Scala analysis: xen09-chalmers-tritriadic-7-8-11
Tritriadic scale built from 7:8:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 121/98 364.984072 3: 14/11 417.507964 undecimal diminished fourth or major third 4: 16/11 648.682058 undecimal semi-diminished fifth 5: 11/7 782.492036 undecimal augmented fifth 6: 88/49 1013.666129 undecimal minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 49/44 186.3339 undecimal minor whole tone 1: 8/7 231.1741 septimal whole tone 2: 121/112 133.8100 3: 1372/1331 52.5239 4: 8/7 231.1741 septimal whole tone 5: 121/112 133.8100 6: 8/7 231.1741 septimal whole tone 7: 49/44 186.3339 undecimal minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1372/1331 52.524 cents 1: 2 121/112 133.810 cents 1: 1 49/44 186.334 cents undecimal minor whole tone 1: 3 8/7 231.174 cents septimal whole tone 2: 1 49/44 186.334 cents undecimal minor whole tone 2: 1 1568/1331 283.698 cents 2: 3 121/98 364.984 cents 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 3 14/11 417.508 cents undecimal diminished fourth or major third 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 484/343 596.158 cents 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 343/242 603.842 cents 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 3 11/7 782.492 cents undecimal augmented fifth 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 3 196/121 835.016 cents two (undecimal diminished fourth or major third) 5: 1 1331/784 916.302 cents 5: 1 88/49 1013.666 cents undecimal minor seventh 6: 3 7/4 968.826 cents harmonic seventh 6: 1 88/49 1013.666 cents undecimal minor seventh 6: 2 224/121 1066.190 cents 6: 1 1331/686 1147.476 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 231.2 365.0 417.5 648.7 782.5 1013.7 1200.0 231.2 : 133.8 186.3 417.5 551.3 782.5 968.8 1200.0 365.0 : 52.5 283.7 417.5 648.7 835.0 1066.2 1200.0 417.5 : 231.2 365.0 596.2 782.5 1013.7 1147.5 1200.0 648.7 : 133.8 365.0 551.3 782.5 916.3 968.8 1200.0 782.5 : 231.2 417.5 648.7 782.5 835.0 1066.2 1200.0 1013.7: 186.3 417.5 551.3 603.8 835.0 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 52.5239 .. 231.1741 cents 2662/2401, 178.6502 cents 1372/1331, 52.5239 cents 2: 186.3339 .. 417.5080 cents 8/7, 231.1741 cents 343/352,-44.8402 cents 3: 417.5080 .. 648.6821 cents 8/7, 231.1741 cents 1/1, 0.0000 cents 4: 551.3179 .. 782.4920 cents 8/7, 231.1741 cents 121/128,-97.3641 cents 5: 782.4920 .. 1013.6661 cents 8/7, 231.1741 cents 1/1, 0.0000 cents 6: 968.8259 .. 1147.4761 cents 2662/2401, 178.6502 cents 343/352,-44.8402 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1372/1331, 52.5239 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 3.263821 Largest / Average step : 1.348516 Largest / Smallest step : 4.401313 Median interval of one step : 49/44, 186.3339 cents, amount: 1 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 165.73465 cents, oct.: 1160.14257 cents Scale is not proper Step pattern alph. order: ABCABAD Step pattern size order : DBADBDC Scale is not a Constant Structure Scale diversity : 1.411240 Lumma stability : 0.087540 Lumma impropriety factor : 0.155870 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 117649/117128, 7.6837 cents Most common intervals : 14/11, 417.5080 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 231.174 782.492 cents Most common triad is 0.0 417.508 782.492 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 7 11 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 : 0.011062 Average absolute harmonicity : 0.175803 Specific harmonicity : 0.061705 Fundamental : 1/1078, -10.0741 octaves, 0.2427 Hz. Guide tone : 13552, 13.7262 octaves, 3545549.661 Hz. Exponens Consonantiae : 1.460906E+07, 23.80036 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 222.0, average 31.71429 Mersenne's string divisions : 13501350 Sum of van Prooijen's expressibility: 7.74226, average 1.10604 Sum of Tenney's harmonic distance : 16.07743, average 2.29678 Vogel's harmonic complexity : 25.71429 Wille's k value : 665 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 84.81336, average 3.02905 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.57143 13 1 7: -2 .. 1 -0.71429 7 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 18 24| Scale is weakly epimorphic with val: <7 19 23| Scale is weakly epimorphic with val: <7 20 22|
FIT/MODE
7: 1 1 0 2 0 2 1 N T3 SD: 54.2367 c. M: 96.7778 c. 8: 2 0 1 1 1 2 1 N SD: 45.9215 c. M:-68.8259 c. 9: 2 1 0 2 1 2 1 N T3 SD: 29.8362 c. M:-53.0005 c. 11: 2 1 1 2 1 2 2 N D3 SD: 21.8785 c. M: 37.7113 c. 14: 3 1 1 3 1 3 2 N SD: 20.7100 c. M:-37.0322 c. 15: 3 2 0 3 2 3 2 N T3 SD: 19.5883 c. M:-35.0159 c. 17: 3 2 1 3 2 3 3 N SD: 14.2440 c. M: 25.4308 c. 19: 4 2 1 3 2 4 3 N SD: 17.5980 c. M:-24.5973 c. 20: 4 2 1 4 2 4 3 N SD: 6.3625 c. M:-11.3179 c. 26: 5 3 1 5 3 5 4 N SD: 2.2854 c. M:-4.2467 c. 46: 9 5 2 9 5 9 7 N SD: 2.3656 c. M:-3.7252 c. 72: 14 8 3 14 8 14 11 N SD: 1.6754 c. M:-3.0005 c. 89: 17 10 4 17 10 17 14 N SD: 1.3782 c. M: 2.4302 c. 109: 21 12 5 21 12 21 17 N SD: 0.8988 c. M: 1.6813 c. 115: 22 13 5 22 13 22 18 N SD: 1.0606 c. M: 1.7255 c. 135: 26 15 6 26 15 26 21 N SD: 0.2914 c. M: 0.5396 c. 161: 31 18 7 31 18 31 25 N SD: 0.1468 c. M: 0.2349 c. 296: 57 33 13 57 33 57 46 N SD: 0.0881 c. M: 0.1526 c. 457: 88 51 20 88 51 88 71 N SD: 0.0668 c. M: 0.1044 c. 753: 145 84 33 145 84 145 117 N SD: 0.0685 c. M: 0.1203 c. 960: 185 107 42 185 107 185 149 N SD: 0.0504 c. M:-0.0839 c. 1095: 211 122 48 211 122 211 170 N SD: 0.0476 c. M:-0.0851 c. 1121: 216 125 49 216 125 216 174 N SD: 0.0403 c. M:-0.0716 c. 1256: 242 140 55 242 140 242 195 N SD: 0.0251 c. M:-0.0441 c. 1417: 273 158 62 273 158 273 220 N SD: 0.0138 c. M:-0.0248 c. 1713: 330 191 75 330 191 330 266 N SD: 0.0055 c. M: 0.0103 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: 43.2859 cents 4 x 5 x 6 x 7:8 S SD: 18.2065 cents 5 x 6 x 7:8:9:10 S SD: 17.6654 cents 6:7 x 8:9 x 11:12 SD: 21.7924 cents 7:8 x 9:10:11:13:14 SD: 11.3653 cents 8:9:10 x 12:13:14:16 S SD: 16.1719 cents 9:10:11 x 13:14:16:18 SD: 9.7907 cents 11:13 x 14:16:17:20:22 SD: 11.3721 cents 12:14:15 x 17:19:22:24 SD: 12.0888 cents 13:15:16:17:19:20:23:26 SD: 9.6831 cents 14:16:17:18:20:22:25:28 SD: 6.7187 cents 15:17 x 19:22:24:27:30 SD: 6.3969 cents 16:18:20 x 23:25:29:32 SD: 7.3885 cents 18:21:22:23:26:28:32:36 SD: 6.9892 cents 20:23:25 x 29:31:36:40 SD: 5.7279 cents 21:24:26:27:31:33:38:42 SD: 4.8577 cents 22:25:27:28:32:35:40:44 SD: 4.7727 cents 26:30:32:33:38:41:47:52 SD: 3.3835 cents 29:33:36:37:42:46:52:58 SD: 3.1538 cents 33:38:41:42:48:52:59:66 SD: 2.7497 cents 42:48:52:53:61:66:75:84 SD: 2.6543 cents 44:50:54:56:64:69:79:88 SD: 2.1154 cents 51:58:63:65:74:80:92:102 SD: 1.8395 cents 55:63:68:70:80:86:99:110 SD: 1.5012 cents 63:72:78:80:92:99:113:126 SD: 1.3547 cents 77:88:95:98:112:121:138:154 SD: 0.5442 cents 154:176:190:196:224:242:277:308 SD: 0.4257 cents 161:184:199:205:234:253:289:322 SD: 0.3673 cents 231:264:285:294:336:363:415:462 SD: 0.2045 cents 308:352:380:392:448:484:553:616 SD: 0.1966 cents 315:360:389:401:458:495:566:630 SD: 0.1745 cents 392:448:484:499:570:616:704:784 SD: 0.0908 cents