Scala analysis: 10-13-58
Single chain pseudo-MOS of major and neutral thirds in 58et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 186.207 cents 186.206900 2: 289.655 cents 289.655170 3: 393.103 cents 393.103450 4: 537.931 cents 537.931030 5: 641.379 cents 641.379310 6: 744.828 cents 744.827590 7: 931.034 cents 931.034480 8: 1034.483 cents 1034.482760 9: 1096.552 cents 1096.551720 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 103.4483 cents 103.4483 1: 186.2069 cents 186.2069 2: 103.4483 cents 103.4483 3: 103.4483 cents 103.4483 4: 144.8276 cents 144.8276 5: 103.4483 cents 103.4483 6: 103.4483 cents 103.4483 7: 186.2069 cents 186.2069 8: 103.4483 cents 103.4483 9: 62.0690 cents 62.0690 10: 103.4483 cents 103.4483
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 62.06896 cents 1: 6 103.44827 cents 1: 1 144.82758 cents 1: 2 186.20690 cents 2: 2 165.51724 cents 2: 2 206.89655 cents 2: 2 248.27586 cents 2: 4 289.65517 cents 3: 1 268.96552 cents 3: 5 351.72413 cents 3: 4 393.10345 cents 4: 6 455.17241 cents 4: 2 496.55173 cents 4: 2 537.93103 cents 5: 5 558.62069 cents 5: 5 641.37931 cents 6: 2 662.06897 cents 6: 2 703.44827 cents 6: 6 744.82759 cents 7: 4 806.89655 cents 7: 5 848.27586 cents 7: 1 931.03448 cents 8: 4 910.34482 cents 8: 2 951.72414 cents 8: 2 993.10345 cents 8: 2 1034.48276 cents 9: 2 1013.79310 cents 9: 1 1055.17242 cents 9: 6 1096.55172 cents 9: 1 1137.93104 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 186.2 289.7 393.1 537.9 641.4 744.8 931.0 1034.5 1096.6 1200.0 186.2 : 103.4 206.9 351.7 455.2 558.6 744.8 848.3 910.3 1013.8 1200.0 289.7 : 103.4 248.3 351.7 455.2 641.4 744.8 806.9 910.3 1096.6 1200.0 393.1 : 144.8 248.3 351.7 537.9 641.4 703.4 806.9 993.1 1096.6 1200.0 537.9 : 103.4 206.9 393.1 496.6 558.6 662.1 848.3 951.7 1055.2 1200.0 641.4 : 103.4 289.7 393.1 455.2 558.6 744.8 848.3 951.7 1096.6 1200.0 744.8 : 186.2 289.7 351.7 455.2 641.4 744.8 848.3 993.1 1096.6 1200.0 931.0 : 103.4 165.5 269.0 455.2 558.6 662.1 806.9 910.3 1013.8 1200.0 1034.5: 62.1 165.5 351.7 455.2 558.6 703.4 806.9 910.3 1096.6 1200.0 1096.6: 103.4 289.7 393.1 496.6 641.4 744.8 848.3 1034.5 1137.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.0690 .. 186.2069 cents 124.13794 cents 62.06896 cents 2: 165.5172 .. 289.6552 cents 124.13793 cents -20.68966 cents 3: 268.9655 .. 393.1035 cents 124.13793 cents -20.68965 cents 4: 455.1724 .. 537.9310 cents 82.75862 cents 62.06896 cents 5: 558.6207 .. 641.3793 cents 82.75862 cents 20.68966 cents 6: 662.0690 .. 744.8276 cents 82.75862 cents 20.68966 cents 7: 806.8965 .. 931.0345 cents 124.13793 cents 62.06896 cents 8: 910.3448 .. 1034.4828 cents 124.13794 cents -20.68966 cents 9: 1013.7931 .. 1137.9310 cents 124.13794 cents -20.68966 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 62.06896 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 186.20690 cents Average / Smallest step : 1.933334 Largest / Average step : 1.551724 Largest / Smallest step : 3.000000 Median interval of one step : 103.44827 cents, amount: 6 Most common interval of one step : 103.44827 cents, amount: 6 Least squares average step : 125.80385 cents, oct.: 1258.03851 cents Scale is not proper Scale is a mode of a 58-tone equal temperament with octave 1200.000 cents degrees: 9 14 19 26 31 36 45 50 53 58 Least number of segments generator : 31 of 641.379 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 49 of 1013.793 cents and inv. generated superset size: 26 = 16 more = 260.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBCBBABDB Step pattern size order : DBBCBBDBAB Interval vector is [ 0 0 1 0 6 0 1 2 2 2 0 2 1 4 0 0 5 0 4 0 0 6 0 2 0 2 5 0 0 ] Scale is a Constant Structure, by a margin of 20.68965 cents Scale diversity : 1.412913 Lumma stability : 0.241379 Lumma impropriety factor : 0.068966 Rothenberg efficiency : 0.404206 redundancy: 0.595794 Efficiency x scale size : 4.042063 Number of different interval sizes : 30 = 3.33333 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 20.68965 cents Number of recognisable fifths : 2, average 703.4483 cents Formal octave complements present : 1 = 10.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 8-9 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 2 0 1 1 N T3 SD: 45.0446 c. M: 74.4828 c. 11: 2 1 1 1 1 1 2 1 0 1 N D3 SD: 32.6916 c. M:-56.4263 c. 12: 2 1 1 1 1 1 2 1 1 1 P D3 SD: 27.6938 c. M: 44.8276 c. Minor Pentatonic with leading tones 13: 2 1 1 2 1 1 2 1 1 1 P M ME SD: 12.6623 c. M: 23.8727 c. 21: 3 2 2 2 2 2 3 2 1 2 P D3 SD: 12.0060 c. M: 23.6453 c. 22: 3 2 2 3 2 2 3 2 1 2 P T3 SD: 12.4763 c. M: 22.5705 c. 24: 4 2 2 3 2 2 4 2 1 2 N SD: 10.9723 c. M:-18.9655 c. 31: 5 2 3 4 3 2 5 3 1 3 N SD: 10.4870 c. M: 18.6874 c. 32: 5 3 2 4 3 3 5 3 1 3 N SD: 10.0497 c. M: 18.1035 c. 34: 5 3 3 4 3 3 5 3 2 3 P SD: 7.7452 c. M: 13.3874 c. 36: 6 3 3 4 3 3 6 3 2 3 N SD: 7.6244 c. M:-13.7931 c. 37: 6 3 3 5 3 3 6 3 2 3 N SD: 6.8142 c. M:-13.4203 c. 44: 7 4 3 6 4 3 7 4 2 4 N SD: 7.7949 c. M:-13.1661 c. 45: 7 4 4 5 4 4 7 4 2 4 N SD: 3.6580 c. M:-6.8965 c. 58: 9 5 5 7 5 5 9 5 3 5 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 21.4363 cents 3 x x x 4 x x 5 x x 6 S SD: 20.4655 cents 4 x x 5 x x 6:7 x x 8 S SD: 14.3883 cents 5 x 6 x 7 x 8 x 9 x 10 S SD: 17.5379 cents 6 x 7 x 8 x 9:10:11 x 12 S SD: 13.2792 cents 7:8 x 9 x 10:11:12 x 13:14 S SD: 11.4248 cents 8:9 x 10:11 x 12:14 x 15:16 S SD: 8.8911 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 9.8083 cents 10:11:12:13:14 x 15:17:18:19:20 SD: 10.7371 cents 11:12:13:14:15:16:17:19:20:21:22 SD: 5.2421 cents 13:14:15:16:18:19:20:22:24 x 26 S SD: 10.1040 cents 14:16:17:18:19:20:22:24:25:26:28 S SD: 9.7890 cents 15:17:18:19:20:22:23:26:27:28:30 SD: 7.0285 cents 16:18:19:20:22:23:25:27:29:30:32 SD: 4.7657 cents 17:19:20:21:23:25:26:29:31:32:34 SD: 4.3800 cents 24:27:28:30:33:35:37:41:44:45:48 SD: 3.9031 cents 27:30:32:34:37:39:42:46:49:51:54 SD: 2.5601 cents 35:39:41:44:48:51:54:60:64:66:70 SD: 2.4383 cents 43:48:51:54:59:62:66:74:78:81:86 SD: 1.7546 cents 44:49:52:55:60:64:68:75:80:83:88 SD: 1.5608 cents 55:61:65:69:75:80:85:94:100:104:110 SD: 1.5206 cents 60:67:71:75:82:87:92:103:109:113:120 SD: 1.1360 cents 71:79:84:89:97:103:109:122:129:134:142 SD: 0.8671 cents 87:97:103:109:119:126:134:149:158:164:174 SD: 0.7078 cents 115:128:136:144:157:167:177:197:209:217:230 SD: 0.6902 cents 121:135:143:152:165:175:186:207:220:228:242 SD: 0.4977 cents 132:147:156:166:180:191:203:226:240:249:264 SD: 0.4772 cents 149:166:176:187:203:216:229:255:271:281:298 SD: 0.4085 cents 192:214:227:241:262:278:295:329:349:362:384 SD: 0.2898 cents 236:263:279:296:322:342:363:404:429:445:472 SD: 0.2460 cents 247:275:292:310:337:358:380:423:449:465:494 SD: 0.2051 cents 361:402:427:453:493:523:555:618:656:680:722 SD: 0.2038 cents 368:410:435:462:502:533:566:630:669:693:736 SD: 0.1561 cents 439:489:519:551:599:636:675:752:798:827:878 SD: 0.1093 cents