Scala analysis: xen09-chalmers-tritriadic-21-19-17
Tritriadic scale built from 21:19:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/17 192.557607 quasi-meantone 2: 21/17 365.825498 submajor third 3: 578/441 468.349004 4: 646/441 660.906611 5: 34/21 834.174502 supraminor sixth 6: 38/21 1026.732109 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/19 173.2679 1: 19/17 192.5576 quasi-meantone 2: 21/19 173.2679 3: 9826/9261 102.5235 4: 19/17 192.5576 quasi-meantone 5: 21/19 173.2679 6: 19/17 192.5576 quasi-meantone 7: 21/19 173.2679
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9826/9261 102.524 cents 1: 3 21/19 173.268 cents 1: 3 19/17 192.558 cents quasi-meantone 2: 1 9826/8379 275.791 cents 2: 1 10982/9261 295.081 cents 2: 5 21/17 365.825 cents submajor third 3: 3 578/441 468.349 cents 3: 2 441/323 539.093 cents 3: 2 399/289 558.383 cents 4: 2 578/399 641.617 cents 4: 2 646/441 660.907 cents 4: 3 441/289 731.651 cents two (submajor third) 5: 5 34/21 834.175 cents supraminor sixth 5: 1 9261/5491 904.919 cents 5: 1 8379/4913 924.209 cents 6: 3 34/19 1007.442 cents quasi-mean seventh 6: 3 38/21 1026.732 cents 6: 1 9261/4913 1097.476 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 : 192.6 365.8 468.3 660.9 834.2 1026.7 1200.0 192.6 : 173.3 275.8 468.3 641.6 834.2 1007.4 1200.0 365.8 : 102.5 295.1 468.3 660.9 834.2 1026.7 1200.0 468.3 : 192.6 365.8 558.4 731.7 924.2 1097.5 1200.0 660.9 : 173.3 365.8 539.1 731.7 904.9 1007.4 1200.0 834.2 : 192.6 365.8 558.4 731.7 834.2 1026.7 1200.0 1026.7: 173.3 365.8 539.1 641.6 834.2 1007.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 102.5235 .. 192.5576 cents 175959/167042, 90.0341 cents 9826/9261, 102.5235 cents 2: 275.7914 .. 365.8255 cents 175959/167042, 90.0341 cents 167042/159201, 83.2338 cents 3: 468.3490 .. 558.3831 cents 175959/167042, 90.0341 cents 9826/9261, 102.5235 cents 4: 641.6169 .. 731.6510 cents 175959/167042, 90.0341 cents 167042/159201, 83.2338 cents 5: 834.1745 .. 924.2086 cents 175959/167042, 90.0341 cents 9826/9261, 102.5235 cents 6: 1007.4424 .. 1097.4765 cents 175959/167042, 90.0341 cents 167042/159201, 83.2338 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 9826/9261, 102.5235 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 19/17, 192.5576 cents Average / Smallest step : 1.672090 Largest / Average step : 1.123253 Largest / Smallest step : 1.878180 Median interval of one step : 21/19, 173.2679 cents, amount: 3 Least squares average step : 169.31534 cents, oct.: 1185.20736 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : LMSLMLM Scale is a Constant Structure, by a margin of 83.23379 cents Scale diversity : 1.396562 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.549829 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 : 361/357, 19.2897 cents Most common intervals : 21/17, 365.8255 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 192.558 365.825 cents Most common triad is 0.0 365.825 834.175 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 17 21 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 90.0341 cents: 5 -- Rational properties -- Prime limit : 19 Odd number limit : 9261 (O: 9261 U: 9261) Highest odd numerator or denominator: 441 Scale harmonicity : 0.006086 Average absolute harmonicity : 0.157819 Specific harmonicity : 0.031937 Fundamental : 1/7497, -12.8721 octaves, 0.0349 Hz. Guide tone : 230622, 17.8152 octaves, 60336611.121 Hz. Exponens Consonantiae : 1.728973E+09, 30.68727 octaves Euler's gradus suavitatis : 92 Sum of Mann's harmonic distance : 1148.5, average 164.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.53429, average 1.50490 Sum of Tenney's harmonic distance : 21.97964, average 3.13995 Vogel's harmonic complexity : 43.57143 Wille's k value : 4630 Wilson's harmonic complexity : 100 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 71.19889, average 2.54282 Lattice compactness (without 2's) : 67.57878, average 2.41353 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.71429 5 1 3: -2 .. 1 -0.71429 7 7: -2 .. 1 -0.71429 7 17: -1 .. 2 0.28571 6 3 19: 0 .. 1 0.42857 3 3 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 23 / 7 = 3.28571 Scale is JI-epimorphic with val: <7 10 18 26 27| Scale is weakly epimorphic with val: <7 10 18 27 31| Scale is weakly epimorphic with val: <7 10 18 29 32| Scale is weakly epimorphic with val: <7 10 18 31 33| Scale is weakly epimorphic with val: <7 10 19 26 31| Scale is JI-epimorphic with val: <7 10 19 27 28| Scale is weakly epimorphic with val: <7 10 19 28 32| Scale is weakly epimorphic with val: <7 10 19 30 33| Scale is weakly epimorphic with val: <7 10 20 26 28| Scale is weakly epimorphic with val: <7 10 20 27 32| Scale is JI-epimorphic with val: <7 10 20 28 29| Scale is weakly epimorphic with val: <7 10 20 29 33| Scale is weakly epimorphic with val: <7 10 21 26 32| Scale is weakly epimorphic with val: <7 10 21 27 29| Scale is weakly epimorphic with val: <7 10 21 28 33| Scale is JI-epimorphic with val: <7 10 21 29 30| Scale is weakly epimorphic with val: <7 10 22 26 29| Scale is weakly epimorphic with val: <7 10 22 27 33| Scale is weakly epimorphic with val: <7 10 22 28 30| Scale is JI-epimorphic with val: <7 10 22 30 31| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is JI-epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 18 28 32| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 19 26 28| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is JI-epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 20 26 32| Scale is weakly epimorphic with val: <7 11 20 27 29| Scale is weakly epimorphic with val: <7 11 20 28 33| Scale is JI-epimorphic with val: <7 11 20 29 30| = patent Scale is weakly epimorphic with val: <7 11 21 26 29| Scale is weakly epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 21 28 30| Scale is JI-epimorphic with val: <7 11 21 30 31| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is weakly epimorphic with val: <7 11 22 29 31| Scale is JI-epimorphic with val: <7 11 22 31 32| Scale is weakly epimorphic with val: <7 12 18 26 28| Scale is weakly epimorphic with val: <7 12 18 27 32| Scale is JI-epimorphic with val: <7 12 18 28 29| Scale is weakly epimorphic with val: <7 12 18 29 33| Scale is weakly epimorphic with val: <7 12 19 26 32| Scale is weakly epimorphic with val: <7 12 19 27 29| Scale is weakly epimorphic with val: <7 12 19 28 33| Scale is JI-epimorphic with val: <7 12 19 29 30| Scale is weakly epimorphic with val: <7 12 20 26 29| Scale is weakly epimorphic with val: <7 12 20 27 33| Scale is weakly epimorphic with val: <7 12 20 28 30| Scale is JI-epimorphic with val: <7 12 20 30 31| Scale is weakly epimorphic with val: <7 12 21 27 30| Scale is weakly epimorphic with val: <7 12 21 29 31| Scale is JI-epimorphic with val: <7 12 21 31 32| Scale is weakly epimorphic with val: <7 12 22 26 30| Scale is weakly epimorphic with val: <7 12 22 28 31| Scale is weakly epimorphic with val: <7 12 22 30 32| Scale is JI-epimorphic with val: <7 12 22 32 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 24.5837 c. M:-45.9367 c. Lebeng 12: 2 2 1 2 1 2 2 P D3 I SD: 28.3747 c. M:-39.0934 c. Major-Minor, Melodic Major, Mischung 6, Mixolydian flat 6, Mela Carukesi, Raga Charukeshi, Tarangini, Heptatonia secunda 13: 2 2 1 2 2 2 2 SP M ME S SD: 8.2727 c. M: 14.7528 c. Oukranian 20: 3 3 2 3 3 3 3 SP M ME S SD: 7.6294 c. M: 12.5576 c. 33: 5 5 3 5 5 5 5 SP M DE S SD: 6.0670 c. M: 10.7394 c. 36: 6 5 3 6 5 6 5 SP T3 SD: 4.4141 c. M:-7.4424 c. 49: 8 7 4 8 7 8 7 SP T3 SD: 2.0237 c. M:-3.3608 c. 56: 9 8 5 9 8 9 8 SP T3 SD: 2.0395 c. M:-3.3791 c. 69: 11 10 6 11 10 11 10 SP T3 SD: 0.7752 c. M: 1.2533 c. 118: 19 17 10 19 17 19 17 SP T3 SD: 0.3889 c. M:-0.6627 c. 187: 30 27 16 30 27 30 27 SP T3 SD: 0.0537 c. M:-0.1002 c. 679: 109 98 58 109 98 109 98 SP T3 SD: 0.0477 c. M:-0.0786 c. 866: 139 125 74 139 125 139 125 SP T3 SD: 0.0383 c. M:-0.0634 c. 1053: 169 152 90 169 152 169 152 SP T3 SD: 0.0349 c. M:-0.0621 c. 1240: 199 179 106 199 179 199 179 SP T3 SD: 0.0343 c. M:-0.0611 c. 1427: 229 206 122 229 206 229 206 SP T3 SD: 0.0348 c. M:-0.0605 c. 1558: 250 225 133 250 225 250 225 SP T3 SD: 0.0364 c. M: 0.0594 c. 1614: 259 233 138 259 233 259 233 SP T3 SD: 0.0357 c. M:-0.0599 c. 1627: 261 235 139 261 235 261 235 SP T3 SD: 0.0375 c. M: 0.0584 c. 1745: 280 252 149 280 252 280 252 SP T3 SD: 0.0277 c. M: 0.0470 c. 1932: 310 279 165 310 279 310 279 SP T3 SD: 0.0210 c. M: 0.0370 c. 2119: 340 306 181 340 306 340 306 SP T3 SD: 0.0161 c. M: 0.0288 c. 2306: 370 333 197 370 333 370 333 SP T3 SD: 0.0129 c. M: 0.0220 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: 20.5242 cents 3 x x 4 x 5 x 6 S SD: 19.4374 cents 4 x 5 x 6 x 7:8 S SD: 18.4693 cents 5 x 6 x 7:8:9:10 S SD: 19.1493 cents 6:7 x 8:9:10:11:12 S SD: 17.5752 cents 7:8 x 9:10:11:13:14 SD: 15.9655 cents 8:9:10 x 12:13:14:16 S SD: 12.5023 cents 9:10:11:12:13:15:16:18 SD: 10.4701 cents 11:12 x 14:16:18:20:22 S SD: 11.6656 cents 13:15:16:17:19:21:24:26 SD: 9.4063 cents 15:17:19:20:22:24:27:30 SD: 8.8722 cents 16:18:20:21:23:26:29:32 SD: 5.8342 cents 17:19:21:22:25:28:31:34 SD: 5.6950 cents 24:27:30:31:35:39:43:48 SD: 5.6819 cents 25:28:31:33:37:40:45:50 SD: 4.5808 cents 26:29:32:34:38:42:47:52 SD: 1.4419 cents 58:65:72:76:85:94:105:116 SD: 1.4215 cents 68:76:84:89:100:110:123:136 SD: 1.0531 cents 84:94:104:110:123:136:152:168 SD: 0.6817 cents 110:123:136:144:161:178:199:220 SD: 0.4588 cents 170:190:210:223:249:275:308:340 SD: 0.4286 cents 187:209:231:245:274:303:338:374 SD: 0.3585 cents 213:238:263:279:312:345:385:426 SD: 0.3536 cents 247:276:305:324:362:400:447:494 SD: 0.2705 cents 273:305:337:358:400:442:494:546 SD: 0.2443 cents 331:370:409:434:485:536:599:662 SD: 0.1524 cents 357:399:441:468:523:578:646:714 SD: 0.0551 cents