Scala analysis: starling7
A distributionally even scale in starling temperament, abababc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78.930 cents 78.930000 2: 311.100 cents 311.100000 3: 390.030 cents 390.030000 4: 622.200 cents 622.200000 5: 701.130 cents 701.130000 6: 967.620 cents 967.620000 7: 1199.790 cents 1199.790000
SHOW/INTERVAL
0: 232.1700 cents 232.1700 1: 78.9300 cents 78.9300 2: 232.1700 cents 232.1700 3: 78.9300 cents 78.9300 4: 232.1700 cents 232.1700 5: 78.9300 cents 78.9300 6: 266.4900 cents 266.4900 7: 232.1700 cents 232.1700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 78.93000 cents 1: 3 232.17000 cents 1: 1 266.49000 cents 2: 5 311.10000 cents 2: 1 345.42000 cents 2: 1 498.66000 cents 3: 2 390.03000 cents 3: 2 543.27000 cents 3: 3 577.59000 cents 4: 3 622.20000 cents 4: 2 656.52000 cents 4: 2 809.76000 cents 5: 1 701.13000 cents 5: 1 854.37000 cents 5: 5 888.69000 cents 6: 1 933.30000 cents 6: 3 967.62000 cents 6: 3 1120.86000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 78.9 311.1 390.0 622.2 701.1 967.6 1199.8 78.9 : 232.2 311.1 543.3 622.2 888.7 1120.9 1199.8 311.1 : 78.9 311.1 390.0 656.5 888.7 967.6 1199.8 390.0 : 232.2 311.1 577.6 809.8 888.7 1120.9 1199.8 622.2 : 78.9 345.4 577.6 656.5 888.7 967.6 1199.8 701.1 : 266.5 498.7 577.6 809.8 888.7 1120.9 1199.8 967.6 : 232.2 311.1 543.3 622.2 854.4 933.3 1199.8 1199.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.9300 .. 266.4900 cents 187.56000 cents 78.93000 cents 2: 311.1000 .. 498.6600 cents 187.56000 cents 44.61000 cents 3: 390.0300 .. 577.5900 cents 187.56000 cents -108.63000 cents 4: 622.2000 .. 809.7600 cents 187.56000 cents 44.61000 cents 5: 701.1300 .. 888.6900 cents 187.56000 cents -108.63000 cents 6: 933.3000 .. 1120.8600 cents 187.56000 cents 44.61000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 78.93000 cents, class 1 Average step (divided formal octave): 171.3986 cents Largest one step interval : 266.49000 cents Average / Smallest step : 2.171526 Largest / Average step : 1.554797 Largest / Smallest step : 3.376283 Median interval of one step : 232.17000 cents, amount: 3 Least squares average step : 157.64229 cents, oct.: 1103.49600 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABABACB Step pattern size order : SMSMSLM Scale is a Constant Structure, by a margin of 44.61000 cents Scale diversity : 1.350397 Lumma stability : 0.243118 Lumma impropriety factor : 0.181082 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 34.32000 cents Most common intervals : 311.10000 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 232.170 311.100 cents Most common triad is 0.0 311.100 888.690 cents, amount: 3 Number of recognisable fifths : 1, average 701.1300 cents Number of recognisable fourths : 1, average 498.6600 cents Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
7: 0 1 1 1 1 1 2 N T3 SD: 86.2902 c. M: 139.7014 c. 8: 0 2 0 2 0 2 2 N M DE S SD: 65.2566 c. M: 101.2350 c. 9: 1 1 1 2 0 2 2 N T3 SD: 36.6122 c. M:-54.3800 c. 10: 1 2 0 2 1 2 2 N T3 S SD: 28.9955 c. M:-48.8370 c. 11: 1 2 1 2 1 2 2 P M ME S SD: 34.7108 c. M:-62.3727 c. 12: 1 2 1 2 1 3 2 N T3 SD: 17.7355 c. M:-32.2050 c. 15: 1 3 1 3 1 3 3 N M DE S SD: 11.3528 c. M:-18.7440 c. Kleismic-7, Triolic Diatonic 27: 2 5 2 5 2 6 5 N T3 SD: 7.5003 c. M:-9.9867 c. 31: 2 6 2 6 2 7 6 N T3 SD: 2.4578 c. M: 4.4777 c. 46: 3 9 3 9 3 10 9 N T3 SD: 2.2661 c. M:-3.7774 c. 77: 5 15 5 15 5 17 15 N T3 SD: 0.8558 c. M: 1.5553 c. 108: 7 21 7 21 7 24 21 N T3 SD: 0.8992 c. M: 1.2525 c. 135: 9 26 9 26 9 30 26 N T3 SD: 0.7836 c. M:-1.0993 c. 166: 11 32 11 32 11 37 32 N T3 SD: 0.4882 c. M:-0.8852 c. 212: 14 41 14 41 14 47 41 N T3 SD: 0.3521 c. M:-0.6340 c. 243: 16 47 16 47 16 54 47 N T3 SD: 0.0627 c. M:-0.1119 c. 563: 37 109 37 109 37 125 109 N T3 SD: 0.0637 c. M: 0.1162 c. 806: 53 156 53 156 53 179 156 N T3 SD: 0.0265 c. M: 0.0474 c. 1049: 69 203 69 203 69 233 203 N T3 SD: 0.0091 c. M: 0.0134 c. 2341: 154 453 154 453 154 520 453 N T3 SD: 0.0078 c. M: 0.0139 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.2100 cents 2 x x x x 3 x 4 S SD: 0.4257 cents 3 x x 4 x x 5:6 S SD: 45.4603 cents 4 x x 5 x 6:7:8 S SD: 0.9997 cents 5 x 6 x 7:8:9:10 S SD: 25.8939 cents 6 x 7:8 x 9:11:12 SD: 28.4999 cents 7 x 8:9:10:11:12:14 S SD: 21.2457 cents 8 x x 10:11:12:14:16 S SD: 14.1990 cents 9:10:11 x 13:14:16:18 SD: 21.8022 cents 10:11:12:13:14:15:17:20 SD: 17.7992 cents 11:12:13:14:16 x 19:22 SD: 14.4688 cents 12:13:14:15:17:18:21:24 SD: 10.9713 cents 13:14 x 16:19 x 23:26 SD: 14.1225 cents 14:15:17:18:20:21:24:28 SD: 10.6044 cents 15:16:18:19:21:22:26:30 SD: 9.8219 cents 16:17:19:20:23:24:28:32 SD: 4.3208 cents 20:21:24:25:29:30:35:40 SD: 3.2292 cents 36:38:43:45:52:54:63:72 SD: 3.0350 cents 40:42:48:50:57:60:70:80 SD: 1.7444 cents 44:46:53:55:63:66:77:88 SD: 1.7108 cents 60:63:72:75:86:90:105:120 SD: 1.1813 cents 86:90:103:108:123:129:150:172 SD: 0.9985 cents 88:92:105:110:126:132:154:176 SD: 0.9983 cents 102:107:122:128:146:153:178:204 SD: 0.9235 cents 106:111:127:133:152:159:185:212 SD: 0.7550 cents 127:133:152:159:182:190:222:254 SD: 0.5884 cents 174:182:208:218:249:261:304:348 SD: 0.4975 cents 178:186:213:223:255:267:311:356 SD: 0.4805 cents 194:203:232:243:278:291:339:388 SD: 0.3242 cents 234:245:280:293:335:351:409:468 SD: 0.2740 cents 238:249:285:298:341:357:416:476 SD: 0.2708 cents 340:356:407:426:487:510:595:680 SD: 0.2421 cents 361:378:432:452:517:541:631:722 SD: 0.2409 cents 365:382:437:457:523:547:638:730 SD: 0.2333 cents 391:409:468:490:560:586:684:782 SD: 0.2220 cents 407:426:487:510:583:610:712:814 SD: 0.1582 cents 451:472:540:565:646:676:789:902 SD: 0.1576 cents 518:542:620:649:742:777:906:1036 SD: 0.1533 cents 534:559:639:669:765:801:934:1068 SD: 0.1456 cents