Scala analysis: met24c-cs12-archytan-maqam_cup
Constant Structure, tempered subdivision of Archytas Chromatic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68.555 cents 68.554680 2: 207.422 cents 207.421870 3: 288.867 cents 288.867190 4: 357.422 cents 357.421870 5: 496.289 cents 496.289060 6: 564.844 cents 564.843750 7: 703.711 cents 703.710930 8: 772.266 cents 772.265620 9: 911.133 cents 911.132810 10: 992.578 cents 992.578120 11: 1061.133 cents 1061.132810 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 138.8672 cents 138.8672 1: 68.5547 cents 68.5547 2: 138.8672 cents 138.8672 3: 81.4453 cents 81.4453 4: 68.5547 cents 68.5547 5: 138.8672 cents 138.8672 6: 68.5547 cents 68.5547 7: 138.8672 cents 138.8672 8: 68.5547 cents 68.5547 9: 138.8672 cents 138.8672 10: 81.4453 cents 81.4453 11: 68.5547 cents 68.5547 12: 138.8672 cents 138.8672
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 68.55468 cents 1: 2 81.44532 cents 1: 5 138.86719 cents 2: 2 150.00000 cents 2: 8 207.42187 cents 2: 2 220.31251 cents 3: 3 275.97656 cents 3: 6 288.86719 cents 3: 3 346.28906 cents 4: 4 357.42187 cents 4: 4 414.84374 cents 4: 4 427.73438 cents 5: 1 483.39843 cents 5: 10 496.28906 cents 5: 1 553.71094 cents 6: 5 564.84375 cents 6: 1 577.73438 cents 6: 1 622.26562 cents 6: 5 635.15625 cents 7: 1 646.28906 cents 7: 10 703.71093 cents 7: 1 716.60157 cents 8: 4 772.26562 cents 8: 4 785.15625 cents 8: 4 842.57813 cents 9: 3 853.71094 cents 9: 6 911.13281 cents 9: 3 924.02344 cents 10: 2 979.68749 cents 10: 8 992.57812 cents 10: 2 1050.00000 cents 11: 5 1061.13281 cents 11: 2 1118.55468 cents 11: 5 1131.44532 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 68.6 207.4 288.9 357.4 496.3 564.8 703.7 772.3 911.1 992.6 1061.1 1200.0 68.6 : 138.9 220.3 288.9 427.7 496.3 635.2 703.7 842.6 924.0 992.6 1131.4 1200.0 207.4 : 81.4 150.0 288.9 357.4 496.3 564.8 703.7 785.2 853.7 992.6 1061.1 1200.0 288.9 : 68.6 207.4 276.0 414.8 483.4 622.3 703.7 772.3 911.1 979.7 1118.6 1200.0 357.4 : 138.9 207.4 346.3 414.8 553.7 635.2 703.7 842.6 911.1 1050.0 1131.4 1200.0 496.3 : 68.6 207.4 276.0 414.8 496.3 564.8 703.7 772.3 911.1 992.6 1061.1 1200.0 564.8 : 138.9 207.4 346.3 427.7 496.3 635.2 703.7 842.6 924.0 992.6 1131.4 1200.0 703.7 : 68.6 207.4 288.9 357.4 496.3 564.8 703.7 785.2 853.7 992.6 1061.1 1200.0 772.3 : 138.9 220.3 288.9 427.7 496.3 635.2 716.6 785.2 924.0 992.6 1131.4 1200.0 911.1 : 81.4 150.0 288.9 357.4 496.3 577.7 646.3 785.2 853.7 992.6 1061.1 1200.0 992.6 : 68.6 207.4 276.0 414.8 496.3 564.8 703.7 772.3 911.1 979.7 1118.6 1200.0 1061.1: 138.9 207.4 346.3 427.7 496.3 635.2 703.7 842.6 911.1 1050.0 1131.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.5547 .. 138.8672 cents 70.31251 cents 68.55468 cents 2: 150.0000 .. 220.3125 cents 70.31251 cents 11.13281 cents 3: 275.9766 .. 346.2891 cents 70.31250 cents 55.66405 cents 4: 357.4219 .. 427.7344 cents 70.31251 cents 11.13281 cents 5: 483.3984 .. 553.7109 cents 70.31251 cents 55.66405 cents 6: 564.8437 .. 635.1562 cents 70.31250 cents 11.13281 cents 7: 646.2891 .. 716.6016 cents 70.31251 cents 11.13281 cents 8: 772.2656 .. 842.5781 cents 70.31251 cents 55.66405 cents 9: 853.7109 .. 924.0234 cents 70.31250 cents 11.13281 cents 10: 979.6875 .. 1050.0000 cents 70.31251 cents 55.66405 cents 11: 1061.1328 .. 1131.4453 cents 70.31251 cents 11.13281 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 68.55468 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 138.86719 cents Average / Smallest step : 1.458690 Largest / Average step : 1.388672 Largest / Smallest step : 2.025641 Median interval of one step : 81.44532 cents, amount: 2 Least squares average step : 98.38882 cents, oct.: 1180.66586 cents Scale is strictly proper Scale is a mode of a 2048-tone equal temperament with octave 2/1 degrees: 117 354 493 610 847 964 1201 1318 1555 1694 1811 2048 Least number of segments generator : 1025 of 600.586 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1927 of 1129.102 cents and inv. generated superset size: 264 = 252 more = 2200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABABABCAB Step pattern size order : SLMSLSLSLMSL Scale is a Constant Structure, by a margin of 11.13281 cents Scale diversity : 1.282400 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.355469 Rothenberg efficiency : 0.508565 redundancy: 0.491435 Efficiency x scale size : 6.102778 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 11.13281 cents Most common intervals : 496.28906 cents & inv., amount: 10 Most common triad is 0.0 496.289 703.711 cents, amount: 8 Number of recognisable fifths : 11, average 704.8828 cents Number of appreciable fifths : 10, average 703.7109 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions with margin 70.3125 cents: 1 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 23.6346 c. M:-42.5781 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 1 0 2 1 2 1 1 1 1 2 N D3 SD: 24.7697 c. M: 37.4219 c. 16: 1 2 1 1 2 1 1 1 2 1 1 2 P D3 SD: 19.8341 c. M:-35.1563 c. 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 3.8651 c. M: 6.5142 c. 53: 3 6 4 3 6 3 6 3 6 4 3 6 SP SD: 3.3363 c. M: 5.4724 c. 70: 4 8 5 4 8 4 8 4 8 5 4 8 SP SD: 1.6199 c. M:-2.5781 c. 87: 5 10 6 5 10 5 10 5 10 6 5 10 SP SD: 0.6383 c. M:-1.1988 c. 104: 6 12 7 6 12 6 12 6 12 7 6 12 SP SD: 0.4240 c. M:-0.8113 c. 191: 11 22 13 11 22 11 22 11 22 13 11 22 SP SD: 0.3967 c. M:-0.6933 c. 295: 17 34 20 17 34 17 34 17 34 20 17 34 SP SD: 0.3757 c. M:-0.6157 c. 353: 20 41 24 20 41 20 41 20 41 24 20 41 SP SD: 0.3508 c. M: 0.5942 c. 440: 25 51 30 25 51 25 51 25 51 30 25 51 SP SD: 0.2338 c. M: 0.4474 c. 457: 26 53 31 26 53 26 53 26 53 31 26 53 SP SD: 0.1894 c. M: 0.3103 c. 544: 31 63 37 31 63 31 63 31 63 37 31 63 SP SD: 0.1081 c. M: 0.2068 c. 561: 32 65 38 32 65 32 65 32 65 38 32 65 SP SD: 0.1060 c. M: 0.2026 c. 631: 36 73 43 36 73 36 73 36 73 43 36 73 SP SD: 0.1185 c. M:-0.1978 c. 648: 37 75 44 37 75 37 75 37 75 44 37 75 SP SD: 0.0227 c. M: 0.0434 c. 1400: 80 162 95 80 162 80 162 80 162 95 80 162 SP SD: 0.0105 c. M:-0.0201 c. 2048: 117 237 139 117 237 117 237 117 237 139 117 237 SP SD: 0.0000 c. M:-0.0000 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: 0.8780 cents 3 x x x x 4 x x x 5 x x 6 S SD: 8.9439 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.3608 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.6114 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.1132 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 12.6020 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 10.4533 cents 9 x 10 x 11:12 x x 14:15:16:17:18 S SD: 6.9659 cents 10 x 11:12 x 13:14:15:16:17:18 x 20 S SD: 9.2960 cents 11 x 12:13:14 x 15 x 17:19 x 20:22 SD: 12.4201 cents 12 x x 14:15:16:17:18:19:20:21:22:24 S SD: 6.8868 cents 13:14:15 x 16:17:18 x 20:22:23:24:26 S SD: 8.3313 cents 14:15:16 x 17:19 x 21:22:24:25:26:28 SD: 7.4067 cents 15:16:17:18 x 20:21 x 23:25:27:28:30 SD: 7.5782 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.5352 cents 18:19:20:21:22:24:25:27:28:30:32:33:36 SD: 4.3941 cents 21:22:24:25:26:28:29:32:33:36:37:39:42 SD: 4.2188 cents 22:23:25:26:27:29:30:33:34:37:39:41:44 SD: 3.8427 cents 23:24:26:27:28:31:32:35:36:39:41:42:46 SD: 3.6316 cents 26:27:29:31:32:35:36:39:41:44:46:48:52 SD: 2.9177 cents 32:33:36:38:39:43:44:48:50:54:57:59:64 SD: 2.6886 cents 39:41:44:46:48:52:54:59:61:66:69:72:78 SD: 1.9407 cents 48:50:54:57:59:64:67:72:75:81:85:89:96 SD: 1.5668 cents 54:56:61:64:66:72:75:81:84:91:96:100:108 SD: 1.5588 cents 66:69:74:78:81:88:91:99:103:112:117:122:132 SD: 1.3946 cents 70:73:79:83:86:93:97:105:109:118:124:129:140 SD: 1.1108 cents 78:81:88:92:96:104:108:117:122:132:138:144:156 SD: 0.6584 cents 126:131:142:149:155:168:175:189:197:213:224:233:252 SD: 0.6208 cents 127:132:143:150:156:169:176:191:198:215:225:234:254 SD: 0.5746 cents 148:154:167:175:182:197:205:222:231:251:263:273:296 SD: 0.4762 cents 171:178:193:202:210:228:237:257:267:289:303:316:342 SD: 0.4617 cents 195:203:220:230:240:260:270:293:305:330:346:360:390 SD: 0.4428 cents 196:204:221:232:241:261:272:294:306:332:348:362:392 SD: 0.4164 cents 199:207:224:235:245:265:276:299:311:337:353:367:398 SD: 0.3860 cents 205:213:231:242:252:273:284:308:320:347:364:378:410 SD: 0.3417 cents 221:230:249:261:272:294:306:332:345:374:392:408:442 SD: 0.3275 cents 226:235:255:267:278:301:313:339:353:383:401:417:452 SD: 0.3092 cents 244:254:275:288:300:325:338:366:381:413:433:450:488 SD: 0.2771 cents 253:263:285:299:311:337:351:380:395:428:449:467:506 SD: 0.2641 cents 274:285:309:324:337:365:380:411:428:464:486:506:548 SD: 0.2581 cents 292:304:329:345:359:389:405:438:456:494:518:539:584 SD: 0.2467 cents 293:305:330:346:360:390:406:440:458:496:520:541:586 SD: 0.2418 cents 319:332:360:377:392:425:442:479:498:540:566:589:638 SD: 0.2113 cents 345:359:389:408:424:460:478:518:539:584:612:637:690 SD: 0.2088 cents 370:385:417:437:455:493:513:556:578:626:656:683:740 SD: 0.2049 cents 371:386:418:438:456:494:514:557:580:628:658:685:742 SD: 0.2017 cents 391:407:441:462:481:521:542:587:611:662:694:722:782 SD: 0.1925 cents 423:440:477:500:520:563:586:635:661:716:750:781:846 SD: 0.1820 cents 440:458:496:520:541:586:610:661:687:745:781:812:880 SD: 0.1701 cents 446:464:503:527:548:594:618:670:697:755:791:823:892 SD: 0.1506 cents 479:498:540:566:589:638:664:719:748:811:850:884:958 SD: 0.1484 cents 518:539:584:612:637:690:718:778:809:877:919:956:1036 SD: 0.0949 cents