Scala analysis: gizmo14
Parapyth set, three ~4:6:7:9:11:13 hexads on 1/1, 9/8, 3/2 (MET-24 version)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.422 cents 57.421870 2: 207.422 cents 207.421870 3: 346.289 cents 346.289060 4: 414.844 cents 414.843750 5: 472.266 cents 472.265620 6: 553.711 cents 553.710940 7: 703.711 cents 703.710940 8: 761.133 cents 761.132810 9: 842.578 cents 842.578120 10: 911.133 cents 911.132810 11: 968.555 cents 968.554690 12: 1050.000 cents 1050.000000 13: 1175.977 cents 1175.976560 14: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 24.0234 cents 24.0234 1: 57.4219 cents 57.4219 2: 150.0000 cents 150.0000 3: 138.8672 cents 138.8672 4: 68.5547 cents 68.5547 5: 57.4219 cents 57.4219 6: 81.4453 cents 81.4453 7: 150.0000 cents 150.0000 8: 57.4219 cents 57.4219 9: 81.4453 cents 81.4453 10: 68.5547 cents 68.5547 11: 57.4219 cents 57.4219 12: 81.4453 cents 81.4453 13: 125.9766 cents 125.9766 14: 24.0234 cents 24.0234
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24.02344 cents 1: 4 57.42187 cents 1: 2 68.55469 cents 1: 3 81.44532 cents 1: 1 125.97656 cents 1: 1 138.86719 cents 1: 2 150.00000 cents 2: 1 81.44531 cents 2: 2 125.97656 cents 2: 3 138.86719 cents 2: 2 150.00000 cents 2: 4 207.42187 cents 2: 1 231.44532 cents 2: 1 288.86719 cents 3: 5 207.42188 cents 3: 2 231.44531 cents 3: 2 264.84375 cents 3: 3 288.86719 cents 3: 1 346.28906 cents 3: 1 357.42188 cents 4: 1 264.84375 cents 4: 3 288.86719 cents 4: 1 333.39844 cents 4: 2 346.28907 cents 4: 3 357.42188 cents 4: 2 370.31250 cents 4: 2 414.84375 cents 5: 2 346.28906 cents 5: 1 357.42188 cents 5: 3 414.84375 cents 5: 1 427.73437 cents 5: 3 438.86719 cents 5: 1 472.26562 cents 5: 3 496.28907 cents 6: 1 414.84375 cents 6: 1 438.86719 cents 6: 1 472.26562 cents 6: 6 496.28906 cents 6: 2 553.71094 cents 6: 1 564.84375 cents 6: 1 577.73437 cents 6: 1 646.28907 cents 7: 2 496.28906 cents 7: 1 553.71094 cents 7: 2 564.84375 cents 7: 2 577.73438 cents 7: 2 622.26562 cents 7: 2 635.15625 cents 7: 1 646.28906 cents 7: 2 703.71094 cents 8: 1 553.71093 cents 8: 1 622.26563 cents 8: 1 635.15625 cents 8: 2 646.28906 cents 8: 6 703.71094 cents 8: 1 727.73438 cents 8: 1 761.13281 cents 8: 1 785.15625 cents 9: 3 703.71094 cents 9: 1 727.73438 cents 9: 3 761.13282 cents 9: 1 772.26563 cents 9: 3 785.15625 cents 9: 1 842.57812 cents 9: 2 853.71094 cents 10: 2 785.15625 cents 10: 2 829.68750 cents 10: 3 842.57813 cents 10: 2 853.71093 cents 10: 1 866.60156 cents 10: 3 911.13281 cents 10: 1 935.15625 cents 11: 1 842.57812 cents 11: 1 853.71094 cents 11: 3 911.13281 cents 11: 2 935.15625 cents 11: 2 968.55469 cents 11: 5 992.57813 cents 12: 1 911.13281 cents 12: 1 968.55468 cents 12: 4 992.57813 cents 12: 2 1050.00000 cents 12: 3 1061.13281 cents 12: 2 1074.02344 cents 12: 1 1118.55469 cents 13: 2 1050.00000 cents 13: 1 1061.13281 cents 13: 1 1074.02344 cents 13: 3 1118.55468 cents 13: 2 1131.44531 cents 13: 4 1142.57813 cents 13: 1 1175.97656 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.07692 = 92/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 57.4 207.4 346.3 414.8 472.3 553.7 703.7 761.1 842.6 911.1 968.6 1050.0 1176.0 1200.0 57.4 : 150.0 288.9 357.4 414.8 496.3 646.3 703.7 785.2 853.7 911.1 992.6 1118.6 1142.6 1200.0 207.4 : 138.9 207.4 264.8 346.3 496.3 553.7 635.2 703.7 761.1 842.6 968.6 992.6 1050.0 1200.0 346.3 : 68.6 126.0 207.4 357.4 414.8 496.3 564.8 622.3 703.7 829.7 853.7 911.1 1061.1 1200.0 414.8 : 57.4 138.9 288.9 346.3 427.7 496.3 553.7 635.2 761.1 785.2 842.6 992.6 1131.4 1200.0 472.3 : 81.4 231.4 288.9 370.3 438.9 496.3 577.7 703.7 727.7 785.2 935.2 1074.0 1142.6 1200.0 553.7 : 150.0 207.4 288.9 357.4 414.8 496.3 622.3 646.3 703.7 853.7 992.6 1061.1 1118.6 1200.0 703.7 : 57.4 138.9 207.4 264.8 346.3 472.3 496.3 553.7 703.7 842.6 911.1 968.6 1050.0 1200.0 761.1 : 81.4 150.0 207.4 288.9 414.8 438.9 496.3 646.3 785.2 853.7 911.1 992.6 1142.6 1200.0 842.6 : 68.6 126.0 207.4 333.4 357.4 414.8 564.8 703.7 772.3 829.7 911.1 1061.1 1118.6 1200.0 911.1 : 57.4 138.9 264.8 288.9 346.3 496.3 635.2 703.7 761.1 842.6 992.6 1050.0 1131.4 1200.0 968.6 : 81.4 207.4 231.4 288.9 438.9 577.7 646.3 703.7 785.2 935.2 992.6 1074.0 1142.6 1200.0 1050.0: 126.0 150.0 207.4 357.4 496.3 564.8 622.3 703.7 853.7 911.1 992.6 1061.1 1118.6 1200.0 1176.0: 24.0 81.4 231.4 370.3 438.9 496.3 577.7 727.7 785.2 866.6 935.2 992.6 1074.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.0234 .. 150.0000 cents 125.97656 cents 24.02344 cents 2: 81.4453 .. 288.8672 cents 207.42188 cents -68.55469 cents 3: 207.4219 .. 357.4219 cents 150.00000 cents -81.44531 cents 4: 264.8438 .. 414.8438 cents 150.00000 cents -92.57813 cents 5: 346.2891 .. 496.2891 cents 150.00001 cents -68.55469 cents 6: 414.8438 .. 646.2891 cents 231.44532 cents -81.44532 cents 7: 496.2891 .. 703.7109 cents 207.42188 cents -150.00001 cents 8: 553.7109 .. 785.1563 cents 231.44532 cents -150.00001 cents 9: 703.7109 .. 853.7109 cents 150.00000 cents -81.44531 cents 10: 785.1562 .. 935.1563 cents 150.00000 cents -68.55469 cents 11: 842.5781 .. 992.5781 cents 150.00001 cents -92.57813 cents 12: 911.1328 .. 1118.5547 cents 207.42188 cents -81.44532 cents 13: 1050.0000 .. 1175.9766 cents 125.97656 cents -68.55469 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 24.02344 cents, class 1 Average step (divided formal octave): 85.7143 cents Largest one step interval : 150.00000 cents Average / Smallest step : 3.567944 Largest / Average step : 1.750000 Largest / Smallest step : 6.243902 Median interval of one step : 75.00001 cents, amount: 0 Most common interval of one step : 57.42187 cents, amount: 4 Least squares average step : 90.54726 cents, oct.: 1267.66164 cents Scale is not proper Scale is a mode of a 2048-tone equal temperament with octave 2/1 degrees: 98 354 591 708 806 945 1201 1299 1438 1555 1653 1792 2007 2048 Least number of segments generator : 1025 of 600.586 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1201 of 703.711 cents and inv. generated superset size: 263 = 249 more = 1878.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDAEBAEDAEFG Step pattern size order : BGFCBDGBDCBDEA Scale is not a Constant Structure Scale diversity : 1.342894 Lumma stability : 0.040039 Lumma impropriety factor : 0.768555 Number of different interval sizes : 46 = 3.53846 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 7.07692 = 92/13 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 11.13281 cents Most common intervals : 496.28907 cents & inv., amount: 11 Most common triad is 0.0 496.289 703.711 cents, amount: 8 Number of recognisable fifths : 11, average 703.7109 cents Formal octave complements present : 1 = 7.1429% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
14: 0 2 2 0 1 1 2 0 1 1 1 1 1 1 N SD: 47.9319 c. M: 75.4185 c. 15: 1 2 1 1 1 1 2 1 1 0 1 1 2 0 N SD: 23.1113 c. M:-38.8672 c. 16: 1 2 2 1 0 1 2 1 1 1 1 1 2 0 N SD: 20.6988 c. M:-35.1562 c. 17: 1 2 2 1 1 1 2 1 1 1 1 1 2 0 N SD: 12.6916 c. M:-24.0234 c. 24: 1 3 3 1 1 2 3 1 2 1 1 2 2 1 N SD: 12.5060 c. M: 25.9766 c. 29: 1 4 3 2 1 2 4 1 2 2 1 2 3 1 N SD: 12.9538 c. M: 17.3559 c. 30: 1 4 4 1 2 2 4 1 2 2 1 2 3 1 N SD: 10.8451 c. M: 17.4219 c. 33: 2 4 4 1 2 2 4 2 2 2 2 2 3 1 N SD: 10.3561 c. M:-17.3473 c. 37: 2 4 5 2 2 2 5 1 3 2 2 2 4 1 N SD: 9.0937 c. M: 15.1869 c. 38: 2 5 4 2 2 3 4 2 3 2 2 2 4 1 N SD: 8.0094 c. M:-14.7101 c. 41: 2 5 5 2 2 3 5 2 3 2 2 3 4 1 N SD: 3.6080 c. M:-6.2024 c. 58: 3 7 7 3 3 4 7 3 4 3 3 4 6 1 N SD: 3.7292 c. M:-5.6977 c. 63: 3 8 7 4 3 4 8 3 4 4 3 4 7 1 N SD: 2.9465 c. M:-4.9758 c. 87: 4 11 10 5 4 6 11 4 6 5 4 6 9 2 N SD: 2.0132 c. M: 3.5628 c. 104: 5 13 12 6 5 7 13 5 7 6 5 7 11 2 N SD: 0.4557 c. M:-0.9465 c. 249: 12 31 29 14 12 17 31 12 17 14 12 17 26 5 N SD: 0.4058 c. M:-0.7954 c. 295: 14 37 34 17 14 20 37 14 20 17 14 20 31 6 N SD: 0.3776 c. M: 0.5442 c. 353: 17 44 41 20 17 24 44 17 24 20 17 24 37 7 N SD: 0.2986 c. M:-0.4814 c. 399: 19 50 46 23 19 27 50 19 27 23 19 27 42 8 N SD: 0.2507 c. M: 0.4729 c. 440: 21 55 51 25 21 30 55 21 30 25 21 30 46 9 N SD: 0.2513 c. M: 0.5220 c. 457: 22 57 53 26 22 31 57 22 31 26 22 31 48 9 N SD: 0.2811 c. M:-0.3911 c. 503: 24 63 58 29 24 34 63 24 34 29 24 34 53 10 N SD: 0.2187 c. M: 0.4310 c. 544: 26 68 63 31 26 37 68 26 37 31 26 37 57 11 N SD: 0.1162 c. M: 0.2413 c. 648: 31 81 75 37 31 44 81 31 44 37 31 44 68 13 N SD: 0.0244 c. M: 0.0506 c. 1400: 67 175 162 80 67 95 175 67 95 80 67 95 147 28 N SD: 0.0113 c. M:-0.0234 c. 2048: 98 256 237 117 98 139 256 98 139 117 98 139 215 41 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x 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 x x 4 S SD: 0.8780 cents 3 x x x x 4 x x x x 5 x x x 6 S SD: 12.3892 cents 4 x x x 5 x x 6 x x x 7 x x 8 S SD: 7.1463 cents 5 x x 6 x x 7 x x 8 x x 9 x 10 S SD: 12.0889 cents 6 x 7 x x 8 x 9 x x 10 x 11 x 12 S SD: 11.6894 cents 7 x 8 x 9 x 10 x 11 x 12 x 13 x 14 S SD: 11.4752 cents 8 x 9 x 10 x 11:12 x 13 x 14:15 x 16 S SD: 5.9998 cents 9 x 10:11 x 12 x x 14 x 15:16:17 x 18 S SD: 9.1743 cents 10 x 11:12 x 13:14:15 x 16:17 x 18 x 20 S SD: 8.4897 cents 11 x 12:13:14 x 15 x 17:18 x 19:20 x 22 SD: 9.7196 cents 12 x 14 x 15:16:17:18:19 x 20:21:22 x 24 S SD: 9.6683 cents 13:14:15:16 x 17:18 x 20:21:22:23:24 x 26 S SD: 8.0619 cents 14:15:16:17:18 x 19:21:22:23:24:25:26 x 28 SD: 7.6788 cents 15:16:17:18:19:20:21 x 23:24:25:26:28 x 30 SD: 7.7716 cents 16:17:18 x 20:21:22:24:25:26:27:28:29 x 32 SD: 5.0539 cents 17:18:19:21 x 22:23 x 26:28:29:30:31 x 34 SD: 6.7586 cents 18:19:20:22:23:24:25:27:28:29:30:31:33 x 36 SD: 5.2678 cents 19:20:21:23:24:25:26:29 x 31:32:33:35:37:38 SD: 5.0079 cents 22:23:25:27:28:29:30:33:34:36:37:38:40:43:44 SD: 3.3681 cents 26:27:29:32:33:34:36:39:40:42:44:45:48:51:52 SD: 2.9470 cents 29:30:33:35:37:38:40:44:45:47:49:51:53:57:58 SD: 2.5771 cents 32:33:36:39:41:42:44:48:50:52:54:56:59:63:64 SD: 1.6225 cents 54:56:61:66:69:71:74:81:84:88:91:94:99:107:108 SD: 1.4853 cents 55:57:62:67:70:72:76:83:85:89:93:96:101:108:110 SD: 1.4755 cents 56:58:63:68:71:74:77:84:87:91:95:98:103:110:112 SD: 1.3444 cents 62:64:70:76:79:81:85:93:96:101:105:108:114:122:124 SD: 1.3211 cents 63:65:71:77:80:83:87:95:98:102:107:110:116:124:126 SD: 1.2641 cents 64:66:72:78:81:84:88:96:99:104:108:112:117:126:128 SD: 1.0418 cents 80:83:90:98:102:105:110:120:124:130:135:140:147:158:160 SD: 0.9463 cents 85:88:96:104:108:112:117:128:132:138:144:149:156:168:170 SD: 0.7828 cents 96:99:108:117:122:126:132:144:149:156:162:168:176:189:192 SD: 0.7071 cents 112:116:126:137:142:147:154:168:174:182:190:196:205:221:224 SD: 0.6801 cents 117:121:132:143:149:154:161:176:182:190:198:205:215:231:234 SD: 0.6598 cents 118:122:133:144:150:155:162:177:183:192:200:206:216:233:236 SD: 0.5935 cents 140:145:158:171:178:184:193:210:217:228:237:245:257:276:280 SD: 0.4310 cents 172:178:194:210:219:226:237:258:267:280:291:301:315:339:344 SD: 0.3988 cents 181:187:204:221:230:238:249:272:281:294:306:317:332:357:362 SD: 0.3474 cents 204:211:230:249:259:268:281:306:317:332:345:357:374:402:408 SD: 0.3039 cents 236:244:266:288:300:310:325:354:366:384:399:413:433:465:472 SD: 0.2878 cents 265:274:299:324:337:348:365:398:411:431:449:464:486:523:530 SD: 0.2817 cents 284:294:320:347:361:373:391:426:441:462:481:497:521:560:568 SD: 0.2560 cents 289:299:326:353:367:380:398:434:449:470:489:506:530:570:578 SD: 0.2534 cents 297:307:335:363:377:390:409:446:461:483:503:520:545:586:594 SD: 0.2303 cents 299:309:337:365:380:393:412:449:464:486:506:523:548:590:598 SD: 0.2140 cents 321:332:362:392:408:422:442:482:498:522:543:562:589:633:642 SD: 0.1996 cents 329:340:371:402:418:432:453:494:511:535:557:576:603:649:658 SD: 0.1767 cents 361:373:407:441:459:474:497:542:560:587:611:632:662:712:722 SD: 0.1643 cents 411:425:463:502:522:540:566:617:638:669:696:719:754:811:822 SD: 0.1628 cents 440:455:496:537:559:578:606:661:683:716:745:770:807:868:880 SD: 0.1438 cents 469:485:529:573:596:616:646:704:728:763:794:821:860:925:938 SD: 0.1281 cents 536:554:604:655:681:704:738:805:832:872:907:938:983:1057:1072 SD: 0.0999 cents