Scala analysis: xen12-chalmers-tritriadic-mt-23-19-7
Tritriadic M->T scale built from 23:19:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 532/529 9.790228 2: 23/19 330.761331 3: 28/23 340.551559 4: 722/529 538.477338 5: 28/19 671.312890 6: 38/23 869.238669 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/19 330.7613 1: 532/529 9.7902 2: 12167/10108 320.9711 3: 532/529 9.7902 4: 361/322 197.9258 5: 7406/6859 132.8356 6: 361/322 197.9258 7: 23/19 330.7613
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 532/529 9.790 cents 1: 1 7406/6859 132.836 cents 1: 2 361/322 197.926 cents 1: 1 12167/10108 320.971 cents 1: 1 23/19 330.761 cents 2: 1 13718/12167 207.716 cents 2: 4 23/19 330.761 cents 2: 1 28/23 340.552 cents 2: 1 19/14 528.687 cents 3: 2 28/23 340.552 cents 3: 2 19/14 528.687 cents 3: 1 722/529 538.477 cents 3: 2 529/361 661.523 cents 4: 2 722/529 538.477 cents 4: 1 529/361 661.523 cents 4: 2 28/19 671.313 cents 4: 2 23/14 859.448 cents 5: 1 28/19 671.313 cents 5: 1 23/14 859.448 cents 5: 4 38/23 869.239 cents 5: 1 12167/6859 992.284 cents 6: 1 38/23 869.239 cents 6: 1 20216/12167 879.029 cents 6: 2 644/361 1002.074 cents 6: 1 6859/3703 1067.164 cents 6: 2 529/266 1190.210 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 9.8 330.8 340.6 538.5 671.3 869.2 1200.0 9.8 : 321.0 330.8 528.7 661.5 859.4 1190.2 1200.0 330.8 : 9.8 207.7 340.6 538.5 869.2 879.0 1200.0 340.6 : 197.9 330.8 528.7 859.4 869.2 1190.2 1200.0 538.5 : 132.8 330.8 661.5 671.3 992.3 1002.1 1200.0 671.3 : 197.9 528.7 538.5 859.4 869.2 1067.2 1200.0 869.2 : 330.8 340.6 661.5 671.3 869.2 1002.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 9.7902 .. 330.7613 cents 12167/10108, 320.9711 cents 532/529, 9.7902 cents 2: 207.7160 .. 528.6871 cents 12167/10108, 320.9711 cents 260642/279841,-123.0453 cents 3: 340.5516 .. 661.5227 cents 12167/10108, 320.9711 cents 392/437,-188.1356 cents 4: 538.4773 .. 859.4484 cents 12167/10108, 320.9711 cents 260642/279841,-123.0453 cents 5: 671.3129 .. 992.2840 cents 12167/10108, 320.9711 cents 392/437,-188.1356 cents 6: 869.2387 .. 1190.2098 cents 12167/10108, 320.9711 cents 260642/279841,-123.0453 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 532/529, 9.7902 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 23/19, 330.7613 cents Average / Smallest step : 17.510171 Largest / Average step : 1.929441 Largest / Smallest step : 33.784844 Median interval of one step : 361/322, 197.9258 cents, amount: 2 Least squares average step : 148.70624 cents, oct.: 1040.94367 cents Scale is not proper Step pattern alph. order: ABACDCE Step pattern size order : ADACBCE Scale is not a Constant Structure Scale diversity : 1.157896 Lumma stability : 0.016317 Lumma impropriety factor : 0.621173 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 : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 532/529, 9.7902 cents Most common intervals : 23/19, 330.7613 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 340.552 869.239 cents Most common triad is 0.0 330.761 869.239 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 19 23 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.004152 Average absolute harmonicity : 0.154315 Specific harmonicity : 0.022744 Fundamental : 1/10051, -13.2951 octaves, 0.0260 Hz. Guide tone : 232484, 17.8268 octaves, 60823757.923 Hz. Exponens Consonantiae : 2.336697E+09, 31.12182 octaves Euler's gradus suavitatis : 129 Sum of Mann's harmonic distance : 1258.0, average 179.71429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.81085, average 1.54441 Sum of Tenney's harmonic distance : 22.44918, average 3.20703 Vogel's harmonic complexity : 58.28571 Wille's k value : 6083 Wilson's harmonic complexity : 133 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 65.93708, average 2.35490 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.28571 9 1 7: 0 .. 1 0.42857 3 19: -1 .. 2 0.28571 6 1 23: -2 .. 1 -0.71429 7 5 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 18 27 30| Scale is weakly epimorphic with val: <7 18 28 29| Scale is weakly epimorphic with val: <7 18 29 35| Scale is weakly epimorphic with val: <7 18 30 34| Scale is weakly epimorphic with val: <7 18 31 33| Scale is weakly epimorphic with val: <7 19 27 32| Scale is weakly epimorphic with val: <7 19 28 31| Scale is weakly epimorphic with val: <7 19 29 30| Scale is weakly epimorphic with val: <7 19 31 35| Scale is weakly epimorphic with val: <7 19 32 34| Scale is weakly epimorphic with val: <7 20 28 33| Scale is weakly epimorphic with val: <7 20 29 32| Scale is weakly epimorphic with val: <7 20 30 31| Scale is weakly epimorphic with val: <7 20 33 35| Scale is weakly epimorphic with val: <7 21 27 29| Scale is weakly epimorphic with val: <7 21 29 34| Scale is weakly epimorphic with val: <7 21 30 33| Scale is weakly epimorphic with val: <7 21 31 32| Scale is weakly epimorphic with val: <7 22 27 31| Scale is weakly epimorphic with val: <7 22 28 30| Scale is weakly epimorphic with val: <7 22 30 35| Scale is weakly epimorphic with val: <7 22 31 34| Scale is weakly epimorphic with val: <7 22 32 33|
FIT/MODE
7: 0 2 0 1 1 1 2 N T3 SD: 13.0188 c. M: 24.1916 c. 11: 0 3 0 2 1 2 3 N SD: 9.4593 c. M: 16.7674 c. 18: 0 5 0 3 2 3 5 N SD: 5.4672 c. M: 9.7902 c. 62: 1 16 1 10 7 10 17 N SD: 5.4525 c. M:-9.5646 c. 66: 1 17 1 11 7 11 18 N SD: 4.9205 c. M:-8.3916 c. 69: 1 18 1 11 8 11 19 N SD: 4.7751 c. M:-7.6011 c. 70: 1 18 1 11 8 12 19 N SD: 4.8920 c. M:-7.3526 c. 73: 1 19 1 12 8 12 20 N SD: 3.7185 c. M:-6.6481 c. 75: 1 20 0 13 8 12 21 N SD: 4.5534 c. M:-6.2098 c. 76: 1 20 1 12 9 12 21 N SD: 4.5475 c. M:-7.6345 c. 77: 1 20 1 13 8 13 21 N SD: 4.0233 c. M:-6.9772 c. 80: 1 21 1 13 9 13 22 N SD: 3.0238 c. M:-5.2098 c. 84: 1 22 1 14 9 14 23 N SD: 2.7855 c. M:-4.4955 c. 91: 1 24 1 15 10 15 25 N SD: 1.9075 c. M:-3.3966 c. 98: 1 26 1 16 11 16 27 N SD: 1.5178 c. M:-2.4547 c. 102: 1 27 1 17 11 17 28 N SD: 1.4996 c. M:-2.6991 c. 109: 1 29 1 18 12 18 30 N SD: 0.7073 c. M:-1.2189 c. 116: 1 31 1 19 13 19 32 N SD: 0.6156 c. M:-1.1009 c. 127: 1 34 1 21 14 21 35 N SD: 0.2641 c. M: 0.4467 c. 243: 2 65 2 40 27 40 67 N SD: 0.1656 c. M:-0.2920 c. 370: 3 99 3 61 41 61 102 N SD: 0.0534 c. M: 0.0990 c. 849: 7 227 7 140 94 140 234 N SD: 0.0590 c. M:-0.1038 c. 867: 7 232 7 143 96 143 239 N SD: 0.0574 c. M: 0.1016 c. 976: 8 261 8 161 108 161 269 N SD: 0.0291 c. M:-0.0473 c. 1346: 11 360 11 222 149 222 371 N SD: 0.0094 c. M:-0.0166 c. 1716: 14 459 14 283 190 283 473 N SD: 0.0099 c. M: 0.0158 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 15.3211 cents 3 x x x 4 x 5:6 S SD: 14.3890 cents 4 x x 5 x 6:7:8 S SD: 28.4503 cents 5 x 6 x 7 x 8:10 S SD: 18.1207 cents 6 x 7 x 8:9:10:12 S SD: 16.5944 cents 7 x 8:9 x 10:12:14 S SD: 32.1454 cents 8 x x 10:11:12:13:16 SD: 12.6843 cents 9 x x 11:12:13:15:18 SD: 11.1609 cents 10:11:12 x 14:15:17:20 SD: 28.6931 cents 11:12:13 x 15:16:18:22 SD: 24.9198 cents 12:13 x 15:16:18:20:24 SD: 24.4276 cents 13:14 x 16:18:19:21:26 SD: 21.5687 cents 14:15 x 17:19:21:23:28 SD: 19.1296 cents 15:16:18 x 20:22:25:30 SD: 18.6728 cents 16:17:19 x 22:24:26:32 SD: 18.3258 cents 17:18 x 21:23:25:28:34 SD: 15.6887 cents 18:19 x 22:25:27:30:36 SD: 15.9458 cents 19:20:23 x 26:28:31:38 SD: 13.6777 cents 20:21:24 x 27:29:33:40 SD: 13.8999 cents 21:22:25:26:29:31:35:42 SD: 12.2422 cents 22:23 x 27:30:32:36:44 SD: 12.3589 cents 23:24 x 28:31:34:38:46 SD: 11.2822 cents 24:25:29 x 33:35:40:48 SD: 11.1038 cents 25:26:30 x 34:37:41:50 SD: 10.3574 cents 26:27:31:32:35:38:43:52 SD: 10.0108 cents 27:28 x 33:37:40:45:54 SD: 9.4799 cents 28:29 x 34:38:41:46:56 SD: 9.0231 cents 29:30:35 x 40:43:48:58 SD: 8.9358 cents 30:31:36:37:41:44:50:60 SD: 8.1379 cents 31:32 x 38:42:46:51:62 SD: 8.4022 cents 32:33 x 39:44:47:53:64 SD: 7.6581 cents 33:34:40 x 45:49:55:66 SD: 7.7492 cents 34:35:41 x 46:50:56:68 SD: 7.3557 cents 35:36:42:43:48:52:58:70 SD: 6.8411 cents 36:37 x 44:49:53:59:72 SD: 6.8411 cents 37:38 x 45:51:55:61:74 SD: 7.1805 cents 38:39:46 x 52:56:63:76 SD: 5.9953 cents 39:40:47 x 53:57:64:78 SD: 6.7018 cents 40:41:48:49:55:59:66:80 SD: 5.7209 cents 41:42 x 50:56:60:68:82 SD: 5.8238 cents 42:43 x 51:57:62:69:84 SD: 5.7194 cents 43:44:52 x 59:63:71:86 SD: 5.5048 cents 44:45:53:54:60:65:73:88 SD: 4.9270 cents 46:47 x 56:63:68:76:92 SD: 4.7659 cents 47:48:57 x 64:69:78:94 SD: 4.8307 cents 48:49:58 x 66:71:79:96 SD: 5.0868 cents 49:50:59:60:67:72:81:98 SD: 4.1834 cents 50:51 x 61:68:74:83:100 SD: 4.6344 cents 51:52 x 62:70:75:84:102 SD: 4.4434 cents 52:53:63 x 71:77:86:104 SD: 4.1238 cents 54:55:65:66:74:80:89:108 SD: 3.9797 cents 55:56 x 67:75:81:91:110 SD: 3.6100 cents 56:57 x 68:76:83:93:112 SD: 4.4971 cents 57:58:69 x 78:84:94:114 SD: 3.5106 cents 60:61 x 73:82:88:99:120 SD: 3.4734 cents 61:62:74 x 83:90:101:122 SD: 3.3210 cents 62:63:75 x 85:91:102:124 SD: 3.6726 cents 63:64:76:77:86:93:104:126 SD: 2.8536 cents 65:66 x 79:89:96:107:130 SD: 3.2076 cents 66:67:80 x 90:97:109:132 SD: 2.8571 cents 68:69:82:83:93:100:112:136 SD: 2.7082 cents 69:70 x 84:94:102:114:138 SD: 2.7268 cents 70:71 x 85:96:103:116:140 SD: 3.0786 cents 71:72:86 x 97:105:117:142 SD: 2.7354 cents 72:73:87:88:98:106:119:144 SD: 2.3954 cents 74:75 x 90:101:109:122:148 SD: 2.3453 cents 75:76:91 x 102:111:124:150 SD: 2.8030 cents 76:77:92:93:104:112:126:152 SD: 2.4783 cents 77:78:93:94:105:113:127:154 SD: 2.3012 cents 79:80 x 96:108:116:131:158 SD: 2.5877 cents 80:81:97 x 109:118:132:160 SD: 2.1189 cents 82:83:99:100:112:121:135:164 SD: 2.0191 cents 84:85 x 102:115:124:139:168 SD: 2.2261 cents 85:86:103 x 116:125:140:170 SD: 2.0724 cents 86:87:104:105:117:127:142:172 SD: 1.9047 cents 87:88:105:106:119:128:144:174 SD: 1.8134 cents 88:89 x 107:120:130:145:176 SD: 1.9844 cents 89:90:108 x 121:131:147:178 SD: 2.1009 cents 90:91:109:110:123:133:149:180 SD: 1.8947 cents 91:92:110:111:124:134:150:182 SD: 1.6086 cents 93:94 x 113:127:137:154:186 SD: 1.6988 cents 94:95:114 x 128:139:155:188 SD: 2.0092 cents 95:96:115:116:130:140:157:190 SD: 1.5477 cents 98:99 x 119:134:144:162:196 SD: 1.8004 cents 99:100:120:121:135:146:164:198 SD: 1.6606 cents 100:101:121:122:136:147:165:200 SD: 1.6375 cents 101:102:122:123:138:149:167:202 SD: 1.2445 cents 103:104:125 x 141:152:170:206 SD: 1.6920 cents 104:105:126:127:142:153:172:208 SD: 1.3474 cents 106:107:128:129:145:156:175:212 SD: 1.2994 cents 107:108 x 130:146:158:177:214 SD: 1.3808 cents 108:109:131 x 147:159:178:216 SD: 1.6103 cents 109:110:132:133:149:161:180:218 SD: 1.2470 cents 110:111:133:134:150:162:182:220 SD: 1.0080 cents 112:113 x 136:153:165:185:224 SD: 1.2226 cents 114:115:138:139:156:168:188:228 SD: 1.1656 cents 115:116:139:140:157:169:190:230 SD: 1.0842 cents 117:118:142 x 160:172:193:234 SD: 1.5053 cents 118:119:143:144:161:174:195:236 SD: 0.9685 cents 120:121:145:146:164:177:198:240 SD: 0.9563 cents 123:124:149:150:168:181:203:246 SD: 0.9020 cents 124:125:150:151:169:183:205:248 SD: 0.8096 cents 126:127 x 153:172:186:208:252 SD: 1.1251 cents 127:128:154:155:173:187:210:254 SD: 1.0847 cents 128:129:155:156:175:189:211:256 SD: 1.0426 cents 129:130:156:157:176:190:213:258 SD: 0.6152 cents 131:132:159 x 179:193:216:262 SD: 1.1641 cents 132:133:160:161:180:195:218:264 SD: 0.9814 cents 133:134:161:162:182:196:220:266 SD: 0.8544 cents 137:138:166:167:187:202:226:274 SD: 0.6936 cents 143:144:173:174:195:211:236:286 SD: 0.6008 cents 156:157:189:190:213:230:258:312 SD: 0.4168 cents 175:176:212:213:239:258:289:350 SD: 0.2905 cents 304:306:368:370:415:448:502:608 SD: 0.2692 cents 323:325:391:393:441:476:534:646 SD: 0.2623 cents 342:344:414:416:467:504:565:684 SD: 0.2433 cents 351:353:425:427:479:517:580:702 SD: 0.2302 cents 376:378:455:458:513:554:621:752 SD: 0.2278 cents 414:416:501:504:565:610:684:828 SD: 0.2258 cents 483:486:585:588:659:712:798:966 SD: 0.2179 cents 488:491:591:594:666:719:806:976 SD: 0.1917 cents 507:510:614:617:692:747:838:1014 SD: 0.1894 cents 515:518:623:627:703:759:851:1030 SD: 0.1812 cents 523:526:633:637:714:771:864:1046 SD: 0.1672 cents 532:535:644:648:726:784:879:1064 SD: 0.1374 cents 551:554:667:671:752:812:910:1102 SD: 0.1361 cents 570:573:690:694:778:840:942:1140 SD: 0.1261 cents