Scala analysis: xen10-chalmers-tritriadic-7-25-23
Tritriadic scale built from 7:25:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/23 144.353080 2: 28/23 340.551559 3: 529/392 518.896882 4: 575/392 663.249962 5: 23/14 859.448441 6: 25/14 1003.801521 middle minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 25/23 144.3531 2: 28/25 196.1985 middle second 3: 12167/10976 178.3453 4: 25/23 144.3531 5: 28/25 196.1985 middle second 6: 25/23 144.3531 7: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 25/23 144.353 cents 1: 1 12167/10976 178.345 cents 1: 3 28/25 196.198 cents middle second 2: 1 13225/10976 322.698 cents 2: 5 28/23 340.552 cents 2: 1 12167/9800 374.544 cents 3: 2 700/529 484.905 cents 3: 3 529/392 518.897 cents 3: 2 784/575 536.750 cents 4: 2 575/392 663.250 cents 4: 3 784/529 681.103 cents 4: 2 529/350 715.095 cents 5: 1 19600/12167 825.456 cents 5: 5 23/14 859.448 cents 5: 1 21952/13225 877.302 cents 6: 3 25/14 1003.802 cents middle minor seventh 6: 1 21952/12167 1021.655 cents 6: 3 46/25 1055.647 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 : 144.4 340.6 518.9 663.2 859.4 1003.8 1200.0 144.4 : 196.2 374.5 518.9 715.1 859.4 1055.6 1200.0 340.6 : 178.3 322.7 518.9 663.2 859.4 1003.8 1200.0 518.9 : 144.4 340.6 484.9 681.1 825.5 1021.7 1200.0 663.2 : 196.2 340.6 536.8 681.1 877.3 1055.6 1200.0 859.4 : 144.4 340.6 484.9 681.1 859.4 1003.8 1200.0 1003.8: 196.2 340.6 536.8 715.1 859.4 1055.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 144.3531 .. 196.1985 cents 644/625, 51.8454 cents 25/23, 144.3531 cents 2: 322.6984 .. 374.5438 cents 644/625, 51.8454 cents 330625/307328, 126.4999 cents 3: 484.9046 .. 536.7500 cents 644/625, 51.8454 cents 6860000/6436343, 110.3608 cents 4: 663.2500 .. 715.0954 cents 644/625, 51.8454 cents 330625/307328, 126.4999 cents 5: 825.4562 .. 877.3016 cents 644/625, 51.8454 cents 6860000/6436343, 110.3608 cents 6: 1003.8015 .. 1055.6469 cents 644/625, 51.8454 cents 330625/307328, 126.4999 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/23, 144.3531 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 1.187564 Largest / Average step : 1.144491 Largest / Smallest step : 1.359157 Median interval of one step : 12167/10976, 178.3453 cents, amount: 1 Least squares average step : 169.67999 cents, oct.: 1187.75990 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : SLMSLSL Scale is a Constant Structure, by a margin of 110.36084 cents Scale diversity : 1.264774 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.740773 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 : 307328/304175, 17.8532 cents Most common intervals : 28/23, 340.5516 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 144.353 340.552 cents Most common triad is 0.0 340.552 859.448 cents, amount: 3 Number of recognisable fifths : 2, average 715.0954 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 23 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 51.8454 cents: 4 -- Rational properties -- Prime limit : 23 Odd number limit : 13225 (O: 13225 U: 13225) Highest odd numerator or denominator: 575 Scale harmonicity : 0.005717 Average absolute harmonicity : 0.159841 Specific harmonicity : 0.031342 Fundamental : 1/9016, -13.1383 octaves, 0.0290 Hz. Guide tone : 370300, 18.4983 octaves, 96879946.831 Hz. Exponens Consonantiae : 3.338625E+09, 31.63661 octaves Euler's gradus suavitatis : 98 Sum of Mann's harmonic distance : 1033.0, average 147.57143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.00246, average 1.57178 Sum of Tenney's harmonic distance : 21.59120, average 3.08446 Vogel's harmonic complexity : 45.14286 Wille's k value : 6612 Wilson's harmonic complexity : 100 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 92.25990, average 3.29500 Lattice compactness (without 2's) : 66.59060, average 2.37824 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.71429 11 1 5: 0 .. 2 0.85714 6 7: -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 weakly epimorphic with val: <7 15 18 35| Scale is weakly epimorphic with val: <7 15 19 34| Scale is weakly epimorphic with val: <7 15 20 33| Scale is weakly epimorphic with val: <7 15 21 32| Scale is weakly epimorphic with val: <7 15 22 31| Scale is JI-epimorphic with val: <7 16 19 31| Scale is weakly epimorphic with val: <7 16 20 30| Scale is weakly epimorphic with val: <7 16 21 29| Scale is weakly epimorphic with val: <7 16 22 35| Scale is weakly epimorphic with val: <7 17 18 29| Scale is weakly epimorphic with val: <7 17 19 35| Scale is JI-epimorphic with val: <7 17 21 33| Scale is weakly epimorphic with val: <7 17 22 32| Scale is weakly epimorphic with val: <7 18 18 33| Scale is weakly epimorphic with val: <7 18 19 32| Scale is weakly epimorphic with val: <7 18 20 31| Scale is weakly epimorphic with val: <7 18 21 30|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 16.4020 c. M:-27.0755 c. Lebeng 18: 2 3 3 2 3 2 3 SP M ME S SD: 8.1080 c. M:-14.4365 c. Dicot-7 25: 3 4 4 3 4 3 4 SP M ME S SD: 5.5884 c. M:-9.1031 c. Dicot-7 42: 5 7 6 5 7 5 7 SP T3 SD: 3.5027 c. M: 6.1071 c. 49: 6 8 7 6 8 6 8 SP T3 SD: 2.4716 c. M: 4.6112 c. 60: 7 10 9 7 10 7 10 SP T3 SD: 2.5576 c. M: 4.3531 c. 67: 8 11 10 8 11 8 11 SP T3 SD: 0.5991 c. M: 1.0695 c. 141: 17 23 21 17 23 17 23 SP T3 SD: 0.3262 c. M:-0.5798 c. 208: 25 34 31 25 34 25 34 SP T3 SD: 0.1808 c. M:-0.3339 c. 349: 42 57 52 42 57 42 57 SP T3 SD: 0.2115 c. M:-0.3604 c. 391: 47 64 58 47 64 47 64 SP T3 SD: 0.1887 c. M: 0.3344 c. 465: 56 76 69 56 76 56 76 SP T3 SD: 0.1099 c. M: 0.1872 c. 532: 64 87 79 64 87 64 87 SP T3 SD: 0.0601 c. M: 0.0999 c. 673: 81 110 100 81 110 81 110 SP T3 SD: 0.0428 c. M:-0.0749 c. 740: 89 121 110 89 121 89 121 SP T3 SD: 0.0165 c. M: 0.0288 c. 1413: 170 231 210 170 231 170 231 SP T3 SD: 0.0132 c. M:-0.0206 c. 2153: 259 352 320 259 352 259 352 SP T3 SD: 0.0060 c. M:-0.0106 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: 19.3525 cents 3 x x 4 x 5 x 6 S SD: 10.8286 cents 4 x 5 x 6 x 7:8 S SD: 17.3485 cents 5 x 6:7 x 8:9:10 S SD: 16.6756 cents 6 x 7:8:9:10:11:12 S SD: 16.7150 cents 7:8 x 9:10 x 13:14 SD: 29.1665 cents 8:9:10:11:12:13:14:16 S SD: 14.1217 cents 9:10:11:12:13:15:16:18 SD: 8.2300 cents 14:15:17:19:21:23:25:28 SD: 6.7522 cents 19:21:23:26:28:31:34:38 SD: 5.9489 cents 20:22:24:27:29:33:36:40 SD: 5.8790 cents 22:24:27:30:32:36:39:44 SD: 4.4727 cents 23:25:28:31:34:38:41:46 SD: 2.4323 cents 37:40:45:50:54:61:66:74 SD: 2.0867 cents 45:49:55:61:66:74:80:90 SD: 1.9116 cents 55:60:67:74:81:90:98:110 SD: 1.9010 cents 56:61:68:76:82:92:100:112 SD: 1.6795 cents 60:65:73:81:88:99:107:120 SD: 1.4047 cents 69:75:84:93:101:113:123:138 SD: 1.0751 cents 92:100:112:124:135:151:164:184 SD: 0.5847 cents 137:149:167:185:201:225:245:274 SD: 0.5381 cents 160:174:195:216:235:263:286:320 SD: 0.5322 cents 171:186:208:231:251:281:305:342 SD: 0.5035 cents 174:189:212:235:255:286:311:348 SD: 0.4757 cents 197:214:240:266:289:324:352:394 SD: 0.4151 cents 221:240:269:298:324:363:395:442 SD: 0.3999 cents 229:249:279:309:336:376:409:458 SD: 0.2681 cents 266:289:324:359:390:437:475:532 SD: 0.2086 cents 289:314:352:390:424:475:516:578 SD: 0.2038 cents 358:389:436:483:525:588:639:716 SD: 0.1992 cents 392:426:477:529:575:644:700:784 SD: 0.1235 cents 529:575:644:714:776:869:945:1058 SD: 0.1052 cents