Scala analysis: synchtrinesplus2
The 12-tone equal temperament with 2:3:4 brats of +2.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.784 cents 99.784000 2: 199.566 cents 199.566000 3: 299.350 cents 299.350000 4: 399.132 cents 399.132000 5: 498.916 cents 498.916000 6: 598.698 cents 598.698000 7: 698.480 cents 698.480000 8: 798.264 cents 798.264000 9: 898.046 cents 898.046000 10: 997.830 cents 997.830000 11: 1097.612 cents 1097.612000 12: 1197.394 cents 1197.394000
SHOW/INTERVAL
0: 99.7820 cents 99.7820 1: 99.7840 cents 99.7840 2: 99.7820 cents 99.7820 3: 99.7840 cents 99.7840 4: 99.7820 cents 99.7820 5: 99.7840 cents 99.7840 6: 99.7820 cents 99.7820 7: 99.7820 cents 99.7820 8: 99.7840 cents 99.7840 9: 99.7820 cents 99.7820 10: 99.7840 cents 99.7840 11: 99.7820 cents 99.7820 12: 99.7820 cents 99.7820
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 99.78200 cents 1: 5 99.78400 cents 2: 2 199.56400 cents 2: 10 199.56600 cents 3: 9 299.34800 cents 3: 3 299.35000 cents 4: 4 399.13000 cents 4: 8 399.13200 cents 5: 11 498.91400 cents 5: 1 498.91600 cents 6: 6 598.69600 cents 6: 6 598.69800 cents 7: 1 698.47800 cents 7: 11 698.48000 cents 8: 8 798.26200 cents 8: 4 798.26400 cents 9: 3 898.04400 cents 9: 9 898.04600 cents 10: 10 997.82800 cents 10: 2 997.83000 cents 11: 5 1097.61000 cents 11: 7 1097.61200 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 : 99.8 199.6 299.4 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 99.8 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 199.6 : 99.8 199.6 299.4 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 299.4 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 399.1 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 498.9 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 598.7 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 698.5 : 99.8 199.6 299.4 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 798.3 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 898.0 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 997.8 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 1097.6: 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 1197.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.7820 .. 99.7840 cents 0.00200 cents 99.78200 cents 2: 199.5640 .. 199.5660 cents 0.00200 cents 99.78000 cents 3: 299.3480 .. 299.3500 cents 0.00200 cents 99.78200 cents 4: 399.1300 .. 399.1320 cents 0.00200 cents 99.78000 cents 5: 498.9140 .. 498.9160 cents 0.00200 cents 99.78200 cents 6: 598.6960 .. 598.6980 cents 0.00200 cents 99.78000 cents 7: 698.4780 .. 698.4800 cents 0.00200 cents 99.78000 cents 8: 798.2620 .. 798.2640 cents 0.00200 cents 99.78200 cents 9: 898.0440 .. 898.0460 cents 0.00200 cents 99.78000 cents 10: 997.8280 .. 997.8300 cents 0.00200 cents 99.78200 cents 11: 1097.6100 .. 1097.6120 cents 0.00200 cents 99.78000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 99.78200 cents, class 1 Average step (divided formal octave): 99.7828 cents Largest one step interval : 99.78400 cents Average / Smallest step : 1.000008 Largest / Average step : 1.000012 Largest / Smallest step : 1.000020 Median interval of one step : 99.78200 cents, amount: 7 Most common interval of one step : 99.78200 cents, amount: 7 Least squares average step : 99.78294 cents, oct.: 1197.39522 cents Scale is strictly proper Scale has Myhill's property chromas: 0.00200 cents and 99.78000 cents, ratio: 49889.999991 generators: 498.91400 cents and 7 of 698.48000 cents ET pair of linear temperament : 12&598685 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 12-tone equal temperament with octave 1197.394 cents degrees: 1 2 3 4 5 6 7 8 9 10 11 12 generators: 5 and 7 Number of contiguous 1-step segments: 1 Step pattern alph. order: ABABABBABABB Step pattern size order : LSLSLSSLSLSS Interval vector is [ 5 10 3 8 1 3 ] Scale is a Constant Structure, by a margin of 99.78000 cents Scale diversity : 1.001744 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.999982 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 : 0.00200 cents Most common intervals : 498.91400 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 598.698 698.480 cents Most common triad is 0.0 498.914 698.480 cents, amount: 10 Number of recognisable fifths : 12, average 698.4798 cents Number of recognisable fourths : 12, average 498.9142 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 1 2 3 4 5 6 7 8 9 10 11 Inversional symmetry on degrees : 0 1 2 3 4 5 6 7 8 9 10 11 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0011 c. M: 0.0018 c. Twelve-tone Chromatic (1/11-comma)
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 2.6060 cents 2 x x x x x x 3 x x x x 4 S SD: 2.1718 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.6535 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.0016 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.8198 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.9859 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.8999 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9806 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.1376 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0544 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.2624 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1804 cents 13:14:15 x 16:17:18:19:21:22:23:25:26 SD: 9.6846 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.2052 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.8842 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0643 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.9859 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.6388 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2633 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.6203 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1869 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.9778 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.8252 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.6450 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.5581 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.2529 cents 65:69:73:77:82:87:92:97:103:109:116:123:130 SD: 1.2257 cents 68:72:76:81:86:91:96:102:108:114:121:128:136 SD: 1.1645 cents 80:85:90:95:101:107:113:120:127:134:142:151:160 SD: 1.0601 cents 84:89:94:100:106:112:119:126:133:141:149:158:168 SD: 0.9729 cents 85:90:95:101:107:113:120:127:135:143:151:160:170 SD: 0.9728 cents 90:95:101:107:113:120:127:135:143:151:160:170:180 SD: 0.9182 cents 96:102:108:114:121:128:136:144:152:161:171:181:192 SD: 0.8660 cents 99:105:111:118:125:132:140:148:157:166:176:187:198 SD: 0.7840 cents 116:123:130:138:146:155:164:174:184:195:206:219:232 SD: 0.6419 cents 123:130:138:146:155:164:174:184:195:207:219:232:246 SD: 0.5769 cents 131:139:147:156:165:175:185:196:208:220:233:247:262 SD: 0.5142 cents 155:164:174:184:195:207:219:232:246:260:276:292:310 SD: 0.4929 cents 165:175:185:196:208:220:233:247:262:277:294:311:330 SD: 0.4707 cents 181:192:203:215:228:241:256:271:287:304:322:341:361 SD: 0.4400 cents 201:213:226:239:253:268:284:301:319:338:358:379:401 SD: 0.4087 cents 203:215:228:241:256:271:287:304:322:341:361:383:405 SD: 0.3973 cents 213:226:239:253:268:284:301:319:338:358:379:402:425 SD: 0.3866 cents 237:251:266:282:298:316:335:355:376:398:422:447:473 SD: 0.3282 cents 254:269:285:302:320:339:359:380:403:427:452:479:507 SD: 0.2076 cents 350:371:393:416:441:467:495:524:555:588:623:660:699 SD: 0.2024 cents 386:409:433:459:486:515:545:578:612:648:687:728:771 SD: 0.2015 cents 401:425:450:477:505:535:567:600:636:674:714:756:801 SD: 0.2004 cents 408:432:458:485:514:544:577:611:647:685:726:769:815 SD: 0.1999 cents 409:433:459:486:515:546:578:612:649:687:728:771:817 SD: 0.1938 cents 425:450:477:505:535:567:601:636:674:714:756:801:849 SD: 0.1781 cents 435:461:488:517:548:580:615:651:690:731:774:820:869 SD: 0.1662 cents 440:466:494:523:554:587:622:659:698:739:783:829:879 SD: 0.1647 cents 509:539:571:605:641:679:719:762:807:855:906:960:1016 SD: 0.1429 cents 540:572:606:642:680:720:763:808:856:907:961:1018:1078 SD: 0.1297 cents 572:606:642:680:720:763:808:856:907:961:1018:1078:1142 SD: 0.1180 cents