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Landscape microtemperaments: Difference between revisions

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Line 8: Line 8:
* ''[[Sextile]]'' (+33554432/33480783) → [[Garischismic clan #Sextile|Garischismic clan]]
* ''[[Sextile]]'' (+33554432/33480783) → [[Garischismic clan #Sextile|Garischismic clan]]
* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]
* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]
* [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]]
* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Terture|Vulture family]]
* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Terture|Vulture family]]
* ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal|Keemic temperaments]]
* ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal|Keemic temperaments]]
Line 22: Line 21:
* ''[[Trivish]]'' (+134217728/133984375) → [[Vishnu family #Trivish|Vishnu family]]
* ''[[Trivish]]'' (+134217728/133984375) → [[Vishnu family #Trivish|Vishnu family]]
* ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortone family #Domain|Minortone family]]
* ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortone family #Domain|Minortone family]]
* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]]
* [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]]
* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[Mercator family #Aemilic|Mercator family]]


Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, chromium, and phosphorus in the order of increasing [[badness]].
Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, chromium, and phosphorus in the order of increasing [[badness]].
Line 49: Line 49:
Comma list: 9801/9800, 151263/151250, 234375/234256
Comma list: 9801/9800, 151263/151250, 234375/234256


Mapping: {{mapping| 6 1 -15 -24 -32 | 0 5 17 24 31 }}
{{Mapping|legend=0| 6 1 -15 -24 -32 | 0 5 17 24 31 }}
: mapping generators: ~55/49, ~375/308
: mapping generators: ~55/49, ~375/308


Line 65: Line 65:
Comma list: 1716/1715, 2080/2079, 34398/34375, 85293/85184
Comma list: 1716/1715, 2080/2079, 34398/34375, 85293/85184


Mapping: {{mapping| 6 1 -15 -24 -32 -68 | 0 5 17 24 31 53 }}
{{Mapping|legend=0| 6 1 -15 -24 -32 -68 | 0 5 17 24 31 53 }}


Optimal tunings:  
Optimal tunings:  
Line 80: Line 80:
Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952
Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952


Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 | 0 5 17 24 31 53 15 }}
{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 | 0 5 17 24 31 53 15 }}


Optimal tunings:  
Optimal tunings:  
Line 95: Line 95:
Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 23409/23408
Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 23409/23408


Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 34 | 0 5 17 24 31 53 15 -5 }}
{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 34 | 0 5 17 24 31 53 15 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 110: Line 110:
Comma list: 936/935, 1701/1700, 1716/1715, 1863/1862, 2024/2023, 2025/2023, 2376/2375
Comma list: 936/935, 1701/1700, 1716/1715, 1863/1862, 2024/2023, 2025/2023, 2376/2375


Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 34 -12 | 0 5 17 24 31 53 15 -5 23 }}
{{Mapping|legend=0| 6 1 -15 -24 -32 -68 -1 34 -12 | 0 5 17 24 31 53 15 -5 23 }}


Optimal tunings:  
Optimal tunings:  
Line 149: Line 149:
Comma list: 3025/3024, 102487/102400, {{monzo| 39 -4 -11 -5 2 }}
Comma list: 3025/3024, 102487/102400, {{monzo| 39 -4 -11 -5 2 }}


Mapping: {{mapping| 21 4 39 98 58 | 0 6 2 -8 3 3 }}
{{Mapping|legend=0| 21 4 39 98 58 | 0 6 2 -8 3 3 }}
: mapping generators: ~1323/1280, ~6615/5632
: mapping generators: ~1323/1280, ~6615/5632


Line 165: Line 165:
Comma list: 3025/3024, 4096/4095, 14641/14625, 85750/85683
Comma list: 3025/3024, 4096/4095, 14641/14625, 85750/85683


Mapping: {{mapping| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }}
{{Mapping|legend=0| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }}


Optimal tunings:  
Optimal tunings:  
Line 180: Line 180:
Comma list: 2601/2600, 3025/3024, 4096/4095, 8624/8619, 14641/14625
Comma list: 2601/2600, 3025/3024, 4096/4095, 8624/8619, 14641/14625


Mapping: {{mapping| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }}
{{Mapping|legend=0| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }}


Optimal tunings:  
Optimal tunings:  
Line 195: Line 195:
Comma list: 2376/2375, 2601/2600, 2926/2925, 3025/3024, 3213/3211, 4096/4095
Comma list: 2376/2375, 2601/2600, 2926/2925, 3025/3024, 3213/3211, 4096/4095


Mapping: {{mapping| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }}
{{Mapping|legend=0| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }}


Optimal tunings:  
Optimal tunings:  
Line 210: Line 210:
Comma list: 1496/1495, 2376/2375, 2601/2600, 2646/2645, 2926/2925, 3025/3024, 3213/3211
Comma list: 1496/1495, 2376/2375, 2601/2600, 2646/2645, 2926/2925, 3025/3024, 3213/3211


Mapping: {{mapping| 21 4 39 98 58 107 120 16 95 | 0 6 2 -8 3 -6 -7 15 0 }}
{{Mapping|legend=0| 21 4 39 98 58 107 120 16 95 | 0 6 2 -8 3 -6 -7 15 0 }}


Optimal tunings:  
Optimal tunings:  
Line 264: Line 264:
Comma list: 9801/9800, 151263/151250, 184549376/184528125
Comma list: 9801/9800, 151263/151250, 184549376/184528125


Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}
{{Mapping|legend=0| 12 0 161 338 517 | 0 1 -7 -16 -25 }}


Optimal tunings:  
Optimal tunings:  
Line 281: Line 281:
Comma list: 9801/9800, 151263/151250, 371293/371250, 184549376/184528125
Comma list: 9801/9800, 151263/151250, 371293/371250, 184549376/184528125


Mapping: {{mapping| 60 0 805 1690 2585 1173 | 0 1 7 -16 -25 -10 }}
{{Mapping|legend=0| 60 0 805 1690 2585 1173 | 0 1 7 -16 -25 -10 }}
: mapping generators: ~2704/2673, ~3
: mapping generators: ~2704/2673, ~3


Line 297: Line 297:
Comma list: 9801/9800, 12376/12375, 28561/28560, 151263/151250, 11275335/11275264
Comma list: 9801/9800, 12376/12375, 28561/28560, 151263/151250, 11275335/11275264


Mapping: {{mapping| 60 0 805 1690 2585 1173 1957 | 0 1 7 -16 -25 -10 -18 }}
{{Mapping|legend=0| 60 0 805 1690 2585 1173 1957 | 0 1 7 -16 -25 -10 -18 }}


Optimal tunings:  
Optimal tunings:  
Line 312: Line 312:
Comma list: 9801/9800, 12376/12375, 12636/12635, 23409/23408, 28561/28560, 151263/151250
Comma list: 9801/9800, 12376/12375, 12636/12635, 23409/23408, 28561/28560, 151263/151250


Mapping: {{mapping| 60 60 385 730 1085 573 877 -61 | 0 1 7 -16 -25 -10 -18 9 }}
{{Mapping|legend=0| 60 60 385 730 1085 573 877 -61 | 0 1 7 -16 -25 -10 -18 9 }}


Optimal tunings:  
Optimal tunings:  
Line 329: Line 329:
Comma list: 9801/9800, 151263/151250, 184549376/184528125, 308915776/308828625
Comma list: 9801/9800, 151263/151250, 184549376/184528125, 308915776/308828625


Mapping: {{mapping| 72 0 966 2028 3102 2777 | 0 1 -7 -16 -25 -22 }}
{{Mapping|legend=0| 72 0 966 2028 3102 2777 | 0 1 -7 -16 -25 -22 }}
: mapping generators: ~105/104, ~3
: mapping generators: ~105/104, ~3


Line 345: Line 345:
Comma list: 9801/9800, 12376/12375, 151263/151250, 1713660/1713481, 97144749/97140736
Comma list: 9801/9800, 12376/12375, 151263/151250, 1713660/1713481, 97144749/97140736


Mapping: {{mapping| 72 0 966 2028 3102 2777 979 | 0 1 -7 -16 -25 -22 -6 }}
{{Mapping|legend=0| 72 0 966 2028 3102 2777 979 | 0 1 -7 -16 -25 -22 -6 }}
: mapping generators: ~105/104, ~3
: mapping generators: ~105/104, ~3


Line 361: Line 361:
Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625
Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625


Subgroup-val mapping: {{mapping| 72 0 966 2028 3102 2777 979 -328 | 0 1 -7 -16 -25 -22 -6 6 }}
{{Mapping|legend=2| 72 0 966 2028 3102 2777 979 -328 | 0 1 -7 -16 -25 -22 -6 6 }}


Optimal tunings:  
Optimal tunings:  
Line 376: Line 376:
Comma list: 9801/9800, 10881/10880, 12376/12375, 16576/16575, 57629/57624, 93093/93092, 179712/179707
Comma list: 9801/9800, 10881/10880, 12376/12375, 16576/16575, 57629/57624, 93093/93092, 179712/179707


Subgroup-val mapping: {{mapping| 72 0 966 2028 3102 2777 979 -328 3228 | 0 1 -7 -16 -25 -22 -6 6 -25 }}
{{Mapping|legend=2| 72 0 966 2028 3102 2777 979 -328 3228 | 0 1 -7 -16 -25 -22 -6 6 -25 }}


Optimal tunings:  
Optimal tunings:  
Line 411: Line 411:
Comma list: 3025/3024, 102487/102400, 180224/180075
Comma list: 3025/3024, 102487/102400, 180224/180075


Mapping: {{mapping| 15 0 17 54 40 | 0 4 3 -2 2 }}
{{Mapping|legend=0| 15 0 17 54 40 | 0 4 3 -2 2 }}


Optimal tunings:  
Optimal tunings:  
Line 426: Line 426:
Comma list: 1716/1715, 3025/3024, 4096/4095, 14641/14625
Comma list: 1716/1715, 3025/3024, 4096/4095, 14641/14625


Mapping: {{mapping| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }}
{{Mapping|legend=0| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }}


Optimal tunings:  
Optimal tunings:  
Line 459: Line 459:
Comma list: 3025/3024, 5632/5625, 102487/102400
Comma list: 3025/3024, 5632/5625, 102487/102400


Mapping: {{mapping| 3 2 8 16 9 | 0 8 -3 -22 4 }}
{{Mapping|legend=0| 3 2 8 16 9 | 0 8 -3 -22 4 }}


Optimal tunings:  
Optimal tunings:  
Line 474: Line 474:
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095


Mapping: {{mapping| 3 2 8 16 9 8 | 0 8 -3 -22 4 9 }}
{{Mapping|legend=0| 3 2 8 16 9 8 | 0 8 -3 -22 4 9 }}


Optimal tunings:  
Optimal tunings:  
Line 489: Line 489:
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4096/4095
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4096/4095


Mapping: {{mapping| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}
{{Mapping|legend=0| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}


Optimal tunings:  
Optimal tunings:  
Line 504: Line 504:
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1729/1728
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1729/1728


Mapping: {{mapping| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}
{{Mapping|legend=0| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}


Optimal tunings:  
Optimal tunings:  
Line 539: Line 539:
Comma list: 9801/9800, 151263/151250, {{monzo| -27 -6 4 6 3 }}
Comma list: 9801/9800, 151263/151250, {{monzo| -27 -6 4 6 3 }}


Mapping: {{mapping| 30 2 15 66 122 | 0 5 6 2 -2 }}
{{Mapping|legend=0| 30 2 15 66 122 | 0 5 6 2 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 554: Line 554:
Comma list: 9801/9800, 10648/10647, 105644/105625, 196625/196608
Comma list: 9801/9800, 10648/10647, 105644/105625, 196625/196608


Mapping: {{mapping| 30 2 15 66 122 193 | 0 5 6 2 -2 -9 }}
{{Mapping|legend=0| 30 2 15 66 122 193 | 0 5 6 2 -2 -9 }}


Optimal tunings:  
Optimal tunings:  
Line 571: Line 571:
Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 89376/89375
Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 89376/89375


Mapping: {{mapping| 30 2 15 66 122 193 91 | 0 5 6 2 -2 -9 4 }}
{{Mapping|legend=0| 30 2 15 66 122 193 91 | 0 5 6 2 -2 -9 4 }}


Optimal tunings:  
Optimal tunings:  
Line 588: Line 588:
Comma list: 9801/9800, 10648/10647, 31213/31212, 105644/105625, 196625/196608
Comma list: 9801/9800, 10648/10647, 31213/31212, 105644/105625, 196625/196608


Mapping: {{mapping| 60 4 30 132 244 386 391 | 0 5 6 2 -2 -9 -8 }}
{{Mapping|legend=0| 60 4 30 132 244 386 391 | 0 5 6 2 -2 -9 -8 }}
: mapping generators: ~612/605, ~216/175
: mapping generators: ~612/605, ~216/175


Line 604: Line 604:
Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 23409/23408, 89376/89375
Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 23409/23408, 89376/89375


Mapping: {{mapping| 60 4 30 132 244 386 391 182 | 0 5 6 2 -2 -9 -8 4 }}
{{Mapping|legend=0| 60 4 30 132 244 386 391 182 | 0 5 6 2 -2 -9 -8 4 }}


Optimal tunings:  
Optimal tunings:  
Line 661: Line 661:
Comma list: 9801/9800, 19712/19683, 151263/151250
Comma list: 9801/9800, 19712/19683, 151263/151250


Mapping: {{mapping| 30 0 -73 -106 -134 | 0 1 3 4 5 }}
{{Mapping|legend=0| 30 0 -73 -106 -134 | 0 1 3 4 5 }}


Optimal tunings:  
Optimal tunings:  
Line 676: Line 676:
Comma list: 1001/1000, 4225/4224, 4459/4455, 19712/19683
Comma list: 1001/1000, 4225/4224, 4459/4455, 19712/19683


Mapping: {{mapping| 30 0 -73 -106 -134 111 | 0 1 3 4 5 0 }}
{{Mapping|legend=0| 30 0 -73 -106 -134 111 | 0 1 3 4 5 0 }}


Optimal tunings:  
Optimal tunings:  
Line 713: Line 713:
Comma list: 9801/9800, 46656/46585, 151263/151250
Comma list: 9801/9800, 46656/46585, 151263/151250


Mapping: {{mapping| 24 1 -6 18 46 | 0 3 5 4 3 }}
{{Mapping|legend=0| 24 1 -6 18 46 | 0 3 5 4 3 }}


Optimal tunings:  
Optimal tunings:  
Line 728: Line 728:
Comma list: 1716/1715, 2080/2079, 34398/34375, 39366/39325
Comma list: 1716/1715, 2080/2079, 34398/34375, 39366/39325


Mapping: {{mapping| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 }}
{{Mapping|legend=0| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 }}


Optimal tunings:  
Optimal tunings:  
Line 743: Line 743:
Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 11016/11011
Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 11016/11011


Mapping: {{mapping| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 9 }}
{{Mapping|legend=0| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 9 }}


Optimal tunings:  
Optimal tunings:  
Line 772: Line 772:


[[Category:Landscape microtemperaments| ]] <!-- main article -->
[[Category:Landscape microtemperaments| ]] <!-- main article -->
[[Category:Landscape| ]] <!-- key article -->
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Landscape_microtemperaments"