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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>
| | The 2.3.7-[[Just_intonation_subgroups|subgroup]] comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3>. For any member of the clan, for the rank three [[Gamelismic_family#Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[Slendric|slendric]], this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo|36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo|72edo]], [[77edo|77edo]] or [[118edo|118edo]] might be preferred. |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-12-21 12:36:21 UTC</tt>.<br>
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| : The original revision id was <tt>570593683</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]]
| |
| The 2.3.7-[[Just intonation subgroups|subgroup]] comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3>. For any member of the clan, for the rank three [[Gamelismic family#Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[slendric]], this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred. | |
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| 7-limit minimax | | 7-limit minimax |
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| [|1 0 0 0>, |5/2 3/4 0 -3/4>, | | [|1 0 0 0>, |5/2 3/4 0 -3/4>, |
| |5/2 -1/4 1 -3/4>, |5/2 -1/4 0 1/4>] | | |5/2 -1/4 1 -3/4>, |5/2 -1/4 0 1/4>] |
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| Eigenmonzos: 2, 7/6, 6/5 | | Eigenmonzos: 2, 7/6, 6/5 |
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| 9-limit minimax | | 9-limit minimax |
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| [|1 0 0 0>, |10/7 6/7 0 -3/7>, | | [|1 0 0 0>, |10/7 6/7 0 -3/7>, |
| |10/7 -1/7 1 -3/7>, |20/7 -2/7 0 1/7>] | | |10/7 -1/7 1 -3/7>, |20/7 -2/7 0 1/7>] |
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| Eigenmonzos: 2, 6/5, 9/7 | | Eigenmonzos: 2, 6/5, 9/7 |
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| Lattice basis: 8/7 0.5192 5/4 2.3219 | | Lattice basis: 8/7 0.5192 5/4 2.3219 |
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| Angle(8/7, 5/4) = 90 degrees | | Angle(8/7, 5/4) = 90 degrees |
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| Map to lattice: [<0 3 0 -1|, <0 0 1 0|] | | Map to lattice: [<0 3 0 -1|, <0 0 1 0|] |
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| Map: [<1 1 0 3|, <0 3 0 -1|, < 0 0 1 0|] | | Map: [<1 1 0 3|, <0 3 0 -1|, < 0 0 1 0|] |
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| Generators: 2, 5, 7 | | Generators: 2, 5, 7 |
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| No-fives [[POTE tuning|POTE generator]]: 233.688 | | No-fives [[POTE_tuning|POTE generator]]: 233.688 |
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| EDOs: 5, 36, 77, 190 | | EDOs: 5, 36, 77, 190 |
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| ==Full seven limit children== | | ==Full seven limit children== |
| To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period. | | To the gamelisma itself we need to add the comma which appears next on the modified [[Normal_lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period. |
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| =Miracle= | | =Miracle= |
| [[Comma|Commas]]: 1029/1024, 225/224 | | [[Comma|Commas]]: 1029/1024, 225/224 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
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| 7-limit: [|1 0 0 0>, |25/13 6/13 -6/13 0>, | | 7-limit: [|1 0 0 0>, |25/13 6/13 -6/13 0>, |
| |25/13 -7/13 7/13 0>, |35/13 -2/13 2/13 0>] | | |25/13 -7/13 7/13 0>, |35/13 -2/13 2/13 0>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 6/5 | | [[Eigenmonzo|Eigenmonzos]]: 2, 6/5 |
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| 9-limit: [|1 0 0 0>, |25/19 12/19 -6/19 0>, | | 9-limit: [|1 0 0 0>, |25/19 12/19 -6/19 0>, |
| |50/19 -14/19 7/19 0>, |55/19 -4/19 2/19 0>] | | |50/19 -14/19 7/19 0>, |55/19 -4/19 2/19 0>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 10/9 | | [[Eigenmonzo|Eigenmonzos]]: 2, 10/9 |
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| [[POTE tuning|POTE generator]]: 116.675 | | [[POTE_tuning|POTE generator]]: 116.675 |
| Algebraic generator: Secor59, [[Algebraic number|positive root]] of 15x^6-8x^4-12 | | |
| | Algebraic generator: Secor59, [[Algebraic_number|positive root]] of 15x^6-8x^4-12 |
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| Map: [<1 1 3 3|, <0 6 -7 -2|] | | Map: [<1 1 3 3|, <0 6 -7 -2|] |
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| Wedgie: <<6 -7 -2 -25 -20 15|| | | Wedgie: <<6 -7 -2 -25 -20 15|| |
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| EDOs: 10, 21, 31, 41, 72, [[175edo|175]] | | EDOs: 10, 21, 31, 41, 72, [[175edo|175]] |
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| Badness: 0.0167 | | Badness: 0.0167 |
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| ==11-limit== | | ==11-limit== |
| [[Comma|Commas]]: 1029/1024, 225/224, 243/242 | | [[Comma|Commas]]: 1029/1024, 225/224, 243/242 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
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| [|1 0 0 0 0>, |25/19 12/19 -6/19 0 0>, | | [|1 0 0 0 0>, |25/19 12/19 -6/19 0 0>, |
| |50/19 -14/19 7/19 0 0>, |55/19 -4/19 2/19 0 0>, | | |50/19 -14/19 7/19 0 0>, |55/19 -4/19 2/19 0 0>, |
| |53/19 30/19 -15/19 0 0>] | | |53/19 30/19 -15/19 0 0>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 10/9 | | [[Eigenmonzo|Eigenmonzos]]: 2, 10/9 |
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| [[POTE tuning|POTE generator]]: 116.633 | | [[POTE_tuning|POTE generator]]: 116.633 |
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| Algebraic generator: Secor59 | | Algebraic generator: Secor59 |
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| Map: [<1 1 3 3 2|, <0 6 -7 -2 15|] | | Map: [<1 1 3 3 2|, <0 6 -7 -2 15|] |
| [[edo|EDOs]]: 10, 31, 41, [[72edo|72]], 247c, 319bcde, [[391edo|391bcde]], 463bcde | | |
| | [[EDO|EDOs]]: 10, 31, 41, [[72edo|72]], 247c, 319bcde, [[391edo|391bcde]], 463bcde |
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| Badness: 0.0107 | | Badness: 0.0107 |
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| [[Chords of miracle]] | | [[Chords_of_miracle|Chords of miracle]] |
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| ==Revelation== | | ==Revelation== |
| Commas: 99/98, 176/175, 1029/1024 | | Commas: 99/98, 176/175, 1029/1024 |
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| Line 76: |
Line 89: |
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| Map: [<1 1 3 3 5|, <0 6 -7 -2 -16|] | | Map: [<1 1 3 3 5|, <0 6 -7 -2 -16|] |
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| EDOs: 10, 21, 31 | | EDOs: 10, 21, 31 |
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| Badness: 0.0329 | | Badness: 0.0329 |
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| ===13-limit=== | | ===13-limit=== |
| Commas: 66/65, 99/98, 105/104, 1001/1000 | | Commas: 66/65, 99/98, 105/104, 1001/1000 |
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| Line 85: |
Line 100: |
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| Map: [<1 1 3 3 5 4|, <0 6 -7 -2 -16 -3|] | | Map: [<1 1 3 3 5 4|, <0 6 -7 -2 -16 -3|] |
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| EDOs: 10, 21, 31 | | EDOs: 10, 21, 31 |
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| Badness: 0.0295 | | Badness: 0.0295 |
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| ==Miraculous== | | ==Miraculous== |
| Commas: 105/104, 144/143, 196/195, 275/273 | | Commas: 105/104, 144/143, 196/195, 275/273 |
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| Line 94: |
Line 111: |
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| Map: [<1 1 3 3 2 4|, <0 6 -7 -2 15 -3|] | | Map: [<1 1 3 3 2 4|, <0 6 -7 -2 15 -3|] |
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| EDOs: 10, 31, 41, 72f, 113f, 185cf | | EDOs: 10, 31, 41, 72f, 113f, 185cf |
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| Badness: 0.0187 | | Badness: 0.0187 |
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| ==Benediction== | | ==Benediction== |
| Commas: 225/224, 243/242, 351/350, 441/440 | | Commas: 225/224, 243/242, 351/350, 441/440 |
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| Line 103: |
Line 122: |
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| Map: [<1 1 3 3 2 7|, <0 6 -7 -2 15 -34|] | | Map: [<1 1 3 3 2 7|, <0 6 -7 -2 15 -34|] |
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| EDOs: 31, 72, 103, [[175edo|175f]] | | EDOs: 31, 72, 103, [[175edo|175f]] |
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| Badness: 0.0157 | | Badness: 0.0157 |
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| ===17-limit=== | | ===17-limit=== |
| Commas: 225/224, 243/242, 273/272, 351/350, 385/384 | | Commas: 225/224, 243/242, 273/272, 351/350, 385/384 |
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| Line 112: |
Line 133: |
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| Map: [<1 1 3 3 2 7 7|, <0 6 -7 -2 15 -34 -30|] | | Map: [<1 1 3 3 2 7 7|, <0 6 -7 -2 15 -34 -30|] |
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| EDOs: 31, 72, 103, [[175edo|175f]] | | EDOs: 31, 72, 103, [[175edo|175f]] |
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| ==Manna== | | ==Manna== |
| Commas: 225/224, 243/242, 325/324, 385/384 | | Commas: 225/224, 243/242, 325/324, 385/384 |
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| Line 120: |
Line 142: |
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| Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 38|] | | Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 38|] |
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| EDOs: 10f, 31f, 41, 72, 113, 185cf, 257cf | | EDOs: 10f, 31f, 41, 72, 113, 185cf, 257cf |
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| Badness: 0.0170 | | Badness: 0.0170 |
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| ==Semimiracle== | | ==Semimiracle== |
| Commas: 169/168, 225/224, 243/242, 385/384 | | Commas: 169/168, 225/224, 243/242, 385/384 |
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| Line 129: |
Line 153: |
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| Map: [<2 2 6 6 4 7|, <0 6 -7 -2 15 2|] | | Map: [<2 2 6 6 4 7|, <0 6 -7 -2 15 2|] |
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| EDOs: 10, 62, 72 | | EDOs: 10, 62, 72 |
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| Badness: 0.0246 | | Badness: 0.0246 |
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| ===17-limit=== | | ===17-limit=== |
| Commas: 169/168, 221/220, 225/224, 243/242, 385/384 | | Commas: 169/168, 221/220, 225/224, 243/242, 385/384 |
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| Line 138: |
Line 164: |
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| Map: [<2 2 6 6 4 7 7|, <0 6 -7 -2 15 2 6|] | | Map: [<2 2 6 6 4 7 7|, <0 6 -7 -2 15 2 6|] |
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| EDOs: 10, 62, 72 | | EDOs: 10, 62, 72 |
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| Badness: 0.0161 | | Badness: 0.0161 |
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| ==Hemimiracle== | | ==Hemimiracle== |
| Commas: 225/224, 245/242, 1029/1024 | | Commas: 225/224, 245/242, 1029/1024 |
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| Line 147: |
Line 175: |
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| Map: [<1 1 3 3 4|, <0 12 -14 -4 -11|] | | Map: [<1 1 3 3 4|, <0 12 -14 -4 -11|] |
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| EDOs: 20, 21, 41, 123c, 144e, 185ce, 226ce | | EDOs: 20, 21, 41, 123c, 144e, 185ce, 226ce |
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| Badness: 0.0592 | | Badness: 0.0592 |
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| ===13-limit=== | | ===13-limit=== |
| Commas: 105/104, 196/195, 245/242, 512/507 | | Commas: 105/104, 196/195, 245/242, 512/507 |
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| Line 156: |
Line 186: |
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| Map: [<1 1 3 3 4 4|, <0 12 -14 -4 -11 -6|] | | Map: [<1 1 3 3 4 4|, <0 12 -14 -4 -11 -6|] |
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| EDOs: 20, 21, 41, 123cf, 144ef, 185cef | | EDOs: 20, 21, 41, 123cf, 144ef, 185cef |
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| Badness: 0.0432 | | Badness: 0.0432 |
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| ==Oracle== | | ==Oracle== |
| Commas: 121/120, 225/224, 1029/1024 | | Commas: 121/120, 225/224, 1029/1024 |
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| Line 165: |
Line 197: |
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| Map: [<1 7 -4 1 3|, <0 -12 14 4 1|] | | Map: [<1 7 -4 1 3|, <0 -12 14 4 1|] |
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| EDOs: 11, 20, 31, 51, 82e, 113e, 144e | | EDOs: 11, 20, 31, 51, 82e, 113e, 144e |
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| Line 173: |
Line 206: |
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| Map: [<1 1 3 3 2 2|, <0 12 -14 -4 30 35|] | | Map: [<1 1 3 3 2 2|, <0 12 -14 -4 30 35|] |
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| EDOs: 41, 62, 103, 247c, 350bcde | | EDOs: 41, 62, 103, 247c, 350bcde |
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| Badness: 0.0256 | | Badness: 0.0256 |
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| ===17-limit=== | | ===17-limit=== |
| Commas: 225/224, 243/242, 273/272, 441/440, 847/845 | | Commas: 225/224, 243/242, 273/272, 441/440, 847/845 |
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| Line 182: |
Line 217: |
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| Map: [<1 1 3 3 2 2 2|, <0 12 -14 -4 30 35 43|] | | Map: [<1 1 3 3 2 2 2|, <0 12 -14 -4 30 35 43|] |
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| EDOs: 41, 62, 103 | | EDOs: 41, 62, 103 |
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| Badness: 0.0225 | | Badness: 0.0225 |
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| Line 191: |
Line 228: |
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| Map: [<1 7 -4 1 17 4|, <0 -18 21 6 -45 -1|] | | Map: [<1 7 -4 1 17 4|, <0 -18 21 6 -45 -1|] |
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| EDOs: 10, 103, 113, 216c | | EDOs: 10, 103, 113, 216c |
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| Badness: 0.0332 | | Badness: 0.0332 |
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| Line 200: |
Line 239: |
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| Map: [<1 7 -4 1 17 4 8|, <0 -18 21 6 -45 -1 -13|] | | Map: [<1 7 -4 1 17 4 8|, <0 -18 21 6 -45 -1 -13|] |
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| EDOs: 10, 103, 113, 216c | | EDOs: 10, 103, 113, 216c |
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| Badness: 0.0247 | | Badness: 0.0247 |
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| ==Music== | | ==Music== |
| By [[Gene Ward Smith]] | | By [[Gene_Ward_Smith|Gene Ward Smith]] |
| [[http://www.archive.org/details/RachmaninoffPlaysBlackjack|Rachmaninoff Plays Blackjack]] [[http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3|play]]
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| By [[Joseph Pehrson]] | | [http://www.archive.org/details/RachmaninoffPlaysBlackjack Rachmaninoff Plays Blackjack] [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play] |
| [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3|Black and Jill]]
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| [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3|Blacklight]]
| | By [[Joseph_Pehrson|Joseph Pehrson]] |
| [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3|Blackjack]]
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| | [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3 Black and Jill] |
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| | [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3 Blacklight] |
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| | [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3 Blackjack] |
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| =Rodan= | | =Rodan= |
| [[Comma|Commas]]: 1029/1024, 245/243 | | [[Comma|Commas]]: 1029/1024, 245/243 |
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| 7+9 limit minimax tuning: [|1 0 0 0>, |5/3 0 1/6 -1/6>, | | 7+9 limit minimax tuning: [|1 0 0 0>, |5/3 0 1/6 -1/6>, |
| |25/9 0 17/18 -17/18>, |25/9 0 -1/18 1/18>] | | |25/9 0 17/18 -17/18>, |25/9 0 -1/18 1/18>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 | | [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 |
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| [[POTE tuning|POTE generator]]: 234.417 | | [[POTE_tuning|POTE generator]]: 234.417 |
| Algebraic generator: [[Algebraic number|larger root]] of 20x^2-36x+15, or (9+√6)/10. | | |
| | Algebraic generator: [[Algebraic_number|larger root]] of 20x^2-36x+15, or (9+√6)/10. |
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| Map: [<1 1 -1 3|, <0 3 17 -1|] | | Map: [<1 1 -1 3|, <0 3 17 -1|] |
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| EDOs: 41, 87, 128 | | EDOs: 41, 87, 128 |
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| Badness: 0.0371 | | Badness: 0.0371 |
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| ==11-limit== | | ==11-limit== |
| [[Comma|Commas]]: 441/440, 245/243, 385/384 | | [[Comma|Commas]]: 441/440, 245/243, 385/384 |
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| [[Minimax tuning]]: [|1 0 0 0 0>, |31/19 6/19 0 0 -3/19>, | | [[Minimax_tuning|Minimax tuning]]: [|1 0 0 0 0>, |31/19 6/19 0 0 -3/19>, |
| |49/19 34/19 0 0 -17/19>, |53/19 -2/19 0 0 1/19>, | | |49/19 34/19 0 0 -17/19>, |53/19 -2/19 0 0 1/19>, |
| |62/19 -26/19 0 0 13/19>] | | |62/19 -26/19 0 0 13/19>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 11/9 | | [[Eigenmonzo|Eigenmonzos]]: 2, 11/9 |
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| [[POTE tuning|POTE generator]]: 234.459 | | [[POTE_tuning|POTE generator]]: 234.459 |
| Algebraic generator: [[Algebraic number|positive root]] of x^2+16x-31, or √95-8. | | |
| | Algebraic generator: [[Algebraic_number|positive root]] of x^2+16x-31, or √95-8. |
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| Map: [<1 1 -1 3 6|, <0 3 17 -1 -13|] | | Map: [<1 1 -1 3 6|, <0 3 17 -1 -13|] |
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| EDOs: 41, 87, 389d | | EDOs: 41, 87, 389d |
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| Badness: 0.0231 | | Badness: 0.0231 |
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| [[Chords of rodan]] | | [[Chords_of_rodan|Chords of rodan]] |
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| ==13-limit== | | ==13-limit== |
| Commas: 196/195, 245/243, 352/351, 364/363 | | Commas: 196/195, 245/243, 352/351, 364/363 |
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| 13 and 15 limit minimax | | 13 and 15 limit minimax |
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| [|1 0 0 0 0 0>, |23/14 3/14 0 0 0 -3/28>, | | [|1 0 0 0 0 0>, |23/14 3/14 0 0 0 -3/28>, |
| |37/14 17/14 0 0 0 -17/28>, |39/14 -1/14 0 0 0 1/28>, | | |37/14 17/14 0 0 0 -17/28>, |39/14 -1/14 0 0 0 1/28>, |
| |45/14 -13/14 0 0 0 13/28>, |23/7 -11/7 0 0 0 11/14>] | | |45/14 -13/14 0 0 0 13/28>, |23/7 -11/7 0 0 0 11/14>] |
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| Eigenmonzos: 2, 13/9 | | Eigenmonzos: 2, 13/9 |
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| [[POTE tuning|POTE generator]]: 234.482 | | [[POTE_tuning|POTE generator]]: 234.482 |
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| Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly. | | Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly. |
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| Map: [<1 1 -1 3 6 8|, <0 3 17 -1 -13 -22|] | | Map: [<1 1 -1 3 6 8|, <0 3 17 -1 -13 -22|] |
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| Generators: 2, 8/7 | | Generators: 2, 8/7 |
| [[edo|Edos]]: 41, 46, [[87edo|87]] | | |
| | [[EDO|Edos]]: 41, 46, [[87edo|87]] |
| | |
| Badness: 0.0184 | | Badness: 0.0184 |
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| ==17-limit== | | ==17-limit== |
| Commas: 154/153, 196/195, 245/243, 273/272, 364/363 | | Commas: 154/153, 196/195, 245/243, 273/272, 364/363 |
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| Eigenmonzos: 2, 18/17 | | Eigenmonzos: 2, 18/17 |
| [[POTE tuning|POTE generator]]: ~8/7 = 234.524 | | |
| | [[POTE_tuning|POTE generator]]: ~8/7 = 234.524 |
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| Map: [<1 1 -1 3 6 8 8|, <0 3 17 -1 -13 -22 -20|] | | Map: [<1 1 -1 3 6 8 8|, <0 3 17 -1 -13 -22 -20|] |
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| Edos: 41, 46, 87, 220dg, 307dg | | Edos: 41, 46, 87, 220dg, 307dg |
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| Badness: 0.0167 | | Badness: 0.0167 |
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| ===Music=== | | ===Music=== |
| By [[Gene Ward Smith]] | | By [[Gene_Ward_Smith|Gene Ward Smith]] |
| [[http://www.archive.org/details/Pianodactyl|Pianodactyl]] [[http://www.archive.org/download/Pianodactyl/pianodactyl.mp3|play]]
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| ==Aerodactyl== | | [http://www.archive.org/details/Pianodactyl Pianodactyl] [http://www.archive.org/download/Pianodactyl/pianodactyl.mp3 play] |
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| | ==Aerodactyl== |
| Commas: 91/90, 245/243, 385/384, 441/440 | | Commas: 91/90, 245/243, 385/384, 441/440 |
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| [[POTE tuning|POTE generator]]: ~8/7 = 234.639 | | [[POTE_tuning|POTE generator]]: ~8/7 = 234.639 |
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| Map: [<1 1 -1 3 6 -1|, <0 3 17 -1 -13 24| | | Map: [<1 1 -1 3 6 -1|, <0 3 17 -1 -13 24| |
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| EDOs: 41f, 46, 51c | | EDOs: 41f, 46, 51c |
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| Badness: 0.0340 | | Badness: 0.0340 |
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| ==Aerodino== | | ==Aerodino== |
| Commas: 176/175, 245/243, 1029/1024 | | Commas: 176/175, 245/243, 1029/1024 |
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| Line 288: |
Line 354: |
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| Map: [<1 1 -1 3 -3|, <0 3 17 -1 33| | | Map: [<1 1 -1 3 -3|, <0 3 17 -1 33| |
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| EDOS: 46 | | EDOS: 46 |
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| Badness: 0.0543 | | Badness: 0.0543 |
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| ===13-limit=== | | ===13-limit=== |
| Commas: 91/90, 176/175, 245/243, 847/845 | | Commas: 91/90, 176/175, 245/243, 847/845 |
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| Line 297: |
Line 365: |
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| Map: [<1 1 -1 3 -3 -1|, <0 3 17 -1 33 24| | | Map: [<1 1 -1 3 -3 -1|, <0 3 17 -1 33 24| |
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| EDOs: 46 | | EDOs: 46 |
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| Badness: 0.0358 | | Badness: 0.0358 |
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| ==Varan== | | ==Varan== |
| Commas: 100/99, 245/243, 2835/2816 | | Commas: 100/99, 245/243, 2835/2816 |
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| Line 306: |
Line 376: |
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| Map: [<1 1 -1 3 -2|, <0 3 17 -1 28| | | Map: [<1 1 -1 3 -2|, <0 3 17 -1 28| |
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| EDOs: 41, 46e | | EDOs: 41, 46e |
| | |
| Badness: 0.0449 | | Badness: 0.0449 |
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| ===13-limit=== | | ===13-limit=== |
| Commas: 100/99, 105/104, 245/243, 352/351 | | Commas: 100/99, 105/104, 245/243, 352/351 |
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| Line 315: |
Line 387: |
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| Map: [<1 1 -1 3 -2 0|, <0 3 17 -1 28 19| | | Map: [<1 1 -1 3 -2 0|, <0 3 17 -1 28 19| |
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| EDOs: 41 | | EDOs: 41 |
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| Badness: 0.0323 | | Badness: 0.0323 |
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| =Valentine= | | =Valentine= |
| ==7-limit== | | |
| | ==7-limit== |
| [[Comma|Commas]]: 1029/1024, 126/125 | | [[Comma|Commas]]: 1029/1024, 126/125 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
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| 7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, | | 7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, |
| |17/6 5/12 0 -5/12>, [5/2 -1/4 0 1/4>] | | |17/6 5/12 0 -5/12>, [5/2 -1/4 0 1/4>] |
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| Eigenmonzos: 2, 7/6 | | Eigenmonzos: 2, 7/6 |
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| 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, | | 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |
| |47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>] | | |47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>] |
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| Eigenmonzos: 2, 9/7 | | Eigenmonzos: 2, 9/7 |
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| [[POTE tuning|POTE generator]]: 77.864 | | [[POTE_tuning|POTE generator]]: 77.864 |
| Algebraic generator: [[Algebraic number|smaller root]] of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents. | | |
| | Algebraic generator: [[Algebraic_number|smaller root]] of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents. |
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| Map: [<1 1 2 3|, <0 9 5 -3|] | | Map: [<1 1 2 3|, <0 9 5 -3|] |
| | |
| Wedgie: <<9 5 -3 -13 -30 -21|| | | Wedgie: <<9 5 -3 -13 -30 -21|| |
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| EDOs: 15, 31, 46, 77, 185, 262cd | | EDOs: 15, 31, 46, 77, 185, 262cd |
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| Badness: 0.0311 | | Badness: 0.0311 |
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| ==11-limit== | | ==11-limit== |
| [[Comma|Commas]]: 121/120, 126/125, 176/175 | | [[Comma|Commas]]: 121/120, 126/125, 176/175 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
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| [|1 0 0 0 0>, |1 0 0 -9/10 9/10>, | | [|1 0 0 0 0>, |1 0 0 -9/10 9/10>, |
| |2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>] | | |2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>] |
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| Eigenmonzos: 2, 11/7 | | Eigenmonzos: 2, 11/7 |
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| [[POTE tuning|POTE generator]]: 77.881 | | [[POTE_tuning|POTE generator]]: 77.881 |
| Algebraic generator: [[Algebraic number|positive root]] of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5. | | |
| | Algebraic generator: [[Algebraic_number|positive root]] of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5. |
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| Map: [<1 1 2 3 3|, <0 9 5 -3 7|] | | Map: [<1 1 2 3 3|, <0 9 5 -3 7|] |
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| Generators: 2, 21/20 | | Generators: 2, 21/20 |
| [[edo|Edos]]: 15, 31, 46, 77, 262cde, 339cde | | |
| | [[EDO|Edos]]: 15, 31, 46, 77, 262cde, 339cde |
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| Badness: 0.0167 | | Badness: 0.0167 |
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| [[Chords of valentine]] | | [[Chords_of_valentine|Chords of valentine]] |
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| =Unidec= | | =Unidec= |
| Comma: 31381059609/31250000000 | | Comma: 31381059609/31250000000 |
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| Line 363: |
Line 451: |
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| Map: [<2 5 8|, <0 -6 -11|] | | Map: [<2 5 8|, <0 -6 -11|] |
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| EDOs: 26, 46, 72, 118, 2524, 2642, 2760, 5002bc | | EDOs: 26, 46, 72, 118, 2524, 2642, 2760, 5002bc |
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| Badness: 0.0824 | | Badness: 0.0824 |
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| ==7-limit== | | ==7-limit== |
| [[Comma|Commas]]: 1029/1024, 4375/4374 | | [[Comma|Commas]]: 1029/1024, 4375/4374 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
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| 7-limit: [|1 0 0 0>, |47/26 0 6/13 -6/13>, | | 7-limit: [|1 0 0 0>, |47/26 0 6/13 -6/13>, |
| |71/26 0 11/13 -11/13>, |71/26 0 -2/13 2/13>] | | |71/26 0 11/13 -11/13>, |71/26 0 -2/13 2/13>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 | | [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 |
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| 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, | | 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |
| |57/28 11/7 0 -11/14>, |20/7 -2/7 0 1/7>] | | |57/28 11/7 0 -11/14>, |20/7 -2/7 0 1/7>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 | | [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 |
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| [[POTE tuning|POTE generator]]: ~10/9 = 183.161 | | [[POTE_tuning|POTE generator]]: ~10/9 = 183.161 |
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| Map: [<2 5 8 5|, <0 -6 -11 2|] | | Map: [<2 5 8 5|, <0 -6 -11 2|] |
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| Wedgie: <<12 22 -4 7 -40 -71|| | | Wedgie: <<12 22 -4 7 -40 -71|| |
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| EDOs: 26, 46, 72, 118, 190 | | EDOs: 26, 46, 72, 118, 190 |
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| ==11-limit== | | ==11-limit== |
| [[Comma|Commas]]: 385/384, 441/440, 4375/4374 | | [[Comma|Commas]]: 385/384, 441/440, 4375/4374 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
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| [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |57/28 11/7 0 -11/14 0>, | | [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |57/28 11/7 0 -11/14 0>, |
| |20/7 -2/7 0 1/7 0>, |99/28 -3/7 0 3/14 0>] | | |20/7 -2/7 0 1/7 0>, |99/28 -3/7 0 3/14 0>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 | | [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 |
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| [[POTE tuning|POTE generator]]: 183.165 | | [[POTE_tuning|POTE generator]]: 183.165 |
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| Map: [<2 5 8 5 6|, <0 -6 -11 2 3|] | | Map: [<2 5 8 5 6|, <0 -6 -11 2 3|] |
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| EDOs: 26, 46, 72, 118, 190 | | EDOs: 26, 46, 72, 118, 190 |
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| | [[Chords_of_unidec|Chords of unidec]] |
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| [[Chords of unidec]]
| | ==Ekadash== |
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| ==Ekadash== | |
| Commas: 385/384, 441/440, 625/624, 729/728 | | Commas: 385/384, 441/440, 625/624, 729/728 |
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| [[POTE tuning|POTE generator]]: ~10/9 = 183.187 | | [[POTE_tuning|POTE generator]]: ~10/9 = 183.187 |
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| Map: [<2 5 8 5 6 19|, <0 -6 -11 2 3 -38|] | | Map: [<2 5 8 5 6 19|, <0 -6 -11 2 3 -38|] |
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| EDOs: 20cf, 26f, 46f, 72, 118, 190, 262df, 452cdef | | EDOs: 20cf, 26f, 46f, 72, 118, 190, 262df, 452cdef |
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| Bad: 0.0204 | | Bad: 0.0204 |
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| ==Hendec== | | ==Hendec== |
| Commas: 169/168, 325/324, 364/363, 1716/1715 | | Commas: 169/168, 325/324, 364/363, 1716/1715 |
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| [[POTE tuning|POTE generator]]: ~10/9 = 183.187 | | [[POTE_tuning|POTE generator]]: ~10/9 = 183.187 |
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| Map: [<2 5 8 5 6 8|, <0 -6 -11 2 3 -2|] | | Map: [<2 5 8 5 6 8|, <0 -6 -11 2 3 -2|] |
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| EDOs: 26, 46, 72 | | EDOs: 26, 46, 72 |
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| Bad: 0.0177 | | Bad: 0.0177 |
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| ===17-limit=== | | ===17-limit=== |
| Commas: 169/168, 221/220, 273/272, 325/324, 364/363 | | Commas: 169/168, 221/220, 273/272, 325/324, 364/363 |
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| [[POTE tuning|POTE generator]]: ~10/9 = 183.196 | | [[POTE_tuning|POTE generator]]: ~10/9 = 183.196 |
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| Map: [<2 5 8 5 6 8 10|, <0 -6 -11 2 3 -2 -6|] | | Map: [<2 5 8 5 6 8 10|, <0 -6 -11 2 3 -2 -6|] |
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| EDOs: 26, 46, 72 | | EDOs: 26, 46, 72 |
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| ===Music=== | | ===Music=== |
| [[Technical Notes for Newbeams#Track%20notes:-Hypnocloudsmack%202|Hypnocloudsmack 2]] by [[Andrew Heathwaite]] | | [[Technical_Notes_for_Newbeams#Track notes:-Hypnocloudsmack 2|Hypnocloudsmack 2]] by [[Andrew_Heathwaite|Andrew Heathwaite]] |
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| =Hemithirds= | | =Hemithirds= |
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| ==7-limit== | | ==7-limit== |
| [[Comma|Commas]]: 1029/1024, 3136/3125 | | [[Comma|Commas]]: 1029/1024, 3136/3125 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
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| 7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, | | 7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, |
| |11/5 -1/10 0 1/10>, |5/2 -1/4 0 1/4>] | | |11/5 -1/10 0 1/10>, |5/2 -1/4 0 1/4>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 7/6 | | [[Eigenmonzo|Eigenmonzos]]: 2, 7/6 |
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| 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, | | 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |
| |82/35 -4/35 0 2/35>, |20/7 -2/7 0 1/7>] | | |82/35 -4/35 0 2/35>, |20/7 -2/7 0 1/7>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 7/6 | | [[Eigenmonzo|Eigenmonzos]]: 2, 7/6 |
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| ==11-limit== | | ==11-limit== |
| [[Comma|Commas]]: 385/384, 441/440, 3136/3125 | | [[Comma|Commas]]: 385/384, 441/440, 3136/3125 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
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| [|1 0 0 0 0>, |11/9 0 0 -5/9 5/9>, |64/27 0 0 2/27 -2/27>, | | [|1 0 0 0 0>, |11/9 0 0 -5/9 5/9>, |64/27 0 0 2/27 -2/27>, |
| |79/27 0 0 5/27 -5/27>, |79/27 0 0 -22/27 22/27>] | | |79/27 0 0 5/27 -5/27>, |79/27 0 0 -22/27 22/27>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 11/7 | | [[Eigenmonzo|Eigenmonzos]]: 2, 11/7 |
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| POTE generator: ~28/25 = 193.227 | | POTE generator: ~28/25 = 193.227 |
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| | Map: [<1 4 2 2 7|, <0 -15 2 5 -22|] |
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| | [[EDO|Edos]]: [[31edo|31]], [[87edo|87]], [[118edo|118]] |
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| Map: [<1 4 2 2 7|, <0 -15 2 5 -22|]
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| [[edo|Edos]]: [[31edo|31]], [[87edo|87]], [[118edo|118]]
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| Badness: 0.0190 | | Badness: 0.0190 |
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| [[Chords of hemithirds]] | | [[Chords_of_hemithirds|Chords of hemithirds]] |
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| ==13-limit== | | ==13-limit== |
| Commas: 196/195 352/351 1001/1000 1029/1024 | | Commas: 196/195 352/351 1001/1000 1029/1024 |
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| Line 466: |
Line 574: |
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| Map: [<1 4 2 2 7 0|, <0 -15 2 5 -22 23|] | | Map: [<1 4 2 2 7 0|, <0 -15 2 5 -22 23|] |
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| EDOs: 31, 56, 87, 118, 205d | | EDOs: 31, 56, 87, 118, 205d |
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| Badness: 0.0217 | | Badness: 0.0217 |
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| =Hemiseven= | | =Hemiseven= |
| ==7-limit== | | |
| | ==7-limit== |
| Commas: 1029/1024, 19683/19600 | | Commas: 1029/1024, 19683/19600 |
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| Line 476: |
Line 587: |
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| Map: [<1 4 14 2|, <0 -6 -29 2|] | | Map: [<1 4 14 2|, <0 -6 -29 2|] |
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| Wedgie: <<6 29 -2 32 -20 -86|| | | Wedgie: <<6 29 -2 32 -20 -86|| |
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| EDOs: 5, 72, 77, 149, 221, 514bd, 735bcd | | EDOs: 5, 72, 77, 149, 221, 514bd, 735bcd |
| | |
| Badness: 0.0566 | | Badness: 0.0566 |
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| ==11-limit== | | ==11-limit== |
| Commas: 385/384, 441/440, 19683/19600 | | Commas: 385/384, 441/440, 19683/19600 |
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| Line 486: |
Line 600: |
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| Map: [<1 4 14 2 -5|, <0 -6 -29 2 21|] | | Map: [<1 4 14 2 -5|, <0 -6 -29 2 21|] |
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| EDOs: 72, 77, 149, 221e, 293de | | EDOs: 72, 77, 149, 221e, 293de |
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| Badness: 0.0285 | | Badness: 0.0285 |
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| ==13-limit== | | ==13-limit== |
| Commas: 351/350, 385/384, 441/440, 676/675 | | Commas: 351/350, 385/384, 441/440, 676/675 |
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| Line 495: |
Line 611: |
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| Map: [<1 4 14 2 -5 19|, <0 -6 -29 2 21 -38|] | | Map: [<1 4 14 2 -5 19|, <0 -6 -29 2 21 -38|] |
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| EDOs: 72, 77, 149, 221ef | | EDOs: 72, 77, 149, 221ef |
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| ==17-limit== | | ==17-limit== |
| Commas: 273/272, 351/350, 385/384, 441/440, 676/675 | | Commas: 273/272, 351/350, 385/384, 441/440, 676/675 |
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| Line 503: |
Line 620: |
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| Map: [<1 4 14 2 -5 19 21|, <0 -6 -29 2 21 -38 -42|] | | Map: [<1 4 14 2 -5 19 21|, <0 -6 -29 2 21 -38 -42|] |
| | |
| EDOs: 72, 77, 149, 221ef | | EDOs: 72, 77, 149, 221ef |
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| =Tritikleismic= | | =Tritikleismic= |
| ==7-limit== | | |
| | ==7-limit== |
| [[Comma|Commas]]: 1029/1024, 15625/15552 | | [[Comma|Commas]]: 1029/1024, 15625/15552 |
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| [[Minimax tunings]]: | | [[Minimax_tunings|Minimax tunings]]: |
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| 7-limit: [|1 0 0 0>, |2 0 6/7 -6/7>, | | 7-limit: [|1 0 0 0>, |2 0 6/7 -6/7>, |
| |8/3 0 5/7 -5/7>, |8/3 0 -2/7 2/7>] | | |8/3 0 5/7 -5/7>, |8/3 0 -2/7 2/7>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 | | [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 |
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| 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, | | 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |
| |46/21 5/7 0 -5/14>, |20/7 -2/7 0 1/7>] | | |46/21 5/7 0 -5/14>, |20/7 -2/7 0 1/7>] |
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| [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 | | [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 |
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| ==11-limit== | | ==11-limit== |
| [[Comma|Commas]]: 385/384, 441/440, 4000/3993 | | [[Comma|Commas]]: 385/384, 441/440, 4000/3993 |
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| [[Minimax tuning]]: | | [[Minimax_tuning|Minimax tuning]]: |
| | |
| [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |46/21 5/7 0 -5/14 0>, | | [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |46/21 5/7 0 -5/14 0>, |
| |20/7 -2/7 0 1/7 0>, |71/21 3/7 0 -3/14 0>] | | |20/7 -2/7 0 1/7 0>, |71/21 3/7 0 -3/14 0>] |
| | |
| [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 | | [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 |
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| Map: [<3 0 3 10 8|, <0 6 5 -2 3|] | | Map: [<3 0 3 10 8|, <0 6 5 -2 3|] |
| [[edo|EDOs]]: [[72edo|72]], [[159edo|159]], [[231edo|231]]
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| |
|
| ==13-limit== | | [[EDO|EDOs]]: [[72edo|72]], [[159edo|159]], [[231edo|231]] |
| | |
| | ==13-limit== |
| Commas: 325/324, 364/363, 441/440, 625/624 | | Commas: 325/324, 364/363, 441/440, 625/624 |
|
| |
|
| Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|] | | Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|] |
| | |
| EDOs: 15, 72, 87, 159 | | EDOs: 15, 72, 87, 159 |
|
| |
|
| ==17-limit== | | ==17-limit== |
| Commas: 273/272, 325/324, 364/363, 375/374, 385/384 | | Commas: 273/272, 325/324, 364/363, 375/374, 385/384 |
|
| |
|
| Map: [<3 0 3 10 8 0 -2|, <0 6 5 -2 3 14 18|] | | Map: [<3 0 3 10 8 0 -2|, <0 6 5 -2 3 14 18|] |
| | |
| EDOs: 15g, 72, 87, 159 | | EDOs: 15g, 72, 87, 159 |
|
| |
|
| =Superkleismic= | | =Superkleismic= |
| Commas: 1029/1024, 875/864 | | Commas: 1029/1024, 875/864 |
|
| |
|
| Line 547: |
Line 674: |
|
| |
|
| Map: [<1 4 5 2|, <0 -9 -10 3|] | | Map: [<1 4 5 2|, <0 -9 -10 3|] |
| | |
| EDOs: 11, 15, 26, 41 | | EDOs: 11, 15, 26, 41 |
| | |
| Badness: 0.0479 | | Badness: 0.0479 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 100/99, 245/242, 385/384 | | Commas: 100/99, 245/242, 385/384 |
|
| |
|
| Line 556: |
Line 685: |
|
| |
|
| Map: [<1 4 5 2 4|, <0 -9 -10 3 -2|] | | Map: [<1 4 5 2 4|, <0 -9 -10 3 -2|] |
| | |
| EDOs: 15, 26, 41, 261 | | EDOs: 15, 26, 41, 261 |
| | |
| Badness: 0.0257 | | Badness: 0.0257 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 100/99, 105/104, 245/243, 1188/1183 | | Commas: 100/99, 105/104, 245/243, 1188/1183 |
|
| |
|
| Line 565: |
Line 696: |
|
| |
|
| Map: [<1 4 5 2 4 8|, <0 -9 -10 3 -2 -16|] | | Map: [<1 4 5 2 4 8|, <0 -9 -10 3 -2 -16|] |
| | |
| EDOs: 11, 15, 26, 41 | | EDOs: 11, 15, 26, 41 |
| | |
| Badness: 0.0215 | | Badness: 0.0215 |
|
| |
|
| =Gorgo= | | =Gorgo= |
| Commas: 36/35, 1029/1024 | | Commas: 36/35, 1029/1024 |
|
| |
|
| [[POTE tuning|POTE generator]]: 228.334 | | [[POTE_tuning|POTE generator]]: 228.334 |
|
| |
|
| Map: [<1 1 1 3|, <0 3 7 -1|] | | Map: [<1 1 1 3|, <0 3 7 -1|] |
| | |
| Wedgie: <<3 7 -1 4 -10 -22|| | | Wedgie: <<3 7 -1 4 -10 -22|| |
| | |
| EDOs: 5, 16, 21 | | EDOs: 5, 16, 21 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 36/35, 56/55, 1029/1024 | | Commas: 36/35, 56/55, 1029/1024 |
|
| |
|
| Line 583: |
Line 718: |
|
| |
|
| Map: [<1 1 1 3 5 |, <0 3 7 -1 -8|] | | Map: [<1 1 1 3 5 |, <0 3 7 -1 -8|] |
| | |
| EDOs: 5, 16e, 21, 47c, 68bce | | EDOs: 5, 16e, 21, 47c, 68bce |
| | |
| Badness: 0.0627 | | Badness: 0.0627 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 27/26, 36/35, 56/55, 507/500 | | Commas: 27/26, 36/35, 56/55, 507/500 |
|
| |
|
| Line 592: |
Line 729: |
|
| |
|
| Map: [<1 1 1 3 5 2|, <0 3 7 -1 -8 9|] | | Map: [<1 1 1 3 5 2|, <0 3 7 -1 -8 9|] |
| | |
| EDOs 5, 21, 68bcef | | EDOs 5, 21, 68bcef |
| | |
| Badness: 0.0471 | | Badness: 0.0471 |
|
| |
|
| ==Music== | | ==Music== |
| [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3|Gorgo Example]] by [[Herman Miller]]
| | [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman_Miller|Herman Miller]] |
|
| |
|
| =Lemba= | | =Lemba= |
| Commas: 50/49, 525/512 | | Commas: 50/49, 525/512 |
|
| |
|
| [[POTE tuning|POTE generator]]: 232.089 | | [[POTE_tuning|POTE generator]]: 232.089 |
|
| |
|
| Map: [<2 2 5 6|, <3 -1 -1|] | | Map: [<2 2 5 6|, <3 -1 -1|] |
| | |
| Wedgie: <<6 -2 -2 -17 -20 1|| | | Wedgie: <<6 -2 -2 -17 -20 1|| |
| | |
| EDOs: 10, 16, 26 | | EDOs: 10, 16, 26 |
|
| |
|
| ==Music== | | ==Music== |
| By [[Herman Miller]] | | By [[Herman_Miller|Herman Miller]] |
| [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3|Lemba Galatsia]]
| | |
| [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3|GPO Lemba]]
| | [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3 Lemba Galatsia] |
|
| |
|
| =Gidorah= | | [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3 GPO Lemba] |
| | |
| | =Gidorah= |
| Commas: 21/20, 144/125 | | Commas: 21/20, 144/125 |
|
| |
|
| Line 618: |
Line 761: |
|
| |
|
| Map: [<1 1 2 3|, <0 3 2 -1|] | | Map: [<1 1 2 3|, <0 3 2 -1|] |
| | |
| EDOs: 5, 11, 21, 26 | | EDOs: 5, 11, 21, 26 |
| | |
| Badness: 0.0623 | | Badness: 0.0623 |
|
| |
|
| =Clyndro= | | =Clyndro= |
| Commas: 1029/1024, 135/128 | | Commas: 1029/1024, 135/128 |
|
| |
|
| Line 627: |
Line 772: |
|
| |
|
| Map: [<1 1 4 3|, <0 3 -9 -1|] | | Map: [<1 1 4 3|, <0 3 -9 -1|] |
| | |
| EDOs: 16 | | EDOs: 16 |
|
| |
|
| =Necromanteion= | | =Necromanteion= |
| Commas: 1029/1024, 5103/5000 | | Commas: 1029/1024, 5103/5000 |
|
| |
|
| Line 635: |
Line 781: |
|
| |
|
| Map: [<1 7 10 1|, <0 -12 -17 4|] | | Map: [<1 7 10 1|, <0 -12 -17 4|] |
| | |
| EDOs: 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd | | EDOs: 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd |
| | |
| Badness: 0.1177 | | Badness: 0.1177 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 176/175, 243/242, 1029/1024 | | Commas: 176/175, 243/242, 1029/1024 |
|
| |
|
| Line 644: |
Line 792: |
|
| |
|
| Map: [<1 7 10 1 17|, <0 -12 -17 4 -30|] | | Map: [<1 7 10 1 17|, <0 -12 -17 4 -30|] |
| | |
| EDOs: 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde | | EDOs: 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde |
| | |
| Badness: 0.0535 | | Badness: 0.0535 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 144/143, 176/175, 243/242, 343/338 | | Commas: 144/143, 176/175, 243/242, 343/338 |
|
| |
|
| Line 653: |
Line 803: |
|
| |
|
| Map: [<1 7 10 1 17 1|, <0 -12 -17 4 -30 6|] | | Map: [<1 7 10 1 17 1|, <0 -12 -17 4 -30 6|] |
| | |
| EDOs: 31, 51ce, 82cf, 113cf, 144cf | | EDOs: 31, 51ce, 82cf, 113cf, 144cf |
| | |
| Badness: 0.0470 | | Badness: 0.0470 |
|
| |
|
| =Widefourth= | | =Widefourth= |
| Commas: 1029/1024, 48828125/48771072 | | Commas: 1029/1024, 48828125/48771072 |
|
| |
|
| Line 662: |
Line 814: |
|
| |
|
| Map: [<1 16 8 -2|, <0 -33 -13 11|] | | Map: [<1 16 8 -2|, <0 -33 -13 11|] |
| | |
| Wedgie: <<33 13 -11 -56 -110 -62|| | | Wedgie: <<33 13 -11 -56 -110 -62|| |
| | |
| EDOs: 16, 71, 87, 103, 190 | | EDOs: 16, 71, 87, 103, 190 |
| | |
| Badness: 0.1541 | | Badness: 0.1541 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 385/384, 441/440, 234375/234256 | | Commas: 385/384, 441/440, 234375/234256 |
|
| |
|
| Line 672: |
Line 827: |
|
| |
|
| Map: [<1 16 8 -2 17|, <0 -33 -13 11 -31|] | | Map: [<1 16 8 -2 17|, <0 -33 -13 11 -31|] |
| | |
| EDOs: 16, 71, 87, 103, 190 | | EDOs: 16, 71, 87, 103, 190 |
| | |
| Badness: 0.0408 | | Badness: 0.0408 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 385/384, 441/440, 625/624, 847/845 | | Commas: 385/384, 441/440, 625/624, 847/845 |
|
| |
|
| Line 681: |
Line 838: |
|
| |
|
| Map: [<1 16 8 -2 17 12|, <0 -33 -13 11 -31 -19|] | | Map: [<1 16 8 -2 17 12|, <0 -33 -13 11 -31 -19|] |
| | |
| EDOs: 16, 71, 87, 103, 190 | | EDOs: 16, 71, 87, 103, 190 |
| Badness: 0.0216</pre></div> | | |
| <h4>Original HTML content:</h4>
| | Badness: 0.0216 |
| <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>Gamelismic clan</title></head><body><!-- ws:start:WikiTextTocRule:140:&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:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 2em;"><a href="#x-Full seven limit children">Full seven limit children</a></div>
| | [[Category:clan]] |
| <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 1em;"><a href="#Miracle">Miracle</a></div>
| | [[Category:family]] |
| <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Miracle-11-limit">11-limit</a></div>
| | [[Category:gamelismic]] |
| <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 2em;"><a href="#Miracle-Revelation">Revelation</a></div>
| | [[Category:listen]] |
| <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 3em;"><a href="#Miracle-Revelation-13-limit">13-limit</a></div>
| | [[Category:miracle]] |
| <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Miracle-Miraculous">Miraculous</a></div>
| | [[Category:theory]] |
| <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Miracle-Benediction">Benediction</a></div>
| |
| <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 3em;"><a href="#Miracle-Benediction-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 2em;"><a href="#Miracle-Manna">Manna</a></div>
| |
| <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 2em;"><a href="#Miracle-Semimiracle">Semimiracle</a></div>
| |
| <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 3em;"><a href="#Miracle-Semimiracle-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 2em;"><a href="#Miracle-Hemimiracle">Hemimiracle</a></div>
| |
| <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 3em;"><a href="#Miracle-Hemimiracle-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Miracle-Oracle">Oracle</a></div>
| |
| <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 2em;"><a href="#Miracle-Hemisecordite">Hemisecordite</a></div>
| |
| <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 3em;"><a href="#Miracle-Hemisecordite-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Miracle-Phicordial">Phicordial</a></div>
| |
| <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 3em;"><a href="#Miracle-Phicordial-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 2em;"><a href="#Miracle-Music">Music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 1em;"><a href="#Rodan">Rodan</a></div>
| |
| <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 2em;"><a href="#Rodan-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 2em;"><a href="#Rodan-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 2em;"><a href="#Rodan-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 3em;"><a href="#Rodan-17-limit-Music">Music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 2em;"><a href="#Rodan-Aerodactyl">Aerodactyl</a></div>
| |
| <!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 2em;"><a href="#Rodan-Aerodino">Aerodino</a></div>
| |
| <!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 3em;"><a href="#Rodan-Aerodino-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Rodan-Varan">Varan</a></div>
| |
| <!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 3em;"><a href="#Rodan-Varan-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --><div style="margin-left: 1em;"><a href="#Valentine">Valentine</a></div>
| |
| <!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 2em;"><a href="#Valentine-7-limit">7-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><div style="margin-left: 2em;"><a href="#Valentine-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --><div style="margin-left: 1em;"><a href="#Unidec">Unidec</a></div>
| |
| <!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --><div style="margin-left: 2em;"><a href="#Unidec-7-limit">7-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --><div style="margin-left: 2em;"><a href="#Unidec-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --><div style="margin-left: 2em;"><a href="#Unidec-Ekadash">Ekadash</a></div>
| |
| <!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --><div style="margin-left: 2em;"><a href="#Unidec-Hendec">Hendec</a></div>
| |
| <!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --><div style="margin-left: 3em;"><a href="#Unidec-Hendec-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --><div style="margin-left: 3em;"><a href="#Unidec-Hendec-Music">Music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --><div style="margin-left: 1em;"><a href="#Hemithirds">Hemithirds</a></div>
| |
| <!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --><div style="margin-left: 2em;"><a href="#Hemithirds-7-limit">7-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --><div style="margin-left: 2em;"><a href="#Hemithirds-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --><div style="margin-left: 2em;"><a href="#Hemithirds-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --><div style="margin-left: 1em;"><a href="#Hemiseven">Hemiseven</a></div>
| |
| <!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --><div style="margin-left: 2em;"><a href="#Hemiseven-7-limit">7-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:185 --><!-- ws:start:WikiTextTocRule:186: --><div style="margin-left: 2em;"><a href="#Hemiseven-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:186 --><!-- ws:start:WikiTextTocRule:187: --><div style="margin-left: 2em;"><a href="#Hemiseven-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:187 --><!-- ws:start:WikiTextTocRule:188: --><div style="margin-left: 2em;"><a href="#Hemiseven-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:188 --><!-- ws:start:WikiTextTocRule:189: --><div style="margin-left: 1em;"><a href="#Tritikleismic">Tritikleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:189 --><!-- ws:start:WikiTextTocRule:190: --><div style="margin-left: 2em;"><a href="#Tritikleismic-7-limit">7-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:190 --><!-- ws:start:WikiTextTocRule:191: --><div style="margin-left: 2em;"><a href="#Tritikleismic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:191 --><!-- ws:start:WikiTextTocRule:192: --><div style="margin-left: 2em;"><a href="#Tritikleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:192 --><!-- ws:start:WikiTextTocRule:193: --><div style="margin-left: 2em;"><a href="#Tritikleismic-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:193 --><!-- ws:start:WikiTextTocRule:194: --><div style="margin-left: 1em;"><a href="#Superkleismic">Superkleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:194 --><!-- ws:start:WikiTextTocRule:195: --><div style="margin-left: 2em;"><a href="#Superkleismic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:195 --><!-- ws:start:WikiTextTocRule:196: --><div style="margin-left: 2em;"><a href="#Superkleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:196 --><!-- ws:start:WikiTextTocRule:197: --><div style="margin-left: 1em;"><a href="#Gorgo">Gorgo</a></div>
| |
| <!-- ws:end:WikiTextTocRule:197 --><!-- ws:start:WikiTextTocRule:198: --><div style="margin-left: 2em;"><a href="#Gorgo-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:198 --><!-- ws:start:WikiTextTocRule:199: --><div style="margin-left: 2em;"><a href="#Gorgo-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:199 --><!-- ws:start:WikiTextTocRule:200: --><div style="margin-left: 2em;"><a href="#Gorgo-Music">Music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:200 --><!-- ws:start:WikiTextTocRule:201: --><div style="margin-left: 1em;"><a href="#Lemba">Lemba</a></div>
| |
| <!-- ws:end:WikiTextTocRule:201 --><!-- ws:start:WikiTextTocRule:202: --><div style="margin-left: 2em;"><a href="#Lemba-Music">Music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:202 --><!-- ws:start:WikiTextTocRule:203: --><div style="margin-left: 1em;"><a href="#Gidorah">Gidorah</a></div>
| |
| <!-- ws:end:WikiTextTocRule:203 --><!-- ws:start:WikiTextTocRule:204: --><div style="margin-left: 1em;"><a href="#Clyndro">Clyndro</a></div>
| |
| <!-- ws:end:WikiTextTocRule:204 --><!-- ws:start:WikiTextTocRule:205: --><div style="margin-left: 1em;"><a href="#Necromanteion">Necromanteion</a></div>
| |
| <!-- ws:end:WikiTextTocRule:205 --><!-- ws:start:WikiTextTocRule:206: --><div style="margin-left: 2em;"><a href="#Necromanteion-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:206 --><!-- ws:start:WikiTextTocRule:207: --><div style="margin-left: 2em;"><a href="#Necromanteion-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:207 --><!-- ws:start:WikiTextTocRule:208: --><div style="margin-left: 1em;"><a href="#Widefourth">Widefourth</a></div>
| |
| <!-- ws:end:WikiTextTocRule:208 --><!-- ws:start:WikiTextTocRule:209: --><div style="margin-left: 2em;"><a href="#Widefourth-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:209 --><!-- ws:start:WikiTextTocRule:210: --><div style="margin-left: 2em;"><a href="#Widefourth-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:210 --><!-- ws:start:WikiTextTocRule:211: --></div>
| |
| <!-- ws:end:WikiTextTocRule:211 -->The 2.3.7-<a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3&gt;. For any member of the clan, for the rank three <a class="wiki_link" href="/Gamelismic%20family#Gamelan">gamelan temperament</a> itself, and for the rank two 2.3.7 temperament <a class="wiki_link" href="/slendric">slendric</a>, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. <a class="wiki_link" href="/36edo">36edo</a> is a good tuning for gamelismic itself, though if the full 7-limit is desired, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/77edo">77edo</a> or <a class="wiki_link" href="/118edo">118edo</a> might be preferred.<br />
| |
| <br />
| |
| 7-limit minimax<br />
| |
| [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,<br /> | |
| |5/2 -1/4 1 -3/4&gt;, |5/2 -1/4 0 1/4&gt;]<br />
| |
| Eigenmonzos: 2, 7/6, 6/5<br />
| |
| <br />
| |
| 9-limit minimax<br />
| |
| [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,<br /> | |
| |10/7 -1/7 1 -3/7&gt;, |20/7 -2/7 0 1/7&gt;]<br />
| |
| Eigenmonzos: 2, 6/5, 9/7<br />
| |
| <br />
| |
| Lattice basis: 8/7 0.5192 5/4 2.3219<br />
| |
| Angle(8/7, 5/4) = 90 degrees<br />
| |
| Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]<br />
| |
| <br />
| |
| Map: [&lt;1 1 0 3|, &lt;0 3 0 -1|, &lt; 0 0 1 0|]<br />
| |
| Generators: 2, 5, 7<br />
| |
| <br />
| |
| No-fives <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 233.688<br />
| |
| EDOs: 5, 36, 77, 190<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Full seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Full seven limit children</h2>
| |
| To the gamelisma itself we need to add the comma which appears next on the modified <a class="wiki_link" href="/Normal%20lists">normal comma list</a>, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Miracle"></a><!-- ws:end:WikiTextHeadingRule:2 -->Miracle</h1>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 225/224<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| 7-limit: [|1 0 0 0&gt;, |25/13 6/13 -6/13 0&gt;,<br />
| |
| |25/13 -7/13 7/13 0&gt;, |35/13 -2/13 2/13 0&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5<br />
| |
| <br />
| |
| 9-limit: [|1 0 0 0&gt;, |25/19 12/19 -6/19 0&gt;,<br />
| |
| |50/19 -14/19 7/19 0&gt;, |55/19 -4/19 2/19 0&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 116.675<br />
| |
| Algebraic generator: Secor59, <a class="wiki_link" href="/Algebraic%20number">positive root</a> of 15x^6-8x^4-12<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3|, &lt;0 6 -7 -2|]<br />
| |
| Wedgie: &lt;&lt;6 -7 -2 -25 -20 15||<br />
| |
| EDOs: 10, 21, 31, 41, 72, <a class="wiki_link" href="/175edo">175</a><br />
| |
| Badness: 0.0167<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Miracle-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 225/224, 243/242<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| [|1 0 0 0 0&gt;, |25/19 12/19 -6/19 0 0&gt;,<br />
| |
| |50/19 -14/19 7/19 0 0&gt;, |55/19 -4/19 2/19 0 0&gt;,<br />
| |
| |53/19 30/19 -15/19 0 0&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 116.633<br />
| |
| Algebraic generator: Secor59<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 2|, &lt;0 6 -7 -2 15|]<br />
| |
| <a class="wiki_link" href="/edo">EDOs</a>: 10, 31, 41, <a class="wiki_link" href="/72edo">72</a>, 247c, 319bcde, <a class="wiki_link" href="/391edo">391bcde</a>, 463bcde<br />
| |
| Badness: 0.0107<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Chords%20of%20miracle">Chords of miracle</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Miracle-Revelation"></a><!-- ws:end:WikiTextHeadingRule:6 -->Revelation</h2>
| |
| Commas: 99/98, 176/175, 1029/1024<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 116.277<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 5|, &lt;0 6 -7 -2 -16|]<br />
| |
| EDOs: 10, 21, 31<br />
| |
| Badness: 0.0329<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Miracle-Revelation-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h3>
| |
| Commas: 66/65, 99/98, 105/104, 1001/1000<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 116.268<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 5 4|, &lt;0 6 -7 -2 -16 -3|]<br />
| |
| EDOs: 10, 21, 31<br />
| |
| Badness: 0.0295<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Miracle-Miraculous"></a><!-- ws:end:WikiTextHeadingRule:10 -->Miraculous</h2>
| |
| Commas: 105/104, 144/143, 196/195, 275/273<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 116.747<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 2 4|, &lt;0 6 -7 -2 15 -3|]<br />
| |
| EDOs: 10, 31, 41, 72f, 113f, 185cf<br />
| |
| Badness: 0.0187<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Miracle-Benediction"></a><!-- ws:end:WikiTextHeadingRule:12 -->Benediction</h2>
| |
| Commas: 225/224, 243/242, 351/350, 441/440<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 116.574<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 2 7|, &lt;0 6 -7 -2 15 -34|]<br />
| |
| EDOs: 31, 72, 103, <a class="wiki_link" href="/175edo">175f</a><br />
| |
| Badness: 0.0157<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Miracle-Benediction-17-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->17-limit</h3>
| |
| Commas: 225/224, 243/242, 273/272, 351/350, 385/384<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 116.585<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 2 7 7|, &lt;0 6 -7 -2 15 -34 -30|]<br />
| |
| EDOs: 31, 72, 103, <a class="wiki_link" href="/175edo">175f</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Miracle-Manna"></a><!-- ws:end:WikiTextHeadingRule:16 -->Manna</h2>
| |
| Commas: 225/224, 243/242, 325/324, 385/384<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 116.739<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 38|]<br />
| |
| EDOs: 10f, 31f, 41, 72, 113, 185cf, 257cf<br />
| |
| Badness: 0.0170<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Miracle-Semimiracle"></a><!-- ws:end:WikiTextHeadingRule:18 -->Semimiracle</h2>
| |
| Commas: 169/168, 225/224, 243/242, 385/384<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 116.624<br />
| |
| <br />
| |
| Map: [&lt;2 2 6 6 4 7|, &lt;0 6 -7 -2 15 2|]<br />
| |
| EDOs: 10, 62, 72<br />
| |
| Badness: 0.0246<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Miracle-Semimiracle-17-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->17-limit</h3>
| |
| Commas: 169/168, 221/220, 225/224, 243/242, 385/384<br />
| |
| <br />
| |
| POTE generator: ~15/14 = 116.628<br />
| |
| <br />
| |
| Map: [&lt;2 2 6 6 4 7 7|, &lt;0 6 -7 -2 15 2 6|]<br />
| |
| EDOs: 10, 62, 72<br />
| |
| Badness: 0.0161<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Miracle-Hemimiracle"></a><!-- ws:end:WikiTextHeadingRule:22 -->Hemimiracle</h2>
| |
| Commas: 225/224, 245/242, 1029/1024<br />
| |
| <br />
| |
| POTE generator: ~33/32 = 58.408<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 4|, &lt;0 12 -14 -4 -11|]<br />
| |
| EDOs: 20, 21, 41, 123c, 144e, 185ce, 226ce<br />
| |
| Badness: 0.0592<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Miracle-Hemimiracle-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h3>
| |
| Commas: 105/104, 196/195, 245/242, 512/507<br />
| |
| <br />
| |
| POTE generator: ~33/32 = 58.430<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 4 4|, &lt;0 12 -14 -4 -11 -6|]<br />
| |
| EDOs: 20, 21, 41, 123cf, 144ef, 185cef<br />
| |
| Badness: 0.0432<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Miracle-Oracle"></a><!-- ws:end:WikiTextHeadingRule:26 -->Oracle</h2>
| |
| Commas: 121/120, 225/224, 1029/1024<br />
| |
| <br />
| |
| POTE generator: ~11/8 = 541.668<br />
| |
| <br />
| |
| Map: [&lt;1 7 -4 1 3|, &lt;0 -12 14 4 1|]<br />
| |
| EDOs: 11, 20, 31, 51, 82e, 113e, 144e<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Miracle-Hemisecordite"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hemisecordite</h2>
| |
| Commas: 225/224, 243/242, 441/440, 847/845<br />
| |
| <br />
| |
| POTE generator: ~27/26 = 58.288<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 2 2|, &lt;0 12 -14 -4 30 35|]<br />
| |
| EDOs: 41, 62, 103, 247c, 350bcde<br />
| |
| Badness: 0.0256<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Miracle-Hemisecordite-17-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->17-limit</h3>
| |
| Commas: 225/224, 243/242, 273/272, 441/440, 847/845<br />
| |
| <br />
| |
| POTE generator: ~27/26 = 58.261<br />
| |
| <br />
| |
| Map: [&lt;1 1 3 3 2 2 2|, &lt;0 12 -14 -4 30 35 43|]<br />
| |
| EDOs: 41, 62, 103<br />
| |
| Badness: 0.0225<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Miracle-Phicordial"></a><!-- ws:end:WikiTextHeadingRule:32 -->Phicordial</h2>
| |
| Commas: 225/224, 243/242, 441/440, 2200/2197<br />
| |
| <br />
| |
| POTE generator: ~16/13 = 361.121<br />
| |
| <br />
| |
| Map: [&lt;1 7 -4 1 17 4|, &lt;0 -18 21 6 -45 -1|]<br />
| |
| EDOs: 10, 103, 113, 216c<br />
| |
| Badness: 0.0332<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Miracle-Phicordial-17-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->17-limit</h3>
| |
| Commas: 225/224, 243/242, 273/272, 441/440, 2200/2197<br />
| |
| <br />
| |
| POTE generator: ~16/13 = 361.123<br />
| |
| <br />
| |
| Map: [&lt;1 7 -4 1 17 4 8|, &lt;0 -18 21 6 -45 -1 -13|]<br />
| |
| EDOs: 10, 103, 113, 216c<br />
| |
| Badness: 0.0247<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Miracle-Music"></a><!-- ws:end:WikiTextHeadingRule:36 -->Music</h2>
| |
| By <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br />
| |
| <a class="wiki_link_ext" href="http://www.archive.org/details/RachmaninoffPlaysBlackjack" rel="nofollow">Rachmaninoff Plays Blackjack</a> <a class="wiki_link_ext" href="http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3" rel="nofollow">play</a><br />
| |
| By <a class="wiki_link" href="/Joseph%20Pehrson">Joseph Pehrson</a><br />
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3" rel="nofollow">Black and Jill</a><br />
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3" rel="nofollow">Blacklight</a><br />
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3" rel="nofollow">Blackjack</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Rodan"></a><!-- ws:end:WikiTextHeadingRule:38 -->Rodan</h1>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 245/243<br />
| |
| <br />
| |
| 7+9 limit minimax tuning: [|1 0 0 0&gt;, |5/3 0 1/6 -1/6&gt;,<br />
| |
| |25/9 0 17/18 -17/18&gt;, |25/9 0 -1/18 1/18&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 234.417<br />
| |
| Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">larger root</a> of 20x^2-36x+15, or (9+√6)/10.<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3|, &lt;0 3 17 -1|]<br />
| |
| EDOs: 41, 87, 128<br />
| |
| Badness: 0.0371<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Rodan-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 441/440, 245/243, 385/384<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>: [|1 0 0 0 0&gt;, |31/19 6/19 0 0 -3/19&gt;,<br />
| |
| |49/19 34/19 0 0 -17/19&gt;, |53/19 -2/19 0 0 1/19&gt;,<br />
| |
| |62/19 -26/19 0 0 13/19&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 234.459<br />
| |
| Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">positive root</a> of x^2+16x-31, or √95-8.<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3 6|, &lt;0 3 17 -1 -13|]<br />
| |
| EDOs: 41, 87, 389d<br />
| |
| Badness: 0.0231<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Chords%20of%20rodan">Chords of rodan</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Rodan-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2>
| |
| Commas: 196/195, 245/243, 352/351, 364/363<br />
| |
| <br />
| |
| 13 and 15 limit minimax<br />
| |
| [|1 0 0 0 0 0&gt;, |23/14 3/14 0 0 0 -3/28&gt;,<br />
| |
| |37/14 17/14 0 0 0 -17/28&gt;, |39/14 -1/14 0 0 0 1/28&gt;,<br />
| |
| |45/14 -13/14 0 0 0 13/28&gt;, |23/7 -11/7 0 0 0 11/14&gt;]<br />
| |
| Eigenmonzos: 2, 13/9<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 234.482<br />
| |
| Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly.<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3 6 8|, &lt;0 3 17 -1 -13 -22|]<br />
| |
| Generators: 2, 8/7<br />
| |
| <a class="wiki_link" href="/edo">Edos</a>: 41, 46, <a class="wiki_link" href="/87edo">87</a><br />
| |
| Badness: 0.0184<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Rodan-17-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->17-limit</h2>
| |
| Commas: 154/153, 196/195, 245/243, 273/272, 364/363<br />
| |
| <br />
| |
| Eigenmonzos: 2, 18/17<br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 234.524<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3 6 8 8|, &lt;0 3 17 -1 -13 -22 -20|]<br />
| |
| Edos: 41, 46, 87, 220dg, 307dg<br />
| |
| Badness: 0.0167<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="Rodan-17-limit-Music"></a><!-- ws:end:WikiTextHeadingRule:46 -->Music</h3>
| |
| By <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br />
| |
| <a class="wiki_link_ext" href="http://www.archive.org/details/Pianodactyl" rel="nofollow">Pianodactyl</a> <a class="wiki_link_ext" href="http://www.archive.org/download/Pianodactyl/pianodactyl.mp3" rel="nofollow">play</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Rodan-Aerodactyl"></a><!-- ws:end:WikiTextHeadingRule:48 -->Aerodactyl</h2>
| |
| Commas: 91/90, 245/243, 385/384, 441/440<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 234.639<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3 6 -1|, &lt;0 3 17 -1 -13 24|<br />
| |
| EDOs: 41f, 46, 51c<br />
| |
| Badness: 0.0340<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Rodan-Aerodino"></a><!-- ws:end:WikiTextHeadingRule:50 -->Aerodino</h2>
| |
| Commas: 176/175, 245/243, 1029/1024<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 234.728<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3 -3|, &lt;0 3 17 -1 33|<br />
| |
| EDOS: 46<br />
| |
| Badness: 0.0543<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc26"><a name="Rodan-Aerodino-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h3>
| |
| Commas: 91/90, 176/175, 245/243, 847/845<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 234.782<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3 -3 -1|, &lt;0 3 17 -1 33 24|<br />
| |
| EDOs: 46<br />
| |
| Badness: 0.0358<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Rodan-Varan"></a><!-- ws:end:WikiTextHeadingRule:54 -->Varan</h2>
| |
| Commas: 100/99, 245/243, 2835/2816<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 234.145<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3 -2|, &lt;0 3 17 -1 28|<br />
| |
| EDOs: 41, 46e<br />
| |
| Badness: 0.0449<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:56:&lt;h3&gt; --><h3 id="toc28"><a name="Rodan-Varan-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h3>
| |
| Commas: 100/99, 105/104, 245/243, 352/351<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 234.089<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 3 -2 0|, &lt;0 3 17 -1 28 19|<br />
| |
| EDOs: 41<br />
| |
| Badness: 0.0323<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Valentine"></a><!-- ws:end:WikiTextHeadingRule:58 -->Valentine</h1>
| |
| <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Valentine-7-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->7-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 126/125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| 7-limit: [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,<br />
| |
| |17/6 5/12 0 -5/12&gt;, [5/2 -1/4 0 1/4&gt;]<br />
| |
| Eigenmonzos: 2, 7/6<br />
| |
| <br />
| |
| 9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,<br />
| |
| |47/21 10/21 0 -5/21&gt;, |20/7 -2/7 0 1/7&gt;]<br />
| |
| Eigenmonzos: 2, 9/7<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 77.864<br />
| |
| Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">smaller root</a> of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents.<br />
| |
| <br />
| |
| Map: [&lt;1 1 2 3|, &lt;0 9 5 -3|]<br />
| |
| Wedgie: &lt;&lt;9 5 -3 -13 -30 -21||<br />
| |
| EDOs: 15, 31, 46, 77, 185, 262cd<br />
| |
| Badness: 0.0311<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Valentine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| [|1 0 0 0 0&gt;, |1 0 0 -9/10 9/10&gt;,<br />
| |
| |2 0 0 -1/2 1/2&gt;, |3 0 0 3/10 -3/10&gt;, |3 0 0 -7/10 7/10&gt;]<br />
| |
| Eigenmonzos: 2, 11/7<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 77.881<br />
| |
| Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">positive root</a> of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5.<br />
| |
| <br />
| |
| Map: [&lt;1 1 2 3 3|, &lt;0 9 5 -3 7|]<br />
| |
| Generators: 2, 21/20<br />
| |
| <a class="wiki_link" href="/edo">Edos</a>: 15, 31, 46, 77, 262cde, 339cde<br />
| |
| Badness: 0.0167<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Chords%20of%20valentine">Chords of valentine</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Unidec"></a><!-- ws:end:WikiTextHeadingRule:64 -->Unidec</h1>
| |
| Comma: 31381059609/31250000000<br />
| |
| <br />
| |
| POTE generator: ~10/9 = 183.047<br />
| |
| <br />
| |
| Map: [&lt;2 5 8|, &lt;0 -6 -11|]<br />
| |
| EDOs: 26, 46, 72, 118, 2524, 2642, 2760, 5002bc<br />
| |
| Badness: 0.0824<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Unidec-7-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->7-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 4375/4374<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| 7-limit: [|1 0 0 0&gt;, |47/26 0 6/13 -6/13&gt;,<br />
| |
| |71/26 0 11/13 -11/13&gt;, |71/26 0 -2/13 2/13&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br />
| |
| <br />
| |
| 9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,<br />
| |
| |57/28 11/7 0 -11/14&gt;, |20/7 -2/7 0 1/7&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 183.161<br />
| |
| <br />
| |
| Map: [&lt;2 5 8 5|, &lt;0 -6 -11 2|]<br />
| |
| Wedgie: &lt;&lt;12 22 -4 7 -40 -71||<br />
| |
| EDOs: 26, 46, 72, 118, 190<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Unidec-11-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 4375/4374<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| [|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;, |57/28 11/7 0 -11/14 0&gt;,<br />
| |
| |20/7 -2/7 0 1/7 0&gt;, |99/28 -3/7 0 3/14 0&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 183.165<br />
| |
| <br />
| |
| Map: [&lt;2 5 8 5 6|, &lt;0 -6 -11 2 3|]<br />
| |
| EDOs: 26, 46, 72, 118, 190<br />
| |
| <br />
| |
| <br />
| |
| <a class="wiki_link" href="/Chords%20of%20unidec">Chords of unidec</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Unidec-Ekadash"></a><!-- ws:end:WikiTextHeadingRule:70 -->Ekadash</h2>
| |
| Commas: 385/384, 441/440, 625/624, 729/728<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 183.187<br />
| |
| <br />
| |
| Map: [&lt;2 5 8 5 6 19|, &lt;0 -6 -11 2 3 -38|]<br />
| |
| EDOs: 20cf, 26f, 46f, 72, 118, 190, 262df, 452cdef<br />
| |
| Bad: 0.0204<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Unidec-Hendec"></a><!-- ws:end:WikiTextHeadingRule:72 -->Hendec</h2>
| |
| Commas: 169/168, 325/324, 364/363, 1716/1715<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 183.187<br />
| |
| <br />
| |
| Map: [&lt;2 5 8 5 6 8|, &lt;0 -6 -11 2 3 -2|]<br />
| |
| EDOs: 26, 46, 72<br />
| |
| Bad: 0.0177<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:74:&lt;h3&gt; --><h3 id="toc37"><a name="Unidec-Hendec-17-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->17-limit</h3>
| |
| Commas: 169/168, 221/220, 273/272, 325/324, 364/363<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 183.196<br />
| |
| <br />
| |
| Map: [&lt;2 5 8 5 6 8 10|, &lt;0 -6 -11 2 3 -2 -6|]<br />
| |
| EDOs: 26, 46, 72<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:76:&lt;h3&gt; --><h3 id="toc38"><a name="Unidec-Hendec-Music"></a><!-- ws:end:WikiTextHeadingRule:76 -->Music</h3>
| |
| <a class="wiki_link" href="/Technical%20Notes%20for%20Newbeams#Track%20notes:-Hypnocloudsmack%202">Hypnocloudsmack 2</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:78:&lt;h1&gt; --><h1 id="toc39"><a name="Hemithirds"></a><!-- ws:end:WikiTextHeadingRule:78 -->Hemithirds</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Hemithirds-7-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->7-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 3136/3125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| 7-limit: [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,<br />
| |
| |11/5 -1/10 0 1/10&gt;, |5/2 -1/4 0 1/4&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6<br />
| |
| <br />
| |
| 9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,<br />
| |
| |82/35 -4/35 0 2/35&gt;, |20/7 -2/7 0 1/7&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Hemithirds-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 3136/3125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| [|1 0 0 0 0&gt;, |11/9 0 0 -5/9 5/9&gt;, |64/27 0 0 2/27 -2/27&gt;,<br />
| |
| |79/27 0 0 5/27 -5/27&gt;, |79/27 0 0 -22/27 22/27&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/7<br />
| |
| <br />
| |
| POTE generator: ~28/25 = 193.227<br />
| |
| <br />
| |
| <br />
| |
| Map: [&lt;1 4 2 2 7|, &lt;0 -15 2 5 -22|]<br />
| |
| <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/118edo">118</a><br />
| |
| Badness: 0.0190<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Chords%20of%20hemithirds">Chords of hemithirds</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="Hemithirds-13-limit"></a><!-- ws:end:WikiTextHeadingRule:84 -->13-limit</h2>
| |
| Commas: 196/195 352/351 1001/1000 1029/1024<br />
| |
| <br />
| |
| POTE generator: ~28/25 = 193.166<br />
| |
| <br />
| |
| Map: [&lt;1 4 2 2 7 0|, &lt;0 -15 2 5 -22 23|]<br />
| |
| EDOs: 31, 56, 87, 118, 205d<br />
| |
| Badness: 0.0217<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:86:&lt;h1&gt; --><h1 id="toc43"><a name="Hemiseven"></a><!-- ws:end:WikiTextHeadingRule:86 -->Hemiseven</h1>
| |
| <!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc44"><a name="Hemiseven-7-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->7-limit</h2>
| |
| Commas: 1029/1024, 19683/19600<br />
| |
| <br />
| |
| POTE generator: ~320/243 = 483.267<br />
| |
| <br />
| |
| Map: [&lt;1 4 14 2|, &lt;0 -6 -29 2|]<br />
| |
| Wedgie: &lt;&lt;6 29 -2 32 -20 -86||<br />
| |
| EDOs: 5, 72, 77, 149, 221, 514bd, 735bcd<br />
| |
| Badness: 0.0566<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc45"><a name="Hemiseven-11-limit"></a><!-- ws:end:WikiTextHeadingRule:90 -->11-limit</h2>
| |
| Commas: 385/384, 441/440, 19683/19600<br />
| |
| <br />
| |
| POTE generator: ~320/243 = 483.276<br />
| |
| <br />
| |
| Map: [&lt;1 4 14 2 -5|, &lt;0 -6 -29 2 21|]<br />
| |
| EDOs: 72, 77, 149, 221e, 293de<br />
| |
| Badness: 0.0285<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:92:&lt;h2&gt; --><h2 id="toc46"><a name="Hemiseven-13-limit"></a><!-- ws:end:WikiTextHeadingRule:92 -->13-limit</h2>
| |
| Commas: 351/350, 385/384, 441/440, 676/675<br />
| |
| <br />
| |
| POTE generator: ~320/243 = 483.256<br />
| |
| <br />
| |
| Map: [&lt;1 4 14 2 -5 19|, &lt;0 -6 -29 2 21 -38|]<br />
| |
| EDOs: 72, 77, 149, 221ef<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Hemiseven-17-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->17-limit</h2>
| |
| Commas: 273/272, 351/350, 385/384, 441/440, 676/675<br />
| |
| <br />
| |
| POTE generator: ~320/243 = 483.261<br />
| |
| <br />
| |
| Map: [&lt;1 4 14 2 -5 19 21|, &lt;0 -6 -29 2 21 -38 -42|]<br />
| |
| EDOs: 72, 77, 149, 221ef<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:96:&lt;h1&gt; --><h1 id="toc48"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:96 -->Tritikleismic</h1>
| |
| <!-- ws:start:WikiTextHeadingRule:98:&lt;h2&gt; --><h2 id="toc49"><a name="Tritikleismic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:98 -->7-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 15625/15552<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tunings">Minimax tunings</a>:<br />
| |
| 7-limit: [|1 0 0 0&gt;, |2 0 6/7 -6/7&gt;,<br />
| |
| |8/3 0 5/7 -5/7&gt;, |8/3 0 -2/7 2/7&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br />
| |
| <br />
| |
| 9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,<br />
| |
| |46/21 5/7 0 -5/14&gt;, |20/7 -2/7 0 1/7&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:100:&lt;h2&gt; --><h2 id="toc50"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:100 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 4000/3993<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
| |
| [|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;, |46/21 5/7 0 -5/14 0&gt;,<br />
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| |20/7 -2/7 0 1/7 0&gt;, |71/21 3/7 0 -3/14 0&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
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| <br />
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| Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]<br />
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| <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:102:&lt;h2&gt; --><h2 id="toc51"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:102 -->13-limit</h2>
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| Commas: 325/324, 364/363, 441/440, 625/624<br />
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| <br />
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| Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]<br />
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| EDOs: 15, 72, 87, 159<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:104:&lt;h2&gt; --><h2 id="toc52"><a name="Tritikleismic-17-limit"></a><!-- ws:end:WikiTextHeadingRule:104 -->17-limit</h2>
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| Commas: 273/272, 325/324, 364/363, 375/374, 385/384<br />
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| <br />
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| Map: [&lt;3 0 3 10 8 0 -2|, &lt;0 6 5 -2 3 14 18|]<br />
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| EDOs: 15g, 72, 87, 159<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:106:&lt;h1&gt; --><h1 id="toc53"><a name="Superkleismic"></a><!-- ws:end:WikiTextHeadingRule:106 -->Superkleismic</h1>
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| Commas: 1029/1024, 875/864<br />
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| <br />
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| POTE generator: ~6/5 = 321.930<br />
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| <br />
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| Map: [&lt;1 4 5 2|, &lt;0 -9 -10 3|]<br />
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| EDOs: 11, 15, 26, 41<br />
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| Badness: 0.0479<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:108:&lt;h2&gt; --><h2 id="toc54"><a name="Superkleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:108 -->11-limit</h2>
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| Commas: 100/99, 245/242, 385/384<br />
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| <br />
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| POTE generator: ~6/5 = 321.847<br />
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| <br />
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| Map: [&lt;1 4 5 2 4|, &lt;0 -9 -10 3 -2|]<br />
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| EDOs: 15, 26, 41, 261<br />
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| Badness: 0.0257<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:110:&lt;h2&gt; --><h2 id="toc55"><a name="Superkleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:110 -->13-limit</h2>
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| Commas: 100/99, 105/104, 245/243, 1188/1183<br />
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| <br />
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| POTE generator: ~6/5 = 321.994<br />
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| <br />
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| Map: [&lt;1 4 5 2 4 8|, &lt;0 -9 -10 3 -2 -16|]<br />
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| EDOs: 11, 15, 26, 41<br />
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| Badness: 0.0215<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:112:&lt;h1&gt; --><h1 id="toc56"><a name="Gorgo"></a><!-- ws:end:WikiTextHeadingRule:112 -->Gorgo</h1>
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| Commas: 36/35, 1029/1024<br />
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| <br />
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| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 228.334<br />
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| <br />
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| Map: [&lt;1 1 1 3|, &lt;0 3 7 -1|]<br />
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| Wedgie: &lt;&lt;3 7 -1 4 -10 -22||<br />
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| EDOs: 5, 16, 21<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:114:&lt;h2&gt; --><h2 id="toc57"><a name="Gorgo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:114 -->11-limit</h2>
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| Commas: 36/35, 56/55, 1029/1024<br />
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| <br />
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| POTE generator: ~8/7 = 229.535<br />
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| <br />
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| Map: [&lt;1 1 1 3 5 |, &lt;0 3 7 -1 -8|]<br />
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| EDOs: 5, 16e, 21, 47c, 68bce<br />
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| Badness: 0.0627<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:116:&lt;h2&gt; --><h2 id="toc58"><a name="Gorgo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:116 -->13-limit</h2>
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| Commas: 27/26, 36/35, 56/55, 507/500<br />
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| <br />
| |
| POTE generator: ~8/7 = 229.059<br />
| |
| <br />
| |
| Map: [&lt;1 1 1 3 5 2|, &lt;0 3 7 -1 -8 9|]<br />
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| EDOs 5, 21, 68bcef<br />
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| Badness: 0.0471<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:118:&lt;h2&gt; --><h2 id="toc59"><a name="Gorgo-Music"></a><!-- ws:end:WikiTextHeadingRule:118 -->Music</h2>
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3" rel="nofollow">Gorgo Example</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:120:&lt;h1&gt; --><h1 id="toc60"><a name="Lemba"></a><!-- ws:end:WikiTextHeadingRule:120 -->Lemba</h1>
| |
| Commas: 50/49, 525/512<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 232.089<br />
| |
| <br />
| |
| Map: [&lt;2 2 5 6|, &lt;3 -1 -1|]<br />
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| Wedgie: &lt;&lt;6 -2 -2 -17 -20 1||<br />
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| EDOs: 10, 16, 26<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:122:&lt;h2&gt; --><h2 id="toc61"><a name="Lemba-Music"></a><!-- ws:end:WikiTextHeadingRule:122 -->Music</h2>
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| By <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br />
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3" rel="nofollow">Lemba Galatsia</a><br />
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3" rel="nofollow">GPO Lemba</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:124:&lt;h1&gt; --><h1 id="toc62"><a name="Gidorah"></a><!-- ws:end:WikiTextHeadingRule:124 -->Gidorah</h1>
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| Commas: 21/20, 144/125<br />
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| <br />
| |
| POTE generator: ~8/7 = 230.762<br />
| |
| <br />
| |
| Map: [&lt;1 1 2 3|, &lt;0 3 2 -1|]<br />
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| EDOs: 5, 11, 21, 26<br />
| |
| Badness: 0.0623<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:126:&lt;h1&gt; --><h1 id="toc63"><a name="Clyndro"></a><!-- ws:end:WikiTextHeadingRule:126 -->Clyndro</h1>
| |
| Commas: 1029/1024, 135/128<br />
| |
| <br />
| |
| POTE generator: ~8/7 = 226.469<br />
| |
| <br />
| |
| Map: [&lt;1 1 4 3|, &lt;0 3 -9 -1|]<br />
| |
| EDOs: 16<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:128:&lt;h1&gt; --><h1 id="toc64"><a name="Necromanteion"></a><!-- ws:end:WikiTextHeadingRule:128 -->Necromanteion</h1>
| |
| Commas: 1029/1024, 5103/5000<br />
| |
| <br />
| |
| POTE generator: ~48/35 = 541.779<br />
| |
| <br />
| |
| Map: [&lt;1 7 10 1|, &lt;0 -12 -17 4|]<br />
| |
| EDOs: 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd<br />
| |
| Badness: 0.1177<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:130:&lt;h2&gt; --><h2 id="toc65"><a name="Necromanteion-11-limit"></a><!-- ws:end:WikiTextHeadingRule:130 -->11-limit</h2>
| |
| Commas: 176/175, 243/242, 1029/1024<br />
| |
| <br />
| |
| POTE generator: ~15/11 = 541.729<br />
| |
| <br />
| |
| Map: [&lt;1 7 10 1 17|, &lt;0 -12 -17 4 -30|]<br />
| |
| EDOs: 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde<br />
| |
| Badness: 0.0535<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:132:&lt;h2&gt; --><h2 id="toc66"><a name="Necromanteion-13-limit"></a><!-- ws:end:WikiTextHeadingRule:132 -->13-limit</h2>
| |
| Commas: 144/143, 176/175, 243/242, 343/338<br />
| |
| <br />
| |
| POTE generator: ~15/11 = 541.606<br />
| |
| <br />
| |
| Map: [&lt;1 7 10 1 17 1|, &lt;0 -12 -17 4 -30 6|]<br />
| |
| EDOs: 31, 51ce, 82cf, 113cf, 144cf<br />
| |
| Badness: 0.0470<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:134:&lt;h1&gt; --><h1 id="toc67"><a name="Widefourth"></a><!-- ws:end:WikiTextHeadingRule:134 -->Widefourth</h1>
| |
| Commas: 1029/1024, 48828125/48771072<br />
| |
| <br />
| |
| POTE generator: ~3125/2304 = 524.210<br />
| |
| <br />
| |
| Map: [&lt;1 16 8 -2|, &lt;0 -33 -13 11|]<br />
| |
| Wedgie: &lt;&lt;33 13 -11 -56 -110 -62||<br />
| |
| EDOs: 16, 71, 87, 103, 190<br />
| |
| Badness: 0.1541<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:136:&lt;h2&gt; --><h2 id="toc68"><a name="Widefourth-11-limit"></a><!-- ws:end:WikiTextHeadingRule:136 -->11-limit</h2>
| |
| Commas: 385/384, 441/440, 234375/234256<br />
| |
| <br />
| |
| POTE generator: ~3125/2304 = 524.210<br />
| |
| <br />
| |
| Map: [&lt;1 16 8 -2 17|, &lt;0 -33 -13 11 -31|]<br />
| |
| EDOs: 16, 71, 87, 103, 190<br />
| |
| Badness: 0.0408<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:138:&lt;h2&gt; --><h2 id="toc69"><a name="Widefourth-13-limit"></a><!-- ws:end:WikiTextHeadingRule:138 -->13-limit</h2>
| |
| Commas: 385/384, 441/440, 625/624, 847/845<br />
| |
| <br />
| |
| POTE generator: ~65/48 = 524.209<br />
| |
| <br />
| |
| Map: [&lt;1 16 8 -2 17 12|, &lt;0 -33 -13 11 -31 -19|]<br />
| |
| EDOs: 16, 71, 87, 103, 190<br />
| |
| Badness: 0.0216</body></html></pre></div>
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