Scala analysis: O3-zalzalian12_D
Sampling of Zalzalian maqam/dastgah modes, slendro/pelog modes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 138.281 cents 138.281250 2: 207.422 cents 207.421870 3: 264.844 cents 264.843750 4: 345.703 cents 345.703120 5: 472.266 cents 472.265630 6: 680.859 cents 680.859370 7: 704.297 cents 704.296870 8: 842.578 cents 842.578130 9: 969.141 cents 969.140630 10: 1050.000 cents 1050.000000 11: 1176.562 cents 1176.562490 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23.4375 cents 23.4375 1: 138.2813 cents 138.2813 2: 69.1406 cents 69.1406 3: 57.4219 cents 57.4219 4: 80.8594 cents 80.8594 5: 126.5625 cents 126.5625 6: 208.5937 cents 208.5937 7: 23.4375 cents 23.4375 8: 138.2813 cents 138.2813 9: 126.5625 cents 126.5625 10: 80.8594 cents 80.8594 11: 126.5625 cents 126.5625 12: 23.4375 cents 23.4375
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 23.43750 cents 1: 1 57.42188 cents 1: 1 69.14062 cents 1: 2 80.85937 cents 1: 3 126.56251 cents 1: 2 138.28125 cents 1: 1 208.59374 cents 2: 1 126.56250 cents 2: 1 138.28125 cents 2: 1 150.00000 cents 2: 2 161.71876 cents 2: 4 207.42187 cents 2: 1 232.03124 cents 2: 1 264.84376 cents 2: 1 335.15625 cents 3: 1 207.42187 cents 3: 2 230.85937 cents 3: 2 264.84375 cents 3: 2 288.28126 cents 3: 1 333.98436 cents 3: 1 345.70313 cents 3: 1 358.59375 cents 3: 1 370.31250 cents 3: 1 416.01562 cents 4: 1 288.28126 cents 4: 1 333.98438 cents 4: 1 345.70312 cents 4: 2 357.42187 cents 4: 2 369.14063 cents 4: 1 439.45312 cents 4: 1 472.26562 cents 4: 1 473.43750 cents 4: 2 496.87501 cents 5: 1 369.14063 cents 5: 1 414.84375 cents 5: 1 438.28124 cents 5: 1 472.26563 cents 5: 3 495.70312 cents 5: 1 496.87500 cents 5: 1 542.57812 cents 5: 2 577.73438 cents 5: 1 623.43751 cents 6: 3 495.70312 cents 6: 1 519.14063 cents 6: 1 564.84374 cents 6: 1 566.01562 cents 6: 1 633.98438 cents 6: 1 635.15626 cents 6: 1 680.85937 cents 6: 3 704.29688 cents 7: 1 576.56249 cents 7: 2 622.26562 cents 7: 1 657.42188 cents 7: 1 703.12500 cents 7: 3 704.29687 cents 7: 1 727.73437 cents 7: 1 761.71876 cents 7: 1 785.15625 cents 7: 1 830.85937 cents 8: 2 703.12499 cents 8: 1 726.56250 cents 8: 1 727.73438 cents 8: 1 760.54688 cents 8: 2 830.85938 cents 8: 2 842.57813 cents 8: 1 854.29688 cents 8: 1 866.01562 cents 8: 1 911.71874 cents 9: 1 783.98438 cents 9: 1 829.68750 cents 9: 1 841.40625 cents 9: 1 854.29687 cents 9: 1 866.01564 cents 9: 2 911.71875 cents 9: 2 935.15625 cents 9: 2 969.14063 cents 9: 1 992.57813 cents 10: 1 864.84375 cents 10: 1 935.15624 cents 10: 1 967.96876 cents 10: 4 992.57813 cents 10: 2 1038.28124 cents 10: 1 1050.00000 cents 10: 1 1061.71875 cents 10: 1 1073.43750 cents 11: 1 991.40626 cents 11: 2 1061.71875 cents 11: 3 1073.43749 cents 11: 2 1119.14063 cents 11: 1 1130.85938 cents 11: 1 1142.57812 cents 11: 2 1176.56249 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 8.36364 = 92/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 138.3 207.4 264.8 345.7 472.3 680.9 704.3 842.6 969.1 1050.0 1176.6 1200.0 138.3 : 69.1 126.6 207.4 334.0 542.6 566.0 704.3 830.9 911.7 1038.3 1061.7 1200.0 207.4 : 57.4 138.3 264.8 473.4 496.9 635.2 761.7 842.6 969.1 992.6 1130.9 1200.0 264.8 : 80.9 207.4 416.0 439.5 577.7 704.3 785.2 911.7 935.2 1073.4 1142.6 1200.0 345.7 : 126.6 335.2 358.6 496.9 623.4 704.3 830.9 854.3 992.6 1061.7 1119.1 1200.0 472.3 : 208.6 232.0 370.3 496.9 577.7 704.3 727.7 866.0 935.2 992.6 1073.4 1200.0 680.9 : 23.4 161.7 288.3 369.1 495.7 519.1 657.4 726.6 784.0 864.8 991.4 1200.0 704.3 : 138.3 264.8 345.7 472.3 495.7 634.0 703.1 760.5 841.4 968.0 1176.6 1200.0 842.6 : 126.6 207.4 334.0 357.4 495.7 564.8 622.3 703.1 829.7 1038.3 1061.7 1200.0 969.1 : 80.9 207.4 230.9 369.1 438.3 495.7 576.6 703.1 911.7 935.2 1073.4 1200.0 1050.0: 126.6 150.0 288.3 357.4 414.8 495.7 622.3 830.9 854.3 992.6 1119.1 1200.0 1176.6: 23.4 161.7 230.9 288.3 369.1 495.7 704.3 727.7 866.0 992.6 1073.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 23.4375 .. 208.5937 cents 185.15624 cents 23.43750 cents 2: 126.5625 .. 335.1563 cents 208.59375 cents -82.03124 cents 3: 207.4219 .. 416.0156 cents 208.59375 cents -127.73438 cents 4: 288.2813 .. 496.8750 cents 208.59375 cents -127.73436 cents 5: 369.1406 .. 623.4375 cents 254.29688 cents -127.73438 cents 6: 495.7031 .. 704.2969 cents 208.59376 cents -127.73439 cents 7: 576.5625 .. 830.8594 cents 254.29688 cents -127.73439 cents 8: 703.1250 .. 911.7187 cents 208.59375 cents -127.73438 cents 9: 783.9844 .. 992.5781 cents 208.59375 cents -127.73436 cents 10: 864.8438 .. 1073.4375 cents 208.59375 cents -127.73438 cents 11: 991.4063 .. 1176.5625 cents 185.15623 cents -82.03124 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 23.43750 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 208.59374 cents Average / Smallest step : 4.266667 Largest / Average step : 2.085937 Largest / Smallest step : 8.900000 Median interval of one step : 103.71094 cents, amount: 0 Most common interval of one step : 126.56251 cents, amount: 3 Least squares average step : 103.71094 cents, oct.: 1244.53125 cents Scale is not proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 118 177 226 295 403 581 601 719 827 896 1004 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 783 of 917.578 cents and inv. generated superset size: 364 = 352 more = 3033.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGAEDEG Step pattern size order : FCBDEGAFEDEA Scale is not a Constant Structure Scale diversity : 1.487912 Lumma stability : 0.039063 Lumma impropriety factor : 0.789062 Rothenberg efficiency : 0.260997 redundancy: 0.739003 Efficiency x scale size : 3.131962 Number of different interval sizes : 70 = 6.36364 / class Number of one step interval sizes : 7 Highest interval variety : 9 Mean interval variety : 8.36364 = 92/11 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 1.17187 cents Most common intervals : 495.70312 cents & inv., amount: 6 Number of recognisable fifths : 9, average 703.9063 cents Formal octave complements present : 1 = 8.3333% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 0 1 1 2 1 1 1 1 1 1 N T3 SD: 53.6565 c. M: 80.8594 c. 13: 1 1 1 0 2 2 0 2 1 1 1 1 N SD: 41.2443 c. M: 68.8702 c. 14: 2 0 1 1 2 2 0 2 1 1 2 0 N SD: 23.2875 c. M:-42.0201 c. 16: 2 1 1 1 1 3 0 2 2 1 2 0 N SD: 20.0450 c. M:-35.1562 c. 17: 2 1 1 1 2 3 0 2 2 1 2 0 N SD: 14.4460 c. M:-25.0230 c. 21: 2 2 1 1 2 4 0 3 2 1 3 0 N SD: 16.5585 c. M: 23.9955 c. 23: 3 1 1 2 2 4 1 2 3 1 3 0 N SD: 14.6402 c. M:-26.1379 c. 24: 3 1 1 2 2 5 0 3 2 2 3 0 N SD: 13.7918 c. M:-23.4375 c. 26: 3 1 2 1 3 5 0 3 3 2 2 1 N SD: 14.0135 c. M: 22.8065 c. 27: 3 2 1 2 3 4 1 3 3 2 3 0 N SD: 12.1563 c. M:-23.4375 c. 28: 3 2 1 2 3 5 0 4 3 2 2 1 N SD: 12.5880 c. M:-21.4286 c. 29: 3 2 1 2 3 5 1 3 3 2 3 1 N SD: 14.2207 c. M: 18.7904 c. 31: 4 1 2 2 3 6 0 4 3 2 3 1 N SD: 10.0892 c. M:-16.5575 c. 34: 4 2 1 3 3 6 1 4 3 3 3 1 N SD: 9.9397 c. M: 17.7849 c. 35: 4 2 2 2 4 6 1 4 3 3 3 1 N SD: 9.1748 c. M:-15.7031 c. 36: 4 2 2 2 4 6 1 4 4 2 4 1 N SD: 8.9183 c. M: 16.6667 c. 37: 4 2 2 3 4 6 1 4 4 2 4 1 N SD: 8.7561 c. M:-14.2209 c. 40: 5 2 2 3 4 7 1 4 4 3 4 1 N SD: 8.6515 c. M:-15.7031 c. 41: 5 2 2 3 4 7 1 5 4 3 4 1 N SD: 4.8211 c. M:-8.0602 c. 46: 5 3 2 3 5 8 1 5 5 3 5 1 N SD: 4.6721 c. M: 7.8465 c. 51: 6 3 2 4 5 9 1 6 5 4 5 1 N SD: 4.4818 c. M:-8.8235 c. 53: 6 3 3 3 6 9 1 6 6 3 6 1 N SD: 4.4515 c. M: 8.4906 c. 58: 7 3 3 4 6 10 1 7 6 4 6 1 N SD: 3.9908 c. M:-6.5463 c. 63: 7 4 3 4 7 11 1 7 7 4 7 1 N SD: 3.2887 c. M: 4.9479 c. 87: 10 5 4 6 9 15 2 10 9 6 9 2 N SD: 2.5852 c. M: 4.9973 c. 94: 11 5 5 6 10 16 2 11 10 6 10 2 N SD: 2.3236 c. M: 4.2636 c. 104: 12 6 5 7 11 18 2 12 11 7 11 2 N SD: 0.3744 c. M:-0.8113 c. 511: 59 29 25 34 54 89 10 59 54 34 54 10 N SD: 0.4227 c. M: 0.7682 c. 513: 59 30 24 35 54 89 10 59 54 35 54 10 N SD: 0.4211 c. M:-0.7653 c. 521: 60 30 25 35 55 91 10 60 55 35 55 10 N SD: 0.3934 c. M:-0.9065 c. 562: 65 32 27 38 59 98 11 65 59 38 59 11 N SD: 0.3856 c. M:-0.8382 c. 567: 65 33 27 38 60 99 11 65 60 38 60 11 N SD: 0.4098 c. M: 0.7296 c. 607: 70 35 29 41 64 105 12 70 64 41 64 12 N SD: 0.3588 c. M: 0.7935 c. 608: 70 35 29 41 64 106 12 70 64 41 64 12 N SD: 0.2562 c. M: 0.5551 c. 712: 82 41 34 48 75 124 14 82 75 48 75 14 N SD: 0.1641 c. M: 0.3555 c. 816: 94 47 39 55 86 142 16 94 86 55 86 16 N SD: 0.0954 c. M: 0.2068 c. 920: 106 53 44 62 97 160 18 106 97 62 97 18 N SD: 0.0423 c. M: 0.0917 c. 1024: 118 59 49 69 108 178 20 118 108 69 108 20 N 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: 1.1709 cents 3 x x x x 4 x x 5 x x x 6 S SD: 16.3646 cents 4 x x x 5 x x 6 x 7 x x 8 S SD: 10.1698 cents 5 x x x 6 x 7 x 8 x 9 x 10 S SD: 22.3254 cents 6 x x 7 x 8 x 9:10 x 11 x 12 S SD: 8.1992 cents 7 x 8 x x 9:10 x 11:12:13 x 14 S SD: 15.2133 cents 8 x 9 x 10:11 x 12:13:14:15 x 16 S SD: 12.1096 cents 9 x 10 x 11:12:13:14:15:16:17 x 18 S SD: 12.1731 cents 10:11 x x 12:13 x 15:16 x 18 x 20 SD: 8.8455 cents 11:12 x 13 x 14:16:17:18:19:20 x 22 S SD: 9.9793 cents 12:13 x 14:15:16 x 18:20:21:22 x 24 S SD: 7.0882 cents 13:14 x 15:16:17:19:20:21:23:24 x 26 SD: 5.9692 cents 14:15:16 x 17:18 x 21:23:25:26 x 28 SD: 7.3330 cents 15:16:17 x 18:20:22:23:24:26:28 x 30 S SD: 7.7491 cents 16:17:18:19:20:21 x 24:26:28:29 x 32 SD: 6.5334 cents 17:18:19:20:21:22:25:26:28:30:31 x 34 SD: 6.4416 cents 18 x 20:21:22:24 x 27:29:32:33 x 36 SD: 5.3468 cents 19 x 21:22:23:25:28:29:31:33:35:37:38 SD: 5.1106 cents 20:22 x 23:24:26 x 30:33:35:37:39:40 SD: 6.0903 cents 21:23:24 x 26:28:31:32:34:37:39:41:42 SD: 5.6385 cents 22:24:25:26:27:29 x 33:36:39:40:43:44 SD: 4.2026 cents 23:25:26:27:28:30:34:35:37:40:42:45:46 SD: 3.4360 cents 24:26:27:28:29:32 x 36:39:42:44:47:48 SD: 3.1327 cents 26:28:29:30:32:34 x 39:42:46:48:51:52 SD: 3.7686 cents 29:31:33:34:35:38:43:44:47:51:53:57:58 SD: 3.5544 cents 31:34:35:36:38:41:46:47:50:54:57:61:62 SD: 3.0024 cents 32:35:36:37:39:42:47:48:52:56:59:63:64 SD: 2.4089 cents 36:39:41:42:44:47:53:54:59:63:66:71:72 SD: 2.2510 cents 37:40:42:43:45:49:55:56:60:65:68:73:74 SD: 2.2199 cents 46:50:52:54:56:60:68:69:75:81:84:91:92 SD: 2.0775 cents 47:51:53:55:57:62:70:71:76:82:86:93:94 SD: 2.0610 cents 48:52:54:56:59:63:71:72:78:84:88:95:96 SD: 1.1767 cents 72:78:81:84:88:95:107:108:117:126:132:142:144 SD: 0.8885 cents 85:92:96:99:104:112:126:128:138:149:156:168:170 SD: 0.8487 cents 96:104:108:112:117:126:142:144:156:168:176:189:192 SD: 0.6649 cents 108:117:122:126:132:142:160:162:176:189:198:213:216 SD: 0.5105 cents 156:169:176:182:190:205:231:234:254:273:286:308:312 SD: 0.5013 cents 157:170:177:183:192:206:233:236:255:275:288:310:314 SD: 0.4729 cents 180:195:203:210:220:236:267:270:293:315:330:355:360 SD: 0.4500 cents 181:196:204:211:221:238:268:272:294:317:332:357:362 SD: 0.3286 cents 217:235:245:253:265:285:322:326:353:380:398:428:434 SD: 0.3249 cents 249:270:281:290:304:327:369:374:405:436:457:491:498 SD: 0.2856 cents 253:274:285:295:309:332:375:380:412:443:464:499:506 SD: 0.2625 cents 289:313:326:337:353:380:428:434:470:506:530:570:578 SD: 0.2382 cents 290:314:327:338:354:381:430:436:472:508:532:572:580 SD: 0.2329 cents 313:339:353:365:382:411:464:470:509:548:574:618:626 SD: 0.2083 cents 338:366:381:394:413:444:501:508:550:592:620:667:676 SD: 0.1872 cents 376:407:424:438:459:494:557:565:612:658:690:742:752 SD: 0.1834 cents 386:418:435:450:471:507:572:580:628:676:708:762:772 SD: 0.1766 cents 434:470:489:506:530:570:643:652:706:760:796:856:868 SD: 0.1484 cents 494:535:557:576:603:649:732:742:804:865:906:975:988 SD: 0.1372 cents 520:563:586:606:635:683:771:781:846:910:954:1026:1040 SD: 0.1290 cents 552:598:622:643:674:725:818:829:898:966:1012:1089:1104 SD: 0.1113 cents