Landscape microtemperaments: Difference between revisions

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* [[Misty]] (+3136/3125 or 5120/5103) → [[Misty family]]
* [[Misty]] (+3136/3125 or 5120/5103) → [[Misty family]]
* ''[[Term (temperament)|Term]]'' (+32805/32768) → [[Schismatic family #Term|Schismatic family]]
* ''[[Term (temperament)|Term]]'' (+32805/32768) → [[Schismatic family #Term|Schismatic family]]
* ''[[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 #Domain|Vulture family]]
* ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal|Keemic temperaments]]
* ''[[Chromat]]'' (10976/10935) → [[Hemimage temperaments #Chromat|Hemimage temperaments]]
* ''[[Chromat]]'' (+10976/10935) → [[Amity family #Chromat|Amity family]]
* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
Line 18: Line 19:
* ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]
* ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]
* ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]
* ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]
* ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortonic family #Domain|Minortonic family]]
* ''[[Trivish]]'' (+134217728/133984375) → [[Vishnu family #Trivish|Vishnu family]]
* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]]
* ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortone family #Domain|Minortone family]]
* [[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, sextile, zinc, magnesium, poe, and chromium 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]].


== Septichrome ==
== Septichrome ==
Line 46: 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 62: 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 73: Line 76:


==== 17-limit ====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13.17


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 92: 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 107: 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 146: 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 162: 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 177: 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 192: 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 207: 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 261: 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 278: 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 294: 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 309: 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 320: Line 323:


==== Hafnium ====
==== Hafnium ====
Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4.  
Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4 (see also [[Berylic]]).


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 326: 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 342: 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 358: 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 373: 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 408: 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 423: 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 456: 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 471: 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 486: 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 501: 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 510: Line 513:


Badness (Sintel): 0.928
Badness (Sintel): 0.928
== Sextile ==
: ''For the 5-limit version, see [[Schismic–commatic equivalence continuum #Sextile (5-limit)]].''
Sextile tempers out the [[garischisma]] with a 1/6-octave period and is the {{nowrap| 12 & 270 }} temperament.
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 250047/250000, 33554432/33480783
{{Mapping|legend=1| 6 0 71 150 | 0 1 -6 -14 }}
: mapping generators: ~4096/3645, ~3
[[Optimal tuning]]s:
* [[WE]]: ~4096/3645 = 199.9828{{c}}, ~3/2 = 702.1521{{c}}
: [[error map]]: {{val| -0.103 +0.094 +0.173 -0.088 }}
* [[CWE]]: ~4096/3645 = 200.0000{{c}}, ~3/2 = 702.2187{{c}}
: error map: {{val| 0.000 +0.264 +0.374 +0.112 }}
{{Optimal ET sequence|legend=1| 12, …, 258, 270, 1362c, 1632c, …, 2442bc, 2712bc }}
[[Badness]] (Sintel): 1.77
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 151263/151250
Mapping: {{mapping| 6 0 71 150 230 | 0 1 -6 -14 -22 }}
Optimal tunings:
* CTE: ~55/49 = 199.9817{{c}}, ~3/2 = 702.1383{{c}}
* POTE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2080{{c}}
{{Optimal ET sequence|legend=0| 12, …, 258e, 270, 822, 1092, 1362c }}
Badness (Sintel): 0.981
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 5632/5625, 10648/10647
Mapping: {{mapping| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }}
Optimal tunings:
* WE: ~55/49 = 199.9804{{c}}, ~3/2 = 702.1260{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2001{{c}}
{{Optimal ET sequence|legend=0| 12f, …, 258ef, 270, 552, 822, 1092, 1914cde }}
Badness (Sintel): 0.788
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1701/1700, 1716/1715, 5632/5625, 7744/7735
Mapping: {{mapping| 6 0 71 150 230 279 -4 | 0 1 -6 -14 -22 -27 3 }}
Optimal tunings:
* WE: ~55/49 = 199.9669{{c}}, ~3/2 = 702.0643{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.1869{{c}}
{{Optimal ET sequence|legend=0| 12f, 270, 552g }}
Badness (Sintel): 1.06
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 936/935, 1216/1215, 1701/1700, 1716/1715, 2376/2375, 4200/4199
Mapping: {{mapping| 6 0 71 150 230 279 -4 35 | 0 1 -6 -14 -22 -27 3 -1 }}
Optimal tunings:
* CTE: ~55/49 = 199.9711{{c}}, ~3/2 = 702.0829{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.1890{{c}}
{{Optimal ET sequence|legend=0| 12f, 270, 552g, 822gg }}
Badness (Sintel): 0.948
=== Sextilia ===
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 4096/4095, 4459/4455, 20449/20412
Mapping: {{mapping| 6 0 71 150 230 -149 | 0 1 -6 -14 -22 18 }}
Optimal tunings:
* WE: ~55/49 = 199.9975{{c}}, ~3/2 = 702.2196{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2285{{c}}
{{Optimal ET sequence|legend=0| 12, 258e, 270 }}
Badness (Sintel): 1.62
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 1001/1000, 1701/1700, 4096/4095, 4459/4455
Mapping: {{mapping| 6 0 71 150 230 -149 -4 | 0 1 -6 -14 -22 18 3 }}
Optimal tunings:
* WE: ~55/49 = 199.9862{{c}}, ~3/2 = 702.1714{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2207{{c}}
{{Optimal ET sequence|legend=0| 12, 258e, 270 }}
Badness (Sintel): 1.95
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 715/714, 1001/1000, 1216/1215, 1701/1700, 1729/1728, 2912/2907
Mapping: {{mapping| 6 0 71 150 230 -149 -4 35 | 0 1 -6 -14 -22 18 3 -1 }}
Optimal tunings:
* WE: ~55/49 = 199.9866{{c}}, ~3/2 = 702.1731{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2208{{c}}
{{Optimal ET sequence|legend=0| 12, 258e, 270 }}
Badness (Sintel): 1.53


== Zinc ==
== Zinc ==
{{See also| 10th-octave temperaments #Neon }}
Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament, and is a [[weak extension]] of [[miscellaneous 5-limit temperaments #Neon|neon]]. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.
 
Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 665: 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 680: 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 690: Line 564:
Badness (Sintel): 0.640
Badness (Sintel): 0.640


==== 2.3.5.7.11.13.19 subgroup (neozinc) ====
==== 2.3.5.7.11.13.19 subgroup ====
A 2.7.11.19 restriction worth considering is [[30th-octave temperaments#Oyster|oyster]].
 
Subgroup: 2.3.5.7.11.13.19
Subgroup: 2.3.5.7.11.13.19


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 712: 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 728: 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 785: 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 800: 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 837: 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 852: 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 867: 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 877: Line 753:
Badness (Sintel): 1.06
Badness (Sintel): 1.06


== Phosphorus ==
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 250047/250000, {{monzo| 60 -96 1 32 }}
[[Mapping]]: {{mapping| 15 8 -4 -4 | 0 13 32 38 }}
: mapping generators: ~{{monzo| -21 34 4 -15 }}, ~210827008/199290375
[[Optimal tuning]]s:
* [[WE]]: ~{{monzo|-21 34 4 -15}} = 80.000039{{c}}, ~210827008/199290375 = 97.073339{{c}}
: [[error map]]: {{val| +0.0006 -0.0013 +0.0330 -0.0392 }}
* [[CWE]]: ~{{monzo|-21 34 4 -15}} = 80.000000{{c}}, ~210827008/199290375 = 97.073314{{c}}
: error map: {{val| 0.0000 -0.0019 +0.0323 -0.0400 }}
{{Optimal ET sequence|legend=1| 210, …, 1125, 1335, 2460 }}
[[Badness]] (Sintel): 9.66
[[Category:Landscape microtemperaments| ]] <!-- main article -->
[[Category:Landscape| ]] <!-- key article -->
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Landscape microtemperaments| ]] <!-- main article -->
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Rank 2]]