Scala analysis: xen09-chalmers-tritriadic-34-39-51
Tritriadic scale built from 34:39:51
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: 39/34 237.527253 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 26/17 735.572252 6: 117/68 939.482254 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 136/117 260.5177 1: 9/8 203.9100 major whole tone 2: 52/51 33.6173 3: 136/117 260.5177 4: 9/8 203.9100 major whole tone 5: 52/51 33.6173 6: 9/8 203.9100 major whole tone 7: 136/117 260.5177
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 : 203.9 237.5 498.0 702.0 735.6 939.5 1200.0 203.9 : 33.6 294.1 498.0 531.7 735.6 996.1 1200.0 237.5 : 260.5 464.4 498.0 702.0 962.5 1166.4 1200.0 498.0 : 203.9 237.5 441.4 702.0 905.9 939.5 1200.0 702.0 : 33.6 237.5 498.0 702.0 735.6 996.1 1200.0 735.6 : 203.9 464.4 668.3 702.0 962.5 1166.4 1200.0 939.5 : 260.5 464.4 498.0 758.6 962.5 996.1 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 : 162.11196 cents, oct.: 1134.78371 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MSLMSML 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 0.0 237.527 701.955 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: 117 Scale harmonicity : 0.015321 Average absolute harmonicity : 0.237205 Specific harmonicity : 0.068492 Fundamental : 1/408, -8.6724 octaves, 0.6412 Hz. Guide tone : 468, 8.8704 octaves, 122440.765 Hz. Exponens Consonantiae : 1.909440E+05, 17.54279 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 166.5, average 23.78571 Mersenne's string divisions : 207315255 Sum of van Prooijen's expressibility: 6.79818, average 0.97117 Sum of Tenney's harmonic distance : 13.68436, average 1.95491 Vogel's harmonic complexity : 23.00000 Wille's k value : 229 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 76.33125, average 2.72612 Lattice compactness (without 2's) : 47.16374, average 1.68442 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 11 1 3: -1 .. 2 0.71429 7 3 13: 0 .. 1 0.42857 3 17: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 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 0 2 1 0 1 2 N T3 SD: 46.6249 c. M: 82.3394 c. 10: 2 0 2 2 0 2 2 N M DE S SD: 19.3587 c. M:-36.0900 c. 14: 2 1 3 2 1 2 3 P T3 SD: 21.5950 c. M:-35.8563 c. 15: 3 0 3 3 0 3 3 N M DE S SD: 19.3587 c. M:-36.0900 c. 17: 3 0 4 3 0 3 4 N T3 SD: 17.3803 c. M: 29.6899 c. 19: 3 1 4 3 1 3 4 N T3 SD: 12.5427 c. M:-22.3225 c. 24: 4 1 5 4 1 4 5 N T3 SD: 8.4286 c. M:-14.4277 c. 29: 5 1 6 5 1 5 6 N T3 SD: 7.2154 c. M:-12.2419 c. 31: 5 1 7 5 1 5 7 N T3 SD: 6.5249 c. M: 10.4500 c. 36: 6 1 8 6 1 6 8 N T3 SD: 3.4505 c. M: 6.1489 c. 41: 7 1 9 7 1 7 9 N T3 SD: 2.2730 c. M: 3.8649 c. 65: 11 2 14 11 2 11 14 N T3 SD: 1.6789 c. M:-2.8893 c. 70: 12 2 15 12 2 12 15 N T3 SD: 1.8843 c. M:-3.3749 c. 101: 17 3 22 17 3 17 22 N T3 SD: 1.0335 c. M: 1.9298 c. 106: 18 3 23 18 3 18 23 N T3 SD: 0.1548 c. M:-0.2768 c. 359: 61 10 78 61 10 61 78 N T3 SD: 0.1319 c. M: 0.2065 c. 465: 79 13 101 79 13 79 101 N T3 SD: 0.0737 c. M: 0.1274 c. 571: 97 16 124 97 16 97 124 N T3 SD: 0.0444 c. M: 0.0777 c. 677: 115 19 147 115 19 115 147 N T3 SD: 0.0376 c. M: 0.0695 c. 1248: 212 35 271 212 35 212 271 N T3 SD: 0.0385 c. M: 0.0638 c. 1359: 231 38 295 231 38 231 295 N T3 SD: 0.0339 c. M:-0.0635 c. 1465: 249 41 318 249 41 249 318 N T3 SD: 0.0281 c. M:-0.0490 c. 1571: 267 44 341 267 44 267 341 N T3 SD: 0.0270 c. M:-0.0467 c. 1824: 310 51 396 310 51 310 396 N T3 SD: 0.0268 c. M: 0.0459 c. 1930: 328 54 419 328 54 328 419 N T3 SD: 0.0176 c. M: 0.0282 c. 2036: 346 57 442 346 57 346 442 N T3 SD: 0.0105 c. M:-0.0193 c. 2142: 364 60 465 364 60 364 465 N T3 SD: 0.0080 c. M:-0.0135 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 x 5:6 S SD: 18.3745 cents 4 x x 5:6 x 7:8 S SD: 28.8801 cents 5 x 6:7 x 8:9:10 S SD: 31.8999 cents 6 x 7:8:9 x 10:12 S SD: 12.4894 cents 7 x 8:9 x 11:12:14 SD: 15.8067 cents 8:9 x 11:12 x 14:16 SD: 12.1640 cents 9:10 x 12 x 14:15:18 S SD: 13.2094 cents 10:11 x 13:15 x 17:20 SD: 12.4405 cents 11:12:13:15 x 17:19:22 SD: 14.3315 cents 12 x 14:16:18 x 21:24 S SD: 8.2996 cents 13 x 15:17 x 20:22:26 SD: 9.2994 cents 14 x 16:19:21 x 24:28 SD: 6.3864 cents 15:17 x 20 x 23:26:30 SD: 3.7210 cents 16:18 x 21:24 x 28:32 S SD: 8.0109 cents 17:19:20:23 x 26:29:34 SD: 8.9902 cents 18:20:21:24:27:28:31:36 SD: 6.6813 cents 19:21:22:25 x 29:33:38 SD: 7.4666 cents 20 x 23:27:30:31:34:40 SD: 6.3517 cents 21 x 24:28 x 32:36:42 S SD: 2.2008 cents 22 x 25:29:33:34:38:44 SD: 5.3383 cents 23:26 x 31 x 35:40:46 SD: 5.7968 cents 24:27:28:32:36:37:41:48 SD: 4.9592 cents 25:28:29:33 x 38:43:50 SD: 4.8705 cents 26:29:30:35:39:40:45:52 SD: 4.0614 cents 27:30:31:36 x 41:46:54 SD: 5.0273 cents 28 x 32:37:42:43:48:56 SD: 3.2167 cents 29 x 33:39 x 44:50:58 SD: 4.9646 cents 30:34 x 40:45:46:52:60 SD: 3.1008 cents 31:35:36:41 x 47:53:62 SD: 5.3746 cents 32:36:37:43:48:49:55:64 SD: 2.7854 cents 33:37:38:44 x 50:57:66 SD: 3.2797 cents 34:38:39:45:51:52:59:68 SD: 3.2237 cents 36 x 41:48:54:55:62:72 SD: 2.1033 cents 37:42 x 49:56:57:64:74 SD: 4.8923 cents 38:43:44:51:57:58:65:76 SD: 3.5316 cents 39:44:45:52:59:60:67:78 SD: 3.0541 cents 40:45:46:53:60:61:69:80 SD: 1.9280 cents 44 x 50:59:66:67:76:88 SD: 3.5816 cents 45:51:52:60:68:69:77:90 SD: 3.5017 cents 46:52:53:61:69:70:79:92 SD: 2.4914 cents 47:53:54:63:71:72:81:94 SD: 2.3682 cents 48:54:55:64:72:73:83:96 SD: 1.8756 cents 54:61:62:72:81:83:93:108 SD: 1.6293 cents 66:74:76:88:99:101:114:132 SD: 1.5987 cents 72:81:83:96:108:110:124:144 SD: 1.2798 cents 87:98:100:116:131:133:150:174 SD: 1.2352 cents 90:101:103:120:135:138:155:180 SD: 1.0717 cents 96:108:110:128:144:147:165:192 SD: 0.4775 cents 136:153:156:181:204:208:234:272 SD: 0.4550 cents 144:162:165:192:216:220:248:288 SD: 0.4415 cents 168:189:193:224:252:257:289:336 SD: 0.3847 cents 232:261:266:309:348:355:399:464 SD: 0.3319 cents 240:270:275:320:360:367:413:480 SD: 0.2696 cents 264:297:303:352:396:404:454:528 SD: 0.2407 cents 272:306:312:363:408:416:468:544 SD: 0.2272 cents 312:351:358:416:468:477:537:624 SD: 0.1469 cents 408:459:468:544:612:624:702:816 SD: 0.0000 cents