Scala analysis: zartehijaz1
Scale from Zarlino temperament extraordinaire -- lower Hijaz tetrachord
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120.948 cents 120.948260 2: 433.517 cents 433.517220 3: 504.190 cents 504.189650 4: 625.138 cents 625.137920 5: 708.379 cents 708.379300 6: 925.138 cents 925.137920 7: 1008.379 cents 1008.379300 8: 1129.328 cents 1129.327570 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 70.6724 cents 70.6724 1: 120.9483 cents 120.9483 2: 312.5690 cents 312.5690 3: 70.6724 cents 70.6724 4: 120.9483 cents 120.9483 5: 83.2414 cents 83.2414 6: 216.7586 cents 216.7586 7: 83.2414 cents 83.2414 8: 120.9483 cents 120.9483 9: 70.6724 cents 70.6724
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 70.67243 cents 1: 2 83.24138 cents 1: 3 120.94826 cents 1: 1 216.75862 cents 1: 1 312.56896 cents 2: 3 191.62070 cents 2: 2 204.18965 cents 2: 2 300.00000 cents 2: 1 383.24139 cents 2: 1 433.51722 cents 3: 2 274.86208 cents 3: 1 312.56896 cents 3: 1 383.24138 cents 3: 2 420.94827 cents 3: 3 504.18965 cents 4: 1 395.81034 cents 4: 2 491.62070 cents 4: 2 504.18965 cents 4: 1 574.86208 cents 4: 1 587.43104 cents 4: 2 625.13792 cents 5: 2 574.86208 cents 5: 1 612.56896 cents 5: 1 625.13792 cents 5: 2 695.81035 cents 5: 2 708.37930 cents 5: 1 804.18966 cents 6: 3 695.81035 cents 6: 2 779.05173 cents 6: 1 816.75862 cents 6: 1 887.43104 cents 6: 2 925.13792 cents 7: 1 766.48278 cents 7: 1 816.75861 cents 7: 2 900.00000 cents 7: 2 995.81035 cents 7: 3 1008.37930 cents 8: 1 887.43104 cents 8: 1 983.24138 cents 8: 3 1079.05174 cents 8: 2 1116.75862 cents 8: 2 1129.32757 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.25000 = 21/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 120.9 433.5 504.2 625.1 708.4 925.1 1008.4 1129.3 1200.0 120.9 : 312.6 383.2 504.2 587.4 804.2 887.4 1008.4 1079.1 1200.0 433.5 : 70.7 191.6 274.9 491.6 574.9 695.8 766.5 887.4 1200.0 504.2 : 120.9 204.2 420.9 504.2 625.1 695.8 816.8 1129.3 1200.0 625.1 : 83.2 300.0 383.2 504.2 574.9 695.8 1008.4 1079.1 1200.0 708.4 : 216.8 300.0 420.9 491.6 612.6 925.1 995.8 1116.8 1200.0 925.1 : 83.2 204.2 274.9 395.8 708.4 779.1 900.0 983.2 1200.0 1008.4: 120.9 191.6 312.6 625.1 695.8 816.8 900.0 1116.8 1200.0 1129.3: 70.7 191.6 504.2 574.9 695.8 779.1 995.8 1079.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 312.5690 cents 241.89653 cents 70.67243 cents 2: 191.6207 .. 433.5172 cents 241.89652 cents -120.94826 cents 3: 274.8621 .. 504.1897 cents 229.32757 cents -158.65514 cents 4: 395.8103 .. 625.1379 cents 229.32758 cents -108.37931 cents 5: 574.8621 .. 804.1897 cents 229.32758 cents -50.27584 cents 6: 695.8104 .. 925.1379 cents 229.32757 cents -108.37931 cents 7: 766.4828 .. 1008.3793 cents 241.89652 cents -158.65514 cents 8: 887.4310 .. 1129.3276 cents 241.89653 cents -120.94826 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 70.67243 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 312.56896 cents Average / Smallest step : 1.886639 Largest / Average step : 2.344267 Largest / Smallest step : 4.422785 Median interval of one step : 120.94826 cents, amount: 3 Most common interval of one step : 120.94826 cents, amount: 3 Least squares average step : 143.81440 cents, oct.: 1294.32957 cents Scale is not proper Step pattern alph. order: ABCADEDAC Step pattern size order : CEACBDBCA Scale is not a Constant Structure Scale diversity : 1.431533 Lumma stability : 0.117787 Lumma impropriety factor : 0.562845 Rothenberg efficiency : 0.358025 redundancy: 0.641975 Efficiency x scale size : 3.222222 Number of different interval sizes : 34 = 4.25000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.25000 = 21/4 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 12.56895 cents Most common intervals : 504.18965 cents & inv., amount: 5 Most common triad is 0.0 504.190 695.810 cents, amount: 3 Number of recognisable fifths : 7, average 699.4015 cents Formal octave complements present : 1 = 11.1111% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
9: 1 2 1 1 0 2 1 0 1 N T3 SD: 37.9791 c. M: 62.6609 c. 12: 1 3 1 1 1 2 1 1 1 N T3 SD: 20.6671 c. M: 33.5172 c. 14: 1 4 1 1 1 3 1 1 1 N T3 SD: 19.6112 c. M: 35.2340 c. 16: 2 4 1 1 1 3 1 2 1 N SD: 23.7105 c. M: 33.3793 c. 17: 2 4 1 2 1 3 1 2 1 N SD: 11.4585 c. M:-20.2282 c. 19: 2 5 1 2 1 4 1 2 1 N SD: 9.9252 c. M:-22.2305 c. 27: 3 7 1 3 2 5 2 2 2 N SD: 11.1231 c. M: 18.2165 c. 29: 3 7 2 3 2 5 2 3 2 N SD: 11.0550 c. M: 19.7241 c. 30: 3 8 2 3 2 5 2 3 2 N SD: 9.6173 c. M:-15.8103 c. 31: 3 8 2 3 2 6 2 3 2 N SD: 5.9267 c. M: 11.6051 c. 48: 5 12 3 5 3 9 3 5 3 N SD: 5.4335 c. M: 8.5172 c. 50: 5 13 3 5 4 9 3 5 3 N SD: 5.3693 c. M:-11.6207 c. 52: 5 14 3 5 4 9 4 5 3 N SD: 4.4271 c. M:-7.0053 c. 61: 6 16 4 6 4 11 4 6 4 N SD: 4.3694 c. M: 8.0161 c. 69: 7 18 4 7 5 12 5 7 4 N SD: 2.0490 c. M:-4.6642 c. 86: 9 22 5 9 6 15 6 9 5 N SD: 2.9156 c. M:-4.6331 c. 88: 9 23 5 9 6 16 6 9 5 N SD: 1.7551 c. M:-2.8464 c. 100: 10 26 6 10 7 18 7 10 6 N SD: 0.9355 c. M: 1.5172 c. 169: 17 44 10 17 12 30 12 17 10 N SD: 0.9114 c. M: 2.0610 c. 188: 19 49 11 19 13 34 13 19 11 N SD: 0.3239 c. M:-0.5253 c. 288: 29 75 17 29 20 52 20 29 17 N SD: 0.1134 c. M: 0.1839 c. 476: 48 124 28 48 33 86 33 48 28 N SD: 0.0593 c. M:-0.0962 c. 764: 77 199 45 77 53 138 53 77 45 N SD: 0.0058 c. M: 0.0094 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 3.2121 cents 3 x x 4 x x 5 x x 6 S SD: 13.7465 cents 4 x 5 x x 6 x 7 x 8 S SD: 15.4797 cents 5 x 6 x 7:8 x 9 x 10 S SD: 32.7940 cents 6:7 x 8 x 9:10:11 x 12 S SD: 26.2017 cents 7:8:9 x 10:11:12 x 13:14 S SD: 20.7453 cents 8:9:10:11 x 12 x 14:15:16 S SD: 17.2754 cents 9:10 x 12:13:14:15:16:17:18 S SD: 12.3469 cents 10:11:13 x 14:15:17:18:19:20 SD: 8.5543 cents 13:14:17 x 19:20:22:23:25:26 SD: 7.9670 cents 14:15:18:19:20:21:24:25:27:28 SD: 3.2374 cents 16:17 x 21:23:24:27:29:31:32 SD: 6.2382 cents 18:19:23:24:26:27:31:32:35:36 SD: 4.8796 cents 24:26:31:32:34:36:41:43:46:48 SD: 3.4881 cents 27:29:35:36:39:41:46:48:52:54 SD: 3.2049 cents 28:30:36:37:40:42:48:50:54:56 SD: 2.9782 cents 38:41:49:51:55:57:65:68:73:76 SD: 2.4047 cents 39:42:50:52:56:59:67:70:75:78 SD: 2.0373 cents 42:45:54:56:60:63:72:75:81:84 SD: 1.8809 cents 53:57:68:71:76:80:90:95:102:106 SD: 1.3408 cents 67:72:86:90:96:101:114:120:129:134 SD: 1.2158 cents 71:76:91:95:102:107:121:127:136:142 SD: 0.8314 cents 85:91:109:114:122:128:145:152:163:170 SD: 0.7265 cents 95:102:122:127:136:143:162:170:182:190 SD: 0.7041 cents 109:117:140:146:156:164:186:195:209:218 SD: 0.6542 cents 113:121:145:151:162:170:193:202:217:226 SD: 0.6026 cents 140:150:180:187:201:211:239:251:269:280 SD: 0.5661 cents 151:162:194:202:217:227:258:270:290:302 SD: 0.5572 cents 154:165:198:206:221:232:263:276:296:308 SD: 0.4245 cents 166:178:213:222:238:250:283:297:319:332 SD: 0.4036 cents 204:219:262:273:293:307:348:365:392:408 SD: 0.3640 cents 221:237:284:296:317:333:377:396:424:442 SD: 0.3413 cents 225:241:289:301:323:339:384:403:432:450 SD: 0.2927 cents 239:256:307:320:343:360:408:428:459:478 SD: 0.2881 cents 249:267:320:333:357:375:425:446:478:498 SD: 0.2364 cents 320:343:411:428:459:482:546:573:614:640 SD: 0.2092 cents 334:358:429:447:479:503:570:598:641:668 SD: 0.1751 cents 358:384:460:479:514:539:611:641:687:716 SD: 0.1732 cents 372:399:478:498:534:560:635:666:714:744 SD: 0.1706 cents 429:460:551:574:616:646:732:768:824:858 SD: 0.1624 cents 453:486:582:606:650:682:773:811:870:906 SD: 0.1185 cents 524:562:673:701:752:789:894:938:1006:1048 SD: 0.0862 cents 538:577:691:720:772:810:918:963:1033:1076 SD: 0.0702 cents