Scala analysis: rbuzurg-buzurg_hijaz_Cup
Qutb al-Din al-Shirazi's Buzurg plus upper Hijaz (JI 12:11-7:6-22:21)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 133.351 cents 133.350660 2: 361.885 cents 361.884960 3: 495.236 cents 495.235620 4: 628.586 cents 628.586280 5: 704.764 cents 704.764380 6: 857.121 cents 857.120580 7: 1123.822 cents 1123.821900 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 76.1781 cents 76.1781 1: 133.3507 cents 133.3507 2: 228.5343 cents 228.5343 3: 133.3507 cents 133.3507 4: 133.3507 cents 133.3507 5: 76.1781 cents 76.1781 6: 152.3562 cents 152.3562 7: 266.7013 cents 266.7013 8: 76.1781 cents 76.1781
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 76.17810 cents 1: 3 133.35066 cents 1: 1 152.35620 cents 1: 1 228.53430 cents 1: 1 266.70132 cents 2: 2 209.52876 cents 2: 1 228.53430 cents 2: 1 266.70132 cents 2: 1 342.87942 cents 2: 2 361.88496 cents 2: 1 419.05752 cents 3: 1 342.87942 cents 3: 1 361.88496 cents 3: 1 438.06306 cents 3: 1 476.23008 cents 3: 4 495.23562 cents 4: 1 495.23562 cents 4: 3 571.41372 cents 4: 3 628.58628 cents 4: 1 704.76438 cents 5: 4 704.76438 cents 5: 1 723.76992 cents 5: 1 761.93694 cents 5: 1 838.11504 cents 5: 1 857.12058 cents 6: 1 780.94248 cents 6: 2 838.11504 cents 6: 1 857.12058 cents 6: 1 933.29868 cents 6: 1 971.46570 cents 6: 2 990.47124 cents 7: 1 933.29868 cents 7: 1 971.46570 cents 7: 1 1047.64380 cents 7: 3 1066.64934 cents 7: 2 1123.82190 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.14286 = 36/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 133.4 361.9 495.2 628.6 704.8 857.1 1123.8 1200.0 133.4 : 228.5 361.9 495.2 571.4 723.8 990.5 1066.6 1200.0 361.9 : 133.4 266.7 342.9 495.2 761.9 838.1 971.5 1200.0 495.2 : 133.4 209.5 361.9 628.6 704.8 838.1 1066.6 1200.0 628.6 : 76.2 228.5 495.2 571.4 704.8 933.3 1066.6 1200.0 704.8 : 152.4 419.1 495.2 628.6 857.1 990.5 1123.8 1200.0 857.1 : 266.7 342.9 476.2 704.8 838.1 971.5 1047.6 1200.0 1123.8: 76.2 209.5 438.1 571.4 704.8 780.9 933.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.1781 .. 266.7013 cents 190.52322 cents 76.17810 cents 2: 209.5288 .. 419.0575 cents 209.52876 cents -57.17256 cents 3: 342.8794 .. 495.2356 cents 152.35620 cents -76.17810 cents 4: 495.2356 .. 704.7644 cents 209.52876 cents 1/1, 0.0000 cents 5: 704.7644 .. 857.1206 cents 152.35620 cents 1/1, 0.0000 cents 6: 780.9425 .. 990.4712 cents 209.52876 cents -76.17810 cents 7: 933.2987 .. 1123.8219 cents 190.52322 cents -57.17256 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 76.17810 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 266.70132 cents Average / Smallest step : 1.969070 Largest / Average step : 1.778009 Largest / Smallest step : 3.501024 Median interval of one step : 133.35066 cents, amount: 3 Most common interval of one step : 133.35066 cents, amount: 3 Least squares average step : 151.91407 cents, oct.: 1215.31260 cents Scale is not proper Step pattern alph. order: ABAACDEC Step pattern size order : BDBBACEA Scale is not a Constant Structure Scale diversity : 1.474261 Lumma stability : 0.126964 Lumma impropriety factor : 0.222251 Rothenberg efficiency : 0.437500 redundancy: 0.562500 Efficiency x scale size : 3.500000 Number of different interval sizes : 26 = 3.71429 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.14286 = 36/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 19.00554 cents Most common intervals : 495.23562 cents & inv., amount: 5 Most common triad is 0.0 495.236 704.764 cents, amount: 2 Number of recognisable fifths : 5, average 704.7644 cents Formal octave complements present : 3 = 37.5000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 45.1455 c. M: 73.8219 c. 9: 1 2 1 1 0 1 2 1 N SD: 39.2671 c. M: 57.1552 c. 10: 1 2 1 1 1 1 2 1 P D3 I SD: 21.4380 c. M: 43.8219 c. 12: 1 3 1 1 1 2 2 1 N T3 SD: 27.0040 c. M:-42.8794 c. Raga Bhankar, Bhatiyar, Jaikauns 14: 1 3 2 1 1 2 3 1 N I SD: 23.0901 c. M: 47.6364 c. 15: 2 3 1 2 1 2 3 1 N G SD: 20.2964 c. M:-38.1150 c. 16: 2 3 2 1 1 2 4 1 N SD: 22.5592 c. M: 32.1206 c. 17: 2 3 2 2 1 2 4 1 N SD: 6.3365 c. M: 10.0618 c. 36: 4 7 4 4 2 5 8 2 N SD: 5.8352 c. M:-9.5461 c. 42: 5 8 4 5 3 5 9 3 N SD: 7.5308 c. M:-9.5436 c. 43: 5 8 5 5 2 6 9 3 N SD: 7.3877 c. M:-13.2742 c. 44: 5 8 5 5 3 5 10 3 N SD: 5.8097 c. M: 11.6660 c. 46: 5 9 5 5 3 6 10 3 N SD: 2.3610 c. M:-3.7490 c. 63: 7 12 7 7 4 8 14 4 N SD: 0.0140 c. M:-0.0223 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 1.4047 cents 3 x x 4 x x 5 x 6 S SD: 9.1275 cents 4 x 5 x x 6:7 x 8 S SD: 28.5949 cents 5 x 6 x 7 x 8 x 10 S SD: 19.6020 cents 6 x 7:8 x 9:10:11:12 S SD: 20.6354 cents 7:8 x 9:10 x 11:13:14 SD: 24.4930 cents 8:9:10:11 x 12:13:15:16 SD: 14.4758 cents 9:10:11:12:13:14:15:17:18 SD: 10.8736 cents 12:13:15:16:17:18:20:23:24 SD: 5.6494 cents 21:23:26:28:30:32:34:40:42 SD: 5.5467 cents 22:24:27:29:32:33:36:42:44 SD: 4.1309 cents 25:27:31:33:36:38:41:48:50 SD: 3.4608 cents 30:32:37:40:43:45:49:57:60 SD: 3.3826 cents 34:37:42:45:49:51:56:65:68 SD: 2.3683 cents 36:39:44:48:52:54:59:69:72 SD: 2.2598 cents 39:42:48:52:56:59:64:75:78 SD: 1.9967 cents 48:52:59:64:69:72:79:92:96 SD: 1.2563 cents 64:69:79:85:92:96:105:122:128 SD: 1.1767 cents 73:79:90:97:105:110:120:140:146 SD: 1.0582 cents 78:84:96:104:112:117:128:149:156 SD: 0.9939 cents 100:108:123:133:144:150:164:191:200 SD: 0.8166 cents 103:111:127:137:148:155:169:197:206 SD: 0.6560 cents 112:121:138:149:161:168:184:214:224 SD: 0.6035 cents 137:148:169:182:197:206:225:262:274 SD: 0.5846 cents 139:150:171:185:200:209:228:266:278 SD: 0.5034 cents 151:163:186:201:217:227:248:289:302 SD: 0.3286 cents 275:297:339:366:395:413:451:526:550 SD: 0.2845 cents 301:325:371:401:433:452:494:576:602 SD: 0.2579 cents 323:349:398:430:464:485:530:618:646 SD: 0.2565 cents 326:352:402:434:469:490:535:624:652 SD: 0.2180 cents 336:363:414:447:483:505:551:643:672 SD: 0.2071 cents 374:404:461:498:538:562:614:716:748 SD: 0.2053 cents 384:415:473:511:552:577:630:735:768 SD: 0.2019 cents 386:417:476:514:555:580:633:739:772 SD: 0.1910 cents 434:469:535:578:624:652:712:831:868 SD: 0.1868 cents 438:473:540:583:630:658:719:838:876 SD: 0.1857 cents 464:501:572:618:667:697:761:888:928 SD: 0.1714 cents 486:525:599:647:699:730:797:930:972 SD: 0.1454 cents 498:538:614:663:716:748:817:953:996 SD: 0.1184 cents 537:580:662:715:772:807:881:1028:1074 SD: 0.1026 cents