Scala analysis: xen18-darreg-djami-isfahan-1
Maqam Isfahan, bakiye between seventh and eighth degrees
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 204.000 cents 204.000000 2: 384.000 cents 384.000000 3: 498.000 cents 498.000000 4: 702.000 cents 702.000000 5: 882.000 cents 882.000000 6: 996.000 cents 996.000000 7: 1176.000 cents 1176.000000 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 24.0000 cents 24.0000 1: 204.0000 cents 204.0000 2: 180.0000 cents 180.0000 3: 114.0000 cents 114.0000 4: 204.0000 cents 204.0000 5: 180.0000 cents 180.0000 6: 114.0000 cents 114.0000 7: 180.0000 cents 180.0000 8: 24.0000 cents 24.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24.00000 cents 1: 2 114.00000 cents 1: 3 180.00000 cents 1: 2 204.00000 cents 2: 1 204.00000 cents 2: 1 228.00000 cents 2: 3 294.00000 cents 2: 1 318.00000 cents 2: 2 384.00000 cents 3: 1 318.00000 cents 3: 2 408.00000 cents 3: 1 474.00000 cents 3: 4 498.00000 cents 4: 1 498.00000 cents 4: 2 522.00000 cents 4: 1 588.00000 cents 4: 1 612.00000 cents 4: 2 678.00000 cents 4: 1 702.00000 cents 5: 4 702.00000 cents 5: 1 726.00000 cents 5: 2 792.00000 cents 5: 1 882.00000 cents 6: 2 816.00000 cents 6: 1 882.00000 cents 6: 3 906.00000 cents 6: 1 972.00000 cents 6: 1 996.00000 cents 7: 2 996.00000 cents 7: 3 1020.00000 cents 7: 2 1086.00000 cents 7: 1 1176.00000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.57143 = 32/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 204.0 384.0 498.0 702.0 882.0 996.0 1176.0 1200.0 204.0 : 180.0 294.0 498.0 678.0 792.0 972.0 996.0 1200.0 384.0 : 114.0 318.0 498.0 612.0 792.0 816.0 1020.0 1200.0 498.0 : 204.0 384.0 498.0 678.0 702.0 906.0 1086.0 1200.0 702.0 : 180.0 294.0 474.0 498.0 702.0 882.0 996.0 1200.0 882.0 : 114.0 294.0 318.0 522.0 702.0 816.0 1020.0 1200.0 996.0 : 180.0 204.0 408.0 588.0 702.0 906.0 1086.0 1200.0 1176.0: 24.0 228.0 408.0 522.0 726.0 906.0 1020.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.0000 .. 204.0000 cents 180.00000 cents 24.00000 cents 2: 204.0000 .. 384.0000 cents 180.00000 cents 1/1, 0.0000 cents 3: 318.0000 .. 498.0000 cents 180.00000 cents -66.00000 cents 4: 498.0000 .. 702.0000 cents 204.00000 cents 1/1, 0.0000 cents 5: 702.0000 .. 882.0000 cents 180.00000 cents 1/1, 0.0000 cents 6: 816.0000 .. 996.0000 cents 180.00000 cents -66.00000 cents 7: 996.0000 .. 1176.0000 cents 180.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 24.00000 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 204.00000 cents Average / Smallest step : 6.250000 Largest / Average step : 1.360000 Largest / Smallest step : 8.500000 Median interval of one step : 180.00000 cents, amount: 3 Most common interval of one step : 180.00000 cents, amount: 3 Least squares average step : 164.17647 cents, oct.: 1313.41176 cents Scale is not proper Scale is a mode of a 200-tone equal temperament with octave 1200.000 cents degrees: 34 64 83 117 147 166 196 200 Least number of segments generator : 101 of 606.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 117 of 702.000 cents and inv. generated superset size: 15 = 7 more = 187.500% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABCBD Step pattern size order : DCBDCBCA Interval vector is [ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 5 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 ] Scale is not a Constant Structure Scale diversity : 1.465310 Lumma stability : 0.040000 Lumma impropriety factor : 0.110000 Rothenberg efficiency : 0.430804 redundancy: 0.569196 Efficiency x scale size : 3.446429 Number of different interval sizes : 26 = 3.71429 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.57143 = 32/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 24.00000 cents Most common intervals : 498.00000 cents & inv., amount: 5 Most common triad is 0.0 498.000 702.000 cents, amount: 3 Number of recognisable fifths : 5, average 702.0000 cents Scale contains two identical conjunct tetrachords Formal octave complements present : 5 = 62.5000% -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 90.2746 c. M: 132.0000 c. 9: 1 1 1 2 1 1 1 1 P M ME SD: 80.7916 c. M: 117.3333 c. 10: 2 1 1 2 1 1 2 0 P D3 SD: 27.7399 c. M: 42.0000 c. 12: 2 2 1 2 2 1 2 0 N T3 SD: 12.2270 c. M:-24.0000 c. 19: 3 3 2 3 3 2 3 0 N SD: 11.9056 c. M:-24.0000 c. 29: 5 4 3 5 4 3 4 1 N SD: 8.8540 c. M: 17.3793 c. 31: 5 5 3 5 5 3 4 1 N SD: 8.4285 c. M: 14.7097 c. 34: 6 5 3 6 5 3 5 1 N SD: 6.0863 c. M: 11.2941 c. 41: 7 6 4 7 6 4 6 1 N SD: 2.6840 c. M: 5.2683 c. 53: 9 8 5 9 8 5 8 1 N SD: 0.6921 c. M:-1.3585 c. 147: 25 22 14 25 22 14 22 3 N SD: 0.2495 c. M: 0.4898 c. 200: 34 30 19 34 30 19 30 4 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 0.0225 cents 3 x x 4 x 5 x x 6 S SD: 0.7864 cents 4 x 5 x 6 x 7 x 8 S SD: 6.8181 cents 5 x 6:7 x 8:9 x 10 S SD: 26.0372 cents 6:7 x 8:9:10:11 x 12 S SD: 13.7497 cents 7:8:9 x 11:12 x x 14 SD: 22.3080 cents 8:9:10:11:12:13:14 x 16 S SD: 10.4066 cents 9:10:11:12:14:15:16 x 18 S SD: 10.8509 cents 10:11:12:13:15:17:18 x 20 SD: 14.2283 cents 11:12:14:15:17:18:20 x 22 SD: 14.6660 cents 12:14:15:16:18:20:21 x 24 S SD: 9.7960 cents 13:15:16:17:20:22:23 x 26 SD: 11.4786 cents 14:16:17:19:21:23:25 x 28 SD: 9.6269 cents 15:17:19:20:23:25:27 x 30 SD: 7.4431 cents 16:18:20:21:24:27:28 x 32 S SD: 6.4748 cents 17:19:21:23:26:28:30 x 34 SD: 7.4492 cents 18:20:22:24:27:30:32 x 36 S SD: 6.0793 cents 21:24:26:28:32:35:37:41:42 SD: 5.9164 cents 22:25:27:29:33:37:39:43:44 SD: 5.8024 cents 23:26:29:31:35:38:41:45:46 SD: 5.1856 cents 24:27:30:32:36:40:43:47:48 SD: 2.3380 cents 32:36:40:43:48:53:57:63:64 SD: 2.1026 cents 40:45:50:53:60:67:71:79:80 SD: 1.9955 cents 48:54:60:64:72:80:85:95:96 SD: 1.1866 cents 72:81:90:96:108:120:128:142:144 SD: 0.4143 cents 226:254:282:301:339:376:402:446:452 SD: 0.3880 cents 230:259:287:307:345:383:409:454:460 SD: 0.3824 cents 238:268:297:317:357:396:423:469:476 SD: 0.3749 cents 246:277:307:328:369:409:437:485:492 SD: 0.3555 cents 258:290:322:344:387:429:459:509:516 SD: 0.3396 cents 262:295:327:349:393:436:466:517:524 SD: 0.3069 cents 282:317:352:376:423:469:501:556:564 SD: 0.2950 cents 294:331:367:392:441:489:523:580:588 SD: 0.2617 cents 318:358:397:424:477:529:565:627:636 SD: 0.2314 cents 342:385:427:456:513:569:608:675:684 SD: 0.2081 cents 360:405:449:480:540:599:640:710:720 SD: 0.2058 cents 366:412:457:488:549:609:651:722:732 SD: 0.1906 cents 390:439:487:520:585:649:693:769:780 SD: 0.1806 cents 408:459:509:544:612:679:725:805:816 SD: 0.1757 cents 414:466:517:552:621:689:736:817:828 SD: 0.1707 cents 432:486:539:576:648:719:768:852:864 SD: 0.1166 cents 504:567:629:672:756:839:896:994:1008 SD: 0.0733 cents