Scala analysis: xen10-chalmers-tritriadic-7-23-19
Tritriadic scale built from 7:23:19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 437/392 188.135550 2: 23/19 330.761331 3: 19/14 528.687110 4: 28/19 671.312890 5: 23/14 859.448441 6: 361/196 1057.374219 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 392/361 142.6258 1: 437/392 188.1356 2: 392/361 142.6258 3: 361/322 197.9258 4: 392/361 142.6258 5: 437/392 188.1356 6: 361/322 197.9258 7: 392/361 142.6258
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 392/361 142.626 cents 1: 2 437/392 188.136 cents 1: 2 361/322 197.926 cents 2: 3 23/19 330.761 cents 2: 3 28/23 340.552 cents 2: 1 6859/5488 386.061 cents 3: 1 9016/6859 473.387 cents 3: 1 10976/8303 483.177 cents 3: 5 19/14 528.687 cents 4: 5 28/19 671.313 cents 4: 1 8303/5488 716.823 cents 4: 1 6859/4508 726.613 cents 5: 1 10976/6859 813.939 cents 5: 3 23/14 859.448 cents 5: 3 38/23 869.239 cents 6: 2 644/361 1002.074 cents 6: 2 784/437 1011.864 cents 6: 3 361/196 1057.374 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 : 188.1 330.8 528.7 671.3 859.4 1057.4 1200.0 188.1 : 142.6 340.6 483.2 671.3 869.2 1011.9 1200.0 330.8 : 197.9 340.6 528.7 726.6 869.2 1057.4 1200.0 528.7 : 142.6 330.8 528.7 671.3 859.4 1002.1 1200.0 671.3 : 188.1 386.1 528.7 716.8 859.4 1057.4 1200.0 859.4 : 197.9 340.6 528.7 671.3 869.2 1011.9 1200.0 1057.4: 142.6 330.8 473.4 671.3 813.9 1002.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 142.6258 .. 197.9258 cents 130321/126224, 55.3000 cents 392/361, 142.6258 cents 2: 330.7613 .. 386.0613 cents 130321/126224, 55.3000 cents 7406/6859, 132.8356 cents 3: 473.3871 .. 528.6871 cents 130321/126224, 55.3000 cents 49479808/47045881, 87.3258 cents 4: 671.3129 .. 726.6129 cents 130321/126224, 55.3000 cents 392/361, 142.6258 cents 5: 813.9387 .. 869.2387 cents 130321/126224, 55.3000 cents 49479808/47045881, 87.3258 cents 6: 1002.0742 .. 1057.3742 cents 130321/126224, 55.3000 cents 7406/6859, 132.8356 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 392/361, 142.6258 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 361/322, 197.9258 cents Average / Smallest step : 1.201947 Largest / Average step : 1.154567 Largest / Smallest step : 1.387728 Median interval of one step : 437/392, 188.1356 cents, amount: 2 Most common interval of one step : 392/361, 142.6258 cents, amount: 3 Least squares average step : 172.58899 cents, oct.: 1208.12293 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : MSLSMLS Scale is a Constant Structure, by a margin of 87.32578 cents Scale diversity : 1.257780 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.723500 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 : 532/529, 9.7902 cents Most common intervals : 19/14, 528.6871 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 330.761 671.313 cents Most common triad is 0.0 528.687 671.313 cents, amount: 3 Number of recognisable fifths : 1, average 716.8227 cents Number of appreciable fifths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 7 19 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 55.3000 cents: 3 -- Rational properties -- Prime limit : 23 Odd number limit : 8303 (O: 8303 U: 8303) Highest odd numerator or denominator: 437 Scale harmonicity : 0.005548 Average absolute harmonicity : 0.156641 Specific harmonicity : 0.029026 Fundamental : 1/7448, -12.8626 octaves, 0.0351 Hz. Guide tone : 232484, 17.8268 octaves, 60823757.923 Hz. Exponens Consonantiae : 1.731541E+09, 30.68941 octaves Euler's gradus suavitatis : 100 Sum of Mann's harmonic distance : 774.0, average 110.57143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.47895, average 1.49699 Sum of Tenney's harmonic distance : 20.68369, average 2.95481 Vogel's harmonic complexity : 45.71429 Wille's k value : 4151 Wilson's harmonic complexity : 101 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 80.52962, average 2.87606 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.57143 10 1 7: -2 .. 1 -0.71429 7 19: -1 .. 2 0.28571 6 3 23: 0 .. 1 0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 18 27 33| Scale is JI-epimorphic with val: <7 18 28 30| Scale is weakly epimorphic with val: <7 18 29 34| Scale is weakly epimorphic with val: <7 18 30 31| Scale is weakly epimorphic with val: <7 18 31 35| Scale is weakly epimorphic with val: <7 19 27 30| Scale is weakly epimorphic with val: <7 19 28 34| Scale is JI-epimorphic with val: <7 19 29 31| Scale is weakly epimorphic with val: <7 19 30 35| Scale is weakly epimorphic with val: <7 19 31 32| Scale is weakly epimorphic with val: <7 20 28 31| Scale is weakly epimorphic with val: <7 20 29 35| Scale is JI-epimorphic with val: <7 20 30 32| = patent Scale is weakly epimorphic with val: <7 20 32 33| Scale is weakly epimorphic with val: <7 21 27 31| Scale is weakly epimorphic with val: <7 21 29 32| Scale is JI-epimorphic with val: <7 21 31 33| Scale is weakly epimorphic with val: <7 21 33 34| Scale is weakly epimorphic with val: <7 22 27 35| Scale is weakly epimorphic with val: <7 22 28 32| Scale is weakly epimorphic with val: <7 22 30 33| Scale is JI-epimorphic with val: <7 22 32 34|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 15.4695 c. M: 28.8028 c. Lebeng 18: 3 2 3 2 3 3 2 SP M ME S SD: 6.8557 c. M:-11.8644 c. 25: 4 3 4 3 4 4 3 SP M ME S SD: 3.0689 c. M:-5.2387 c. 66: 10 8 11 8 10 11 8 SP T3 SD: 3.5481 c. M: 6.3174 c. 68: 11 8 11 8 11 11 8 SP M DE S SD: 3.5279 c. M:-5.9821 c. 70: 11 8 12 8 11 12 8 SP T3 SD: 3.2966 c. M:-5.4829 c. 77: 12 9 13 9 12 13 9 SP T3 SD: 1.9692 c. M: 3.4886 c. 84: 13 10 14 10 13 14 10 SP T3 SD: 1.5144 c. M: 2.4213 c. 102: 16 12 17 12 16 17 12 SP T3 SD: 0.8761 c. M:-1.4493 c. 109: 17 13 18 13 17 18 13 SP T3 SD: 0.5475 c. M: 0.9796 c. 127: 20 15 21 15 20 21 15 SP T3 SD: 0.5428 c. M:-0.8935 c. 134: 21 16 22 16 21 22 16 SP T3 SD: 0.3887 c. M: 0.6578 c. 236: 37 28 39 28 37 39 28 SP T3 SD: 0.1585 c. M:-0.2529 c. 370: 58 44 61 44 58 61 44 SP T3 SD: 0.0417 c. M: 0.0769 c. 606: 95 72 100 72 95 100 72 SP T3 SD: 0.0391 c. M: 0.0683 c. 976: 153 116 161 116 153 161 116 SP T3 SD: 0.0146 c. M: 0.0236 c. 1346: 211 160 222 160 211 222 160 SP T3 SD: 0.0133 c. M: 0.0226 c. 2213: 347 263 365 263 347 365 263 SP T3 SD: 0.0141 c. M:-0.0253 c. 2322: 364 276 383 276 364 383 276 SP T3 SD: 0.0123 c. M: 0.0219 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: 15.3211 cents 3 x x 4 x 5 x 6 S SD: 13.1633 cents 4 x 5 x 6 x 7:8 S SD: 27.2326 cents 5 x 6:7 x 8:9:10 S SD: 16.4951 cents 6 x 7:8:9:10:11:12 S SD: 13.5857 cents 7:8 x x 10:12:13:14 S SD: 20.3800 cents 8:9:10:11:12:13:15:16 SD: 11.1561 cents 9:10:11:12:13:15:17:18 SD: 10.0817 cents 11:12:13:15:16:18:20:22 SD: 9.3251 cents 14:16:17:19:21:23:26:28 SD: 7.8576 cents 17:19:21:23:25:28:31:34 SD: 5.7317 cents 19:21:23:26:28:31:35:38 SD: 3.4065 cents 25:28:30:34:37:41:46:50 SD: 2.7618 cents 34:38:41:46:50:56:63:68 SD: 2.1841 cents 42:47:51:57:62:69:77:84 SD: 1.7207 cents 51:57:62:69:75:84:94:102 SD: 1.6715 cents 53:59:64:72:78:87:98:106 SD: 1.2824 cents 70:78:85:95:103:115:129:140 SD: 0.8736 cents 95:106:115:129:140:156:175:190 SD: 0.2853 cents 252:281:305:342:371:414:464:504 SD: 0.2680 cents 314:350:380:426:463:516:578:628 SD: 0.2405 cents 342:381:414:464:504:562:630:684 SD: 0.1989 cents 367:409:444:498:541:603:676:734 SD: 0.1878 cents 384:428:465:521:566:631:707:768 SD: 0.1666 cents 409:456:495:555:603:672:753:818 SD: 0.1651 cents 437:487:529:593:644:718:805:874 SD: 0.0994 cents 532:593:644:722:784:874:980:1064 SD: 0.0468 cents