Scala analysis: starling11_tuning-math_19356_19356
A distributionally even scale in starling temperament, abacbabcabc
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: 266.490 cents 266.490000 3: 311.100 cents 311.100000 4: 390.030 cents 390.030000 5: 577.590 cents 577.590000 6: 656.520 cents 656.520000 7: 701.130 cents 701.130000 8: 888.690 cents 888.690000 9: 967.620 cents 967.620000 10: 1155.180 cents 1155.180000 11: 1199.790 cents 1199.790000
SHOW/INTERVAL
0: 44.6100 cents 44.6100 1: 78.9300 cents 78.9300 2: 187.5600 cents 187.5600 3: 44.6100 cents 44.6100 4: 78.9300 cents 78.9300 5: 187.5600 cents 187.5600 6: 78.9300 cents 78.9300 7: 44.6100 cents 44.6100 8: 187.5600 cents 187.5600 9: 78.9300 cents 78.9300 10: 187.5600 cents 187.5600 11: 44.6100 cents 44.6100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 44.61000 cents 1: 4 78.93000 cents 1: 4 187.56000 cents 2: 3 123.54000 cents 2: 3 232.17000 cents 2: 5 266.49000 cents 3: 9 311.10000 cents 3: 1 345.42000 cents 3: 1 454.05000 cents 4: 1 355.71000 cents 4: 5 390.03000 cents 4: 5 498.66000 cents 5: 2 434.64000 cents 5: 2 543.27000 cents 5: 7 577.59000 cents 6: 7 622.20000 cents 6: 2 656.52000 cents 6: 2 765.15000 cents 7: 5 701.13000 cents 7: 5 809.76000 cents 7: 1 844.08000 cents 8: 1 745.74000 cents 8: 1 854.37000 cents 8: 9 888.69000 cents 9: 5 933.30000 cents 9: 3 967.62000 cents 9: 3 1076.25000 cents 10: 4 1012.23000 cents 10: 4 1120.86000 cents 10: 3 1155.18000 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 8 9 10 11 0.0 : 78.9 266.5 311.1 390.0 577.6 656.5 701.1 888.7 967.6 1155.2 1199.8 78.9 : 187.6 232.2 311.1 498.7 577.6 622.2 809.8 888.7 1076.3 1120.9 1199.8 266.5 : 44.6 123.5 311.1 390.0 434.6 622.2 701.1 888.7 933.3 1012.2 1199.8 311.1 : 78.9 266.5 345.4 390.0 577.6 656.5 844.1 888.7 967.6 1155.2 1199.8 390.0 : 187.6 266.5 311.1 498.7 577.6 765.2 809.8 888.7 1076.3 1120.9 1199.8 577.6 : 78.9 123.5 311.1 390.0 577.6 622.2 701.1 888.7 933.3 1012.2 1199.8 656.5 : 44.6 232.2 311.1 498.7 543.3 622.2 809.8 854.4 933.3 1120.9 1199.8 701.1 : 187.6 266.5 454.0 498.7 577.6 765.1 809.8 888.7 1076.2 1155.2 1199.8 888.7 : 78.9 266.5 311.1 390.0 577.6 622.2 701.1 888.7 967.6 1012.2 1199.8 967.6 : 187.6 232.2 311.1 498.7 543.3 622.2 809.8 888.7 933.3 1120.9 1199.8 1155.2: 44.6 123.5 311.1 355.7 434.6 622.2 701.1 745.7 933.3 1012.2 1199.8 1199.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.6100 .. 187.5600 cents 142.95000 cents 44.61000 cents 2: 123.5400 .. 266.4900 cents 142.95000 cents -64.02000 cents 3: 311.1000 .. 454.0500 cents 142.95000 cents 44.61000 cents 4: 355.7100 .. 498.6600 cents 142.95000 cents -98.34000 cents 5: 434.6400 .. 577.5900 cents 142.95000 cents -64.02000 cents 6: 622.2000 .. 765.1500 cents 142.95000 cents 44.61000 cents 7: 701.1300 .. 844.0800 cents 142.95000 cents -64.02000 cents 8: 745.7400 .. 888.6900 cents 142.95000 cents -98.34000 cents 9: 933.3000 .. 1076.2500 cents 142.95000 cents 44.61000 cents 10: 1012.2300 .. 1155.1800 cents 142.95000 cents -64.02000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 44.61000 cents, class 1 Average step (divided formal octave): 109.0718 cents Largest one step interval : 187.56000 cents Average / Smallest step : 2.445008 Largest / Average step : 1.719601 Largest / Smallest step : 4.204438 Median interval of one step : 78.93000 cents, amount: 4 Least squares average step : 109.50178 cents, oct.: 1204.51957 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABACBABC Step pattern size order : MLSMLMSLMLS Scale is a Constant Structure, by a margin of 10.29000 cents Scale diversity : 1.394841 Lumma stability : 0.185908 Lumma impropriety factor : 0.345010 Rothenberg efficiency : 0.513420 redundancy: 0.486580 Efficiency x scale size : 5.647619 Number of different interval sizes : 30 = 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 : 10.29000 cents Most common intervals : 311.10000 cents & inv., amount: 9 Scale is a chain of 5 triads 0.0 390.030 888.690 cents Most common triad is 0.0 311.100 888.690 cents, amount: 7 Number of recognisable fifths : 5, average 701.1300 cents Number of recognisable fourths : 5, average 498.6600 cents Formal octave complements present : 3 = 27.2727% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 0 2 1 2 0 N T3 S SD: 32.0736 c. M: 48.3464 c. 12: 1 2 0 1 2 1 0 2 1 2 0 N T3 SD: 25.7886 c. M:-44.6100 c. 15: 1 2 1 1 2 1 1 2 1 2 1 P M ME S SD: 17.0892 c. M: 35.3760 c. 16: 1 3 0 1 3 1 0 3 1 2 1 N SD: 19.3296 c. M:-33.4575 c. 19: 1 3 1 1 3 1 1 3 1 3 1 N M DE S SD: 13.9024 c. M: 25.0516 c. 22: 1 4 1 1 4 1 1 3 2 3 1 N S SD: 13.7507 c. M: 24.3941 c. 24: 2 3 1 2 4 1 1 4 1 4 1 N SD: 13.3203 c. M:-22.3050 c. 26: 2 4 1 1 5 1 1 4 2 4 1 N SD: 12.4229 c. M:-22.3050 c. 27: 2 4 1 2 4 2 1 4 2 4 1 N T3 SD: 6.7043 c. M:-10.0300 c. 31: 2 5 1 2 5 2 1 5 2 5 1 N T3 SD: 3.0306 c. M:-5.9071 c. 58: 4 9 2 4 9 4 2 9 4 9 2 N T3 SD: 3.0091 c. M:-5.4331 c. 77: 5 12 3 5 12 5 3 12 5 12 3 N T3 SD: 1.2395 c. M: 2.1351 c. 108: 7 17 4 7 17 7 4 17 7 17 4 N T3 SD: 0.7904 c. M: 1.2525 c. 135: 9 21 5 9 21 9 5 21 9 21 5 N T3 SD: 0.7169 c. M:-1.1427 c. 166: 11 26 6 11 26 11 6 26 11 26 6 N T3 SD: 0.7144 c. M:-1.2441 c. 212: 14 33 8 14 33 14 8 33 14 33 8 N T3 SD: 0.3799 c. M: 0.6651 c. 243: 16 38 9 16 38 16 9 38 16 38 9 N T3 SD: 0.0956 c. M:-0.1733 c. 563: 37 88 21 37 88 37 21 88 37 88 21 N T3 SD: 0.0876 c. M: 0.1518 c. 806: 53 126 30 53 126 53 30 126 53 126 30 N T3 SD: 0.0331 c. M: 0.0592 c. 1049: 69 164 39 69 164 69 39 164 69 164 39 N T3 SD: 0.0080 c. M: 0.0134 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.2100 cents 2 x x x x x x 3 x x x 4 S SD: 0.4257 cents 3 x x x x 4 x x 5 x x 6 S SD: 26.5544 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 0.9997 cents 5 x x 6 x 7 x x 8:9 x 10 S SD: 18.0755 cents 6 x 7 x x 8 x 9:10:11 x 12 S SD: 19.0241 cents 7 x 8 x 9 x 10:11 x 12 x 14 S SD: 18.7157 cents 8 x 9 x 10:11 x 12:13:14 x 16 S SD: 11.9027 cents 9 x x 11 x x 13:14:15:16 x 18 SD: 13.5527 cents 10:11 x 12:13:14 x 15:17 x 19:20 SD: 15.0028 cents 11:12 x 13:14:15:16 x 18:19:21:22 SD: 11.7205 cents 12:13:14 x 15:17 x 18:20:21:23:24 SD: 7.9121 cents 13:14:15 x 16:18:19 x 22:23:25:26 SD: 8.1277 cents 14:15:16:17:18 x 20:21:23:24:27:28 SD: 9.7174 cents 15:16 x 18:19:21:22 x 25:26:29:30 SD: 4.9439 cents 16:17 x 19:20:22:23:24:27:28:31:32 SD: 5.2572 cents 17:18:20 x 21:24:25 x 28:30:33:34 SD: 5.6856 cents 19:20:22:23:24:27:28 x 32:33:37:38 SD: 4.8483 cents 20:21:23:24:25:28:29:30:33:35:39:40 SD: 3.3305 cents 21:22:24:25:26:29:31 x 35:37:41:42 SD: 5.1093 cents 22:23 x 26:28:31:32:33:37:38:43:44 SD: 4.6617 cents 23:24:27:28:29:32:34 x 38:40:45:46 SD: 4.5849 cents 24:25:28:29:30:34:35:36:40:42:47:48 SD: 3.0192 cents 25:26:29:30:31:35:37 x 42:44:49:50 SD: 3.7011 cents 28:29:33:34:35:39:41:42:47:49:55:56 SD: 3.6069 cents 30:31:35:36:38:42:44:45:50:52:58:60 SD: 3.3965 cents 35:37:41:42:44:49:51:52:58:61:68:70 SD: 2.8359 cents 36:38:42:43:45:50:53:54:60:63:70:72 SD: 2.0883 cents 40:42:47:48:50:56:58:60:67:70:78:80 SD: 1.9244 cents 48:50:56:57:60:67:70:72:80:84:94:96 SD: 1.7462 cents 56:59:65:67:70:78:82:84:94:98:109:112 SD: 1.6171 cents 60:63:70:72:75:84:88:90:100:105:117:120 SD: 1.1282 cents 80:84:93:96:100:112:117:120:134:140:156:160 SD: 1.1036 cents 83:87:97:99:104:116:121:124:139:145:162:166 SD: 1.0596 cents 86:90:100:103:108:120:126:129:144:150:168:172 SD: 1.0110 cents 91:95:106:109:114:127:133:136:152:159:177:182 SD: 0.7740 cents 106:111:124:127:133:148:155:159:177:185:207:212 SD: 0.7345 cents 122:128:142:146:153:170:178:183:204:213:238:244 SD: 0.7337 cents 126:132:147:151:158:176:184:189:211:220:246:252 SD: 0.6152 cents 132:138:154:158:165:184:193:198:221:231:257:264 SD: 0.5988 cents 151:158:176:181:189:211:221:226:252:264:294:302 SD: 0.5595 cents 152:159:177:182:190:212:222:228:254:266:296:304 SD: 0.5040 cents 167:175:195:200:209:233:244:250:279:292:325:334 SD: 0.4625 cents 174:182:203:208:218:243:254:261:291:304:339:348 SD: 0.3557 cents 210:220:245:251:263:293:307:315:351:367:409:420 SD: 0.3382 cents 234:245:273:280:293:327:342:351:391:409:456:468 SD: 0.2245 cents 258:270:301:309:323:360:377:387:431:451:503:516 SD: 0.2058 cents 371:388:433:444:465:518:542:556:620:649:723:742 SD: 0.2031 cents 386:404:450:462:484:539:564:579:645:675:752:772 SD: 0.2010 cents 391:409:456:468:490:546:571:586:653:684:762:782 SD: 0.1848 cents 407:426:475:487:510:568:595:610:680:712:793:814 SD: 0.1709 cents 427:447:498:511:535:596:624:640:713:747:832:854 SD: 0.1431 cents 553:579:645:662:693:772:808:829:924:967:1078:1106 SD: 0.1013 cents