Scala analysis: xen09-chalmers-tritriadic-26-34-39
Tritriadic scale built from 26:34:39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 17/13 464.427748 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 68/39 962.472747 6: 51/26 1166.382749 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 52/51 33.6173 1: 9/8 203.9100 major whole tone 2: 136/117 260.5177 3: 52/51 33.6173 4: 9/8 203.9100 major whole tone 5: 136/117 260.5177 6: 9/8 203.9100 major whole tone 7: 52/51 33.6173
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 52/51 33.617 cents 1: 3 9/8 203.910 cents major whole tone 1: 2 136/117 260.518 cents 2: 3 39/34 237.527 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 17/13 464.428 cents 3: 1 351/272 441.437 cents 3: 5 4/3 498.045 cents perfect fourth 3: 1 153/104 668.338 cents 4: 1 208/153 531.662 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 544/351 758.563 cents 5: 3 26/17 735.572 cents 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 68/39 962.473 cents 6: 2 117/68 939.482 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 51/26 1166.383 cents 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 : 203.9 464.4 498.0 702.0 962.5 1166.4 1200.0 203.9 : 260.5 294.1 498.0 758.6 962.5 996.1 1200.0 464.4 : 33.6 237.5 498.0 702.0 735.6 939.5 1200.0 498.0 : 203.9 464.4 668.3 702.0 905.9 1166.4 1200.0 702.0 : 260.5 464.4 498.0 702.0 962.5 996.1 1200.0 962.5 : 203.9 237.5 441.4 702.0 735.6 939.5 1200.0 1166.4: 33.6 237.5 498.0 531.7 735.6 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 260.5177 cents 578/507, 226.9005 cents 52/51, 33.6173 cents 2: 237.5273 .. 464.4277 cents 578/507, 226.9005 cents 4563/4624,-22.9905 cents 3: 441.4373 .. 668.3377 cents 578/507, 226.9005 cents 4563/4624,-22.9905 cents 4: 531.6623 .. 758.5627 cents 578/507, 226.9005 cents 21632/23409,-136.6755 cents 5: 735.5723 .. 962.4727 cents 578/507, 226.9005 cents 4563/4624,-22.9905 cents 6: 939.4823 .. 1166.3827 cents 578/507, 226.9005 cents 4563/4624,-22.9905 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 136/117, 260.5177 cents Average / Smallest step : 5.099423 Largest / Average step : 1.519687 Largest / Smallest step : 7.749525 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 183.18129 cents, oct.: 1282.26904 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MLSMLMS Scale is a Constant Structure, by a margin of 22.99049 cents Scale diversity : 1.222238 Lumma stability : 0.056029 Lumma impropriety factor : 0.190531 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 : 4624/4563, 22.9905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 464.428 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Scale contains a complete diamond : 1 3 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 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 17 Odd number limit : 351 (O: 351 U: 351) Highest odd numerator or denominator: 51 Scale harmonicity : 0.015321 Average absolute harmonicity : 0.237369 Specific harmonicity : 0.068762 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 612, 9.2574 octaves, 160114.846 Hz. Exponens Consonantiae : 1.909440E+05, 17.54279 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 123.0, average 17.57143 Mersenne's string divisions : 4201890 Sum of van Prooijen's expressibility: 6.43757, average 0.91965 Sum of Tenney's harmonic distance : 12.90620, average 1.84374 Vogel's harmonic complexity : 21.57143 Wille's k value : 175 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 75.48330, average 2.69583 Lattice compactness (without 2's) : 46.44630, average 1.65880 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 10 1 3: -1 .. 2 0.28571 6 3 13: -1 .. 0 -0.42857 3 17: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 24 29| Scale is weakly epimorphic with val: <7 10 25 30| Scale is weakly epimorphic with val: <7 10 26 31| Scale is weakly epimorphic with val: <7 10 27 32| Scale is JI-epimorphic with val: <7 11 24 26| Scale is JI-epimorphic with val: <7 11 25 27| Scale is JI-epimorphic with val: <7 11 26 28| Scale is JI-epimorphic with val: <7 11 27 29| Scale is JI-epimorphic with val: <7 11 28 30| Scale is JI-epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 12 24 30| Scale is weakly epimorphic with val: <7 12 25 31| Scale is weakly epimorphic with val: <7 12 26 32|
FIT/MODE
7: 1 2 0 1 2 1 0 N T3 SD: 36.9701 c. M:-66.0987 c. 10: 2 2 0 2 2 2 0 N M DE S SD: 21.8189 c. M:-36.0900 c. 12: 2 3 0 2 3 2 0 N T3 SD: 23.3811 c. M:-37.5273 c. 15: 3 3 0 3 3 3 0 N M DE S SD: 21.8189 c. M:-36.0900 c. 17: 3 4 0 3 4 3 0 N T3 SD: 19.8849 c. M:-33.6173 c. 19: 3 4 1 3 4 3 1 N T3 SD: 16.5257 c. M: 29.5406 c. 20: 3 5 0 4 4 3 1 N SD: 17.5970 c. M: 26.3827 c. 21: 4 4 1 3 5 3 1 N S SD: 16.1353 c. M:-24.6614 c. 24: 4 5 1 4 5 4 1 N T3 SD: 9.6736 c. M: 16.3827 c. 29: 5 6 1 5 6 5 1 N T3 SD: 6.2658 c. M: 10.7486 c. 31: 5 7 1 5 7 5 1 N T3 SD: 5.5388 c. M: 10.3616 c. 34: 6 7 1 6 7 6 1 N T3 SD: 5.5756 c. M: 9.5316 c. 36: 6 8 1 6 8 6 1 N T3 SD: 2.5527 c. M:-4.1939 c. 41: 7 9 1 7 9 7 1 N T3 SD: 2.5826 c. M:-4.3490 c. 65: 11 14 2 11 14 11 2 N T3 SD: 1.9432 c. M: 3.3058 c. 70: 12 15 2 12 15 12 2 N T3 SD: 1.4097 c. M: 2.4727 c. 101: 17 22 3 17 22 17 3 N T3 SD: 1.2437 c. M: 2.0263 c. 106: 18 23 3 18 23 18 3 N T3 SD: 0.1953 c. M: 0.3450 c. 359: 61 78 10 61 78 61 10 N T3 SD: 0.1286 c. M:-0.2013 c. 465: 79 101 13 79 101 79 13 N T3 SD: 0.0615 c. M:-0.1079 c. 571: 97 124 16 97 124 97 16 N T3 SD: 0.0334 c. M: 0.0571 c. 1248: 212 271 35 212 271 212 35 N T3 SD: 0.0343 c. M: 0.0638 c. 1465: 249 318 41 249 318 249 41 N T3 SD: 0.0269 c. M:-0.0490 c. 1571: 267 341 44 267 341 267 44 N T3 SD: 0.0206 c. M:-0.0365 c. 1930: 328 419 54 328 419 328 54 N T3 SD: 0.0237 c. M:-0.0421 c. 2036: 346 442 57 346 442 346 57 N T3 SD: 0.0131 c. M:-0.0220 c. 2142: 364 465 60 364 465 364 60 N T3 SD: 0.0063 c. M:-0.0116 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: 26.0380 cents 4 x 5 x 6:7 x 8 S SD: 19.5930 cents 5:6 x 7:8:9 x 10 S SD: 37.4919 cents 6:7 x 8:9:10 x 12 S SD: 20.0658 cents 7:8:9 x 11:12 x 14 SD: 18.9226 cents 8:9:10:11:12:14 x 16 S SD: 15.7940 cents 9:10 x 12:14:16 x 18 S SD: 14.9087 cents 10:11:13 x 15:17 x 20 SD: 11.8981 cents 11:12:14:15:17:19 x 22 SD: 16.2354 cents 12:14 x 16:18:21 x 24 S SD: 12.6561 cents 13:15:17 x 20:23 x 26 SD: 13.3882 cents 14:16:18:19:21:24:27:28 SD: 9.3300 cents 15:17 x 20:23:26:29:30 SD: 8.0694 cents 16:18:21 x 24:28:31:32 SD: 3.8601 cents 18:20 x 24:27:31:35:36 SD: 5.6466 cents 19:21:25 x 29:33:37:38 SD: 7.7501 cents 20:23:26:27:30:35:39:40 SD: 6.6384 cents 22:25:29 x 33:38:43:44 SD: 4.7059 cents 24:27:31:32:36:42:47:48 SD: 3.2074 cents 25:28:33 x 38:44:49:50 SD: 5.5607 cents 26:29:34:35:39:45:51:52 SD: 3.6660 cents 28:32 x 37:42:49:55:56 SD: 5.3506 cents 29:33:38:39:44:51:57:58 SD: 5.0492 cents 30:34:39:40:45:52:59:60 SD: 2.8296 cents 31:35 x 41:47:54:61:62 SD: 4.1174 cents 32:36:42:43:48:56:63:64 SD: 2.4851 cents 42:47:55:56:63:73:82:84 SD: 1.9468 cents 48:54:63:64:72:84:94:96 SD: 1.3457 cents 72:81:94:96:108:126:141:144 SD: 1.0728 cents 78:88:102:104:117:136:153:156 SD: 0.7036 cents 120:135:157:160:180:209:235:240 SD: 0.5028 cents 160:180:209:213:240:279:314:320 SD: 0.4891 cents 176:198:230:235:264:307:345:352 SD: 0.4343 cents 192:216:251:256:288:335:377:384 SD: 0.3139 cents 234:263:306:312:351:408:459:468 SD: 0.2350 cents 312:351:408:416:468:544:612:624 SD: 0.0000 cents