Scala analysis: xen18-schulter-zalzal-d
Zalzal's scale in 17-WT, on D
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 214.440 cents 214.440000 2: 347.920 cents 347.920000 3: 492.780 cents 492.780000 4: 707.220 cents 707.220000 5: 843.550 cents 843.550000 6: 985.560 cents 985.560000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 214.4400 cents 214.4400 1: 214.4400 cents 214.4400 2: 133.4800 cents 133.4800 3: 144.8600 cents 144.8600 4: 214.4400 cents 214.4400 5: 136.3300 cents 136.3300 6: 142.0100 cents 142.0100 7: 214.4400 cents 214.4400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 133.48000 cents 1: 1 136.33000 cents 1: 1 142.01000 cents 1: 1 144.86000 cents 1: 3 214.44000 cents 2: 2 278.34000 cents 2: 1 347.92000 cents 2: 1 350.77000 cents 2: 1 356.45000 cents 2: 1 359.30000 cents 2: 1 428.88000 cents 3: 4 492.78000 cents 3: 1 495.63000 cents 3: 1 562.36000 cents 3: 1 570.89000 cents 4: 1 629.11000 cents 4: 1 637.64000 cents 4: 1 704.37000 cents 4: 4 707.22000 cents 5: 1 771.12000 cents 5: 1 840.70000 cents 5: 1 843.55000 cents 5: 1 849.23000 cents 5: 1 852.08000 cents 5: 2 921.66000 cents 6: 3 985.56000 cents 6: 1 1055.14000 cents 6: 1 1057.99000 cents 6: 1 1063.67000 cents 6: 1 1066.52000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 214.4 347.9 492.8 707.2 843.5 985.6 1200.0 214.4 : 133.5 278.3 492.8 629.1 771.1 985.6 1200.0 347.9 : 144.9 359.3 495.6 637.6 852.1 1066.5 1200.0 492.8 : 214.4 350.8 492.8 707.2 921.7 1055.1 1200.0 707.2 : 136.3 278.3 492.8 707.2 840.7 985.6 1200.0 843.5 : 142.0 356.5 570.9 704.4 849.2 1063.7 1200.0 985.6 : 214.4 428.9 562.4 707.2 921.7 1058.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.4800 .. 214.4400 cents 80.96000 cents 133.48000 cents 2: 278.3400 .. 428.8800 cents 150.54000 cents 63.90000 cents 3: 492.7800 .. 570.8900 cents 78.11000 cents 63.90000 cents 4: 629.1100 .. 707.2200 cents 78.11000 cents 58.22000 cents 5: 771.1200 .. 921.6600 cents 150.54000 cents 63.90000 cents 6: 985.5600 .. 1066.5200 cents 80.96000 cents 63.90000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 133.48000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 214.44000 cents Average / Smallest step : 1.284302 Largest / Average step : 1.250900 Largest / Smallest step : 1.606533 Median interval of one step : 144.86000 cents, amount: 1 Most common interval of one step : 214.44000 cents, amount: 3 Least squares average step : 169.63293 cents, oct.: 1187.43050 cents Scale is strictly proper Step pattern alph. order: ABCADEA Step pattern size order : EADEBCE Scale is a Constant Structure, by a margin of 58.22000 cents Scale diversity : 1.404311 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.483983 Rothenberg efficiency : 0.383673 redundancy: 0.616327 Efficiency x scale size : 2.685714 Number of different interval sizes : 30 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2.85000 cents Most common intervals : 492.78000 cents & inv., amount: 4 Most common triad is 0.0 492.780 707.220 cents, amount: 3 Number of recognisable fifths : 5, average 706.6500 cents Formal octave complements present : 5 = 71.4286% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 26.2824 c. M:-43.0114 c. Lebeng 10: 2 1 1 2 1 1 2 P D3 I SD: 15.9992 c. M:-25.5600 c. 17: 3 2 2 3 2 2 3 SP D3 I SD: 2.8137 c. M:-5.0212 c. Safi al-Din's maqam Rast 61: 11 7 7 11 7 7 11 SP D3 I SD: 2.7579 c. M:-6.1784 c. 73: 13 8 9 13 8 9 13 SP SD: 2.2589 c. M: 5.1938 c. 80: 14 9 10 14 9 10 14 SP SD: 3.1716 c. M:-4.4400 c. 83: 15 9 10 15 9 10 15 SP SD: 2.4071 c. M: 4.9958 c. 90: 16 10 11 16 10 11 16 SP SD: 1.5691 c. M: 3.5500 c. 107: 19 12 13 19 12 13 19 SP SD: 1.2282 c. M: 2.4285 c. 117: 21 13 14 21 13 14 21 SP SD: 1.1489 c. M: 2.5244 c. 124: 22 14 15 22 14 15 22 SP SD: 1.1167 c. M: 1.6145 c. 134: 24 15 16 24 15 16 24 SP SD: 0.8833 c. M: 1.7590 c. 151: 27 17 18 27 17 18 27 SP SD: 0.7982 c. M:-1.7489 c. 229: 41 25 28 41 26 27 41 SP SD: 0.8200 c. M: 2.0685 c. 239: 43 26 29 43 27 28 43 SP SD: 1.0356 c. M: 1.4765 c. 241: 43 27 29 43 27 29 43 SP SD: 0.8365 c. M: 2.0562 c. 246: 44 27 30 44 28 29 44 SP SD: 0.6222 c. M: 1.5785 c. 256: 46 28 31 46 29 30 46 SP SD: 0.8144 c. M:-1.1850 c. 258: 46 29 31 46 29 31 46 SP SD: 0.7826 c. M: 1.6895 c. 263: 47 29 32 47 30 31 47 SP SD: 0.4836 c. M: 1.1519 c. 273: 49 30 33 49 31 32 49 SP SD: 0.6371 c. M:-0.9446 c. 280: 50 31 34 50 32 33 50 SP SD: 0.4149 c. M: 0.7771 c. 290: 52 32 35 52 33 34 52 SP SD: 0.5068 c. M:-0.7324 c. 297: 53 33 36 53 34 35 53 SP SD: 0.4177 c. M:-0.8944 c. 324: 58 36 39 58 37 38 58 SP SD: 0.4146 c. M:-0.8944 c. 380: 68 42 46 68 43 45 68 SP SD: 0.3113 c. M: 0.5516 c. 397: 71 44 48 71 45 47 71 SP SD: 0.1775 c. M: 0.3129 c. 414: 74 46 50 74 47 49 74 SP SD: 0.0547 c. M: 0.0939 c. 845: 151 94 102 151 96 100 151 SP SD: 0.0036 c. M:-0.0090 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 2.6325 cents 3 x x 4 x 5 x 6 S SD: 13.7156 cents 4 x 5 x 6 x 7:8 S SD: 10.5529 cents 5 x 6:7 x 8:9:10 S SD: 20.9876 cents 6:7 x 8:9:10:11:12 S SD: 15.4026 cents 7:8 x 9 x 11:12:14 SD: 20.0857 cents 8:9:10:11:12:13:14:16 S SD: 10.4281 cents 13:15:16:17:20:21:23:26 SD: 8.7075 cents 14:16:17:19:21:23:25:28 SD: 6.8833 cents 18:20:22:24:27:29:32:36 SD: 5.5562 cents 21:24:26:28:32:34:37:42 SD: 5.3088 cents 22:25:27:29:33:36:39:44 SD: 3.0063 cents 30:34:37:40:45:49:53:60 SD: 2.5726 cents 40:45:49:53:60:65:71:80 SD: 2.2671 cents 45:51:55:60:68:73:80:90 SD: 2.1953 cents 46:52:56:61:69:75:81:92 SD: 1.7377 cents 54:61:66:72:81:88:95:108 SD: 1.6210 cents 67:76:82:89:101:109:118:134 SD: 1.1391 cents 76:86:93:101:114:124:134:152 SD: 1.1111 cents 85:96:104:113:128:138:150:170 SD: 0.9509 cents 91:103:111:121:137:148:161:182 SD: 0.7056 cents 107:121:131:142:161:174:189:214 SD: 0.6389 cents 113:128:138:150:170:184:200:226 SD: 0.6338 cents 121:137:148:161:182:197:214:242 SD: 0.3656 cents 188:213:230:250:283:306:332:376 SD: 0.3644 cents 198:224:242:263:298:322:350:396 SD: 0.3568 cents 228:258:279:303:343:371:403:456 SD: 0.2715 cents 274:310:335:364:412:446:484:548 SD: 0.2522 cents 288:326:352:383:433:469:509:576 SD: 0.2480 cents 319:361:390:424:480:519:564:638 SD: 0.2040 cents 355:402:434:472:534:578:627:710 SD: 0.1864 cents 373:422:456:496:561:607:659:746 SD: 0.1859 cents 395:447:483:525:594:643:698:790 SD: 0.1455 cents 486:550:594:646:731:791:859:972 SD: 0.1376 cents 553:626:676:735:832:900:977:1106 SD: 0.0862 cents