Scala analysis: xen12-chalmers-tritriadic-mt-13-17-19
Tritriadic M->T scale built from 13:17:19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/17 192.557607 quasi-meantone 2: 17/13 464.427748 3: 19/13 656.985354 4: 26/17 735.572252 5: 289/169 928.855495 6: 323/169 1121.413102 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 338/323 78.5869 1: 19/17 192.5576 quasi-meantone 2: 289/247 271.8701 3: 19/17 192.5576 quasi-meantone 4: 338/323 78.5869 5: 4913/4394 193.2832 6: 19/17 192.5576 quasi-meantone 7: 338/323 78.5869
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 338/323 78.587 cents 1: 3 19/17 192.558 cents quasi-meantone 1: 1 4913/4394 193.283 cents 1: 1 289/247 271.870 cents 2: 3 338/289 271.145 cents 2: 1 289/247 271.870 cents 2: 1 5491/4394 385.841 cents 2: 2 17/13 464.428 cents 3: 1 6422/4913 463.702 cents 3: 3 17/13 464.428 cents 3: 2 26/19 543.015 cents 3: 1 19/13 656.985 cents 4: 1 26/19 543.015 cents 4: 2 19/13 656.985 cents 4: 3 26/17 735.572 cents 4: 1 4913/3211 736.298 cents 5: 2 26/17 735.572 cents 5: 1 8788/5491 814.159 cents 5: 1 494/289 928.130 cents 5: 3 289/169 928.855 cents 6: 1 494/289 928.130 cents 6: 1 8788/4913 1006.717 cents 6: 3 34/19 1007.442 cents quasi-mean seventh 6: 2 323/169 1121.413 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 192.6 464.4 657.0 735.6 928.9 1121.4 1200.0 192.6 : 271.9 464.4 543.0 736.3 928.9 1007.4 1200.0 464.4 : 192.6 271.1 464.4 657.0 735.6 928.1 1200.0 657.0 : 78.6 271.9 464.4 543.0 735.6 1007.4 1200.0 735.6 : 193.3 385.8 464.4 657.0 928.9 1121.4 1200.0 928.9 : 192.6 271.1 463.7 735.6 928.1 1006.7 1200.0 1121.4: 78.6 271.1 543.0 735.6 814.2 1007.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.5869 .. 271.8701 cents 4913/4394, 193.2832 cents 338/323, 78.5869 cents 2: 271.1445 .. 464.4277 cents 4913/4394, 193.2832 cents 83486/83521,-0.7256 cents 3: 463.7021 .. 656.9854 cents 4913/4394, 193.2832 cents 83486/83521,-0.7256 cents 4: 543.0146 .. 736.2979 cents 4913/4394, 193.2832 cents 338/361,-113.9707 cents 5: 735.5723 .. 928.8555 cents 4913/4394, 193.2832 cents 83486/83521,-0.7256 cents 6: 928.1299 .. 1121.4131 cents 4913/4394, 193.2832 cents 83486/83521,-0.7256 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 338/323, 78.5869 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 289/247, 271.8701 cents Average / Smallest step : 2.181389 Largest / Average step : 1.585909 Largest / Smallest step : 3.459484 Median interval of one step : 19/17, 192.5576 cents, amount: 3 Most common interval of one step : 19/17, 192.5576 cents, amount: 3 Least squares average step : 184.33867 cents, oct.: 1290.37071 cents Scale is not proper Step pattern alph. order: ABACDAC Step pattern size order : BDBACBA Scale is not a Constant Structure Scale diversity : 1.303787 Lumma stability : 0.130978 Lumma impropriety factor : 0.097394 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 83521/83486, 0.7256 cents Most common intervals : 17/13, 464.4277 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 192.558 735.572 cents Most common triad is 0.0 464.428 735.572 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 13 17 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 193.2832 cents: 3 -- Rational properties -- Prime limit : 19 Odd number limit : 5491 (O: 5491 U: 5491) Highest odd numerator or denominator: 323 Scale harmonicity : 0.005211 Average absolute harmonicity : 0.155718 Specific harmonicity : 0.027551 Fundamental : 1/2873, -11.4883 octaves, 0.0911 Hz. Guide tone : 142766, 17.1233 octaves, 37351235.456 Hz. Exponens Consonantiae : 4.101667E+08, 28.61164 octaves Euler's gradus suavitatis : 104 Sum of Mann's harmonic distance : 547.0, average 78.14286 Mersenne's string divisions : 581366880 Sum of van Prooijen's expressibility: 9.98851, average 1.42693 Sum of Tenney's harmonic distance : 19.61862, average 2.80266 Vogel's harmonic complexity : 47.00000 Wille's k value : 2745 Wilson's harmonic complexity : 109 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 60.07276, average 2.14546 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.28571 2 1 13: -2 .. 1 -0.71429 7 17: -1 .. 2 0.28571 6 3 19: 0 .. 1 0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 24 26 32| Scale is weakly epimorphic with val: <7 24 27 29| Scale is weakly epimorphic with val: <7 24 28 33| Scale is weakly epimorphic with val: <7 24 29 30| Scale is weakly epimorphic with val: <7 25 26 29| Scale is weakly epimorphic with val: <7 25 27 33| Scale is weakly epimorphic with val: <7 25 28 30| Scale is weakly epimorphic with val: <7 25 30 31| Scale is weakly epimorphic with val: <7 26 27 30| Scale is weakly epimorphic with val: <7 26 29 31| Scale is weakly epimorphic with val: <7 26 31 32| Scale is weakly epimorphic with val: <7 27 28 31| Scale is weakly epimorphic with val: <7 27 30 32| Scale is weakly epimorphic with val: <7 27 32 33| Scale is weakly epimorphic with val: <7 28 29 32| Scale is weakly epimorphic with val: <7 28 31 33| Scale is weakly epimorphic with val: <7 29 30 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 86.0541 c. M: 142.6996 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 40.3684 c. M: 71.4131 c. 9: 1 2 2 0 2 1 1 N T3 SD: 47.0826 c. M: 68.9056 c. 10: 2 2 1 1 2 1 1 P D3 S SD: 35.1895 c. M: 56.9854 c. 11: 2 2 2 1 2 1 1 N D3 SD: 29.2117 c. M:-52.9627 c. 13: 2 3 2 1 2 2 1 N G T3 S SD: 7.7344 c. M: 13.7208 c. 18: 3 4 3 1 3 3 1 N G T3 S SD: 6.7748 c. M:-11.9202 c. 31: 5 7 5 2 5 5 2 N G T3 S SD: 0.7128 c. M:-1.1675 c. 106: 17 24 17 7 17 17 7 N G T3 S SD: 0.3873 c. M: 0.6584 c. 137: 22 31 22 9 22 22 9 N G T3 S SD: 0.2103 c. M: 0.3883 c. 168: 27 38 27 11 27 27 11 N G T3 S SD: 0.1835 c. M:-0.2995 c. 305: 49 69 49 20 49 49 20 N G T3 S SD: 0.1817 c. M: 0.3309 c. 473: 76 107 76 31 76 76 31 N G T3 S SD: 0.1796 c. M: 0.3143 c. 855: 137 194 137 56 138 137 56 N SD: 0.1709 c. M: 0.2769 c. 886: 142 201 142 58 143 142 58 N SD: 0.1558 c. M:-0.2641 c. 917: 147 208 147 60 148 147 60 N SD: 0.1451 c. M:-0.2612 c. 948: 152 215 152 62 153 152 62 N SD: 0.1390 c. M:-0.2584 c. 961: 154 218 154 63 155 154 63 N SD: 0.1458 c. M: 0.2579 c. 979: 157 222 157 64 158 157 64 N SD: 0.1370 c. M:-0.2558 c. 992: 159 225 159 65 160 159 65 N SD: 0.1274 c. M: 0.2189 c. 1023: 164 232 164 67 165 164 67 N SD: 0.1127 c. M: 0.1822 c. 1054: 169 239 169 69 170 169 69 N SD: 0.1022 c. M:-0.1768 c. 1085: 174 246 174 71 175 174 71 N SD: 0.0961 c. M:-0.1768 c. 1116: 179 253 179 73 180 179 73 N SD: 0.0945 c. M:-0.1768 c. 1129: 181 256 181 74 182 181 74 N SD: 0.0980 c. M: 0.1750 c. 1147: 184 260 184 75 185 184 75 N SD: 0.0969 c. M:-0.1768 c. 1160: 186 263 186 76 187 186 76 N SD: 0.0827 c. M: 0.1438 c. 1191: 191 270 191 78 192 191 78 N SD: 0.0709 c. M: 0.1143 c. 1222: 196 277 196 80 197 196 80 N SD: 0.0636 c. M:-0.1134 c. 1253: 201 284 201 82 202 201 82 N SD: 0.0615 c. M:-0.1150 c. 1284: 206 291 206 84 207 206 84 N SD: 0.0642 c. M:-0.1165 c. 1297: 208 294 208 85 209 208 85 N SD: 0.0634 c. M: 0.1135 c. 1328: 213 301 213 87 214 213 87 N SD: 0.0496 c. M: 0.0877 c. 1359: 218 308 218 89 219 218 89 N SD: 0.0395 c. M: 0.0631 c. 1390: 223 315 223 91 224 223 91 N SD: 0.0352 c. M:-0.0654 c. 1421: 228 322 228 93 229 228 93 N SD: 0.0379 c. M:-0.0678 c. 1465: 235 332 235 96 236 235 96 N SD: 0.0386 c. M: 0.0661 c. 1496: 240 339 240 98 241 240 98 N SD: 0.0248 c. M: 0.0442 c. 1527: 245 346 245 100 246 245 100 N SD: 0.0150 c. M:-0.0247 c. 1558: 250 353 250 102 251 250 102 N SD: 0.0164 c. M:-0.0277 c. 1664: 267 377 267 109 268 267 109 N SD: 0.0106 c. M: 0.0189 c. 1695: 272 384 272 111 273 272 111 N SD: 0.0049 c. M:-0.0088 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 16.8086 cents 3 x 4 x x 5 x 6 S SD: 18.5894 cents 4 x 5 x 6:7 x 8 S SD: 23.4914 cents 5:6 x 7:8:9 x 10 S SD: 37.2411 cents 6:7:8 x 9:10:11:12 S SD: 20.3810 cents 7:8:9:10:11:12:13:14 H SD: 13.2506 cents 8:9:10 x 12:14:15:16 S SD: 16.7141 cents 9:10:12:13:14:15:17:18 SD: 10.0040 cents 10:11:13 x 15:17:19:20 SD: 7.8214 cents 12:13:16 x 18:21:23:24 SD: 13.7400 cents 13:15:17:19:20:22:25:26 SD: 8.5596 cents 15:17:20:22:23:26:29:30 SD: 7.4400 cents 17:19:22:25:26:29:32:34 SD: 4.8525 cents 23:26:30:34:35:39:44:46 SD: 4.7132 cents 24:27:31:35:37:41:46:48 SD: 4.0835 cents 26:29:34:38:40:44:50:52 SD: 3.3721 cents 32:36:42:47:49:55:61:64 SD: 2.6485 cents 41:46:54:60:63:70:78:82 SD: 2.6325 cents 42:47:55:61:64:72:80:84 SD: 2.1294 cents 45:50:59:66:69:77:86:90 SD: 1.9225 cents 52:58:68:76:80:89:99:104 SD: 1.8291 cents 58:65:76:85:89:99:111:116 SD: 1.4642 cents 59:66:77:86:90:101:113:118 SD: 1.2188 cents 68:76:89:99:104:116:130:136 SD: 1.1557 cents 78:87:102:114:119:133:149:156 SD: 1.0725 cents 87:97:114:127:133:149:166:174 SD: 1.0113 cents 91:102:119:133:139:156:174:182 SD: 0.9966 cents 93:104:122:136:142:159:178:186 SD: 0.9720 cents 100:112:131:146:153:171:191:200 SD: 0.7507 cents 104:116:136:152:159:178:199:208 SD: 0.6226 cents 134:150:175:196:205:229:256:268 SD: 0.5795 cents 162:181:212:237:248:277:310:324 SD: 0.4939 cents 169:189:221:247:258:289:323:338 SD: 0.4763 cents 179:200:234:262:274:306:342:358 SD: 0.4497 cents 189:211:247:276:289:323:361:378 SD: 0.4386 cents 204:228:267:298:312:349:390:408 SD: 0.2785 cents 221:247:289:323:338:378:422:442 SD: 0.2309 cents 238:266:311:348:364:407:455:476 SD: 0.2240 cents 306:342:400:447:468:523:585:612 SD: 0.2172 cents 325:363:425:475:497:556:621:650 SD: 0.2021 cents 338:378:442:494:517:578:646:676 SD: 0.1565 cents 442:494:578:646:676:756:845:884 SD: 0.0842 cents