE temperament]]: ~7/5 = 568.865 | | [[POTE_tuning|POTE temperament]]: ~7/5 = 568.865 |
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| Map: [<1 0 6 7|, <0 3 -7 -8|] | | Map: [<1 0 6 7|, <0 3 -7 -8|] |
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| Wedgie: <<3 -7 -8 -18 -21 1|| | | Wedgie: <<3 -7 -8 -18 -21 1|| |
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| EDOs: 17d, 19, 78bd, 97bd | | EDOs: 17d, 19, 78bd, 97bd |
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| Badness: 0.0592 | | Badness: 0.0592 |
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| ==11-limit== | | ==11-limit== |
| Commas: 45/44, 56/55, 1029/1000 | | Commas: 45/44, 56/55, 1029/1000 |
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| Map: [<1 0 6 7 4|, <0 3 -7 -8 -1|] | | Map: [<1 0 6 7 4|, <0 3 -7 -8 -1|] |
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| EDOs: 19, 59bde, 78bde, 97bde | | EDOs: 19, 59bde, 78bde, 97bde |
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| Badness: 0.0457 | | Badness: 0.0457 |
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| =Tritonic= | | =Tritonic= |
| Comnma: 553584375/536870912 | | Comnma: 553584375/536870912 |
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| Map: [<1 4 -3|, <0 -5 11|] | | Map: [<1 4 -3|, <0 -5 11|] |
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| EDOs: 29, 31, 60, 91 | | EDOs: 29, 31, 60, 91 |
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| Badness: 0.3785 | | Badness: 0.3785 |
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| ==7-limit== | | ==7-limit== |
| Commas: 225/224, 50421/50000 | | Commas: 225/224, 50421/50000 |
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| [[POTE tuning|POTE temperament]]: 580.286 | | [[POTE_tuning|POTE temperament]]: 580.286 |
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| Map: [<1 4 -3 -3|, <0 -5 11 12|] | | Map: [<1 4 -3 -3|, <0 -5 11 12|] |
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| Wedgie: <<5 -11 -12 -29 -33 3|| | | Wedgie: <<5 -11 -12 -29 -33 3|| |
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| EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], 213bcd | | EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], 213bcd |
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| ==11-limit== | | ==11-limit== |
| Commas: 121/120, 225/224, 441/440 | | Commas: 121/120, 225/224, 441/440 |
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| [[POTE tuning|POTE generator]]: ~7/5 = 580.267 | | [[POTE_tuning|POTE generator]]: ~7/5 = 580.267 |
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| Map: [<1 4 -3 -3 2|, <0 -5 11 12 3|] | | Map: [<1 4 -3 -3 2|, <0 -5 11 12 3|] |
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| EDOs: 29, 31, 60e | | EDOs: 29, 31, 60e |
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| Badness: 0.0237 | | Badness: 0.0237 |
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| ==13-limit== | | ==13-limit== |
| Commas: 105/104, 121/120, 196/195, 275/273 | | Commas: 105/104, 121/120, 196/195, 275/273 |
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| Map: [<1 4 -3 -3 2 -5|, <0 -5 11 12 3 18|] | | Map: [<1 4 -3 -3 2 -5|, <0 -5 11 12 3 18|] |
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| EDOs: 29, 31, 60e, 151cde | | EDOs: 29, 31, 60e, 151cde |
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| Badness: 0.0230 | | Badness: 0.0230 |
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| ==Tritoni== | | ==Tritoni== |
| Commas: 225/224, 385/384, 27783/27500 | | Commas: 225/224, 385/384, 27783/27500 |
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| Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|] | | Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|] |
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| EDOs: 31, 91, 122 | | EDOs: 31, 91, 122 |
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| Badness: 0.0455 | | Badness: 0.0455 |
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| =Merman= | | =Merman= |
| Comma: 1121008359375/1099511627776 | | Comma: 1121008359375/1099511627776 |
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| Map: [<1 5 -5|, <0 -7 15|] | | Map: [<1 5 -5|, <0 -7 15|] |
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| EDOs: 41, 84, 125, 209, 334c, 543bc | | EDOs: 41, 84, 125, 209, 334c, 543bc |
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| Badness: 0.4538 | | Badness: 0.4538 |
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| ==7-limit== | | ==7-limit== |
| Commas: 225/224, 2500000/2470629 | | Commas: 225/224, 2500000/2470629 |
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| Map: [<1 5 -5 -5|, <0 -7 15 16|] | | Map: [<1 5 -5 -5|, <0 -7 15 16|] |
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| Wedgie: <<7 -15 -16 -40 -45 5|| | | Wedgie: <<7 -15 -16 -40 -45 5|| |
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| EDOs: 41, 84, 125 | | EDOs: 41, 84, 125 |
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| Badness: 0.0551 | | Badness: 0.0551 |
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| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 441/440, 1344/1331 | | Commas: 225/224, 441/440, 1344/1331 |
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| Map: [<1 5 -5 -5 2|, <0 -7 15 16 3]] | | Map: [<1 5 -5 -5 2|, <0 -7 15 16 3]] |
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| EDOs: 41, 84, 125e | | EDOs: 41, 84, 125e |
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| Badness: 0.0364 | | Badness: 0.0364 |
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| ==13-limit== | | ==13-limit== |
| Commas: 144/143, 225/224, 364/363, 441/440 | | Commas: 144/143, 225/224, 364/363, 441/440 |
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| Map: [<1 5 -5 -5 2 12|, <0 -7 15 16 3 -17|] | | Map: [<1 5 -5 -5 2 12|, <0 -7 15 16 3 -17|] |
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| EDOs: 41, 84, 125e, 209ef, 293ef | | EDOs: 41, 84, 125e, 209ef, 293ef |
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| Badness: 0.0275 | | Badness: 0.0275 |
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| =Septimin= | | =Septimin= |
| Comma: 35595703125/34359738368 | | Comma: 35595703125/34359738368 |
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| Line 293: |
Line 348: |
|
| |
|
| Map: [<1 4 1|, <0 -11 6|] | | Map: [<1 4 1|, <0 -11 6|] |
| | |
| EDOs: 9, 32, 41, 91, 132, 223c, 355bc | | EDOs: 9, 32, 41, 91, 132, 223c, 355bc |
| | |
| Badness: 0.6709 | | Badness: 0.6709 |
|
| |
|
| ==7-limit== | | ==7-limit== |
| Commas: 225/224, 84035/82944 | | Commas: 225/224, 84035/82944 |
|
| |
|
| [[POTE tuning|POTE temperament]]: 263.632 | | [[POTE_tuning|POTE temperament]]: 263.632 |
|
| |
|
| Map: [<1 4 1 5|, <0 -11 6 -10|] | | Map: [<1 4 1 5|, <0 -11 6 -10|] |
| | |
| Wedgie: <<11 -6 10 -35 -15 40|| | | Wedgie: <<11 -6 10 -35 -15 40|| |
| | |
| EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]] | | EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]] |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 385/384, 2401/2376 | | Commas: 225/224, 385/384, 2401/2376 |
|
| |
|
| [[POTE tuning|POTE temperament]]: 263.634 | | [[POTE_tuning|POTE temperament]]: 263.634 |
|
| |
|
| Map: [<1 4 1 5 5|, <0 -11 6 -10 -7|] | | Map: [<1 4 1 5 5|, <0 -11 6 -10 -7|] |
| | |
| EDOs: 9, 32, 41, 91, 223cdef | | EDOs: 9, 32, 41, 91, 223cdef |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 105/104, 144/143, 196/195, 245/242 | | Commas: 105/104, 144/143, 196/195, 245/242 |
|
| |
|
| [[POTE tuning|POTE temperament]]: 263.700 | | [[POTE_tuning|POTE temperament]]: 263.700 |
|
| |
|
| Map: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|] | | Map: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|] |
| | |
| EDOs: 9, 41, 91 | | EDOs: 9, 41, 91 |
|
| |
|
| =Slender= | | =Slender= |
| Commas: 225/224, 589824/588245 | | Commas: 225/224, 589824/588245 |
|
| |
|
| [[POTE tuning|POTE temperament]]: ~49/48 = 38.413 | | [[POTE_tuning|POTE temperament]]: ~49/48 = 38.413 |
|
| |
|
| Map: [<1 2 2 3|, <0 -13 10 -6|] | | Map: [<1 2 2 3|, <0 -13 10 -6|] |
| | |
| Wedgie: <<13 -10 6 -46 -27 42|| | | Wedgie: <<13 -10 6 -46 -27 42|| |
| | |
| EDOs: 31, 94, 125 | | EDOs: 31, 94, 125 |
| | |
| Badness: 0.0569 | | Badness: 0.0569 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 385/384, 1331/1323 | | Commas: 225/224, 385/384, 1331/1323 |
|
| |
|
| [[POTE tuning|POTE temperament]]: ~49/48 = 38.387 | | [[POTE_tuning|POTE temperament]]: ~49/48 = 38.387 |
|
| |
|
| Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|] | | Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|] |
| | |
| EDOs: 31, 63, 94, 125 | | EDOs: 31, 63, 94, 125 |
| | |
| Badness: 25.342 | | Badness: 25.342 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 225/224, 275/273, 385/384, 1331/1323 | | Commas: 225/224, 275/273, 385/384, 1331/1323 |
|
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|
| Line 346: |
Line 412: |
|
| |
|
| Map: [<1 2 2 3 4 3|, <0 -13 10 -6 -17 22|] | | Map: [<1 2 2 3 4 3|, <0 -13 10 -6 -17 22|] |
| | |
| EDOs: 31, 63, 94 | | EDOs: 31, 63, 94 |
| | |
| Badness: 25.913 | | Badness: 25.913 |
|
| |
|
| =Marvo= | | =Marvo= |
| Commas: 225/224, 78125000/78121827 | | Commas: 225/224, 78125000/78121827 |
|
| |
|
| [[POTE tuning|POTE temperament]]: ~27/20 = 516.694 | | [[POTE_tuning|POTE temperament]]: ~27/20 = 516.694 |
|
| |
|
| Map: [<1 5 12 29|, <0 -6 -17 -46|] | | Map: [<1 5 12 29|, <0 -6 -17 -46|] |
| | |
| Wedgie: <<6, 17, 46, 13, 56 59|| | | Wedgie: <<6, 17, 46, 13, 56 59|| |
| | |
| EDOs: 65, 72 | | EDOs: 65, 72 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 243/242, 4000/3993 | | Commas: 225/224, 243/242, 4000/3993 |
|
| |
|
| [[POTE tuning|POTE temperament]]: ~27/20 = 516.699 | | [[POTE_tuning|POTE temperament]]: ~27/20 = 516.699 |
|
| |
|
| Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|] | | Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|] |
| | |
| EDOs: 65, 72, 281, 497 | | EDOs: 65, 72, 281, 497 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 243/242, 225/224, 351/350, 1625/1617 | | Commas: 243/242, 225/224, 351/350, 1625/1617 |
|
| |
|
| Line 372: |
Line 443: |
|
| |
|
| Map: [<1 5 12 29 12 39|, <0 -6 -17 -46 -15 -62|] | | Map: [<1 5 12 29 12 39|, <0 -6 -17 -46 -15 -62|] |
| | |
| EDOs: 72, 137, 209, 281f, 490bcf | | EDOs: 72, 137, 209, 281f, 490bcf |
| | |
| Badness: 0.0269 | | Badness: 0.0269 |
|
| |
|
| =Marvolo= | | =Marvolo= |
| Commas: 225/224, 156250000/155649627 | | Commas: 225/224, 156250000/155649627 |
|
| |
|
| Line 381: |
Line 454: |
|
| |
|
| Map: [<1 2 1 1|, <0 -6 19 26|] | | Map: [<1 2 1 1|, <0 -6 19 26|] |
| | |
| Wedgie: <<6 -19 -26 -44 -58 -7|| | | Wedgie: <<6 -19 -26 -44 -58 -7|| |
| | |
| EDOs: 29, 43, 72, 619bcd, 691bcd | | EDOs: 29, 43, 72, 619bcd, 691bcd |
| | |
| Badness: 0.0833 | | Badness: 0.0833 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 441/440, 4000/3993 | | Commas: 225/224, 441/440, 4000/3993 |
|
| |
|
| Line 391: |
Line 467: |
|
| |
|
| Map: [<1 2 1 1 2|, <0 -6 19 26 21|] | | Map: [<1 2 1 1 2|, <0 -6 19 26 21|] |
| | |
| EDOs: 29, 43, 72 | | EDOs: 29, 43, 72 |
| | |
| Badness: 0.0290 | | Badness: 0.0290 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 169/168, 225/224, 364/363, 441/440 | | Commas: 169/168, 225/224, 364/363, 441/440 |
|
| |
|
| Line 400: |
Line 478: |
|
| |
|
| Map: [<1 2 1 1 2 3|, <0 -6 19 26 21 10|] | | Map: [<1 2 1 1 2 3|, <0 -6 19 26 21 10|] |
| | |
| EDOs: 29, 43, 72, 115f | | EDOs: 29, 43, 72, 115f |
| | |
| Badness: 0.0215 | | Badness: 0.0215 |
|
| |
|
| =Amavil= | | =Amavil= |
| Commas: 225/224, 17496/16807 | | Commas: 225/224, 17496/16807 |
|
| |
|
| Line 409: |
Line 489: |
|
| |
|
| Map: [<1 6 1 9|, <0 -10 3 -14|] | | Map: [<1 6 1 9|, <0 -10 3 -14|] |
| | |
| Wedgie: <<10 -3 14 -28 -6 41|| | | Wedgie: <<10 -3 14 -28 -6 41|| |
| | |
| EDOs: 9, 34d, 43, 77d | | EDOs: 9, 34d, 43, 77d |
| | |
| Badness: 0.1096 | | Badness: 0.1096 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 99/98, 176/175, 864/847 | | Commas: 99/98, 176/175, 864/847 |
|
| |
|
| Line 419: |
Line 502: |
|
| |
|
| Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|] | | Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|] |
| | |
| EDOs: 9, 34d, 43, 77de | | EDOs: 9, 34d, 43, 77de |
| | |
| Badness: 0.0426 | | Badness: 0.0426 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 78/77, 99/98, 144/143, 176/175 | | Commas: 78/77, 99/98, 144/143, 176/175 |
|
| |
|
| Line 428: |
Line 513: |
|
| |
|
| Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|] | | Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|] |
| | |
| EDOs: 9, 34d, 43, 77de | | EDOs: 9, 34d, 43, 77de |
| | |
| Badness: 0.0258 | | Badness: 0.0258 |
|
| |
|
| =Enneaportent= | | =Enneaportent= |
| Commas: 225/224, 40353607/40310784 | | Commas: 225/224, 40353607/40310784 |
|
| |
|
| Line 437: |
Line 524: |
|
| |
|
| Map: [<9 0 28 11|, <0 2 -1 2|] | | Map: [<9 0 28 11|, <0 2 -1 2|] |
| | |
| Wedgie: <<18 -9 18 -56 -22 67|| | | Wedgie: <<18 -9 18 -56 -22 67|| |
| | |
| EDOs: 9, 54, 63, 72, 495bcd | | EDOs: 9, 54, 63, 72, 495bcd |
| | |
| Badness: 0.0937 | | Badness: 0.0937 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 385/384, 12005/11979 | | Commas: 225/224, 385/384, 12005/11979 |
|
| |
|
| Line 447: |
Line 537: |
|
| |
|
| Map: [<9 0 28 11 24|, <0 2 -1 2 1|] | | Map: [<9 0 28 11 24|, <0 2 -1 2 1|] |
| | |
| EDOs: 9, 54, 63, 72, 423cd, 495bcd | | EDOs: 9, 54, 63, 72, 423cd, 495bcd |
| | |
| Badness: 0.0304 | | Badness: 0.0304 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 169/168, 225/224, 364/363, 1716/1715 | | Commas: 169/168, 225/224, 364/363, 1716/1715 |
|
| |
|
| Line 456: |
Line 548: |
|
| |
|
| Map: [<9 0 28 11 24 19|, <0 2 -1 2 1 2|] | | Map: [<9 0 28 11 24 19|, <0 2 -1 2 1 2|] |
| | |
| EDOs: 9, 54, 63, 72, 279cf | | EDOs: 9, 54, 63, 72, 279cf |
| | |
| Badness: 0.0223 | | Badness: 0.0223 |
|
| |
|
| =Submajor= | | =Submajor= |
| Comma: 69198046875/68719476736 | | Comma: 69198046875/68719476736 |
|
| |
|
| Line 465: |
Line 559: |
|
| |
|
| Map: [<1 4 -1|, <0 -8 11|] | | Map: [<1 4 -1|, <0 -8 11|] |
| | |
| EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc | | EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc |
| | |
| Badness: 0.1302 | | Badness: 0.1302 |
|
| |
|
| ==7-limit== | | ==7-limit== |
| Commas: 225/224, 51200/50421 | | Commas: 225/224, 51200/50421 |
|
| |
|
| Line 474: |
Line 570: |
|
| |
|
| Map: [<1 4 -1 1|, <0 -8 11 6|] | | Map: [<1 4 -1 1|, <0 -8 11 6|] |
| | |
| Wedgie: <<8 -11 -6 -36 -32 17|| | | Wedgie: <<8 -11 -6 -36 -32 17|| |
| | |
| EDOs: 10, 33, 43, 53 | | EDOs: 10, 33, 43, 53 |
| | |
| Badness: 0.0605 | | Badness: 0.0605 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 385/384, 6655/6561 | | Commas: 225/224, 385/384, 6655/6561 |
|
| |
|
| Line 484: |
Line 583: |
|
| |
|
| Map: [<1 4 -1 1 11|, <0 -8 11 6 -25|] | | Map: [<1 4 -1 1 11|, <0 -8 11 6 -25|] |
| | |
| EDOs: 10, 53, 116, 169de, 285cde | | EDOs: 10, 53, 116, 169de, 285cde |
| | |
| Badness: 0.0506 | | Badness: 0.0506 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 169/168, 225/224, 275/273, 385/384 | | Commas: 169/168, 225/224, 275/273, 385/384 |
|
| |
|
| Line 493: |
Line 594: |
|
| |
|
| Map: [<1 4 -1 1 11 4|, <0 -8 11 6 -25 -1|] | | Map: [<1 4 -1 1 11 4|, <0 -8 11 6 -25 -1|] |
| | |
| EDOs: 10, 53, 116, 169de, 285cdef | | EDOs: 10, 53, 116, 169de, 285cdef |
| | |
| Badness: 0.0277 | | Badness: 0.0277 |
|
| |
|
| ==Interpental== | | ==Interpental== |
| Commas: 99/98, 176/175, 51200/50421 | | Commas: 99/98, 176/175, 51200/50421 |
|
| |
|
| Line 502: |
Line 605: |
|
| |
|
| Map: [<1 4 -1 1 -5|, <0 -8 11 6 28|] | | Map: [<1 4 -1 1 -5|, <0 -8 11 6 28|] |
| | |
| EDOs: 43, 53, 96, 149d | | EDOs: 43, 53, 96, 149d |
| | |
| Badness: 0.0518 | | Badness: 0.0518 |
|
| |
|
| ===13-limit=== | | ===13-limit=== |
| Commas: 99/98, 169/168, 176/175, 640/637 | | Commas: 99/98, 169/168, 176/175, 640/637 |
|
| |
|
| Line 511: |
Line 616: |
|
| |
|
| Map: [<1 4 -1 1 -5 4|, <0 -8 11 6 28 -1|] | | Map: [<1 4 -1 1 -5 4|, <0 -8 11 6 28 -1|] |
| | |
| EDOs: 43, 53, 96, 149d | | EDOs: 43, 53, 96, 149d |
| | |
| Badness: 0.0297 | | Badness: 0.0297 |
|
| |
|
| =Alphorn= | | =Alphorn= |
| Commas: 225/224, 5764801/5668704 | | Commas: 225/224, 5764801/5668704 |
|
| |
|
| Line 520: |
Line 627: |
|
| |
|
| Map: [<1 9 0 13|, <0 -16 5 -22|] | | Map: [<1 9 0 13|, <0 -16 5 -22|] |
| | |
| Wedgie: <<16 -5 22 -45 -10 65|| | | Wedgie: <<16 -5 22 -45 -10 65|| |
| | |
| EDOs: 28d, 41, 151cd, 192cd, 233cd | | EDOs: 28d, 41, 151cd, 192cd, 233cd |
| | |
| Badness: 0.1293 | | Badness: 0.1293 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 225/224, 385/384, 12250/11979 | | Commas: 225/224, 385/384, 12250/11979 |
|
| |
|
| Line 530: |
Line 640: |
|
| |
|
| Map: [<1 9 0 13 3|, <0 -16 5 -22 1|] | | Map: [<1 9 0 13 3|, <0 -16 5 -22 1|] |
| | |
| EDOs: 41, 315cde | | EDOs: 41, 315cde |
| Badness: 0.0735</pre></div> | | |
| <h4>Original HTML content:</h4>
| | Badness: 0.0735 |
| <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>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:114:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 1em;"><a href="#Negri">Negri</a></div>
| | [[Category:marvel]] |
| <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Negri-11-limit">11-limit</a></div>
| | [[Category:overview]] |
| <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Negri-13-limit">13-limit</a></div>
| | [[Category:rank_2]] |
| <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 1em;"><a href="#Negril">Negril</a></div>
| | [[Category:temperaments]] |
| <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Negril-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 1em;"><a href="#Negric">Negric</a></div>
| |
| <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 2em;"><a href="#Negric-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 1em;"><a href="#Negroni">Negroni</a></div>
| |
| <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Negroni-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Wizard">Wizard</a></div>
| |
| <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Wizard-7-limit">7-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Wizard-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 2em;"><a href="#Wizard-Lizard">Lizard</a></div>
| |
| <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-19-limit">19-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 2em;"><a href="#Wizard-Gizzard">Gizzard</a></div>
| |
| <!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-19-limit">19-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 2em;"><a href="#Wizard-Mage">Mage</a></div>
| |
| <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 1em;"><a href="#Triton">Triton</a></div>
| |
| <!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#Triton-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Tritonic">Tritonic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Tritonic-7-limit">7-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Tritonic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 2em;"><a href="#Tritonic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 2em;"><a href="#Tritonic-Tritoni">Tritoni</a></div>
| |
| <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 1em;"><a href="#Merman">Merman</a></div>
| |
| <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 2em;"><a href="#Merman-7-limit">7-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Merman-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 2em;"><a href="#Merman-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 1em;"><a href="#Septimin">Septimin</a></div>
| |
| <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Septimin-7-limit">7-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Septimin-11-limit">11-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Septimin-13-limit">13-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 1em;"><a href="#Slender">Slender</a></div>
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| <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 2em;"><a href="#Slender-11-limit">11-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Slender-13-limit">13-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 1em;"><a href="#Marvo">Marvo</a></div>
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| <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 2em;"><a href="#Marvo-11-limit">11-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Marvo-13-limit">13-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 1em;"><a href="#Marvolo">Marvolo</a></div>
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| <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 2em;"><a href="#Marvolo-11-limit">11-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Marvolo-13-limit">13-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 1em;"><a href="#Amavil">Amavil</a></div>
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| <!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 2em;"><a href="#Amavil-11-limit">11-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Amavil-13-limit">13-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 1em;"><a href="#Enneaportent">Enneaportent</a></div>
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| <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 2em;"><a href="#Enneaportent-11-limit">11-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 2em;"><a href="#Enneaportent-13-limit">13-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 1em;"><a href="#Submajor">Submajor</a></div>
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| <!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 2em;"><a href="#Submajor-7-limit">7-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 2em;"><a href="#Submajor-11-limit">11-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 2em;"><a href="#Submajor-13-limit">13-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Submajor-Interpental">Interpental</a></div>
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| <!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 3em;"><a href="#Submajor-Interpental-13-limit">13-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --><div style="margin-left: 1em;"><a href="#Alphorn">Alphorn</a></div>
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| <!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 2em;"><a href="#Alphorn-11-limit">11-limit</a></div>
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| <!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --></div>
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| <!-- ws:end:WikiTextTocRule:172 -->This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =<a class="wiki_link" href="/225_224"> 225/224</a>, the <a class="wiki_link" href="/Marvel%20family">marvel</a> comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are <a class="wiki_link" href="/Meantone%20family">meantone</a>, <a class="wiki_link" href="/Miracle">miracle</a>, <a class="wiki_link" href="/Magic%20family">magic</a>, <a class="wiki_link" href="/Pajara">pajara</a>, <a class="wiki_link" href="/Orwell">orwell</a>, <a class="wiki_link" href="/Kleismic%20family">catakleismic</a>, <a class="wiki_link" href="/Garibaldi%20temperament">garibaldi</a>, <a class="wiki_link" href="/Augmented%20family">august</a>, <a class="wiki_link" href="/Pythagorean%20family">compton</a>, <a class="wiki_link" href="/Dicot%20family">sharp</a>, <a class="wiki_link" href="/Escapade%20family">escapade</a> and <a class="wiki_link" href="/Pelogic%20family">mavila</a>.<br />
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| <br />
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| Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.<br />
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| <br />
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| The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.<br />
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| <br />
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| Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.)<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h1>
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| <a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 225/224<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~15/14 = 125.608<br />
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| <br />
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| <a class="wiki_link" href="/Map">Map</a>: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]<br />
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| <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;4 -3 2 -14 -8 13||<br />
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| EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/86edo">86</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2>
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| Commas: 45/44, 49/48, 56/55<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 126.474<br />
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| <br />
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| Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]<br />
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| EDOs: 9, 10, 19<br />
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| <a class="wiki_link" href="/Badness">Badness</a>: 0.0262<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2>
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| Commas: 45/44, 49/48, 56/55, 78/77<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~14/13 = 126.431<br />
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| <br />
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| Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]<br />
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| EDOs: 9, 10, 19<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Negril"></a><!-- ws:end:WikiTextHeadingRule:6 -->Negril</h1>
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| Commas: 49/48, 100/99, 225/224<br />
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| <br />
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| POTE generator: ~15/14 = 124.767<br />
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| <br />
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| Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]<br />
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| EDOs: 19, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/48edo">48df</a>, <a class="wiki_link" href="/77edo">77cdf</a><br />
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| Badness: 0.0387<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Negril-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2>
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| Commas: 49/48, 65/64, 91/90, 875/858<br />
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| <br />
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| POTE generator: ~15/14 = 124.716<br />
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| <br />
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| Map: [&lt;1 2 2 3 2 4|, &lt;0 -4 3 -2 14 -3|]<br />
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| EDOs: 9, 10, 19, 29, 48, 77<br />
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| Badness: 0.0244<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Negric"></a><!-- ws:end:WikiTextHeadingRule:10 -->Negric</h1>
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| Commas: 33/32, 49/48, 77/75<br />
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| <br />
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| POTE generator: ~15/14 = 127.039<br />
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| <br />
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| Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]<br />
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| EDOs: 9, 19, <a class="wiki_link" href="/85edo">85</a><br />
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| Badness: 0.0306<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Negric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2>
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| Commas: 33/32, 49/48, 65/64, 91/90<br />
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| <br />
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| POTE generator: ~15/14 = 127.039<br />
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| <br />
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| Map: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]<br />
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| EDOs: 9, 19, 85<br />
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| Badness: 0.0202<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Negroni"></a><!-- ws:end:WikiTextHeadingRule:14 -->Negroni</h1>
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| Commas: 49/48, 55/54, 225/224<br />
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| <br />
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| POTE generator: ~15/14 = 124.539<br />
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| <br />
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| Map: [&lt;1 2 2 3 5|, &lt;0 -4 3 -2 -15|]<br />
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| EDOs: 10, 19e, 29, 77cde<br />
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| Badness: 0.0353<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Negroni-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h2>
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| Commas: 49/48, 55/54, 65/64, 91/90<br />
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| <br />
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| POTE generator: ~15/14 = 124.545<br />
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| <br />
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| Map: [&lt;1 2 2 3 5 4|, &lt;0 -4 3 -2 -15 -3|]<br />
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| EDOs: 10, 19e, 29, 77cdef<br />
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| Badness: 0.0216<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:18 -->Wizard</h1>
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| Comma: 2197265625/2147483648<br />
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| <br />
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| POTE generator: ~5/4 = 383.212<br />
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| <br />
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| Map: [&lt;2 1 5|, &lt;0 6 -1|]<br />
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| EDOs: 22, 50, 72, 166, 238c, 310c, 548bc<br />
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| Badness: 0.3864<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Wizard-7-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->7-limit</h2>
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| Commas: 225/224, 118098/117649<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.256<br />
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| <br />
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| Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]<br />
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| Wedgie: &lt;&lt;12 -2 20 -31 -2 52||<br />
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| EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238c</a>, <a class="wiki_link" href="/310edo">310c</a>, <a class="wiki_link" href="/382edo">382c</a><br />
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| Badness: 0.0408<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2>
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| Commas: 225/224, 385/384, 4000/3993<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.232<br />
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| <br />
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| Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]<br />
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| EDOs: 22, 50, 72, 94, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238c</a>, <a class="wiki_link" href="/310edo">310c</a><br />
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| Badness: 0.0185<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Wizard-Lizard"></a><!-- ws:end:WikiTextHeadingRule:24 -->Lizard</h2>
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| Commas: 225/224, 351/350, 364/363, 385/384<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.389<br />
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| <br />
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| Map: [&lt;2 1 5 2 8 11|, &lt;0 6 -1 10 -3 -10|]<br />
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| EDOs: 22, 50, 72, 122, 194df<br />
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| Badness: 0.0218<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Wizard-Lizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->17-limit</h3>
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| Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.381<br />
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| <br />
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| Map: [&lt;2 1 5 2 8 11 6|, &lt;0 6 -1 10 -3 -10 6|]<br />
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| EDOs: 22, 50, 72, 122g, 194dfg<br />
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| Badness: 0.0145<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Wizard-Lizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->19-limit</h3>
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| Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~5/4 = 383.477<br />
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| <br />
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| Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]<br />
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| EDOs: 22h, 50, 72, <a class="wiki_link" href="/122edo">122g</a>, <a class="wiki_link" href="/194edo">194dfg</a><br />
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| Badness: 0.0157<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Wizard-Gizzard"></a><!-- ws:end:WikiTextHeadingRule:30 -->Gizzard</h2>
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| Commas: 225/224, 385/384, 325/324, 1573/1568<br />
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| <br />
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| POTE generator: ~5/4 = 383.170<br />
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| <br />
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| Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]<br />
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| EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/26edo">72</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238cf</a><br />
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| Badness: 0.0203<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Wizard-Gizzard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->17-limit</h3>
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| Commas: 225/224, 289/288, 325/324, 375/374, 385/384<br />
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| <br />
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| POTE generator: ~5/4 = 383.175<br />
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| <br />
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| Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]<br />
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| EDOs: 22f, 72, 94, <a class="wiki_link" href="/166edo">166g</a>, <a class="wiki_link" href="/238edo">238cfg</a><br />
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| Badness: 0.0136<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Wizard-Gizzard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->19-limit</h3>
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| Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399<br />
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| <br />
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| POTE generator: ~5/4 = 383.138<br />
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| <br />
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| Map: [&lt;2 1 5 2 8 -2 6 15|, &lt;0 6 -1 10 -3 26 6 -18|]<br />
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| EDOs: 22f, 72, 94, 166g<br />
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| Badness: 0.0148<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Wizard-Mage"></a><!-- ws:end:WikiTextHeadingRule:36 -->Mage</h2>
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| Commas: 99/98, 176/175, 1331/1296<br />
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| <br />
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| POTE generator: ~55/48 = 216.876<br />
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| <br />
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| Map: [&lt;2 1 5 2 4|, &lt;0 6 -1 10 8|]<br />
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| EDOs: 22, 72e, 94e<br />
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| Badness: 0.0578<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:38 -->Triton</h1>
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| Commas: 225/224, 1029/1000<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~7/5 = 568.865<br />
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| <br />
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| Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]<br />
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| Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||<br />
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| EDOs: 17d, 19, 78bd, 97bd<br />
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| Badness: 0.0592<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Triton-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2>
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| Commas: 45/44, 56/55, 1029/1000<br />
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| <br />
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| POTE generator: ~7/5 = 569.144<br />
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| <br />
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| Map: [&lt;1 0 6 7 4|, &lt;0 3 -7 -8 -1|]<br />
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| EDOs: 19, 59bde, 78bde, 97bde<br />
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| Badness: 0.0457<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:42 -->Tritonic</h1>
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| Comnma: 553584375/536870912<br />
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| <br />
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| POTE generator: ~45/32 = 580.219<br />
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| <br />
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| Map: [&lt;1 4 -3|, &lt;0 -5 11|]<br />
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| EDOs: 29, 31, 60, 91<br />
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| Badness: 0.3785<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Tritonic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->7-limit</h2>
| |
| Commas: 225/224, 50421/50000<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.286<br />
| |
| <br />
| |
| Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]<br />
| |
| Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||<br />
| |
| EDOs: <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/91edo">91</a>, <a class="wiki_link" href="/122edo">122</a>, 213bcd<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2>
| |
| Commas: 121/120, 225/224, 441/440<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/5 = 580.267<br />
| |
| <br />
| |
| Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]<br />
| |
| EDOs: 29, 31, 60e<br />
| |
| Badness: 0.0237<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Tritonic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2>
| |
| Commas: 105/104, 121/120, 196/195, 275/273<br />
| |
| <br />
| |
| POTE generator: ~7/5 = 580.108<br />
| |
| <br />
| |
| Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]<br />
| |
| EDOs: 29, 31, 60e, 151cde<br />
| |
| Badness: 0.0230<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Tritonic-Tritoni"></a><!-- ws:end:WikiTextHeadingRule:50 -->Tritoni</h2>
| |
| Commas: 225/224, 385/384, 27783/27500<br />
| |
| <br />
| |
| POTE generator: ~7/5 = 580.389<br />
| |
| <br />
| |
| Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]<br />
| |
| EDOs: 31, 91, 122<br />
| |
| Badness: 0.0455<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Merman"></a><!-- ws:end:WikiTextHeadingRule:52 -->Merman</h1>
| |
| Comma: 1121008359375/1099511627776<br />
| |
| <br />
| |
| POTE generator: ~45/32 = 585.634<br />
| |
| <br />
| |
| Map: [&lt;1 5 -5|, &lt;0 -7 15|]<br />
| |
| EDOs: 41, 84, 125, 209, 334c, 543bc<br />
| |
| Badness: 0.4538<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Merman-7-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->7-limit</h2>
| |
| Commas: 225/224, 2500000/2470629<br />
| |
| <br />
| |
| POTE generator: ~7/5 = 585.585<br />
| |
| <br />
| |
| Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]<br />
| |
| Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||<br />
| |
| EDOs: 41, 84, 125<br />
| |
| Badness: 0.0551<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Merman-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2>
| |
| Commas: 225/224, 441/440, 1344/1331<br />
| |
| <br />
| |
| POTE generator: ~7/5 = 585.606<br />
| |
| <br />
| |
| Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]<br />
| |
| EDOs: 41, 84, 125e<br />
| |
| Badness: 0.0364<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Merman-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2>
| |
| Commas: 144/143, 225/224, 364/363, 441/440<br />
| |
| <br />
| |
| POTE generator: ~7/5 = 585.657<br />
| |
| <br />
| |
| Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]<br />
| |
| EDOs: 41, 84, 125e, 209ef, 293ef<br />
| |
| Badness: 0.0275<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:60 -->Septimin</h1>
| |
| Comma: 35595703125/34359738368<br />
| |
| <br />
| |
| POTE generator: ~75/64 = 263.658<br />
| |
| <br />
| |
| Map: [&lt;1 4 1|, &lt;0 -11 6|]<br />
| |
| EDOs: 9, 32, 41, 91, 132, 223c, 355bc<br />
| |
| Badness: 0.6709<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Septimin-7-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->7-limit</h2>
| |
| Commas: 225/224, 84035/82944<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.632<br />
| |
| <br />
| |
| Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]<br />
| |
| Wedgie: &lt;&lt;11 -6 10 -35 -15 40||<br />
| |
| EDOs: 9, <a class="wiki_link" href="/32edo">32</a>, 41, 91, <a class="wiki_link" href="/132edo">132</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->11-limit</h2>
| |
| Commas: 225/224, 385/384, 2401/2376<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.634<br />
| |
| <br />
| |
| Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]<br />
| |
| EDOs: 9, 32, 41, 91, 223cdef<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->13-limit</h2>
| |
| Commas: 105/104, 144/143, 196/195, 245/242<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.700<br />
| |
| <br />
| |
| Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]<br />
| |
| EDOs: 9, 41, 91<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:68 -->Slender</h1>
| |
| Commas: 225/224, 589824/588245<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.413<br />
| |
| <br />
| |
| Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]<br />
| |
| Wedgie: &lt;&lt;13 -10 6 -46 -27 42||<br />
| |
| EDOs: 31, 94, 125<br />
| |
| Badness: 0.0569<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->11-limit</h2>
| |
| Commas: 225/224, 385/384, 1331/1323<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.387<br />
| |
| <br />
| |
| Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]<br />
| |
| EDOs: 31, 63, 94, 125<br />
| |
| Badness: 25.342<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Slender-13-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->13-limit</h2>
| |
| Commas: 225/224, 275/273, 385/384, 1331/1323<br />
| |
| <br />
| |
| POTE generator: ~49/48 = 38.314<br />
| |
| <br />
| |
| Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]<br />
| |
| EDOs: 31, 63, 94<br />
| |
| Badness: 25.913<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:74:&lt;h1&gt; --><h1 id="toc37"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:74 -->Marvo</h1>
| |
| Commas: 225/224, 78125000/78121827<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~27/20 = 516.694<br />
| |
| <br />
| |
| Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]<br />
| |
| Wedgie: &lt;&lt;6, 17, 46, 13, 56 59||<br />
| |
| EDOs: 65, 72<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->11-limit</h2>
| |
| Commas: 225/224, 243/242, 4000/3993<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~27/20 = 516.699<br />
| |
| <br />
| |
| Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]<br />
| |
| EDOs: 65, 72, 281, 497<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Marvo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->13-limit</h2>
| |
| Commas: 243/242, 225/224, 351/350, 1625/1617<br />
| |
| <br />
| |
| POTE generator: ~27/20 = 516.730<br />
| |
| <br />
| |
| Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]<br />
| |
| EDOs: 72, 137, 209, 281f, 490bcf<br />
| |
| Badness: 0.0269<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:80:&lt;h1&gt; --><h1 id="toc40"><a name="Marvolo"></a><!-- ws:end:WikiTextHeadingRule:80 -->Marvolo</h1>
| |
| Commas: 225/224, 156250000/155649627<br />
| |
| <br />
| |
| POTE generator: ~21/20 = 83.348<br />
| |
| <br />
| |
| Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]<br />
| |
| Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||<br />
| |
| EDOs: 29, 43, 72, 619bcd, 691bcd<br />
| |
| Badness: 0.0833<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Marvolo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2>
| |
| Commas: 225/224, 441/440, 4000/3993<br />
| |
| <br />
| |
| POTE generator: ~21/20 = 83.340<br />
| |
| <br />
| |
| Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]<br />
| |
| EDOs: 29, 43, 72<br />
| |
| Badness: 0.0290<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="Marvolo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:84 -->13-limit</h2>
| |
| Commas: 169/168, 225/224, 364/363, 441/440<br />
| |
| <br />
| |
| POTE generator: ~21/20 = 83.330<br />
| |
| <br />
| |
| Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]<br />
| |
| EDOs: 29, 43, 72, 115f<br />
| |
| Badness: 0.0215<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:86:&lt;h1&gt; --><h1 id="toc43"><a name="Amavil"></a><!-- ws:end:WikiTextHeadingRule:86 -->Amavil</h1>
| |
| Commas: 225/224, 17496/16807<br />
| |
| <br />
| |
| POTE generator: ~48/35 = 529.979<br />
| |
| <br />
| |
| Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]<br />
| |
| Wedgie: &lt;&lt;10 -3 14 -28 -6 41||<br />
| |
| EDOs: 9, 34d, 43, 77d<br />
| |
| Badness: 0.1096<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc44"><a name="Amavil-11-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->11-limit</h2>
| |
| Commas: 99/98, 176/175, 864/847<br />
| |
| <br />
| |
| POTE generator: ~15/11 = 529.974<br />
| |
| <br />
| |
| Map: [&lt;1 6 1 9 7|, &lt;0 -10 3 -14 -8|]<br />
| |
| EDOs: 9, 34d, 43, 77de<br />
| |
| Badness: 0.0426<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc45"><a name="Amavil-13-limit"></a><!-- ws:end:WikiTextHeadingRule:90 -->13-limit</h2>
| |
| Commas: 78/77, 99/98, 144/143, 176/175<br />
| |
| <br />
| |
| POTE generator: ~15/11 = 529.951<br />
| |
| <br />
| |
| Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]<br />
| |
| EDOs: 9, 34d, 43, 77de<br />
| |
| Badness: 0.0258<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:92:&lt;h1&gt; --><h1 id="toc46"><a name="Enneaportent"></a><!-- ws:end:WikiTextHeadingRule:92 -->Enneaportent</h1>
| |
| Commas: 225/224, 40353607/40310784<br />
| |
| <br />
| |
| POTE generator: ~5/4 = 383.165<br />
| |
| <br />
| |
| Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]<br />
| |
| Wedgie: &lt;&lt;18 -9 18 -56 -22 67||<br />
| |
| EDOs: 9, 54, 63, 72, 495bcd<br />
| |
| Badness: 0.0937<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Enneaportent-11-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->11-limit</h2>
| |
| Commas: 225/224, 385/384, 12005/11979<br />
| |
| <br />
| |
| POTE generator: ~5/4 = 383.146<br />
| |
| <br />
| |
| Map: [&lt;9 0 28 11 24|, &lt;0 2 -1 2 1|]<br />
| |
| EDOs: 9, 54, 63, 72, 423cd, 495bcd<br />
| |
| Badness: 0.0304<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:96:&lt;h2&gt; --><h2 id="toc48"><a name="Enneaportent-13-limit"></a><!-- ws:end:WikiTextHeadingRule:96 -->13-limit</h2>
| |
| Commas: 169/168, 225/224, 364/363, 1716/1715<br />
| |
| <br />
| |
| POTE generator: ~5/4 = 383.047<br />
| |
| <br />
| |
| Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]<br />
| |
| EDOs: 9, 54, 63, 72, 279cf<br />
| |
| Badness: 0.0223<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:98:&lt;h1&gt; --><h1 id="toc49"><a name="Submajor"></a><!-- ws:end:WikiTextHeadingRule:98 -->Submajor</h1>
| |
| Comma: 69198046875/68719476736<br />
| |
| <br />
| |
| POTE generator: ~10125/8192 = 362.321<br />
| |
| <br />
| |
| Map: [&lt;1 4 -1|, &lt;0 -8 11|]<br />
| |
| EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc<br />
| |
| Badness: 0.1302<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:100:&lt;h2&gt; --><h2 id="toc50"><a name="Submajor-7-limit"></a><!-- ws:end:WikiTextHeadingRule:100 -->7-limit</h2>
| |
| Commas: 225/224, 51200/50421<br />
| |
| <br />
| |
| POTE generator: ~49/40 = 362.255<br />
| |
| <br />
| |
| Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]<br />
| |
| Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||<br />
| |
| EDOs: 10, 33, 43, 53<br />
| |
| Badness: 0.0605<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:102:&lt;h2&gt; --><h2 id="toc51"><a name="Submajor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:102 -->11-limit</h2>
| |
| Commas: 225/224, 385/384, 6655/6561<br />
| |
| <br />
| |
| POTE generator: ~27/22 = 362.101<br />
| |
| <br />
| |
| Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]<br />
| |
| EDOs: 10, 53, 116, 169de, 285cde<br />
| |
| Badness: 0.0506<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:104:&lt;h2&gt; --><h2 id="toc52"><a name="Submajor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:104 -->13-limit</h2>
| |
| Commas: 169/168, 225/224, 275/273, 385/384<br />
| |
| <br />
| |
| POTE generator: ~16/13 = 362.105<br />
| |
| <br />
| |
| Map: [&lt;1 4 -1 1 11 4|, &lt;0 -8 11 6 -25 -1|]<br />
| |
| EDOs: 10, 53, 116, 169de, 285cdef<br />
| |
| Badness: 0.0277<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:106:&lt;h2&gt; --><h2 id="toc53"><a name="Submajor-Interpental"></a><!-- ws:end:WikiTextHeadingRule:106 -->Interpental</h2>
| |
| Commas: 99/98, 176/175, 51200/50421<br />
| |
| <br />
| |
| POTE generator: ~49/40 = 362.418<br />
| |
| <br />
| |
| Map: [&lt;1 4 -1 1 -5|, &lt;0 -8 11 6 28|]<br />
| |
| EDOs: 43, 53, 96, 149d<br />
| |
| Badness: 0.0518<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:108:&lt;h3&gt; --><h3 id="toc54"><a name="Submajor-Interpental-13-limit"></a><!-- ws:end:WikiTextHeadingRule:108 -->13-limit</h3>
| |
| Commas: 99/98, 169/168, 176/175, 640/637<br />
| |
| <br />
| |
| POTE generator: ~16/13 = 362.402<br />
| |
| <br />
| |
| Map: [&lt;1 4 -1 1 -5 4|, &lt;0 -8 11 6 28 -1|]<br />
| |
| EDOs: 43, 53, 96, 149d<br />
| |
| Badness: 0.0297<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:110:&lt;h1&gt; --><h1 id="toc55"><a name="Alphorn"></a><!-- ws:end:WikiTextHeadingRule:110 -->Alphorn</h1>
| |
| Commas: 225/224, 5764801/5668704<br />
| |
| <br />
| |
| POTE generator: ~48/35 = 556.221<br />
| |
| <br />
| |
| Map: [&lt;1 9 0 13|, &lt;0 -16 5 -22|]<br />
| |
| Wedgie: &lt;&lt;16 -5 22 -45 -10 65||<br />
| |
| EDOs: 28d, 41, 151cd, 192cd, 233cd<br />
| |
| Badness: 0.1293<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:112:&lt;h2&gt; --><h2 id="toc56"><a name="Alphorn-11-limit"></a><!-- ws:end:WikiTextHeadingRule:112 -->11-limit</h2>
| |
| Commas: 225/224, 385/384, 12250/11979<br />
| |
| <br />
| |
| POTE generator: ~11/8 = 556.144<br />
| |
| <br />
| |
| Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]<br />
| |
| EDOs: 41, 315cde<br />
| |
| Badness: 0.0735</body></html></pre></div>
| |