Scala analysis: archytas12
Archytas[12] (64/63) hobbit, 9-limit minimax
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98.099 cents 98.099240 2: 217.542 cents 217.542050 3: 315.641 cents 315.641290 4: 393.130 cents 393.129740 5: 491.229 cents 491.228980 6: 589.328 cents 589.328220 7: 708.771 cents 708.771020 8: 806.870 cents 806.870260 9: 884.359 cents 884.358710 10: 982.458 cents 982.457950 11: 1101.901 cents 1101.900760 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 98.0992 cents 98.0992 1: 98.0992 cents 98.0992 2: 119.4428 cents 119.4428 3: 98.0992 cents 98.0992 4: 77.4885 cents 77.4885 5: 98.0992 cents 98.0992 6: 98.0992 cents 98.0992 7: 119.4428 cents 119.4428 8: 98.0992 cents 98.0992 9: 77.4884 cents 77.4884 10: 98.0992 cents 98.0992 11: 119.4428 cents 119.4428 12: 98.0992 cents 98.0992
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 77.48845 cents 1: 7 98.09924 cents 1: 3 119.44281 cents 2: 4 175.58769 cents 2: 2 196.19848 cents 2: 6 217.54205 cents 3: 3 273.68693 cents 3: 3 295.03050 cents 3: 6 315.64129 cents 4: 1 371.78617 cents 4: 7 393.12974 cents 4: 3 413.74052 cents 4: 1 435.08410 cents 5: 9 491.22898 cents 5: 1 512.57254 cents 5: 2 533.18334 cents 6: 1 568.71742 cents 6: 5 589.32822 cents 6: 5 610.67178 cents 6: 1 631.28258 cents 7: 2 666.81666 cents 7: 1 687.42746 cents 7: 9 708.77102 cents 8: 1 764.91590 cents 8: 3 786.25947 cents 8: 7 806.87026 cents 8: 1 828.21383 cents 9: 6 884.35871 cents 9: 3 904.96950 cents 9: 3 926.31307 cents 10: 6 982.45795 cents 10: 2 1003.80152 cents 10: 4 1024.41231 cents 11: 3 1080.55719 cents 11: 7 1101.90076 cents 11: 2 1122.51155 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 : 98.1 217.5 315.6 393.1 491.2 589.3 708.8 806.9 884.4 982.5 1101.9 1200.0 98.1 : 119.4 217.5 295.0 393.1 491.2 610.7 708.8 786.3 884.4 1003.8 1101.9 1200.0 217.5 : 98.1 175.6 273.7 371.8 491.2 589.3 666.8 764.9 884.4 982.5 1080.6 1200.0 315.6 : 77.5 175.6 273.7 393.1 491.2 568.7 666.8 786.3 884.4 982.5 1101.9 1200.0 393.1 : 98.1 196.2 315.6 413.7 491.2 589.3 708.8 806.9 905.0 1024.4 1122.5 1200.0 491.2 : 98.1 217.5 315.6 393.1 491.2 610.7 708.8 806.9 926.3 1024.4 1101.9 1200.0 589.3 : 119.4 217.5 295.0 393.1 512.6 610.7 708.8 828.2 926.3 1003.8 1101.9 1200.0 708.8 : 98.1 175.6 273.7 393.1 491.2 589.3 708.8 806.9 884.4 982.5 1080.6 1200.0 806.9 : 77.5 175.6 295.0 393.1 491.2 610.7 708.8 786.3 884.4 982.5 1101.9 1200.0 884.4 : 98.1 217.5 315.6 413.7 533.2 631.3 708.8 806.9 905.0 1024.4 1122.5 1200.0 982.5 : 119.4 217.5 315.6 435.1 533.2 610.7 708.8 806.9 926.3 1024.4 1101.9 1200.0 1101.9: 98.1 196.2 315.6 413.7 491.2 589.3 687.4 806.9 905.0 982.5 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.4885 .. 119.4428 cents 41.95436 cents 77.48845 cents 2: 175.5877 .. 217.5420 cents 41.95436 cents 56.14488 cents 3: 273.6869 .. 315.6413 cents 41.95436 cents 56.14488 cents 4: 371.7862 .. 435.0841 cents 63.29793 cents 56.14488 cents 5: 491.2290 .. 533.1833 cents 41.95436 cents 56.14488 cents 6: 568.7174 .. 631.2826 cents 62.56516 cents 35.53408 cents 7: 666.8167 .. 708.7710 cents 41.95436 cents 35.53408 cents 8: 764.9159 .. 828.2138 cents 63.29793 cents 56.14488 cents 9: 884.3587 .. 926.3131 cents 41.95436 cents 56.14488 cents 10: 982.4579 .. 1024.4123 cents 41.95436 cents 56.14488 cents 11: 1080.5572 .. 1122.5115 cents 41.95436 cents 56.14488 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 77.48845 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 119.44281 cents Average / Smallest step : 1.290515 Largest / Average step : 1.194428 Largest / Smallest step : 1.541427 Median interval of one step : 98.09924 cents, amount: 7 Most common interval of one step : 98.09924 cents, amount: 7 Least squares average step : 99.63972 cents, oct.: 1195.67660 cents Scale is strictly proper Step pattern alph. order: ABACAABACABA Step pattern size order : MLMSMMLMSMLM Scale is a Constant Structure, by a margin of 35.53408 cents Scale diversity : 1.346148 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.562670 Rothenberg efficiency : 0.416997 redundancy: 0.583003 Efficiency x scale size : 5.003968 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 20.61078 cents Most common intervals : 491.22898 cents & inv., amount: 9 Most common triad is 0.0 491.229 708.771 cents, amount: 6 Number of recognisable fifths : 10, average 706.6367 cents Number of appreciable fifths : 9, average 708.7710 cents Scale contains two identical conjunct hexachords Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.0835 c. M:-17.5420 c. Twelve-tone Chromatic (1/11-comma) 22: 2 2 2 1 2 2 2 2 1 2 2 2 P D3 I SD: 8.5782 c. M:-11.6314 c. 27: 2 3 2 2 2 2 3 2 2 2 3 2 SP D3 SD: 6.4114 c. M: 11.5504 c. 34: 3 3 3 2 3 3 3 3 2 3 3 3 SP D3 I SD: 5.5860 c. M:-10.6718 c. "Just" Chromatic 37: 3 4 3 2 3 3 4 3 2 3 4 3 P SD: 6.0469 c. M:-9.4850 c. 39: 3 4 3 3 3 3 4 3 3 3 4 3 SP D3 SD: 5.1777 c. M:-7.9490 c. 49: 4 5 4 3 4 4 5 4 3 4 5 4 SP SD: 1.8542 c. M:-2.8661 c. 61: 5 6 5 4 5 5 6 5 4 5 6 5 SP SD: 0.7014 c. M:-1.1486 c. 110: 9 11 9 7 9 9 11 9 7 9 11 9 SP SD: 0.4528 c. M:-0.7223 c. 171: 14 17 14 11 14 14 17 14 11 14 17 14 SP SD: 0.1123 c. M:-0.1482 c. 745: 61 74 61 48 61 61 74 61 48 61 74 61 SP SD: 0.1091 c. M:-0.2020 c. 916: 75 91 75 59 75 75 91 75 59 75 91 75 SP SD: 0.1072 c. M:-0.1914 c. 943: 77 94 77 61 77 77 94 77 61 77 94 77 SP SD: 0.0795 c. M: 0.1448 c. 1004: 82 100 82 65 82 82 100 82 65 82 100 82 SP SD: 0.0734 c. M:-0.1034 c. 1114: 91 111 91 72 91 91 111 91 72 91 111 91 SP SD: 0.0528 c. M: 0.1002 c. 1175: 96 117 96 76 96 96 117 96 76 96 117 96 SP SD: 0.0465 c. M:-0.0668 c. 1285: 105 128 105 83 105 105 128 105 83 105 128 105 SP SD: 0.0350 c. M: 0.0675 c. 1346: 110 134 110 87 110 110 134 110 87 110 134 110 SP SD: 0.0265 c. M:-0.0395 c. 1456: 119 145 119 94 119 119 145 119 94 119 145 119 SP SD: 0.0251 c. M: 0.0425 c. 1517: 124 151 124 98 124 124 151 124 98 124 151 124 SP SD: 0.0113 c. M:-0.0183 c. 1688: 138 168 138 109 138 138 168 138 109 138 168 138 SP SD: 0.0044 c. M:-0.0083 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: 3.4080 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.2720 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 4.1739 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.2873 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 12.0551 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.6267 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.1020 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.9396 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.2257 cents 11:12 x 13:14:15 x 17 x 18:19:21:22 SD: 11.5412 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.5889 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 8.0821 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.2869 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 4.5098 cents 20:21:23:24:25:27:28:30:32:33:35:38:40 SD: 4.0355 cents 24:25:27:29:30:32:34:36:38:40:42:45:48 SD: 3.6396 cents 29:31:33:35:36:39:41:44:46:48:51:55:58 SD: 3.5421 cents 30:32:34:36:38:40:42:45:48:50:53:57:60 SD: 2.2458 cents 39:41:44:47:49:52:55:59:62:65:69:74:78 SD: 1.8732 cents 51:54:58:61:64:68:72:77:81:85:90:96:102 SD: 1.3632 cents 54:57:61:65:68:72:76:81:86:90:95:102:108 SD: 1.3109 cents 66:70:75:79:83:88:93:99:105:110:116:125:132 SD: 1.2758 cents 67:71:76:80:84:89:94:101:107:112:118:127:134 SD: 1.0847 cents 81:86:92:97:102:108:114:122:129:135:143:153:162 SD: 1.0023 cents 89:94:101:107:112:118:125:134:142:148:157:168:178 SD: 0.7507 cents 106:112:120:127:133:141:149:160:169:177:187:200:212 SD: 0.6752 cents 118:125:134:142:148:157:166:178:188:197:208:223:236 SD: 0.6733 cents 119:126:135:143:149:158:167:179:190:198:210:225:238 SD: 0.6116 cents 135:143:153:162:169:179:190:203:215:225:238:255:270 SD: 0.5534 cents 140:148:159:168:176:186:197:211:223:233:247:265:280 SD: 0.5391 cents 150:159:170:180:188:199:211:226:239:250:265:283:300 SD: 0.4983 cents 156:165:177:187:196:207:219:235:249:260:275:295:312 SD: 0.4244 cents 170:180:193:204:213:226:239:256:271:283:300:321:340 SD: 0.4013 cents 192:203:218:230:241:255:270:289:306:320:339:363:384 SD: 0.3946 cents 204:216:231:245:256:271:287:307:325:340:360:386:408 SD: 0.3559 cents 219:232:248:263:275:291:308:330:349:365:386:414:438 SD: 0.3322 cents 225:238:255:270:282:299:316:339:359:375:397:425:450 SD: 0.3227 cents 239:253:271:287:300:317:336:360:381:398:422:452:478 SD: 0.3178 cents 255:270:289:306:320:339:358:384:406:425:450:482:510 SD: 0.2889 cents 259:274:294:311:325:344:364:390:413:432:457:489:518 SD: 0.2777 cents 271:287:307:325:340:360:381:408:432:452:478:512:542 SD: 0.2356 cents 306:324:347:367:384:406:430:461:488:510:540:578:612 SD: 0.2346 cents 326:345:370:391:409:433:458:491:520:543:575:616:652 SD: 0.2324 cents 330:349:374:396:414:438:464:497:526:550:582:624:660 SD: 0.1886 cents 360:381:408:432:452:478:506:542:574:600:635:680:720 SD: 0.1488 cents 411:435:466:493:516:546:578:619:655:685:725:777:822 SD: 0.1386 cents 530:561:601:636:665:704:745:798:845:883:935:1002:1060 SD: 0.1129 cents