Scala analysis: xen10-chalmers-tritriadic-19-21-23
Tritriadic scale built from 19:21:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/19 173.267891 2: 23/19 330.761331 3: 483/361 504.029222 4: 529/361 661.522662 5: 38/23 869.238669 6: 42/23 1042.506560 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/21 157.4934 1: 21/19 173.2679 2: 23/21 157.4934 3: 21/19 173.2679 4: 23/21 157.4934 5: 13718/12167 207.7160 6: 21/19 173.2679 7: 23/21 157.4934
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 23/21 157.493 cents 1: 3 21/19 173.268 cents 1: 1 13718/12167 207.716 cents 2: 5 23/19 330.761 cents 2: 1 13718/11109 365.209 cents 2: 1 15162/12167 380.984 cents 3: 2 529/399 488.255 cents 3: 2 483/361 504.029 cents 3: 3 722/529 538.477 cents 4: 3 529/361 661.523 cents 4: 2 722/483 695.971 cents 4: 2 798/529 711.745 cents 5: 1 12167/7581 819.016 cents 5: 1 11109/6859 834.791 cents 5: 5 38/23 869.239 cents 6: 1 12167/6859 992.284 cents 6: 3 38/21 1026.732 cents 6: 3 42/23 1042.507 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 : 173.3 330.8 504.0 661.5 869.2 1042.5 1200.0 173.3 : 157.5 330.8 488.3 696.0 869.2 1026.7 1200.0 330.8 : 173.3 330.8 538.5 711.7 869.2 1042.5 1200.0 504.0 : 157.5 365.2 538.5 696.0 869.2 1026.7 1200.0 661.5 : 207.7 381.0 538.5 711.7 869.2 1042.5 1200.0 869.2 : 173.3 330.8 504.0 661.5 834.8 992.3 1200.0 1042.5: 157.5 330.8 488.3 661.5 819.0 1026.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 157.4934 .. 207.7160 cents 288078/279841, 50.2226 cents 23/21, 157.4934 cents 2: 330.7613 .. 380.9839 cents 288078/279841, 50.2226 cents 279841/260642, 123.0453 cents 3: 488.2548 .. 538.4773 cents 288078/279841, 50.2226 cents 6436343/6049638, 107.2709 cents 4: 661.5227 .. 711.7452 cents 288078/279841, 50.2226 cents 279841/260642, 123.0453 cents 5: 819.0161 .. 869.2387 cents 288078/279841, 50.2226 cents 6436343/6049638, 107.2709 cents 6: 992.2840 .. 1042.5066 cents 288078/279841, 50.2226 cents 279841/260642, 123.0453 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 23/21, 157.4934 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 13718/12167, 207.7160 cents Average / Smallest step : 1.088481 Largest / Average step : 1.211677 Largest / Smallest step : 1.318887 Median interval of one step : 21/19, 173.2679 cents, amount: 3 Least squares average step : 171.38715 cents, oct.: 1199.71008 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : MSMSLMS Scale is a Constant Structure, by a margin of 107.27087 cents Scale diversity : 1.249248 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.748887 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 : 441/437, 15.7745 cents Most common intervals : 23/19, 330.7613 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 173.268 330.761 cents Most common triad is 0.0 330.761 869.239 cents, amount: 3 Number of recognisable fifths : 4, average 703.8580 cents 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 : 19 23 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 50.2226 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.004123 Average absolute harmonicity : 0.154264 Specific harmonicity : 0.022583 Fundamental : 1/8303, -13.0194 octaves, 0.0315 Hz. Guide tone : 422142, 18.6874 octaves, 110443139.387 Hz. Exponens Consonantiae : 3.505045E+09, 31.70679 octaves Euler's gradus suavitatis : 130 Sum of Mann's harmonic distance : 972.5, average 138.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.81481, average 1.54497 Sum of Tenney's harmonic distance : 21.99139, average 3.14163 Vogel's harmonic complexity : 58.71429 Wille's k value : 6083 Wilson's harmonic complexity : 136 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 64.20942, average 2.29319 Lattice compactness (without 2's) : 60.28697, average 2.15311 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.42857 3 1 3: 0 .. 1 0.42857 3 7: 0 .. 1 0.42857 3 19: -2 .. 1 -0.71429 7 1 23: -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 JI-epimorphic with val: <7 10 18 27 29| Scale is weakly epimorphic with val: <7 10 18 29 34| Scale is weakly epimorphic with val: <7 10 18 30 33| Scale is weakly epimorphic with val: <7 10 18 31 32| Scale is weakly epimorphic with val: <7 10 19 27 31| Scale is JI-epimorphic with val: <7 10 19 28 30| Scale is weakly epimorphic with val: <7 10 19 30 35| Scale is weakly epimorphic with val: <7 10 19 31 34| Scale is weakly epimorphic with val: <7 10 19 32 33| Scale is weakly epimorphic with val: <7 10 20 27 33| Scale is weakly epimorphic with val: <7 10 20 28 32| Scale is JI-epimorphic with val: <7 10 20 29 31| Scale is weakly epimorphic with val: <7 10 20 32 35| Scale is weakly epimorphic with val: <7 10 20 33 34| Scale is weakly epimorphic with val: <7 10 21 27 35| Scale is weakly epimorphic with val: <7 10 21 28 34| Scale is weakly epimorphic with val: <7 10 21 29 33| Scale is JI-epimorphic with val: <7 10 21 30 32| Scale is weakly epimorphic with val: <7 10 22 27 30| Scale is weakly epimorphic with val: <7 10 22 28 29| Scale is weakly epimorphic with val: <7 10 22 29 35| Scale is weakly epimorphic with val: <7 10 22 30 34| Scale is JI-epimorphic with val: <7 10 22 31 33| Scale is weakly epimorphic with val: <7 11 18 27 31| Scale is JI-epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 18 31 34| Scale is weakly epimorphic with val: <7 11 18 32 33| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 19 28 32| Scale is JI-epimorphic with val: <7 11 19 29 31| Scale is weakly epimorphic with val: <7 11 19 32 35| Scale is weakly epimorphic with val: <7 11 19 33 34| Scale is weakly epimorphic with val: <7 11 20 27 35| Scale is weakly epimorphic with val: <7 11 20 28 34| Scale is weakly epimorphic with val: <7 11 20 29 33| Scale is JI-epimorphic with val: <7 11 20 30 32| = patent Scale is weakly epimorphic with val: <7 11 21 27 30| Scale is weakly epimorphic with val: <7 11 21 28 29| Scale is weakly epimorphic with val: <7 11 21 29 35| Scale is weakly epimorphic with val: <7 11 21 30 34| Scale is JI-epimorphic with val: <7 11 21 31 33| Scale is weakly epimorphic with val: <7 11 22 27 32| Scale is weakly epimorphic with val: <7 11 22 28 31| Scale is weakly epimorphic with val: <7 11 22 29 30| Scale is weakly epimorphic with val: <7 11 22 31 35| Scale is JI-epimorphic with val: <7 11 22 32 34| Scale is weakly epimorphic with val: <7 12 18 27 33| Scale is weakly epimorphic with val: <7 12 18 28 32| Scale is JI-epimorphic with val: <7 12 18 29 31| Scale is weakly epimorphic with val: <7 12 18 32 35| Scale is weakly epimorphic with val: <7 12 18 33 34| Scale is weakly epimorphic with val: <7 12 19 27 35| Scale is weakly epimorphic with val: <7 12 19 28 34| Scale is weakly epimorphic with val: <7 12 19 29 33| Scale is JI-epimorphic with val: <7 12 19 30 32| Scale is weakly epimorphic with val: <7 12 20 27 30| Scale is weakly epimorphic with val: <7 12 20 28 29| Scale is weakly epimorphic with val: <7 12 20 29 35| Scale is weakly epimorphic with val: <7 12 20 30 34| Scale is JI-epimorphic with val: <7 12 20 31 33| Scale is weakly epimorphic with val: <7 12 21 27 32| Scale is weakly epimorphic with val: <7 12 21 28 31| Scale is weakly epimorphic with val: <7 12 21 29 30| Scale is weakly epimorphic with val: <7 12 21 31 35| Scale is JI-epimorphic with val: <7 12 21 32 34| Scale is weakly epimorphic with val: <7 12 22 28 33| Scale is weakly epimorphic with val: <7 12 22 29 32| Scale is weakly epimorphic with val: <7 12 22 30 31| Scale is JI-epimorphic with val: <7 12 22 33 35|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 12.9869 c. M:-24.1916 c. Lebeng 15: 2 2 2 2 3 2 2 SP M ME S SD: 14.4151 c. M: 24.0292 c. 22: 3 3 3 3 4 3 3 SP M ME S SD: 7.3257 c. M: 13.1201 c. 29: 4 4 4 4 5 4 4 SP M ME S SD: 5.0824 c. M: 8.0238 c. 40: 6 5 6 5 7 6 5 SP T3 SD: 4.4817 c. M:-7.4934 c. 47: 7 6 7 6 8 7 6 SP T3 SD: 3.7784 c. M:-6.6091 c. 62: 9 8 9 8 11 9 8 SP T3 SD: 1.9453 c. M: 3.4581 c. 69: 10 9 10 9 12 10 9 SP T3 SD: 0.5479 c. M:-0.9717 c. 145: 21 19 21 19 25 21 19 SP T3 SD: 0.4511 c. M:-0.7984 c. 214: 31 28 31 28 37 31 28 SP T3 SD: 0.3789 c. M:-0.6437 c. 236: 34 31 34 31 41 34 31 SP T3 SD: 0.3703 c. M: 0.6394 c. 243: 35 32 35 32 42 35 32 SP T3 SD: 0.3012 c. M: 0.5313 c. 312: 45 41 45 41 54 45 41 SP T3 SD: 0.1253 c. M: 0.1989 c. 381: 55 50 55 50 66 55 50 SP T3 SD: 0.0620 c. M: 0.1053 c. 838: 121 110 121 110 145 121 110 SP T3 SD: 0.0281 c. M:-0.0525 c. 907: 131 119 131 119 157 131 119 SP T3 SD: 0.0332 c. M:-0.0513 c. 1219: 176 160 176 160 211 176 160 SP T3 SD: 0.0075 c. M: 0.0127 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: 20.2162 cents 3 x x 4 x 5 x 6 S SD: 5.4204 cents 4 x 5 x 6 x 7:8 S SD: 25.1864 cents 5 x 6:7 x 8:9:10 S SD: 20.0946 cents 6 x 7:8:9:10:11:12 S SD: 12.9402 cents 7:8 x 9:10:12:13:14 S SD: 20.3988 cents 8:9:10:11:12:13:15:16 SD: 14.8561 cents 9:10:11:12:13:15:16:18 SD: 8.3296 cents 15:17:18:20:22:25:27:30 SD: 7.8260 cents 17:19:21:23:25:28:31:34 SD: 6.4621 cents 18:20:22:24:26:30:33:36 SD: 5.1354 cents 27:30:33:36:40:45:49:54 SD: 4.7340 cents 28:31:34:37:41:46:51:56 SD: 3.5492 cents 29:32:35:39:42:48:53:58 SD: 3.3155 cents 38:42:46:51:56:63:69:76 SD: 2.2872 cents 47:52:57:63:69:78:86:94 SD: 1.4704 cents 75:83:91:100:110:124:137:150 SD: 1.1141 cents 77:85:93:103:113:127:141:154 SD: 1.0923 cents 86:95:104:115:126:142:157:172 SD: 0.3600 cents 133:147:161:178:195:220:243:266 SD: 0.3563 cents 219:242:265:293:321:362:400:438 SD: 0.1837 cents 305:337:369:408:447:504:557:610 SD: 0.1768 cents 408:451:494:546:598:674:745:816 SD: 0.1019 cents 494:546:598:661:724:816:902:988 SD: 0.0709 cents