Scala analysis: xen09-chalmers-tritriadic-24-35-26
Tritriadic scale built from 24:35:26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 169/144 277.145322 two (tridecimal 2/3-tone) 3: 35/26 514.611959 4: 35/24 653.184619 septimal semi-diminished fifth 5: 455/288 791.757280 6: 24/13 1061.427339 tridecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 2520/2197 237.4666 4: 13/12 138.5727 tridecimal 2/3-tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 6912/5915 269.6701 7: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 13/12 138.573 cents tridecimal 2/3-tone 1: 1 2520/2197 237.467 cents 1: 1 6912/5915 269.670 cents 2: 3 169/144 277.145 cents two (tridecimal 2/3-tone) 2: 2 210/169 376.039 cents 2: 2 576/455 408.243 cents 3: 1 2197/1728 415.718 cents 3: 3 35/26 514.612 cents 3: 3 48/35 546.815 cents septimal semi-augmented fourth 4: 3 35/24 653.185 cents septimal semi-diminished fifth 4: 3 52/35 685.388 cents 4: 1 3456/2197 784.282 cents 5: 2 455/288 791.757 cents 5: 2 169/105 823.961 cents 5: 3 288/169 922.855 cents 6: 1 5915/3456 930.330 cents 6: 1 2197/1260 962.533 cents 6: 5 24/13 1061.427 cents tridecimal neutral seventh 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 : 138.6 277.1 514.6 653.2 791.8 1061.4 1200.0 138.6 : 138.6 376.0 514.6 653.2 922.9 1061.4 1200.0 277.1 : 237.5 376.0 514.6 784.3 922.9 1061.4 1200.0 514.6 : 138.6 277.1 546.8 685.4 824.0 962.5 1200.0 653.2 : 138.6 408.2 546.8 685.4 824.0 1061.4 1200.0 791.8 : 269.7 408.2 546.8 685.4 922.9 1061.4 1200.0 1061.4: 138.6 277.1 415.7 653.2 791.8 930.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 269.6701 cents 82944/76895, 131.0974 cents 13/12, 138.5727 cents 2: 277.1453 .. 408.2427 cents 82944/76895, 131.0974 cents 999635/995328, 7.4753 cents 3: 415.7180 .. 546.8154 cents 82944/76895, 131.0974 cents 999635/995328, 7.4753 cents 4: 653.1846 .. 784.2820 cents 82944/76895, 131.0974 cents 1225/1152, 106.3692 cents 5: 791.7573 .. 922.8547 cents 82944/76895, 131.0974 cents 999635/995328, 7.4753 cents 6: 930.3299 .. 1061.4273 cents 82944/76895, 131.0974 cents 999635/995328, 7.4753 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6912/5915, 269.6701 cents Average / Smallest step : 1.237102 Largest / Average step : 1.573075 Largest / Smallest step : 1.946055 Median interval of one step : 13/12, 138.5727 cents, amount: 5 Most common interval of one step : 13/12, 138.5727 cents, amount: 5 Least squares average step : 168.40563 cents, oct.: 1178.83940 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2087-tone equal temperament with octave 2/1 degrees: 241 482 895 1136 1377 1846 2087 Least number of segments generator : 1044 of 600.287 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1945 of 1118.352 cents and inv. generated superset size: 48 = 41 more = 685.714% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAACA Step pattern size order : SSMSSLS Scale is a Constant Structure, by a margin of 7.47526 cents Scale diversity : 1.299553 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.344513 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 : 999635/995328, 7.4753 cents Most common intervals : 13/12, 138.5727 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 514.612 1061.427 cents Number of recognisable fifths : 0 Best fifths form a closed circle Scale contains a complete diamond : 3 13 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 : 13 Odd number limit : 5915 (O: 5915 U: 5915) Highest odd numerator or denominator: 455 Scale harmonicity : 0.010086 Average absolute harmonicity : 0.168863 Specific harmonicity : 0.053878 Fundamental : 1/3744, -11.8704 octaves, 0.0699 Hz. Guide tone : 141960, 17.1151 octaves, 37140365.250 Hz. Exponens Consonantiae : 5.314982E+08, 28.98549 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 620.5, average 88.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.20192, average 1.45742 Sum of Tenney's harmonic distance : 20.37528, average 2.91075 Vogel's harmonic complexity : 29.14286 Wille's k value : 2957 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 111.86065, average 3.99502 Lattice compactness (without 2's) : 60.28697, average 2.15311 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -1.57143 19 1 3: -2 .. 1 -0.71429 7 5: 0 .. 1 0.42857 3 7: 0 .. 1 0.42857 3 1 13: -1 .. 2 0.28571 6 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 15 18 28| Scale is JI-epimorphic with val: <7 10 15 20 25| Scale is weakly epimorphic with val: <7 10 15 21 27| Scale is weakly epimorphic with val: <7 10 15 22 29| Scale is JI-epimorphic with val: <7 10 16 19 25| Scale is weakly epimorphic with val: <7 10 16 20 27| Scale is weakly epimorphic with val: <7 10 16 21 29| Scale is JI-epimorphic with val: <7 10 17 18 25| Scale is weakly epimorphic with val: <7 10 17 19 27| Scale is weakly epimorphic with val: <7 10 17 20 29| Scale is weakly epimorphic with val: <7 10 17 22 26| Scale is weakly epimorphic with val: <7 10 18 18 27| Scale is weakly epimorphic with val: <7 10 18 19 29| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 18 22 28| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 19 29| Scale is weakly epimorphic with val: <7 11 15 20 24| Scale is JI-epimorphic with val: <7 11 15 21 26| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 19 24| Scale is JI-epimorphic with val: <7 11 16 20 26| = patent Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 17 18 24| Scale is JI-epimorphic with val: <7 11 17 19 26| Scale is weakly epimorphic with val: <7 11 17 20 28| Scale is JI-epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 12 15 19 28| Scale is weakly epimorphic with val: <7 12 15 21 25| Scale is JI-epimorphic with val: <7 12 15 22 27| Scale is weakly epimorphic with val: <7 12 16 18 28| Scale is weakly epimorphic with val: <7 12 16 20 25| Scale is JI-epimorphic with val: <7 12 16 21 27| Scale is weakly epimorphic with val: <7 12 16 22 29| Scale is weakly epimorphic with val: <7 12 17 19 25| Scale is JI-epimorphic with val: <7 12 17 20 27| Scale is weakly epimorphic with val: <7 12 17 21 29| Scale is weakly epimorphic with val: <7 12 17 22 24| Scale is weakly epimorphic with val: <7 12 18 18 25| Scale is JI-epimorphic with val: <7 12 18 19 27| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 18 21 24|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 41.0759 c. M:-65.7118 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 36.8985 c. M: 64.6120 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 10.4533 c. M:-18.7214 c. 26: 3 3 5 3 3 6 3 P T3 SD: 4.6043 c. M: 7.1419 c. 35: 4 4 7 4 4 8 4 P T3 SD: 1.9126 c. M: 3.1859 c. 86: 10 10 17 10 10 19 10 SP T3 SD: 2.0052 c. M:-3.5916 c. 103: 12 12 20 12 12 23 12 SP T3 SD: 1.4085 c. M:-2.4663 c. 112: 13 13 22 13 13 25 13 SP T3 SD: 0.8032 c. M:-1.4261 c. 121: 14 14 24 14 14 27 14 SP T3 SD: 0.9366 c. M:-1.6311 c. 138: 16 16 27 16 16 31 16 SP T3 SD: 0.8907 c. M: 1.5685 c. 147: 17 17 29 17 17 33 17 SP T3 SD: 0.2314 c. M:-0.4057 c. 303: 35 35 60 35 35 68 35 SP T3 SD: 0.1890 c. M:-0.3219 c. 338: 39 39 67 39 39 76 39 SP T3 SD: 0.1273 c. M: 0.2222 c. 450: 52 52 89 52 52 101 52 SP T3 SD: 0.1399 c. M:-0.2427 c. 485: 56 56 96 56 56 109 56 SP T3 SD: 0.0186 c. M: 0.0319 c. 1117: 129 129 221 129 129 251 129 SP T3 SD: 0.0144 c. M:-0.0257 c. 1602: 185 185 317 185 185 360 185 SP T3 SD: 0.0045 c. M:-0.0082 c. 2087: 241 241 413 241 241 469 241 SP T3 SD: 0.0013 c. M:-0.0023 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: 24.3852 cents 3 x x 4 x 5 x 6 S SD: 31.3572 cents 4 x 5 x 6 x 7:8 S SD: 37.8082 cents 5 x 6:7 x 8:9:10 S SD: 18.4330 cents 6 x 7:8:9 x 11:12 SD: 10.7780 cents 7 x 8:9:10:11:13:14 SD: 16.5862 cents 8:9 x 11:12:13:15:16 SD: 17.5546 cents 9:10:11:12:13:14:17:18 SD: 14.0676 cents 11:12:13:15:16:17:20:22 SD: 7.7751 cents 12:13:14:16:18:19:22:24 SD: 7.7177 cents 17:18:20:23:25:27:31:34 SD: 7.0167 cents 21:23:25:28:31:33:39:42 SD: 6.1908 cents 22:24:26:30:32:35:41:44 SD: 4.9943 cents 23:25:27:31:34:36:42:46 SD: 4.9656 cents 24:26:28:32:35:38:44:48 SD: 3.3198 cents 34:37:40:46:50:54:63:68 SD: 3.1580 cents 35:38:41:47:51:55:65:70 SD: 2.1958 cents 46:50:54:62:67:73:85:92 SD: 1.4674 cents 70:76:82:94:102:111:129:140 SD: 1.3954 cents 74:80:87:100:108:117:137:148 SD: 1.3851 cents 81:88:95:109:118:128:150:162 SD: 1.0873 cents 96:104:113:129:140:152:177:192 SD: 1.0620 cents 98:106:115:132:143:155:181:196 SD: 0.5304 cents 155:168:182:209:226:245:286:310 SD: 0.4827 cents 179:194:210:241:261:283:330:358 SD: 0.4172 cents 190:206:223:256:277:300:351:380 SD: 0.3775 cents 214:232:251:288:312:338:395:428 SD: 0.2639 cents 266:288:312:358:388:420:491:532 SD: 0.2618 cents 288:312:338:388:420:455:532:576 SD: 0.2428 cents 312:338:366:420:455:493:576:624 SD: 0.1201 cents 552:598:648:743:805:872:1019:1104 SD: 0.0749 cents