Scala analysis: xen09-chalmers-tritriadic-1-7-11
Tritriadic scale built from 1:7:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 77/64 320.143849 Keemun minor third 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 16/11 648.682058 undecimal semi-diminished fifth 5: 7/4 968.825906 harmonic seventh 6: 121/64 1102.635885 two (undecimal semi-augmented fourth) 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 128/121 97.3641 undecimal semitone 1: 77/64 320.1438 Keemun minor third 2: 128/121 97.3641 undecimal semitone 3: 121/112 133.8100 4: 128/121 97.3641 undecimal semitone 5: 77/64 320.1438 Keemun minor third 6: 121/112 133.8100 7: 128/121 97.3641 undecimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 128/121 97.364 cents undecimal semitone 1: 2 121/112 133.810 cents 1: 2 77/64 320.144 cents Keemun minor third 2: 3 8/7 231.174 cents septimal whole tone 2: 3 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 1331/1024 453.954 cents 3: 1 1024/847 328.538 cents 3: 1 1792/1331 514.872 cents 3: 5 11/8 551.318 cents undecimal semi-augmented fourth 4: 5 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 1331/896 685.128 cents 4: 1 847/512 871.462 cents 5: 1 2048/1331 746.046 cents 5: 3 11/7 782.492 cents undecimal augmented fifth 5: 3 7/4 968.826 cents harmonic seventh 6: 2 128/77 879.856 cents 6: 2 224/121 1066.190 cents 6: 3 121/64 1102.636 cents two (undecimal semi-augmented fourth) 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 : 320.1 417.5 551.3 648.7 968.8 1102.6 1200.0 320.1 : 97.4 231.2 328.5 648.7 782.5 879.9 1200.0 417.5 : 133.8 231.2 551.3 685.1 782.5 1102.6 1200.0 551.3 : 97.4 417.5 551.3 648.7 968.8 1066.2 1200.0 648.7 : 320.1 454.0 551.3 871.5 968.8 1102.6 1200.0 968.8 : 133.8 231.2 551.3 648.7 782.5 879.9 1200.0 1102.6: 97.4 417.5 514.9 648.7 746.0 1066.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.3641 .. 320.1438 cents 9317/8192, 222.7797 cents 128/121, 97.3641 cents 2: 231.1741 .. 453.9538 cents 9317/8192, 222.7797 cents 512/539,-88.9698 cents 3: 328.5382 .. 551.3179 cents 9317/8192, 222.7797 cents 1048576/1127357,-125.4156 cents 4: 648.6821 .. 871.4618 cents 9317/8192, 222.7797 cents 128/121, 97.3641 cents 5: 746.0462 .. 968.8259 cents 9317/8192, 222.7797 cents 1048576/1127357,-125.4156 cents 6: 879.8562 .. 1102.6359 cents 9317/8192, 222.7797 cents 512/539,-88.9698 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 128/121, 97.3641 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 77/64, 320.1438 cents Average / Smallest step : 1.760696 Largest / Average step : 1.867506 Largest / Smallest step : 3.288109 Median interval of one step : 121/112, 133.8100 cents, amount: 2 Most common interval of one step : 128/121, 97.3641 cents, amount: 3 Least squares average step : 180.45562 cents, oct.: 1263.18933 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : LSMSLMS Scale is a Constant Structure, by a margin of 8.39436 cents Scale diversity : 1.399244 Lumma stability : 0.243410 Lumma impropriety factor : 0.357309 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 : 65536/65219, 8.3944 cents Most common intervals : 11/8, 551.3179 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 417.508 648.682 cents Most common triad is 0.0 551.318 648.682 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 1 11 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.013363 Average absolute harmonicity : 0.180034 Specific harmonicity : 0.071791 Fundamental : 1/704, -9.4594 octaves, 0.3716 Hz. Guide tone : 13552, 13.7262 octaves, 3545549.661 Hz. Exponens Consonantiae : 9.540608E+06, 23.18565 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 205.5, average 29.35714 Mersenne's string divisions : 245329425 Sum of van Prooijen's expressibility: 7.93855, average 1.13408 Sum of Tenney's harmonic distance : 15.70734, average 2.24391 Vogel's harmonic complexity : 21.57143 Wille's k value : 665 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 129.20255, average 4.61438 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -1.57143 23 1 7: 0 .. 1 0.42857 3 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 18 22| Scale is JI-epimorphic with val: <7 19 24| Scale is weakly epimorphic with val: <7 20 26| Scale is weakly epimorphic with val: <7 22 23|
FIT/MODE
7: 2 0 1 1 2 0 1 N T3 SD: 50.5491 c. M: 74.6508 c. 8: 2 1 0 1 2 1 1 N T3 S SD: 55.5548 c. M: 101.3179 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 30.1585 c. M: 53.4772 c. 11: 3 1 1 1 3 1 1 N M DE S SD: 10.5657 c. M:-18.8557 c. 15: 4 1 2 1 4 2 1 N T3 SD: 10.9330 c. M: 17.5080 c. 24: 6 2 3 2 6 3 2 N T3 SD: 12.4047 c. M: 20.1438 c. 26: 7 2 3 2 7 3 2 N T3 SD: 2.7157 c. M:-5.0564 c. 37: 10 3 4 3 10 4 3 N T3 SD: 2.7151 c. M:-4.1805 c. 63: 17 5 7 5 17 7 5 N T3 SD: 2.0480 c. M:-3.6657 c. 72: 19 6 8 6 19 8 6 N T3 SD: 1.9958 c. M: 3.4772 c. 89: 24 7 10 7 24 10 7 N T3 SD: 2.0465 c. M:-3.4517 c. 98: 26 8 11 8 26 11 8 N T3 SD: 1.0191 c. M: 1.7765 c. 109: 29 9 12 9 29 12 9 N T3 SD: 0.9186 c. M: 1.7185 c. 124: 33 10 14 10 33 14 10 N T3 SD: 0.7765 c. M: 1.3789 c. 135: 36 11 15 11 36 15 11 N T3 SD: 0.2249 c. M: 0.4137 c. 296: 79 24 33 24 79 33 24 N T3 SD: 0.0706 c. M:-0.1264 c. 431: 115 35 48 35 115 48 35 N T3 SD: 0.0707 c. M:-0.1254 c. 727: 194 59 81 59 194 81 59 N T3 SD: 0.0585 c. M:-0.0986 c. 986: 263 80 110 80 263 110 80 N T3 SD: 0.0414 c. M: 0.0637 c. 1121: 299 91 125 91 299 125 91 N T3 SD: 0.0409 c. M: 0.0725 c. 1282: 342 104 143 104 342 143 104 N T3 SD: 0.0198 c. M: 0.0353 c. 1417: 378 115 158 115 378 158 115 N T3 SD: 0.0180 c. M: 0.0309 c. 1578: 421 128 176 128 421 176 128 N T3 SD: 0.0141 c. M:-0.0257 c. 1713: 457 139 191 139 457 191 139 N T3 SD: 0.0048 c. M: 0.0089 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: 26.6365 cents 3 x x 4 x 5 x 6 S SD: 33.2878 cents 4 x 5 x 6:7 x 8 S SD: 15.4335 cents 5:6 x 7 x 9 x 10 SD: 14.5170 cents 6:7 x 8:9 x 11:12 SD: 21.3092 cents 7:8:9 x 10:12:13:14 S SD: 17.8176 cents 8 x 10:11:12:14:15:16 S SD: 10.5640 cents 9:11 x 12:13:16:17:18 SD: 11.1464 cents 11:13:14:15:16:19:21:22 SD: 6.3224 cents 12:14:15 x 17:21:23:24 SD: 13.3945 cents 13:16:17:18:19:23:25:26 SD: 10.2905 cents 14:17:18:19:20:25:26:28 SD: 9.2911 cents 15:18:19:21:22:26:28:30 SD: 6.4365 cents 18:22:23:25:26:32:34:36 SD: 6.3639 cents 19:23:24:26:28:33:36:38 SD: 4.6278 cents 24:29:31:33:35:42:45:48 SD: 4.3719 cents 26:31:33:36:38:46:49:52 SD: 4.2138 cents 29:35:37:40:42:51:55:58 SD: 2.1877 cents 40:48:51:55:58:70:76:80 SD: 1.6444 cents 48:58:61:66:70:84:91:96 SD: 1.4675 cents 59:71:75:81:86:103:112:118 SD: 1.3700 cents 73:88:93:100:106:128:138:146 SD: 1.2504 cents 80:96:102:110:116:140:151:160 SD: 1.1726 cents 88:106:112:121:128:154:166:176 SD: 0.6298 cents 99:119:126:136:144:173:187:198 SD: 0.5314 cents 128:154:163:176:186:224:242:256 SD: 0.2783 cents 275:331:350:378:400:481:520:550 SD: 0.1888 cents 400:481:509:550:582:700:756:800 SD: 0.1764 cents 403:485:513:554:586:705:762:806 SD: 0.1562 cents 429:516:546:590:624:751:811:858 SD: 0.1210 cents 528:635:672:726:768:924:998:1056 SD: 0.1154 cents 557:670:709:766:810:975:1053:1114 SD: 0.1130 cents 576:693:733:792:838:1008:1089:1152 SD: 0.0618 cents