Scala analysis: tgm
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 73.612 cents 73.612410 2: 192.720 cents 192.719780 3: 311.827 cents 311.827160 4: 385.440 cents 385.439570 5: 504.547 cents 504.546940 6: 578.159 cents 578.159350 7: 697.267 cents 697.266730 8: 816.374 cents 816.374100 9: 889.987 cents 889.986510 10: 1009.094 cents 1009.093890 11: 1082.706 cents 1082.706300 12: 1201.814 cents 1201.813670
SHOW/INTERVAL
0: 119.1074 cents 119.1074 1: 73.6124 cents 73.6124 2: 119.1074 cents 119.1074 3: 119.1074 cents 119.1074 4: 73.6124 cents 73.6124 5: 119.1074 cents 119.1074 6: 73.6124 cents 73.6124 7: 119.1074 cents 119.1074 8: 119.1074 cents 119.1074 9: 73.6124 cents 73.6124 10: 119.1074 cents 119.1074 11: 73.6124 cents 73.6124 12: 119.1074 cents 119.1074
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 73.61241 cents 1: 7 119.10737 cents 2: 10 192.71978 cents 2: 2 238.21475 cents 3: 3 266.33219 cents 3: 9 311.82716 cents 4: 8 385.43957 cents 4: 4 430.93453 cents 5: 1 459.05198 cents 5: 11 504.54694 cents 6: 6 578.15935 cents 6: 6 623.65432 cents 7: 11 697.26673 cents 7: 1 742.76169 cents 8: 4 770.87914 cents 8: 8 816.37410 cents 9: 9 889.98651 cents 9: 3 935.48148 cents 10: 2 963.59892 cents 10: 10 1009.09389 cents 11: 7 1082.70630 cents 11: 5 1128.20126 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 73.6 192.7 311.8 385.4 504.5 578.2 697.3 816.4 890.0 1009.1 1082.7 1201.8 73.6 : 119.1 238.2 311.8 430.9 504.5 623.7 742.8 816.4 935.5 1009.1 1128.2 1201.8 192.7 : 119.1 192.7 311.8 385.4 504.5 623.7 697.3 816.4 890.0 1009.1 1082.7 1201.8 311.8 : 73.6 192.7 266.3 385.4 504.5 578.2 697.3 770.9 890.0 963.6 1082.7 1201.8 385.4 : 119.1 192.7 311.8 430.9 504.5 623.7 697.3 816.4 890.0 1009.1 1128.2 1201.8 504.5 : 73.6 192.7 311.8 385.4 504.5 578.2 697.3 770.9 890.0 1009.1 1082.7 1201.8 578.2 : 119.1 238.2 311.8 430.9 504.5 623.7 697.3 816.4 935.5 1009.1 1128.2 1201.8 697.3 : 119.1 192.7 311.8 385.4 504.5 578.2 697.3 816.4 890.0 1009.1 1082.7 1201.8 816.4 : 73.6 192.7 266.3 385.4 459.1 578.2 697.3 770.9 890.0 963.6 1082.7 1201.8 890.0 : 119.1 192.7 311.8 385.4 504.5 623.7 697.3 816.4 890.0 1009.1 1128.2 1201.8 1009.1: 73.6 192.7 266.3 385.4 504.5 578.2 697.3 770.9 890.0 1009.1 1082.7 1201.8 1082.7: 119.1 192.7 311.8 430.9 504.5 623.7 697.3 816.4 935.5 1009.1 1128.2 1201.8 1201.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6124 .. 119.1074 cents 45.49496 cents 73.61241 cents 2: 192.7198 .. 238.2148 cents 45.49497 cents 73.61241 cents 3: 266.3322 .. 311.8272 cents 45.49497 cents 28.11744 cents 4: 385.4396 .. 430.9345 cents 45.49496 cents 73.61241 cents 5: 459.0520 .. 504.5469 cents 45.49496 cents 28.11745 cents 6: 578.1594 .. 623.6543 cents 45.49497 cents 73.61241 cents 7: 697.2667 .. 742.7617 cents 45.49496 cents 73.61241 cents 8: 770.8791 .. 816.3741 cents 45.49496 cents 28.11745 cents 9: 889.9865 .. 935.4815 cents 45.49497 cents 73.61241 cents 10: 963.5989 .. 1009.0939 cents 45.49497 cents 28.11744 cents 11: 1082.7063 .. 1128.2013 cents 45.49496 cents 73.61241 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 73.61241 cents, class 1 Average step (divided formal octave): 100.1511 cents Largest one step interval : 119.10737 cents Average / Smallest step : 1.360520 Largest / Average step : 1.189276 Largest / Smallest step : 1.618034 Median interval of one step : 119.10737 cents, amount: 7 Most common interval of one step : 119.10737 cents, amount: 7 Least squares average step : 99.64953 cents, oct.: 1195.79434 cents Scale is strictly proper Scale has Myhill's property chromas: 45.49496 cents and 28.11745 cents, ratio: 1.618033 generators: 5 of 504.54694 cents and 7 of 697.26673 cents ET pair of linear temperament : 12&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 898-tone equal temperament with octave 1201.814 cents degrees: 55 144 233 288 377 432 521 610 665 754 809 898 generators: 377 and 521 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABBABAB Step pattern size order : SLLSLSLLSLSL Scale is a Constant Structure, by a margin of 28.11744 cents Scale diversity : 1.220713 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.583592 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 28.11744 cents Most common intervals : 504.54694 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 119.107 697.267 cents Most common triad is 0.0 504.547 697.267 cents, amount: 10 Number of recognisable fifths : 11, average 697.2667 cents Number of recognisable fourths : 11, average 504.5469 cents Scale contains two identical conjunct hexachords Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.2697 c. M:-26.5387 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 2 1 2 1 2 P M ME SD: 5.5700 c. M: 10.3591 c. 31: 2 3 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 2.1099 c. M:-3.9240 c. 50: 3 5 5 3 5 3 5 5 3 5 3 5 SP M DE SD: 0.8085 c. M: 1.5036 c. 81: 5 8 8 5 8 5 8 8 5 8 5 8 SP M DE SD: 0.3084 c. M:-0.5736 c. 131: 8 13 13 8 13 8 13 13 8 13 8 13 SP M DE SD: 0.1179 c. M: 0.2192 c. 212: 13 21 21 13 21 13 21 21 13 21 13 21 SP M DE SD: 0.0450 c. M:-0.0837 c. 343: 21 34 34 21 34 21 34 34 21 34 21 34 SP M DE SD: 0.0172 c. M: 0.0320 c. 555: 34 55 55 34 55 34 55 55 34 55 34 55 SP M DE SD: 0.0066 c. M:-0.0122 c. 898: 55 89 89 55 89 55 89 89 55 89 55 89 SP M DE SD: 0.0025 c. M: 0.0047 c. 1453: 89 144 144 89 144 89 144 144 89 144 89 144 SP M DE SD: 0.0010 c. M:-0.0018 c. 2351: 144 233 233 144 233 144 233 233 144 233 144 233 SP M DE SD: 0.0004 c. M: 0.0007 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 1.8137 cents 2 x x x x x x 3 x x x x 4 S SD: 2.5134 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.9295 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.1475 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 2.1568 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.4752 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.2663 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.9682 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.9507 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1224 cents 11 x 12:13:14:15 x 16:18 x 20:21:22 S SD: 11.1435 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.5458 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.8249 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 8.4081 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.2439 cents 18:19:20:22 x 24:25:27:29:30:32:34:36 SD: 4.5927 cents 20:21:22:24:25:27:28:30:32:33:36:37:40 SD: 3.8123 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.2965 cents 25:26:28:30:31:33:35:37:40:42:45:47:50 SD: 3.1363 cents 33:34:37:40:41:44:46:49:53:55:59:62:66 SD: 3.1326 cents 35:37:39:42:44:47:49:52:56:59:63:65:70 SD: 2.9631 cents 36:38:40:43:45:48:50:54:58:60:64:67:72 SD: 2.6639 cents 40:42:45:48:50:54:56:60:64:67:72:75:80 SD: 2.1200 cents 44:46:49:53:55:59:61:66:71:74:79:82:88 SD: 2.1104 cents 45:47:50:54:56:60:63:67:72:75:81:84:90 SD: 1.7033 cents 51:53:57:61:64:68:71:76:82:85:91:95:102 SD: 1.6092 cents 60:63:67:72:75:80:84:90:96:100:107:112:120 SD: 1.4995 cents 61:64:68:73:76:82:85:91:98:102:109:114:122 SD: 1.3726 cents 67:70:75:80:84:90:94:100:107:112:120:125:134 SD: 1.2908 cents 68:71:76:81:85:91:95:102:109:114:122:127:136 SD: 0.9807 cents 76:79:85:91:95:102:106:114:122:127:136:142:152 SD: 0.8815 cents 91:95:102:109:114:122:127:136:146:152:163:170:182 SD: 0.7011 cents 101:105:113:121:126:135:141:151:162:169:181:189:202 SD: 0.6955 cents 116:121:130:139:145:155:162:174:186:194:208:217:232 SD: 0.6645 cents 121:126:135:145:151:162:169:181:194:202:217:226:242 SD: 0.5680 cents 136:142:152:163:170:182:190:203:218:227:244:254:272 SD: 0.5443 cents 153:160:171:183:191:205:214:229:245:256:274:286:306 SD: 0.5183 cents 161:168:180:193:201:215:225:241:258:269:288:301:322 SD: 0.4849 cents 177:185:198:212:221:237:247:265:284:296:317:331:354 SD: 0.4196 cents 204:213:228:244:255:273:285:305:327:341:365:381:408 SD: 0.3329 cents 254:265:284:304:317:340:355:380:407:425:455:475:509 SD: 0.2822 cents 272:284:304:326:340:364:380:407:436:455:487:508:545 SD: 0.2678 cents 305:318:341:365:381:408:426:456:489:510:546:570:611 SD: 0.2278 cents 345:360:386:413:431:462:482:516:553:577:618:645:691 SD: 0.2015 cents 373:389:417:447:466:499:521:558:598:624:668:697:747 SD: 0.1970 cents 390:407:436:467:487:522:545:583:625:652:699:729:781 SD: 0.1943 cents 417:435:466:499:521:558:582:624:668:697:747:779:835 SD: 0.1736 cents 441:460:493:528:551:590:616:660:707:737:790:824:883 SD: 0.1503 cents 482:503:539:577:602:645:673:721:772:806:863:901:965 SD: 0.1355 cents 577:602:645:691:721:772:806:863:925:965:1034:1078:1155 SD: 0.1349 cents 597:623:667:715:746:799:834:893:957:998:1069:1116:1195 SD: 0.1277 cents