Scala analysis: xen12-chalmers-tritriadic-mt-17-23-25
Tritriadic M->T scale built from 17:23:25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/23 144.353080 2: 23/17 523.318938 3: 25/17 667.672018 4: 34/23 676.681062 5: 529/289 1046.637876 6: 575/289 1190.990956 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 578/575 9.0090 1: 25/23 144.3531 2: 529/425 378.9659 3: 25/23 144.3531 4: 578/575 9.0090 5: 12167/9826 369.9568 6: 25/23 144.3531 7: 578/575 9.0090
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 578/575 9.009 cents 1: 3 25/23 144.353 cents 1: 1 12167/9826 369.957 cents 1: 1 529/425 378.966 cents 2: 3 578/529 153.362 cents 2: 1 529/425 378.966 cents 2: 1 13225/9826 514.310 cents 2: 2 23/17 523.319 cents 3: 1 14450/12167 297.715 cents 3: 3 23/17 523.319 cents 3: 2 34/25 532.328 cents 3: 1 25/17 667.672 cents 4: 1 34/25 532.328 cents 4: 2 25/17 667.672 cents 4: 3 34/23 676.681 cents 4: 1 12167/7225 902.285 cents 5: 2 34/23 676.681 cents 5: 1 19652/13225 685.690 cents 5: 1 850/529 821.034 cents 5: 3 529/289 1046.638 cents 6: 1 850/529 821.034 cents 6: 1 19652/12167 830.043 cents 6: 3 46/25 1055.647 cents 6: 2 575/289 1190.991 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 : 144.4 523.3 667.7 676.7 1046.6 1191.0 1200.0 144.4 : 379.0 523.3 532.3 902.3 1046.6 1055.6 1200.0 523.3 : 144.4 153.4 523.3 667.7 676.7 821.0 1200.0 667.7 : 9.0 379.0 523.3 532.3 676.7 1055.6 1200.0 676.7 : 370.0 514.3 523.3 667.7 1046.6 1191.0 1200.0 1046.6: 144.4 153.4 297.7 676.7 821.0 830.0 1200.0 1191.0: 9.0 153.4 532.3 676.7 685.7 1055.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 9.0090 .. 378.9659 cents 12167/9826, 369.9568 cents 578/575, 9.0090 cents 2: 153.3621 .. 523.3189 cents 12167/9826, 369.9568 cents 245650/279841,-225.6037 cents 3: 297.7152 .. 667.6720 cents 12167/9826, 369.9568 cents 245650/279841,-225.6037 cents 4: 532.3280 .. 902.2848 cents 12167/9826, 369.9568 cents 578/625,-135.3440 cents 5: 676.6811 .. 1046.6379 cents 12167/9826, 369.9568 cents 245650/279841,-225.6037 cents 6: 821.0341 .. 1190.9910 cents 12167/9826, 369.9568 cents 245650/279841,-225.6037 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 578/575, 9.0090 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 529/425, 378.9659 cents Average / Smallest step : 19.028498 Largest / Average step : 2.210634 Largest / Smallest step : 42.065047 Median interval of one step : 25/23, 144.3531 cents, amount: 3 Most common interval of one step : 25/23, 144.3531 cents, amount: 3 Least squares average step : 190.57047 cents, oct.: 1333.99332 cents Scale is not proper Step pattern alph. order: ABACDAC Step pattern size order : BDBACBA Scale is not a Constant Structure Scale diversity : 1.181460 Lumma stability : 0.015015 Lumma impropriety factor : 0.729381 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 : 578/575, 9.0090 cents Most common intervals : 23/17, 523.3189 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 144.353 676.681 cents Most common triad is 0.0 523.319 676.681 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 17 23 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 13225 (O: 13225 U: 13225) Highest odd numerator or denominator: 575 Scale harmonicity : 0.004340 Average absolute harmonicity : 0.154948 Specific harmonicity : 0.023800 Fundamental : 1/6647, -12.6985 octaves, 0.0394 Hz. Guide tone : 449650, 18.7784 octaves, 117639935.438 Hz. Exponens Consonantiae : 2.988824E+09, 31.47693 octaves Euler's gradus suavitatis : 124 Sum of Mann's harmonic distance : 936.0, average 133.71429 Mersenne's string divisions : 234995040 Sum of van Prooijen's expressibility: 11.00246, average 1.57178 Sum of Tenney's harmonic distance : 21.57939, average 3.08277 Vogel's harmonic complexity : 56.00000 Wille's k value : 6612 Wilson's harmonic complexity : 130 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 69.77003, average 2.49179 Lattice compactness (without 2's) : 66.59060, average 2.37824 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.28571 2 1 5: 0 .. 2 0.85714 6 17: -2 .. 1 -0.71429 7 1 23: -1 .. 2 0.28571 6 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 15 26 34| Scale is weakly epimorphic with val: <7 15 27 33| Scale is weakly epimorphic with val: <7 15 28 32| Scale is weakly epimorphic with val: <7 15 29 31| Scale is weakly epimorphic with val: <7 15 32 35| Scale is weakly epimorphic with val: <7 16 26 31| Scale is weakly epimorphic with val: <7 16 27 30| Scale is weakly epimorphic with val: <7 16 28 29| Scale is weakly epimorphic with val: <7 16 29 35| Scale is weakly epimorphic with val: <7 16 30 34| Scale is weakly epimorphic with val: <7 16 31 33| Scale is weakly epimorphic with val: <7 17 26 35| Scale is weakly epimorphic with val: <7 17 28 33| Scale is weakly epimorphic with val: <7 17 29 32| Scale is weakly epimorphic with val: <7 17 30 31| Scale is weakly epimorphic with val: <7 18 26 32| Scale is weakly epimorphic with val: <7 18 27 31| Scale is weakly epimorphic with val: <7 18 28 30| Scale is weakly epimorphic with val: <7 18 30 35| Scale is weakly epimorphic with val: <7 18 31 34| Scale is weakly epimorphic with val: <7 18 32 33|
FIT/MODE
7: 1 2 1 0 2 1 0 N T3 SD: 15.2567 c. M:-27.0755 c. 9: 1 3 1 0 3 1 0 N T3 SD: 10.7261 c. M:-20.0288 c. 16: 2 5 2 0 5 2 0 N T3 SD: 5.1229 c. M:-9.0090 c. 57: 7 18 7 0 18 7 0 N T3 SD: 5.0750 c. M:-9.0090 c. 67: 8 21 8 1 20 8 1 N SD: 5.3082 c. M: 8.9014 c. 69: 8 22 8 1 21 8 1 N SD: 4.7627 c. M: 8.3823 c. 74: 9 23 9 1 23 8 1 N SD: 4.7220 c. M:-7.4162 c. 75: 9 24 9 0 23 9 1 N SD: 4.7150 c. M: 6.9910 c. 76: 9 24 9 1 23 9 1 N SD: 3.8214 c. M: 6.7804 c. 78: 9 25 9 1 24 9 1 N SD: 4.0237 c. M: 6.3756 c. 83: 10 26 10 1 25 10 1 N SD: 3.4816 c. M: 5.6740 c. 85: 10 27 10 1 26 10 1 N SD: 2.9019 c. M: 5.1086 c. 92: 11 29 11 1 28 11 1 N SD: 2.3312 c. M: 4.0344 c. 94: 11 30 11 1 29 11 1 N SD: 2.5170 c. M: 3.9275 c. 99: 12 31 12 1 30 12 1 N SD: 2.3465 c. M: 4.2136 c. 101: 12 32 12 1 31 12 1 N SD: 1.6307 c. M: 2.8721 c. 108: 13 34 13 1 33 13 1 N SD: 1.3445 c. M: 2.1934 c. 117: 14 37 14 1 36 14 1 N SD: 0.7072 c. M: 1.2474 c. 133: 16 42 16 1 41 16 1 N SD: 0.0116 c. M: 0.0213 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: 12.6370 cents 3 x 4 x x x x 6 S SD: 12.6370 cents 4 x 5 x 6:7 x 8 S SD: 39.8935 cents 5:6:7 x x 9 x 10 SD: 45.8850 cents 6:7:8 x 9:11 x 12 SD: 25.5308 cents 7:8:9:10 x 13 x 14 SD: 27.1808 cents 8:9:11 x 12:15 x 16 SD: 16.3742 cents 9:10:12:13 x 16 x 18 SD: 14.9748 cents 10:11:14 x 15:18 x 20 SD: 14.7139 cents 11:12:15:16 x 20 x 22 S SD: 5.3720 cents 12:13:16 x 18:22 x 24 SD: 7.2619 cents 13:14:18:19 x 24 x 26 SD: 9.3718 cents 14:15:19 x 21:26 x 28 SD: 8.7551 cents 15:16:20:22 x 27 x 30 SD: 10.1346 cents 16:17:22 x 24:29 x 32 SD: 11.4297 cents 17:18:23:25 x 31 x 34 SD: 9.1739 cents 18:20:24:26:27:33 x 36 SD: 10.1341 cents 19:21:26:28 x 35 x 38 SD: 7.3702 cents 20:22:27:29:30:37 x 40 SD: 7.4787 cents 21:23:28 x 31:38 x 42 SD: 6.9673 cents 22:24:30:32:33:40 x 44 SD: 6.1469 cents 23:25:31 x 34:42 x 46 SD: 1.5501 cents 24:26:32:35 x 44 x 48 SD: 5.9649 cents 25:27:34 x 37:46 x 50 SD: 3.4060 cents 26:28:35:38 x 48 x 52 SD: 5.1633 cents 27:29:37 x 40:49 x 54 SD: 6.7878 cents 28:30:38:41 x 51 x 56 SD: 5.5778 cents 29:32:39 x 43:53 x 58 SD: 5.7379 cents 30:33:41:44 x 55 x 60 SD: 5.5159 cents 31:34:42 x 46:57 x 62 SD: 3.7522 cents 32:35:43:47 x 59 x 64 SD: 4.0861 cents 33:36:45 x 49:60 x 66 SD: 4.0993 cents 34:37:46:50 x 62 x 68 SD: 1.3733 cents 35:38:47:51:52:64 x 70 SD: 3.7398 cents 36:39:49:53 x 66 x 72 SD: 2.4753 cents 37:40:50:54:55:68 x 74 SD: 3.3585 cents 38:41:51:56 x 70 x 76 SD: 4.4351 cents 39:42:53:57:58:71 x 78 SD: 4.1785 cents 40:43:54 x 59:73 x 80 SD: 4.1092 cents 41:45:55:60:61:75 x 82 SD: 4.4005 cents 42:46:57 x 62:77 x 84 SD: 2.9312 cents 43:47:58:63:64:79 x 86 SD: 3.0829 cents 44:48:60 x 65:81 x 88 SD: 3.5998 cents 45:49:61:66:67:82 x 90 SD: 2.6700 cents 46:50:62 x 68:84 x 92 SD: 1.5501 cents 47:51:64:69 x 86 x 94 SD: 2.3888 cents 48:52:65 x 71:88 x 96 SD: 1.3330 cents 49:53:66:72 x 90:97:98 SD: 2.6100 cents 50:54:68 x 74:92:99:100 SD: 3.1641 cents 51:55:69:75 x 93:101:102 SD: 2.8558 cents 53:58:72:78 x 97:105:106 SD: 2.6040 cents 54:59:73:79:80:99:107:108 SD: 2.1903 cents 55:60:74:81 x 101:109:110 SD: 2.4469 cents 56:61:76:82:83:103:111:112 SD: 2.1686 cents 57:62:77:84 x 104:113:114 SD: 1.5971 cents 59:64:80 x 87:108:117:118 SD: 1.4765 cents 61:66:83 x 90:112:121:122 SD: 2.5116 cents 62:67:84:91:92:113:123:124 SD: 2.2246 cents 63:68:85 x 93:115:125:126 SD: 2.4823 cents 64:70:87:94:95:117:127:128 SD: 2.3268 cents 65:71:88 x 96:119:129:130 SD: 1.6260 cents 67:73:91 x 99:123:133:134 SD: 1.7021 cents 68:74:92:100:101:124:135:136 SD: 1.6217 cents 70:76:95:103 x 128:139:140 SD: 1.1600 cents 72:78:97:106 x 132:143:144 SD: 1.7293 cents 73:79:99:107:108:134:145:146 SD: 1.6989 cents 74:80:100:109 x 135:147:148 SD: 1.9803 cents 76:83:103:112 x 139:151:152 SD: 1.6404 cents 77:84:104:113:114:141:153:154 SD: 1.2262 cents 78:85:106:115 x 143:155:156 SD: 1.7526 cents 79:86:107:116:117:145:157:158 SD: 1.0498 cents 80:87:108 x 118:146:159:160 SD: 1.2868 cents 81:88:110:119:120:148:161:162 SD: 1.2175 cents 82:89:111 x 121:150:163:164 SD: 0.7578 cents 84:91:114 x 124:154:167:168 SD: 1.4654 cents 85:92:115:125:126:156:169:170 SD: 1.4234 cents 88:96:119:129:130:161:175:176 SD: 1.2244 cents 90:98:122:132:133:165:179:180 SD: 1.0116 cents 93:101:126:137 x 170:185:186 SD: 0.7929 cents 94:102:127:138:139:172:187:188 SD: 0.6986 cents 95:103:129:140 x 174:189:190 SD: 1.4300 cents 96:104:130:141:142:176:191:192 SD: 1.0011 cents 97:105:131:143 x 178:193:194 SD: 1.6502 cents 98:107:133:144:145:179:195:196 SD: 1.4790 cents 99:108:134 x 146:181:197:198 SD: 1.3049 cents 100:109:135:147:148:183:199:200 SD: 0.9318 cents 101:110:137 x 149:185:201:202 SD: 1.1265 cents 102:111:138:150:151:187:203:204 SD: 0.6068 cents 113:123:153:166:167:207:225:226 SD: 0.5516 cents 116:126:157:171 x 212:231:232 SD: 0.8969 cents 117:127:158:172:173:214:233:234 SD: 0.6514 cents 118:128:160 x 174:216:235:236 SD: 1.1602 cents 119:129:161:175:176:218:237:238 SD: 0.7476 cents 125:136:169:184:185:229:249:250 SD: 0.5984 cents 136:148:184:200:201:249:271:272 SD: 0.4819 cents 159:173:215:234:235:291:316:318 SD: 0.4394 cents 184:200:249:271:272:337:366:368 SD: 0.4117 cents 195:212:264:287:288:357:388:390 SD: 0.3512 cents 230:250:311:338:340:421:458:460 SD: 0.3052 cents 253:275:342:372:374:463:503:506 SD: 0.2890 cents 255:277:345:375:377:467:507:510 SD: 0.2647 cents 266:289:360:391:393:487:529:532 SD: 0.2553 cents 278:302:376:409:411:509:553:556 SD: 0.2127 cents 289:314:391:425:427:529:575:578 SD: 0.1625 cents 391:425:529:575:578:716:778:782 SD: 0.1033 cents