Scala analysis: archytas12sync
Archytas[12] (64/63) hobbit, sync beating
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.459 cents 96.458890 2: 222.993 cents 222.992620 3: 319.452 cents 319.451500 4: 392.045 cents 392.044810 5: 488.504 cents 488.503690 6: 615.037 cents 615.037420 7: 711.496 cents 711.496310 8: 807.955 cents 807.955190 9: 934.489 cents 934.488920 10: 977.007 cents 977.007380 11: 1103.541 cents 1103.541110 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 96.4589 cents 96.4589 1: 96.4589 cents 96.4589 2: 126.5337 cents 126.5337 3: 96.4589 cents 96.4589 4: 72.5933 cents 72.5933 5: 96.4589 cents 96.4589 6: 126.5337 cents 126.5337 7: 96.4589 cents 96.4589 8: 96.4589 cents 96.4589 9: 126.5337 cents 126.5337 10: 42.5185 cents 42.5185 11: 126.5337 cents 126.5337 12: 96.4589 cents 96.4589
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 42.51846 cents 1: 1 72.59331 cents 1: 6 96.45889 cents 1: 4 126.53373 cents 2: 4 169.05219 cents 2: 2 192.91777 cents 2: 6 222.99262 cents 3: 3 265.51107 cents 3: 3 295.58592 cents 3: 6 319.45150 cents 4: 2 361.96996 cents 4: 6 392.04481 cents 4: 2 415.91038 cents 4: 2 445.98523 cents 5: 9 488.50369 cents 5: 1 518.57853 cents 5: 2 542.44411 cents 6: 6 584.96257 cents 6: 6 615.03742 cents 7: 2 657.55588 cents 7: 1 681.42147 cents 7: 9 711.49631 cents 8: 2 754.01476 cents 8: 2 784.08961 cents 8: 6 807.95519 cents 8: 2 838.03003 cents 9: 6 880.54849 cents 9: 3 904.41408 cents 9: 3 934.48892 cents 10: 6 977.00738 cents 10: 2 1007.08222 cents 10: 4 1030.94781 cents 11: 4 1073.46627 cents 11: 6 1103.54111 cents 11: 1 1127.40669 cents 11: 1 1157.48154 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 96.5 223.0 319.5 392.0 488.5 615.0 711.5 808.0 934.5 977.0 1103.5 1200.0 96.5 : 126.5 223.0 295.6 392.0 518.6 615.0 711.5 838.0 880.5 1007.1 1103.5 1200.0 223.0 : 96.5 169.1 265.5 392.0 488.5 585.0 711.5 754.0 880.5 977.0 1073.5 1200.0 319.5 : 72.6 169.1 295.6 392.0 488.5 615.0 657.6 784.1 880.5 977.0 1103.5 1200.0 392.0 : 96.5 223.0 319.5 415.9 542.4 585.0 711.5 808.0 904.4 1030.9 1127.4 1200.0 488.5 : 126.5 223.0 319.5 446.0 488.5 615.0 711.5 808.0 934.5 1030.9 1103.5 1200.0 615.0 : 96.5 192.9 319.5 362.0 488.5 585.0 681.4 808.0 904.4 977.0 1073.5 1200.0 711.5 : 96.5 223.0 265.5 392.0 488.5 585.0 711.5 808.0 880.5 977.0 1103.5 1200.0 808.0 : 126.5 169.1 295.6 392.0 488.5 615.0 711.5 784.1 880.5 1007.1 1103.5 1200.0 934.5 : 42.5 169.1 265.5 362.0 488.5 585.0 657.6 754.0 880.5 977.0 1073.5 1200.0 977.0 : 126.5 223.0 319.5 446.0 542.4 615.0 711.5 838.0 934.5 1030.9 1157.5 1200.0 1103.5: 96.5 192.9 319.5 415.9 488.5 585.0 711.5 808.0 904.4 1030.9 1073.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.5185 .. 126.5337 cents 84.01527 cents 42.51846 cents 2: 169.0522 .. 222.9926 cents 53.94043 cents 42.51846 cents 3: 265.5111 .. 319.4515 cents 53.94043 cents 42.51845 cents 4: 361.9700 .. 445.9852 cents 84.01527 cents 42.51846 cents 5: 488.5037 .. 542.4441 cents 53.94042 cents 42.51846 cents 6: 584.9626 .. 615.0374 cents 30.07485 cents 42.51846 cents 7: 657.5559 .. 711.4963 cents 53.94043 cents 42.51846 cents 8: 754.0148 .. 838.0300 cents 84.01527 cents 42.51845 cents 9: 880.5485 .. 934.4889 cents 53.94043 cents 42.51846 cents 10: 977.0074 .. 1030.9478 cents 53.94043 cents 42.51846 cents 11: 1073.4663 .. 1157.4815 cents 84.01527 cents 42.51846 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 42.51846 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 126.53373 cents Average / Smallest step : 2.351920 Largest / Average step : 1.265337 Largest / Smallest step : 2.975972 Median interval of one step : 96.45889 cents, amount: 6 Most common interval of one step : 96.45889 cents, amount: 6 Least squares average step : 100.56194 cents, oct.: 1206.74331 cents Scale is strictly proper Scale is a mode of a 1157-tone equal temperament with octave 1200.000 cents degrees: 93 215 308 378 471 593 686 779 901 942 1064 1157 Least number of segments generator : 579 of 600.519 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 907 of 940.709 cents and inv. generated superset size: 61 = 49 more = 508.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABAABDBA Step pattern size order : CDCBCDCCDADC Scale is a Constant Structure, by a margin of 42.51845 cents Scale diversity : 1.432600 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.425185 Rothenberg efficiency : 0.415278 redundancy: 0.584722 Efficiency x scale size : 4.983333 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 23.86557 cents Most common intervals : 488.50369 cents & inv., amount: 9 Most common triad is 0.0 488.504 711.496 cents, amount: 6 Number of recognisable fifths : 9, average 711.4963 cents Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.5007 c. M: 34.4889 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 1 1 1 2 1 1 2 0 2 1 P D3 SD: 14.9045 c. M:-25.5111 c. 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 8.7822 c. M: 15.0374 c. Pajara-12 27: 2 3 2 2 2 3 2 2 3 1 3 2 SP D3 SD: 5.5165 c. M: 8.3404 c. 37: 3 4 3 2 3 4 3 3 4 1 4 3 SP SD: 3.1644 c. M:-6.0516 c. 49: 4 5 4 3 4 5 4 4 5 2 5 4 SP SD: 1.9427 c. M: 3.8767 c. 64: 5 7 5 4 5 7 5 5 7 2 7 5 SP SD: 2.1195 c. M:-3.7126 c. 76: 6 8 6 5 6 8 6 6 8 3 8 6 SP SD: 2.0872 c. M: 3.6620 c. 86: 7 9 7 5 7 9 7 7 9 3 9 7 SP SD: 0.9253 c. M:-1.4787 c. 113: 9 12 9 7 9 12 9 9 12 4 12 9 SP SD: 0.6221 c. M:-0.8918 c. 162: 13 17 13 10 13 17 13 13 17 6 17 13 SP SD: 0.6050 c. M: 1.1556 c. 199: 16 21 16 12 16 21 16 16 21 7 21 16 SP SD: 0.0959 c. M:-0.1844 c. 646: 52 68 52 39 52 68 52 52 68 23 68 52 SP SD: 0.1004 c. M: 0.1767 c. 710: 57 75 57 43 57 75 57 57 75 25 75 57 SP SD: 0.1009 c. M:-0.1738 c. 759: 61 80 61 46 61 80 61 61 80 27 80 61 SP SD: 0.0538 c. M: 0.1016 c. 958: 77 101 77 58 77 101 77 77 101 34 101 77 SP SD: 0.0227 c. M: 0.0422 c. 1157: 93 122 93 70 93 122 93 93 122 41 122 93 SP SD: 0.0026 c. M: 0.0047 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 4.7707 cents 3 x x x x 4 x x x 5 x x 6 S SD: 17.0100 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 3.4534 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 10.4933 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 14.4872 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.5587 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.5155 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.7636 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.7704 cents 11:12 x 13:14:15:16:17:18:19 x 21:22 SD: 11.0164 cents 12:13:14 x 15:16:17:18:19 x 21:23:24 SD: 6.9269 cents 13:14:15 x 16:17:19:20:21:22:23:25:26 SD: 8.2282 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.8816 cents 15:16:17:18:19:20:21:23:24:26 x 28:30 SD: 5.3179 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 5.0767 cents 19:20:22:23:24:25:27:29:30 x 33:36:38 SD: 4.7168 cents 20:21:23:24:25:27:29:30:32:34:35:38:40 SD: 4.4192 cents 21:22:24:25:26:28:30:32:33:36:37:40:42 SD: 4.0358 cents 24:25:27:29:30:32:34:36:38:41:42:45:48 SD: 3.6931 cents 28:30:32:34:35:37:40:42:45:48:49:53:56 SD: 2.9929 cents 30:32:34:36:38:40:43:45:48:51:53:57:60 SD: 2.9382 cents 34:36:39:41:43:45:49:51:54:58:60:64:68 SD: 2.7916 cents 35:37:40:42:44:46:50:53:56:60:62:66:70 SD: 2.0717 cents 49:52:56:59:61:65:70:74:78:84:86:93:98 SD: 1.5432 cents 59:62:67:71:74:78:84:89:94:101:104:112:118 SD: 1.2741 cents 67:71:76:81:84:89:96:101:107:115:118:127:134 SD: 1.2271 cents 71:75:81:85:89:94:101:107:113:122:125:134:142 SD: 1.0682 cents 74:78:84:89:93:98:106:112:118:127:130:140:148 SD: 1.0139 cents 87:92:99:105:109:115:124:131:139:149:153:165:174 SD: 0.9192 cents 89:94:101:107:112:118:127:134:142:153:156:168:178 SD: 0.9121 cents 94:99:107:113:118:125:134:142:150:161:165:178:188 SD: 0.8532 cents 102:108:116:123:128:135:146:154:163:175:179:193:204 SD: 0.8380 cents 103:109:117:124:129:137:147:155:164:177:181:195:206 SD: 0.7446 cents 108:114:123:130:135:143:154:163:172:185:190:204:216 SD: 0.7259 cents 122:129:139:147:153:162:174:184:195:209:215:231:244 SD: 0.6737 cents 138:146:157:166:173:183:197:208:220:237:243:261:276 SD: 0.3208 cents 212:224:241:255:266:281:302:320:338:364:373:401:424 SD: 0.3182 cents 232:245:264:279:291:308:331:350:370:398:408:439:464 SD: 0.2602 cents 276:292:314:332:346:366:394:416:440:474:485:522:552 SD: 0.2559 cents 291:308:331:350:365:386:415:439:464:499:512:550:582 SD: 0.2412 cents 331:350:377:398:415:439:472:499:528:568:582:626:662 SD: 0.2276 cents 335:354:381:403:420:444:478:505:534:575:589:634:670 SD: 0.1892 cents 350:370:398:421:439:464:499:528:558:600:615:662:700 SD: 0.1880 cents 370:391:421:445:464:491:528:558:590:635:651:700:740 SD: 0.1870 cents 405:428:461:487:508:537:578:611:646:695:712:766:810 SD: 0.1553 cents 472:499:537:568:592:626:673:712:753:810:830:893:944 SD: 0.1452 cents 488:516:555:587:612:647:696:736:778:837:858:923:976 SD: 0.0803 cents