Scala analysis: xen09-chalmers-tritriadic-1-5-11
Tritriadic scale built from 1:5:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 16/11 648.682058 undecimal semi-diminished fifth 4: 55/32 937.631656 5: 20/11 1034.995772 large minor 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: 5/4 386.3137 major third 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 128/121 97.3641 undecimal semitone 4: 605/512 288.9496 5: 128/121 97.3641 undecimal semitone 6: 1331/1280 67.6401 7: 128/121 97.3641 undecimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1331/1280 67.640 cents 1: 3 128/121 97.364 cents undecimal semitone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 605/512 288.950 cents 1: 1 5/4 386.314 cents major third 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 64/55 262.368 cents 2: 2 5/4 386.314 cents major third 2: 1 160/121 483.678 cents 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 64/55 262.368 cents 3: 1 1331/1024 453.954 cents 3: 1 160/121 483.678 cents 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 2 11/8 551.318 cents undecimal semi-augmented fourth 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 121/80 716.322 cents 4: 1 2048/1331 746.046 cents 4: 1 55/32 937.632 cents 5: 1 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 121/80 716.322 cents 5: 2 8/5 813.686 cents minor sixth 5: 1 55/32 937.632 cents 5: 2 20/11 1034.996 cents large minor seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 1024/605 911.050 cents 6: 1 20/11 1034.996 cents large minor seventh 6: 3 121/64 1102.636 cents two (undecimal semi-augmented fourth) 6: 1 2560/1331 1132.360 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 386.3 551.3 648.7 937.6 1035.0 1102.6 1200.0 386.3 : 165.0 262.4 551.3 648.7 716.3 813.7 1200.0 551.3 : 97.4 386.3 483.7 551.3 648.7 1035.0 1200.0 648.7 : 288.9 386.3 454.0 551.3 937.6 1102.6 1200.0 937.6 : 97.4 165.0 262.4 648.7 813.7 911.1 1200.0 1035.0: 67.6 165.0 551.3 716.3 813.7 1102.6 1200.0 1102.6: 97.4 483.7 648.7 746.0 1035.0 1132.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.6401 .. 386.3137 cents 1600/1331, 318.6736 cents 1331/1280, 67.6401 cents 2: 165.0042 .. 551.3179 cents 5/4, 386.3137 cents 22/25,-221.3095 cents 3: 262.3683 .. 648.6821 cents 5/4, 386.3137 cents 512/605,-288.9496 cents 4: 551.3179 .. 937.6317 cents 5/4, 386.3137 cents 121/128,-97.3641 cents 5: 648.6821 .. 1034.9958 cents 5/4, 386.3137 cents 512/605,-288.9496 cents 6: 813.6863 .. 1132.3599 cents 1600/1331, 318.6736 cents 22/25,-221.3095 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1331/1280, 67.6401 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 2.534422 Largest / Average step : 2.253497 Largest / Smallest step : 5.711311 Median interval of one step : 128/121, 97.3641 cents, amount: 3 Most common interval of one step : 128/121, 97.3641 cents, amount: 3 Least squares average step : 195.54512 cents, oct.: 1368.81583 cents Scale is not proper Step pattern alph. order: ABCDCEC Step pattern size order : ECBDBAB Scale is not a Constant Structure Scale diversity : 1.430874 Lumma stability : 0.112734 Lumma impropriety factor : 0.724993 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 : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 33275/32768, 26.5813 cents Most common intervals : 11/8, 551.3179 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 386.314 551.318 cents Most common triad is 0.0 551.318 648.682 cents, amount: 3 Number of recognisable fifths : 2, average 716.3222 cents Number of appreciable fifths : 0 Scale contains a complete diamond : 1 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.014095 Average absolute harmonicity : 0.186624 Specific harmonicity : 0.076814 Fundamental : 1/704, -9.4594 octaves, 0.3716 Hz. Guide tone : 9680, 13.2408 octaves, 2532535.472 Hz. Exponens Consonantiae : 6.814720E+06, 22.70022 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 180.5, average 25.78571 Mersenne's string divisions : 85319595 Sum of van Prooijen's expressibility: 7.64630, average 1.09233 Sum of Tenney's harmonic distance : 15.26896, average 2.18128 Vogel's harmonic complexity : 21.00000 Wille's k value : 665 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 127.60047, average 4.55716 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 -1.28571 23 1 5: 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 15 23| Scale is weakly epimorphic with val: <7 16 25| Scale is weakly epimorphic with val: <7 18 22|
FIT/MODE
7: 2 1 1 1 1 0 1 N T3 SD: 48.7508 c. M: 80.4888 c. 8: 3 1 0 2 1 0 1 N SD: 43.4374 c. M:-63.6863 c. 9: 3 1 1 2 1 0 1 N SD: 21.2116 c. M: 35.9692 c. 13: 4 2 1 3 1 1 1 N SD: 11.5054 c. M: 19.6112 c. 22: 7 3 2 5 2 1 2 N SD: 6.9247 c. M: 11.7268 c. 28: 9 4 2 7 2 2 2 N SD: 6.2394 c. M:-11.6498 c. 35: 11 5 3 8 3 2 3 N SD: 6.6832 c. M: 11.9174 c. 37: 12 5 3 9 3 2 3 N SD: 1.8828 c. M:-2.9089 c. 50: 16 7 4 12 4 3 4 N SD: 1.6810 c. M: 2.9958 c. 87: 28 12 7 21 7 5 7 N SD: 0.4398 c. M:-0.8124 c. 196: 63 27 16 47 16 11 16 N SD: 0.5051 c. M: 0.8970 c. 211: 68 29 17 51 17 12 17 N SD: 0.4549 c. M:-0.7570 c. 233: 75 32 19 56 19 13 19 N SD: 0.2637 c. M: 0.4900 c. 283: 91 39 23 68 23 16 23 N SD: 0.3059 c. M: 0.5292 c. 320: 103 44 26 77 26 18 26 N SD: 0.0838 c. M: 0.1359 c. 407: 131 56 33 98 33 23 33 N SD: 0.0596 c. M: 0.1063 c. 727: 234 100 59 175 59 41 59 N SD: 0.0467 c. M: 0.0801 c. 1084: 349 149 88 261 88 61 88 N SD: 0.0356 c. M:-0.0596 c. 1171: 377 161 95 282 95 66 95 N SD: 0.0161 c. M:-0.0285 c. 1491: 480 205 121 359 121 84 121 N SD: 0.0111 c. M: 0.0202 c. 1898: 611 261 154 457 154 107 154 N SD: 0.0081 c. M: 0.0131 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 26.6365 cents 3 x 4 x 5 x x 6 S SD: 25.1131 cents 4:5 x 6:7 x x 8 S SD: 15.4335 cents 5:6:7 x x 9 x 10 SD: 19.7965 cents 6 x 8:9:10:11 x 12 S SD: 18.6767 cents 7:9 x 10:12 x 13:14 SD: 13.1588 cents 8:10:11:12:14 x 15:16 S SD: 10.5640 cents 11:14:15:16:19:20:21:22 SD: 5.5988 cents 12:15 x 17:21:22:23:24 SD: 10.3107 cents 13:16:18:19:22:24:25:26 SD: 8.1092 cents 15:19:21:22:26:27:28:30 SD: 7.4361 cents 16:20:22:23:28:29:30:32 SD: 5.7593 cents 21:26:29:31:36:38:40:42 SD: 5.0290 cents 24:30:33:35:41:44:45:48 SD: 3.3316 cents 29:36:40:42:50:53:55:58 SD: 2.7380 cents 35:44:48:51:60:64:66:70 SD: 2.3255 cents 40:50:55:58:69:73:76:80 SD: 1.9387 cents 48:60:66:70:83:87:91:96 SD: 1.9259 cents 53:66:73:77:91:96:100:106 SD: 1.5265 cents 61:76:84:89:105:111:115:122 SD: 1.4299 cents 64:80:88:93:110:116:121:128 SD: 0.8109 cents 88:110:121:128:151:160:166:176 SD: 0.6920 cents 99:124:136:144:170:180:187:198 SD: 0.6356 cents 128:160:176:186:220:233:242:256 SD: 0.3772 cents 192:240:264:279:330:349:363:384 SD: 0.2501 cents 264:330:363:384:454:480:499:528 SD: 0.1496 cents 440:550:605:640:756:800:832:880 SD: 0.0898 cents 576:720:792:838:990:1047:1089:1152 SD: 0.0838 cents