Ragismic microtemperaments: Difference between revisions
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* [[Ennealimmal]] (+2401/2400) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]] | * [[Ennealimmal]] (+2401/2400) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]] | ||
* [[Octoid]] (+16875/16807) → [[Stearnsmic clan #Octoid|Stearnsmic clan]] | * [[Octoid]] (+16875/16807) → [[Stearnsmic clan #Octoid|Stearnsmic clan]] | ||
* ''[[ | * ''[[Ludizemlic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments #Ludizemlic|37th-octave temperaments]] | ||
Considered below, sorted by [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, quincy, deca, keenanose, counterkleismic, sfourth, aluminium, ragitritonic, quatracot, trideci, moulin, and palladium. | Considered below, sorted by [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, quincy, deca, keenanose, counterkleismic, sfourth, aluminium, ragitritonic, quatracot, trideci, moulin, and palladium. | ||
| Line 59: | Line 59: | ||
Comma list: 3025/3024, 4375/4374, 35156250/35153041 | Comma list: 3025/3024, 4375/4374, 35156250/35153041 | ||
{{Mapping|legend=0| 2 -7 -8 -15 -6 | 0 37 46 75 47 }} | |||
: mapping generators: ~99/70, ~11/10 | : mapping generators: ~99/70, ~11/10 | ||
| Line 99: | Line 99: | ||
Comma list: 540/539, 4375/4374, 16384/16335 | Comma list: 540/539, 4375/4374, 16384/16335 | ||
{{Mapping|legend=0| 19 0 14 -37 126 | 0 1 1 3 -2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 114: | Line 114: | ||
Comma list: 540/539, 625/624, 729/728, 2205/2197 | Comma list: 540/539, 625/624, 729/728, 2205/2197 | ||
{{Mapping|legend=0| 19 0 14 -37 126 -20 | 0 1 1 3 -2 3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 129: | Line 129: | ||
Comma list: 3025/3024, 4375/4374, 234375/234256 | Comma list: 3025/3024, 4375/4374, 234375/234256 | ||
{{Mapping|legend=0| 38 0 28 -74 11 | 0 1 1 3 2 }} | |||
: mapping generators: ~55/54, ~3 | : mapping generators: ~55/54, ~3 | ||
| Line 145: | Line 145: | ||
Comma list: 1716/1715, 2080/2079, 3025/3024, 234375/234256 | Comma list: 1716/1715, 2080/2079, 3025/3024, 234375/234256 | ||
{{Mapping|legend=0| 38 0 28 -74 11 -281 | 0 1 1 3 2 7 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 160: | Line 160: | ||
Comma list: 3025/3024, 4096/4095, 4375/4374, 31250/31213 | Comma list: 3025/3024, 4096/4095, 4375/4374, 31250/31213 | ||
{{Mapping|legend=0| 38 0 28 -74 11 502 | 0 1 1 3 2 -6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 175: | Line 175: | ||
Comma list: 3025/3024, 4225/4224, 4375/4374, 78125/78078 | Comma list: 3025/3024, 4225/4224, 4375/4374, 78125/78078 | ||
{{Mapping|legend=0| 38 1 29 -71 13 111 | 0 2 2 6 4 1 }} | |||
: mapping generators: ~55/54, ~429/250 | : mapping generators: ~55/54, ~429/250 | ||
| Line 193: | Line 193: | ||
Comma list: 2500/2499, 3250/3249, 4225/4224, 4375/4374, 11016/11011, 57375/57344 | Comma list: 2500/2499, 3250/3249, 4225/4224, 4375/4374, 11016/11011, 57375/57344 | ||
{{Mapping|legend=0| 19 3 17 -28 82 92 159 78 | 0 10 10 30 -6 -8 -30 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 252: | Line 252: | ||
Comma list: 4000/3993, 4375/4374, 131072/130977 | Comma list: 4000/3993, 4375/4374, 131072/130977 | ||
{{Mapping|legend=0| 7 2 -8 53 3 | 0 3 8 -11 7 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 267: | Line 267: | ||
Comma list: 1575/1573, 2080/2079, 4096/4095, 4375/4374 | Comma list: 1575/1573, 2080/2079, 4096/4095, 4375/4374 | ||
{{Mapping|legend=0| 7 2 -8 53 3 35 | 0 3 8 -11 7 -3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 306: | Line 306: | ||
Comma list: 3025/3024, 4375/4374, 131072/130977 | Comma list: 3025/3024, 4375/4374, 131072/130977 | ||
{{Mapping|legend=0| 2 -4 -11 18 18 | 0 11 24 -19 -17 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 321: | Line 321: | ||
Comma list: 1716/1715, 2080/2079, 3025/3024, 4096/4095 | Comma list: 1716/1715, 2080/2079, 3025/3024, 4096/4095 | ||
{{Mapping|legend=0| 2 -4 -11 18 18 25 | 0 11 24 -19 -17 -27 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 354: | Line 354: | ||
Comma list: 3025/3024, 4375/4374, 589824/588245 | Comma list: 3025/3024, 4375/4374, 589824/588245 | ||
{{Mapping|legend=0| 2 -11 -20 5 10 | 0 23 40 1 -5 }} | |||
: mapping generators: ~99/70, ~99/80 | : mapping generators: ~99/70, ~99/80 | ||
| Line 370: | Line 370: | ||
Comma list: 1716/1715, 2080/2079, 2200/2197, 3025/3024 | Comma list: 1716/1715, 2080/2079, 2200/2197, 3025/3024 | ||
{{Mapping|legend=0| 2 -11 -20 5 10 -8 | 0 23 40 1 -5 25 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 385: | Line 385: | ||
Comma list: 4375/4374, 14641/14580, 15488/15435 | Comma list: 4375/4374, 14641/14580, 15488/15435 | ||
{{Mapping|legend=0| 1 -40 -70 1 -77 | 0 46 80 2 89 }} | |||
: mapping generators: ~2, ~144/77 | : mapping generators: ~2, ~144/77 | ||
| Line 401: | Line 401: | ||
Comma list: 676/675, 1001/1000, 4375/4374, 14641/14580 | Comma list: 676/675, 1001/1000, 4375/4374, 14641/14580 | ||
{{Mapping|legend=0| 1 -40 -70 1 -77 -131 | 0 46 80 2 89 149 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 440: | Line 440: | ||
Comma list: 3025/3024, 4375/4374, 2791309312/2790703125 | Comma list: 3025/3024, 4375/4374, 2791309312/2790703125 | ||
{{Mapping|legend=0| 2 1 6 -15 -8 | 0 8 -5 76 55 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 475: | Line 475: | ||
Comma list: 3025/3024, 4375/4374, 5767168/5764801 | Comma list: 3025/3024, 4375/4374, 5767168/5764801 | ||
{{Mapping|legend=0| 2 -8 -15 6 10 | 0 29 51 -1 -8 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 490: | Line 490: | ||
Comma list: 1716/1715, 2080/2079, 3025/3024, 15379/15360 | Comma list: 1716/1715, 2080/2079, 3025/3024, 15379/15360 | ||
{{Mapping|legend=0| 2 -8 -15 6 10 -3 | 0 29 51 -1 -8 27 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 526: | Line 526: | ||
Comma list: 4375/4374, 41503/41472, 1879453125/1879048192 | Comma list: 4375/4374, 41503/41472, 1879453125/1879048192 | ||
{{Mapping|legend=0| 17 0 26 -87 207 | 0 2 1 10 -11 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 565: | Line 565: | ||
Comma list: 441/440, 4375/4374, 65536/65219 | Comma list: 441/440, 4375/4374, 65536/65219 | ||
{{Mapping|legend=0| 1 -24 -43 5 2 | 0 35 62 -3 2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 580: | Line 580: | ||
Comma list: 364/363, 441/440, 2200/2197, 4375/4374 | Comma list: 364/363, 441/440, 2200/2197, 4375/4374 | ||
{{Mapping|legend=0| 1 -24 -43 5 2 -27 | 0 35 62 -3 2 42 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 595: | Line 595: | ||
Comma list: 364/363, 441/440, 595/594, 1156/1155, 2200/2197 | Comma list: 364/363, 441/440, 595/594, 1156/1155, 2200/2197 | ||
{{Mapping|legend=0| 1 -24 -43 5 2 -27 -31 | 0 35 62 -3 2 42 48 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 632: | Line 632: | ||
Comma list: 4375/4374, 41503/41472, 184549376/184528125 | Comma list: 4375/4374, 41503/41472, 184549376/184528125 | ||
{{Mapping|legend=0| 1 0 -27 109 -159 | 0 2 37 -134 205 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 647: | Line 647: | ||
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625 | Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625 | ||
{{Mapping|legend=0| 1 0 -27 109 -159 -70 | 0 2 37 -134 205 93 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 684: | Line 684: | ||
Comma list: 3025/3024, 4375/4374, 235298/234375 | Comma list: 3025/3024, 4375/4374, 235298/234375 | ||
{{Mapping|legend=0| 2 -20 -26 -34 -17 | 0 31 41 53 32 }} | |||
: mapping generators: ~99/70, ~35/27 | : mapping generators: ~99/70, ~35/27 | ||
| Line 700: | Line 700: | ||
Comma list: 847/845, 1001/1000, 3025/3024, 4375/4374 | Comma list: 847/845, 1001/1000, 3025/3024, 4375/4374 | ||
{{Mapping|legend=0| 2 -20 -26 -34 -17 -21 | 0 31 41 53 32 38 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 733: | Line 733: | ||
Comma list: 4375/4374, 41503/41472, 172032/171875 | Comma list: 4375/4374, 41503/41472, 172032/171875 | ||
{{Mapping|legend=0| 1 -22 -22 -65 58 | 0 32 33 92 -74 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 748: | Line 748: | ||
Comma list: 676/675, 1001/1000, 4375/4374, 10985/10976 | Comma list: 676/675, 1001/1000, 4375/4374, 10985/10976 | ||
{{Mapping|legend=0| 1 -22 -22 -65 58 -56 | 0 32 33 92 -74 81 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 763: | Line 763: | ||
Comma list: 4375/4374, 5632/5625, 117649/117612 | Comma list: 4375/4374, 5632/5625, 117649/117612 | ||
{{Mapping|legend=0| 1 -22 -22 -65 -141 | 0 32 33 92 196 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 778: | Line 778: | ||
Comma list: 676/675, 1716/1715, 4225/4224, 4375/4374 | Comma list: 676/675, 1716/1715, 4225/4224, 4375/4374 | ||
{{Mapping|legend=0| 1 -22 -22 -65 -141 -56 | 0 32 33 92 196 81 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 815: | Line 815: | ||
Comma list: 3025/3024, 4375/4374, 4296700485/4294967296 | Comma list: 3025/3024, 4375/4374, 4296700485/4294967296 | ||
{{Mapping|legend=0| 4 0 -11 48 43 | 0 5 16 -29 -23 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 830: | Line 830: | ||
Comma list: 2200/2197, 3025/3024, 4096/4095, 4375/4374 | Comma list: 2200/2197, 3025/3024, 4096/4095, 4375/4374 | ||
{{Mapping|legend=0| 4 0 -11 48 43 11 | 0 5 16 -29 -23 3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 863: | Line 863: | ||
Comma list: 441/440, 4000/3993, 4375/4374 | Comma list: 441/440, 4000/3993, 4375/4374 | ||
{{Mapping|legend=0| 1 2 3 3 4 | 0 -30 -49 -14 -39 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 878: | Line 878: | ||
Comma list: 364/363, 441/440, 676/675, 4375/4374 | Comma list: 364/363, 441/440, 676/675, 4375/4374 | ||
{{Mapping|legend=0| 1 2 3 3 4 5 | 0 -30 -49 -14 -39 -94 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 893: | Line 893: | ||
Comma list: 364/363, 441/440, 595/594, 676/675, 1156/1155 | Comma list: 364/363, 441/440, 595/594, 676/675, 1156/1155 | ||
{{Mapping|legend=0| 1 2 3 3 4 5 5 | 0 -30 -49 -14 -39 -94 -66 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 908: | Line 908: | ||
Comma list: 343/342, 364/363, 441/440, 476/475, 595/594, 676/675 | Comma list: 343/342, 364/363, 441/440, 476/475, 595/594, 676/675 | ||
{{Mapping|legend=0| 1 2 3 3 4 5 5 4 | 0 -30 -49 -14 -39 -94 -66 18 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 945: | Line 945: | ||
Comma list: 3025/3024, 4375/4374, 391314/390625 | Comma list: 3025/3024, 4375/4374, 391314/390625 | ||
{{Mapping|legend=0| 10 4 9 2 18 | 0 5 6 11 7 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 960: | Line 960: | ||
Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374 | Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374 | ||
{{Mapping|legend=0| 10 4 9 2 18 37 | 0 5 6 11 7 0 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 975: | Line 975: | ||
Comma list: 1001/1000, 1521/1520, 3025/3024, 4225/4224, 4375/4374 | Comma list: 1001/1000, 1521/1520, 3025/3024, 4225/4224, 4375/4374 | ||
{{Mapping|legend=0| 10 4 9 2 18 37 33 | 0 5 6 11 7 0 4 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,010: | Line 1,010: | ||
Comma list: 4375/4374, 117649/117612, 67110351/67108864 | Comma list: 4375/4374, 117649/117612, 67110351/67108864 | ||
{{Mapping|legend=0| 1 2 3 3 3 | 0 -112 -183 -52 124 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,025: | Line 1,025: | ||
Comma list: 4225/4224, 4375/4374, 6656/6655, 117649/117612 | Comma list: 4225/4224, 4375/4374, 6656/6655, 117649/117612 | ||
{{Mapping|legend=0| 1 2 3 3 3 3 | 0 -112 -183 -52 124 189 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,062: | Line 1,062: | ||
Comma list: 540/539, 4375/4374, 2097152/2096325 | Comma list: 540/539, 4375/4374, 2097152/2096325 | ||
{{Mapping|legend=0| 1 -5 -4 -18 19 | 0 25 24 79 -59 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,077: | Line 1,077: | ||
Comma list: 540/539, 625/624, 729/728, 10985/10976 | Comma list: 540/539, 625/624, 729/728, 10985/10976 | ||
{{Mapping|legend=0| 1 -5 -4 -18 19 -15 | 0 25 24 79 -59 71 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,092: | Line 1,092: | ||
Comma list: 1375/1372, 4375/4374, 496125/495616 | Comma list: 1375/1372, 4375/4374, 496125/495616 | ||
{{Mapping|legend=0| 1 -5 -4 -18 -40 | 0 25 24 79 165 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,107: | Line 1,107: | ||
Comma list: 625/624, 729/728, 1375/1372, 10985/10976 | Comma list: 625/624, 729/728, 1375/1372, 10985/10976 | ||
{{Mapping|legend=0| 1 -5 -4 -18 -40 -15 | 0 25 24 79 165 71 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,142: | Line 1,142: | ||
Comma list: 121/120, 441/440, 4375/4374 | Comma list: 121/120, 441/440, 4375/4374 | ||
{{Mapping|legend=0| 1 2 3 3 4 | 0 -19 -31 -9 -25 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,157: | Line 1,157: | ||
Comma list: 121/120, 169/168, 325/324, 441/440 | Comma list: 121/120, 169/168, 325/324, 441/440 | ||
{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -19 -31 -9 -25 -14 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,172: | Line 1,172: | ||
Comma list: 385/384, 2401/2376, 4375/4374 | Comma list: 385/384, 2401/2376, 4375/4374 | ||
{{Mapping|legend=0| 1 2 3 3 3 | 0 -19 -31 -9 21 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,187: | Line 1,187: | ||
Comma list: 196/195, 364/363, 385/384, 4375/4374 | Comma list: 196/195, 364/363, 385/384, 4375/4374 | ||
{{Mapping|legend=0| 1 2 3 3 3 3 | 0 -19 -31 -9 21 32 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,224: | Line 1,224: | ||
Comma list: 4375/4374, 234375/234256, 2097152/2096325 | Comma list: 4375/4374, 234375/234256, 2097152/2096325 | ||
{{Mapping|legend=0| 13 0 92 -355 148 | 0 1 -3 19 -5 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,239: | Line 1,239: | ||
Comma list: 4096/4095, 4375/4374, 6656/6655, 78125/78078 | Comma list: 4096/4095, 4375/4374, 6656/6655, 78125/78078 | ||
{{Mapping|legend=0| 13 0 92 -355 148 419 | 0 1 -3 19 -5 -18 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,278: | Line 1,278: | ||
Comma list: 4375/4374, 5632/5625, 2621440/2614689 | Comma list: 4375/4374, 5632/5625, 2621440/2614689 | ||
{{Mapping|legend=0| 1 -3 -15 40 -75 | 0 9 34 -73 154 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,293: | Line 1,293: | ||
Comma list: 2080/2079, 2200/2197, 4375/4374, 5632/5625 | Comma list: 2080/2079, 2200/2197, 4375/4374, 5632/5625 | ||
{{Mapping|legend=0| 1 -3 -15 40 -75 -34 | 0 9 34 -73 154 74 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,328: | Line 1,328: | ||
Comma list: 3025/3024, 4375/4374, 1265625/1261568 | Comma list: 3025/3024, 4375/4374, 1265625/1261568 | ||
{{Mapping|legend=0| 2 -6 -1 -36 -22 | 0 13 8 59 41 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,343: | Line 1,343: | ||
Comma list: 625/624, 729/728, 1575/1573, 2200/2197 | Comma list: 625/624, 729/728, 1575/1573, 2200/2197 | ||
{{Mapping|legend=0| 2 -6 -1 -36 -22 -6 | 0 13 8 59 41 19 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,380: | Line 1,380: | ||
Comma list: 245/242, 385/384, 4375/4374 | Comma list: 245/242, 385/384, 4375/4374 | ||
{{Mapping|legend=0| 13 0 -11 57 45 | 0 1 2 -1 0 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,395: | Line 1,395: | ||
Comma list: 169/168, 245/242, 325/324, 385/384 | Comma list: 169/168, 245/242, 325/324, 385/384 | ||
{{Mapping|legend=0| 13 0 -11 57 45 48 | 0 1 2 -1 0 0 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,430: | Line 1,430: | ||
Comma list: 4375/4374, 759375/758912, 100663296/100656875 | Comma list: 4375/4374, 759375/758912, 100663296/100656875 | ||
{{Mapping|legend=0| 1 -16 -9 -75 9 | 0 73 47 323 -23 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,445: | Line 1,445: | ||
Comma list: 4225/4224, 4375/4374, 6656/6655, 78125/78078 | Comma list: 4225/4224, 4375/4374, 6656/6655, 78125/78078 | ||
{{Mapping|legend=0| 1 -16 -9 -75 9 9 | 0 73 47 323 -23 -22 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,482: | Line 1,482: | ||
Comma list: 3025/3024, 4375/4374, 134775333/134217728 | Comma list: 3025/3024, 4375/4374, 134775333/134217728 | ||
{{Mapping|legend=0| 46 0 -39 202 232 | 0 1 2 -1 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,497: | Line 1,497: | ||
Comma list: 3025/3024, 4225/4224, 4375/4374, 26411/26364 | Comma list: 3025/3024, 4225/4224, 4375/4374, 26411/26364 | ||
{{Mapping|legend=0| 46 0 -39 202 232 316 | 0 1 2 -1 -1 -2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,512: | Line 1,512: | ||
Comma list: 833/832, 1089/1088, 1225/1224, 1701/1700, 4225/4224 | Comma list: 833/832, 1089/1088, 1225/1224, 1701/1700, 4225/4224 | ||
{{Mapping|legend=0| 46 0 -39 202 232 316 188 | 0 1 2 -1 -1 -2 0 }} | |||
Optimal tunings: | Optimal tunings: | ||