Scala analysis: xen18-schulter-zalzal-g
Mode of Zalzal's scale in 17-WT, on G
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: 350.770 cents 350.770000 3: 492.780 cents 492.780000 4: 707.220 cents 707.220000 5: 921.660 cents 921.660000 6: 1055.140 cents 1055.140000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 144.8600 cents 144.8600 1: 214.4400 cents 214.4400 2: 136.3300 cents 136.3300 3: 142.0100 cents 142.0100 4: 214.4400 cents 214.4400 5: 214.4400 cents 214.4400 6: 133.4800 cents 133.4800 7: 144.8600 cents 144.8600
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 : 214.4 350.8 492.8 707.2 921.7 1055.1 1200.0 214.4 : 136.3 278.3 492.8 707.2 840.7 985.6 1200.0 350.8 : 142.0 356.4 570.9 704.4 849.2 1063.7 1200.0 492.8 : 214.4 428.9 562.4 707.2 921.7 1058.0 1200.0 707.2 : 214.4 347.9 492.8 707.2 843.5 985.6 1200.0 921.7 : 133.5 278.3 492.8 629.1 771.1 985.6 1200.0 1055.1: 144.9 359.3 495.6 637.6 852.1 1066.5 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 : 175.44529 cents, oct.: 1228.11700 cents Scale is strictly proper Step pattern alph. order: ABCAADE Step pattern size order : EBCEEAD 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 : 3 = 42.8571% Limited inverse transpositions with margin 150.5400 cents: 1 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.1790 c. M: 64.5171 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 39.4352 c. M: 64.4400 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 35.2734 c. M:-52.2267 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 21.2238 c. M:-38.3400 c. Pseudo Rast 16: 3 2 2 2 3 2 2 SP M ME S SD: 21.6149 c. M: 32.2200 c. Antiphrygian 17: 3 2 2 3 3 2 2 SP D3 S SD: 2.5389 c. M: 4.0129 c. Pseudo Rast 73: 13 8 9 13 13 8 9 SP SD: 2.4653 c. M: 5.5645 c. 83: 15 9 10 15 15 9 10 SP SD: 2.2829 c. M: 3.7820 c. 90: 16 10 11 16 16 10 11 SP SD: 1.8782 c. M: 4.1033 c. 100: 18 11 12 18 18 11 12 SP SD: 1.5829 c. M: 2.7700 c. 107: 19 12 13 19 19 12 13 SP SD: 1.5774 c. M: 3.1064 c. 117: 21 13 14 21 21 13 14 SP SD: 1.1446 c. M: 2.0521 c. 134: 24 15 16 24 24 15 16 SP SD: 0.8998 c. M:-1.5764 c. 151: 27 17 18 27 27 17 18 SP SD: 0.8075 c. M:-1.8136 c. 229: 41 26 27 41 41 25 28 SP SD: 0.7749 c. M: 1.8649 c. 246: 44 28 29 44 44 27 30 SP SD: 0.6022 c. M: 1.4815 c. 263: 47 30 31 47 47 29 32 SP SD: 0.4828 c. M: 1.1476 c. 280: 50 32 33 50 50 31 34 SP SD: 0.4230 c. M: 0.8543 c. 297: 53 34 35 53 53 33 36 SP SD: 0.4214 c. M:-0.7452 c. 363: 65 41 43 65 65 40 44 SP SD: 0.4130 c. M:-0.6540 c. 380: 68 43 45 68 68 42 46 SP SD: 0.2809 c. M:-0.4453 c. 397: 71 45 47 71 71 44 48 SP SD: 0.1602 c. M:-0.2544 c. 414: 74 47 49 74 74 46 50 SP SD: 0.0494 c. M:-0.0791 c. 845: 151 96 100 151 151 94 102 SP SD: 0.0034 c. M:-0.0079 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: 12.5570 cents 4 x 5 x 6:7 x 8 S SD: 14.8233 cents 5 x 6:7:8 x 9:10 S SD: 29.6853 cents 6:7 x 8:9:10:11:12 S SD: 10.8387 cents 7:8 x 9:11:12:13:14 SD: 16.3983 cents 8:9:10:11:12:14:15:16 S SD: 12.8974 cents 9:10:11:12:14:15:17:18 SD: 12.6917 cents 10:11:12:13:15:17:18:20 SD: 11.6160 cents 12:14:15:16:18:20:22:24 S SD: 10.5874 cents 13:15:16:17:20:22:24:26 SD: 8.6113 cents 14:16:17:19:21:24:26:28 SD: 6.7268 cents 18:20:22:24:27:31:33:36 SD: 5.5427 cents 22:25:27:29:33:37:40:44 SD: 4.8945 cents 24:27:29:32:36:41:44:48 SD: 3.9517 cents 30:34:37:40:45:51:55:60 SD: 2.2785 cents 45:51:55:60:68:77:83:90 SD: 1.9726 cents 54:61:66:72:81:92:99:108 SD: 1.5144 cents 61:69:75:81:92:104:112:122 SD: 1.3104 cents 67:76:82:89:101:114:123:134 SD: 0.9230 cents 107:121:131:142:161:182:197:214 SD: 0.5966 cents 137:155:168:182:206:233:252:274 SD: 0.5267 cents 151:171:185:201:227:257:278:302 SD: 0.5059 cents 161:182:197:214:242:274:296:322 SD: 0.4882 cents 174:197:213:231:262:296:320:348 SD: 0.4726 cents 182:206:223:242:274:310:335:364 SD: 0.2742 cents 236:267:289:314:355:402:434:472 SD: 0.2739 cents 280:317:343:372:421:477:515:560 SD: 0.2512 cents 303:343:371:403:456:516:557:606 SD: 0.2252 cents 343:388:420:456:516:584:631:686 SD: 0.1639 cents 410:464:502:545:617:698:754:820 SD: 0.1218 cents 592:670:725:787:891:1008:1089:1184 SD: 0.0968 cents