Scala analysis: xen12-chalmers-tritriadic-dm-19-21-17
Tritriadic D->M scale built from 19:21:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/19 173.267891 2: 21/17 365.825498 submajor third 3: 441/323 539.093389 4: 578/399 641.616896 5: 34/21 834.174502 supraminor sixth 6: 34/19 1007.442393 quasi-mean seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 19/17 192.5576 quasi-meantone 1: 21/19 173.2679 2: 19/17 192.5576 quasi-meantone 3: 21/19 173.2679 4: 9826/9261 102.5235 5: 19/17 192.5576 quasi-meantone 6: 21/19 173.2679 7: 19/17 192.5576 quasi-meantone
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 : 173.3 365.8 539.1 641.6 834.2 1007.4 1200.0 173.3 : 192.6 365.8 468.3 660.9 834.2 1026.7 1200.0 365.8 : 173.3 275.8 468.3 641.6 834.2 1007.4 1200.0 539.1 : 102.5 295.1 468.3 660.9 834.2 1026.7 1200.0 641.6 : 192.6 365.8 558.4 731.7 924.2 1097.5 1200.0 834.2 : 173.3 365.8 539.1 731.7 904.9 1007.4 1200.0 1007.4: 192.6 365.8 558.4 731.7 834.2 1026.7 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 : 169.31567 cents, oct.: 1185.20968 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : MLMSLML 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% -- 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 : 0.157545 Specific harmonicity : 0.031588 Fundamental : 1/6783, -12.7277 octaves, 0.0386 Hz. Guide tone : 254898, 17.9596 octaves, 66687833.344 Hz. Exponens Consonantiae : 1.728973E+09, 30.68727 octaves Euler's gradus suavitatis : 92 Sum of Mann's harmonic distance : 965.0, average 137.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.49082, average 1.49869 Sum of Tenney's harmonic distance : 21.63514, average 3.09073 Vogel's harmonic complexity : 43.42857 Wille's k value : 4630 Wilson's harmonic complexity : 100 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 70.56321, average 2.52011 Lattice compactness (without 2's) : 66.76043, average 2.38430 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.57143 4 1 3: -1 .. 2 0.28571 6 7: -1 .. 2 0.28571 6 17: -1 .. 2 0.28571 6 2 19: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 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: 24.0977 c. M:-44.0974 c. Lebeng 12: 2 2 1 1 2 2 2 P D3 S SD: 30.1568 c. M: 41.6169 c. Major Locrian 13: 2 2 2 1 2 2 2 SP M ME I SD: 8.0469 c. M:-14.7528 c. Horthatian 32: 5 5 4 3 5 5 5 SP SD: 9.3507 c. M:-14.2321 c. 33: 5 5 5 3 5 5 5 SP M DE I SD: 7.6124 c. M:-12.9286 c. 36: 5 6 5 3 6 5 6 SP T3 SD: 5.3742 c. M: 8.2836 c. 43: 6 7 6 4 7 6 7 SP T3 SD: 4.4518 c. M: 8.8608 c. 49: 7 8 7 4 8 7 8 SP T3 SD: 2.4855 c. M: 4.8822 c. 56: 8 9 8 5 9 8 9 SP T3 SD: 1.7391 c. M: 3.3791 c. 62: 9 10 9 5 10 9 10 SP T3 SD: 1.9166 c. M: 2.9072 c. 69: 10 11 10 6 11 10 11 SP T3 SD: 0.9406 c. M:-1.8614 c. 118: 17 19 17 10 19 17 19 SP T3 SD: 0.4833 c. M: 0.9389 c. 187: 27 30 27 16 30 27 30 SP T3 SD: 0.0522 c. M:-0.0943 c. 679: 98 109 98 58 109 98 109 SP T3 SD: 0.0573 c. M: 0.0852 c. 866: 125 139 125 74 139 125 139 SP T3 SD: 0.0419 c. M: 0.0634 c. 1053: 152 169 152 90 169 152 169 SP T3 SD: 0.0343 c. M: 0.0621 c. 1240: 179 199 179 106 199 179 199 SP T3 SD: 0.0311 c. M: 0.0611 c. 1427: 206 229 206 122 229 206 229 SP T3 SD: 0.0302 c. M: 0.0605 c. 1558: 225 250 225 133 250 225 250 SP T3 SD: 0.0310 c. M:-0.0594 c. 1614: 233 259 233 138 259 233 259 SP T3 SD: 0.0305 c. M: 0.0599 c. 1627: 235 261 235 139 261 235 261 SP T3 SD: 0.0428 c. M:-0.0584 c. 1745: 252 280 252 149 280 252 280 SP T3 SD: 0.0237 c. M:-0.0470 c. 1932: 279 310 279 165 310 279 310 SP T3 SD: 0.0186 c. M:-0.0370 c. 2119: 306 340 306 181 340 306 340 SP T3 SD: 0.0153 c. M:-0.0288 c. 2306: 333 370 333 197 370 333 370 SP T3 SD: 0.0137 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: 30.1691 cents 3 x x 4 x 5 x 6 S SD: 21.6113 cents 4 x 5 x 6 x 7:8 S SD: 18.6274 cents 5 x 6:7 x 8:9:10 S SD: 14.0378 cents 6:7 x 8:9:10:11:12 S SD: 22.5850 cents 7:8:9 x 10:11:13:14 SD: 20.7715 cents 8:9:10:11:12:13:14:16 S SD: 11.6763 cents 9:10:11:12:13:15:16:18 SD: 9.8768 cents 10:11:12:14 x 16:18:20 S SD: 11.7790 cents 11:12:14:15:16:18:20:22 S SD: 9.4070 cents 13:14:16:18:19:21:23:26 SD: 8.1967 cents 16:18:20:22:23:26:29:32 SD: 6.7256 cents 18:20:22:25:26:29:32:36 SD: 5.5815 cents 20:22:25:27:29:32:36:40 SD: 5.3367 cents 22:24:27:30:32:36:39:44 SD: 5.1469 cents 25:28:31:34:36:40:45:50 SD: 5.0398 cents 27:30:33:37:39:44:48:54 SD: 3.8980 cents 29:32:36:40:42:47:52:58 SD: 2.8831 cents 38:42:47:52:55:62:68:76 SD: 2.0228 cents 47:52:58:64:68:76:84:94 SD: 0.9194 cents 76:84:94:104:110:123:136:152 SD: 0.6817 cents 123:136:152:168:178:199:220:246 SD: 0.3685 cents 200:221:247:273:290:324:358:400 SD: 0.3036 cents 238:263:294:325:345:385:426:476 SD: 0.2835 cents 247:273:305:337:358:400:442:494 SD: 0.2443 cents 276:305:341:377:400:447:494:552 SD: 0.1939 cents 323:357:399:441:468:523:578:646 SD: 0.0551 cents