Scala analysis: xen09-chalmers-tritriadic-24-33-44
Tritriadic scale built from 24:33:44
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 121/96 400.680884 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 121/72 898.725883 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 1331/1152 250.0438 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 121/108 196.7709 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 121/108 196.771 cents 1: 1 1331/1152 250.044 cents 2: 3 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 121/96 400.681 cents 3: 1 1728/1331 451.911 cents 3: 3 4/3 498.045 cents perfect fourth 3: 3 11/8 551.318 cents undecimal semi-augmented fourth 4: 3 16/11 648.682 cents undecimal semi-diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 1331/864 748.089 cents 5: 2 192/121 799.319 cents 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 3 121/72 898.726 cents 6: 1 2304/1331 949.956 cents 6: 1 216/121 1003.229 cents 6: 5 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 150.6 400.7 551.3 702.0 898.7 1049.4 1200.0 150.6 : 250.0 400.7 551.3 748.1 898.7 1049.4 1200.0 400.7 : 150.6 301.3 498.0 648.7 799.3 950.0 1200.0 551.3 : 150.6 347.4 498.0 648.7 799.3 1049.4 1200.0 702.0 : 196.8 347.4 498.0 648.7 898.7 1049.4 1200.0 898.7 : 150.6 301.3 451.9 702.0 852.6 1003.2 1200.0 1049.4: 150.6 301.3 551.3 702.0 852.6 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 250.0438 cents 14641/13824, 99.4068 cents 12/11, 150.6371 cents 2: 301.2741 .. 400.6809 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 3: 451.9112 .. 551.3179 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 4: 648.6821 .. 748.0888 cents 14641/13824, 99.4068 cents 128/121, 97.3641 cents 5: 799.3191 .. 898.7259 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 6: 949.9562 .. 1049.3629 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1331/1152, 250.0438 cents Average / Smallest step : 1.138024 Largest / Average step : 1.458589 Largest / Smallest step : 1.659909 Median interval of one step : 12/11, 150.6371 cents, amount: 5 Most common interval of one step : 12/11, 150.6371 cents, amount: 5 Least squares average step : 175.73986 cents, oct.: 1230.17899 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : SLSSMSS Scale is a Constant Structure, by a margin of 51.23029 cents Scale diversity : 1.396184 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.502966 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 : 1331/1296, 46.1338 cents Most common intervals : 12/11, 150.6371 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 551.318 1049.363 cents Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 3 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 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.014379 Average absolute harmonicity : 0.207794 Specific harmonicity : 0.079500 Fundamental : 1/3168, -11.6294 octaves, 0.0826 Hz. Guide tone : 1452, 10.5038 octaves, 379880.321 Hz. Exponens Consonantiae : 4.599936E+06, 22.13318 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 238.5, average 34.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.76687, average 1.10955 Sum of Tenney's harmonic distance : 14.96896, average 2.13842 Vogel's harmonic complexity : 27.57143 Wille's k value : 1996 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 97.83317, average 3.49404 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.42857 16 1 3: -2 .. 1 -0.28571 6 1 11: -1 .. 2 0.71429 7 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 10 25| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 12 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.8904 c. M: 57.8237 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 31.8772 c. M:-49.3191 c. 9: 1 2 1 1 2 1 1 P M ME S SD: 21.9274 c. M: 35.2883 c. Pelog Saptanada: Sunda 15: 2 3 2 2 2 2 2 SP M ME S SD: 11.5106 c. M: 18.7259 c. Miller's Porcupine-7 Major 17: 2 4 2 2 3 2 2 P T3 SD: 13.3830 c. M:-22.8485 c. 24: 3 5 3 3 4 3 3 SP T3 SD: 1.0992 c. M: 1.9550 c. 111: 14 23 14 14 18 14 14 SP T3 SD: 0.7639 c. M: 1.4286 c. 135: 17 28 17 17 22 17 17 SP T3 SD: 0.5246 c. M: 0.9481 c. 159: 20 33 20 20 26 20 20 SP T3 SD: 0.4091 c. M: 0.6809 c. 183: 23 38 23 23 30 23 23 SP T3 SD: 0.3802 c. M: 0.6809 c. 311: 39 65 39 39 51 39 39 SP T3 SD: 0.3382 c. M:-0.6053 c. 335: 42 70 42 42 55 42 42 SP T3 SD: 0.2931 c. M:-0.5131 c. 359: 45 75 45 45 59 45 45 SP T3 SD: 0.2731 c. M:-0.4385 c. 422: 53 88 53 53 69 53 53 SP T3 SD: 0.2367 c. M:-0.4147 c. 446: 56 93 56 56 73 56 56 SP T3 SD: 0.1690 c. M:-0.2872 c. 470: 59 98 59 59 77 59 59 SP T3 SD: 0.1122 c. M:-0.1727 c. 494: 62 103 62 62 81 62 62 SP T3 SD: 0.0722 c. M:-0.1288 c. 518: 65 108 65 65 85 65 65 SP T3 SD: 0.0657 c. M:-0.1158 c. 653: 82 136 82 82 107 82 82 SP T3 SD: 0.0567 c. M: 0.1041 c. 677: 85 141 85 85 111 85 85 SP T3 SD: 0.0504 c. M: 0.0900 c. 1147: 144 239 144 144 188 144 144 SP T3 SD: 0.0283 c. M:-0.0502 c. 1171: 147 244 147 147 192 147 147 SP T3 SD: 0.0052 c. M:-0.0091 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 18.3921 cents 4 x 5 x 6:7 x 8 S SD: 17.8893 cents 5 x 6:7 x 8:9:10 S SD: 25.6481 cents 6:7 x 8:9:10:11:12 S SD: 21.4442 cents 7:8:9:10:11:12:13:14 H SD: 20.3124 cents 8:9:10:11:12:13:15:16 SD: 12.7336 cents 10:11:13:14:15:17:18:20 SD: 10.5473 cents 12:13:15:17:18:20:22:24 SD: 8.1183 cents 16:17:20:22:24:27:29:32 SD: 7.4719 cents 18:20:23:25:27:30:33:36 SD: 6.5140 cents 19:21:24:26:29:32:35:38 SD: 5.6861 cents 22:24:28:30:33:37:40:44 SD: 3.7734 cents 24:26:30:33:36:40:44:48 SD: 3.3757 cents 32:35:40:44:48:54:59:64 SD: 2.7622 cents 34:37:43:47:51:57:62:68 SD: 2.2215 cents 42:46:53:58:63:71:77:84 SD: 2.0748 cents 46:50:58:63:69:77:84:92 SD: 1.9214 cents 54:59:68:74:81:91:99:108 SD: 1.1644 cents 66:72:83:91:99:111:121:132 SD: 0.8994 cents 88:96:111:121:132:148:161:176 SD: 0.5750 cents 154:168:194:212:231:259:282:308 SD: 0.4719 cents 176:192:222:242:264:296:323:352 SD: 0.3664 cents 200:218:252:275:300:336:367:400 SD: 0.3262 cents 222:242:280:305:333:373:407:444 SD: 0.3257 cents 242:264:305:333:363:407:444:484 SD: 0.3222 cents 254:277:320:349:381:427:466:508 SD: 0.2974 cents 264:288:333:363:396:444:484:528 SD: 0.2627 cents 288:314:363:396:432:484:528:576 SD: 0.1432 cents 384:419:484:528:576:645:704:768 SD: 0.1386 cents 472:515:595:649:708:793:865:944 SD: 0.1303 cents 504:550:635:693:756:847:924:1008 SD: 0.1271 cents 560:611:706:770:840:941:1027:1120 SD: 0.1098 cents