Scala analysis: xen10-chalmers-tritriadic-21-15-23
Tritriadic scale built from 21:15:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/21 157.493440 2: 529/441 314.986880 3: 30/23 459.994367 4: 10/7 617.487807 Euler's tritone 5: 230/147 774.981247 6: 42/23 1042.506560 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/21 157.4934 1: 23/21 157.4934 2: 23/21 157.4934 3: 13230/12167 145.0075 4: 23/21 157.4934 5: 23/21 157.4934 6: 3087/2645 267.5253 7: 23/21 157.4934
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 13230/12167 145.007 cents 1: 5 23/21 157.493 cents 1: 1 3087/2645 267.525 cents 2: 2 630/529 302.501 cents 2: 3 529/441 314.987 cents 2: 2 147/115 425.019 cents 3: 3 30/23 459.994 cents 3: 1 12167/9261 472.480 cents 3: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 3 10/7 617.488 cents Euler's tritone 4: 1 18522/12167 727.520 cents 4: 3 23/15 740.006 cents 5: 2 230/147 774.981 cents 5: 3 882/529 885.013 cents 5: 2 529/315 897.499 cents 6: 1 5290/3087 932.475 cents 6: 5 42/23 1042.507 cents 6: 1 12167/6615 1054.993 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 : 157.5 315.0 460.0 617.5 775.0 1042.5 1200.0 157.5 : 157.5 302.5 460.0 617.5 885.0 1042.5 1200.0 315.0 : 145.0 302.5 460.0 727.5 885.0 1042.5 1200.0 460.0 : 157.5 315.0 582.5 740.0 897.5 1055.0 1200.0 617.5 : 157.5 425.0 582.5 740.0 897.5 1042.5 1200.0 775.0 : 267.5 425.0 582.5 740.0 885.0 1042.5 1200.0 1042.5: 157.5 315.0 472.5 617.5 775.0 932.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 145.0075 .. 267.5253 cents 161/150, 122.5178 cents 13230/12167, 145.0075 cents 2: 302.5009 .. 425.0188 cents 161/150, 122.5178 cents 50/49, 34.9756 cents 3: 459.9944 .. 582.5122 cents 161/150, 122.5178 cents 50/49, 34.9756 cents 4: 617.4878 .. 740.0056 cents 161/150, 122.5178 cents 50/49, 34.9756 cents 5: 774.9812 .. 897.4991 cents 161/150, 122.5178 cents 50/49, 34.9756 cents 6: 932.4747 .. 1054.9925 cents 161/150, 122.5178 cents 50/49, 34.9756 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 13230/12167, 145.0075 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 3087/2645, 267.5253 cents Average / Smallest step : 1.182205 Largest / Average step : 1.560564 Largest / Smallest step : 1.844907 Median interval of one step : 23/21, 157.4934 cents, amount: 5 Most common interval of one step : 23/21, 157.4934 cents, amount: 5 Least squares average step : 165.48105 cents, oct.: 1158.36736 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : MMSMMLM Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.269556 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.387411 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 : 279841/277830, 12.4860 cents Most common intervals : 23/21, 157.4934 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 459.994 1042.507 cents Most common triad is 0.0 157.493 1042.507 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 21 23 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 122.5178 cents: 4 -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.005796 Average absolute harmonicity : 0.162080 Specific harmonicity : 0.032118 Fundamental : 1/10143, -13.3082 octaves, 0.0258 Hz. Guide tone : 111090, 16.7614 octaves, 29063984.049 Hz. Exponens Consonantiae : 1.126786E+09, 30.06957 octaves Euler's gradus suavitatis : 96 Sum of Mann's harmonic distance : 764.5, average 109.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.82105, average 1.40301 Sum of Tenney's harmonic distance : 20.55084, average 2.93583 Vogel's harmonic complexity : 46.57143 Wille's k value : 6083 Wilson's harmonic complexity : 104 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 71.01044, average 2.53609 Lattice compactness (without 2's) : 67.06225, average 2.39508 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.71429 5 1 3: -2 .. 1 -0.28571 6 5: 0 .. 1 0.42857 3 7: -2 .. 1 -0.71429 7 1 23: -1 .. 2 0.28571 6 5 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 15 18 29| Scale is weakly epimorphic with val: <7 10 15 19 35| Scale is weakly epimorphic with val: <7 10 15 20 34| Scale is weakly epimorphic with val: <7 10 15 21 33| Scale is weakly epimorphic with val: <7 10 16 18 31| Scale is JI-epimorphic with val: <7 10 16 19 30| Scale is weakly epimorphic with val: <7 10 16 20 29| Scale is weakly epimorphic with val: <7 10 16 21 35| Scale is weakly epimorphic with val: <7 10 16 22 34| Scale is weakly epimorphic with val: <7 10 17 18 33| Scale is weakly epimorphic with val: <7 10 17 19 32| Scale is JI-epimorphic with val: <7 10 17 20 31| Scale is weakly epimorphic with val: <7 10 17 21 30| Scale is weakly epimorphic with val: <7 10 17 22 29| Scale is weakly epimorphic with val: <7 10 18 19 34| Scale is weakly epimorphic with val: <7 10 18 20 33| Scale is JI-epimorphic with val: <7 10 18 21 32| Scale is weakly epimorphic with val: <7 10 18 22 31| Scale is JI-epimorphic with val: <7 11 15 18 30| Scale is weakly epimorphic with val: <7 11 15 19 29| Scale is weakly epimorphic with val: <7 11 15 20 35| Scale is weakly epimorphic with val: <7 11 15 21 34| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is JI-epimorphic with val: <7 11 16 19 31| Scale is weakly epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 22 35| Scale is weakly epimorphic with val: <7 11 17 18 34| Scale is weakly epimorphic with val: <7 11 17 19 33| Scale is JI-epimorphic with val: <7 11 17 20 32| Scale is weakly epimorphic with val: <7 11 17 21 31| Scale is weakly epimorphic with val: <7 11 17 22 30| Scale is weakly epimorphic with val: <7 11 18 19 35| Scale is weakly epimorphic with val: <7 11 18 20 34| Scale is JI-epimorphic with val: <7 11 18 21 33| Scale is weakly epimorphic with val: <7 11 18 22 32| Scale is JI-epimorphic with val: <7 12 15 18 31| Scale is weakly epimorphic with val: <7 12 15 19 30| Scale is weakly epimorphic with val: <7 12 15 20 29| Scale is weakly epimorphic with val: <7 12 15 21 35| Scale is weakly epimorphic with val: <7 12 16 18 33| Scale is JI-epimorphic with val: <7 12 16 19 32| Scale is weakly epimorphic with val: <7 12 16 20 31| Scale is weakly epimorphic with val: <7 12 16 21 30| Scale is weakly epimorphic with val: <7 12 16 22 29| Scale is weakly epimorphic with val: <7 12 17 18 35| Scale is weakly epimorphic with val: <7 12 17 19 34| Scale is JI-epimorphic with val: <7 12 17 20 33| Scale is weakly epimorphic with val: <7 12 17 21 32| Scale is weakly epimorphic with val: <7 12 17 22 31| Scale is weakly epimorphic with val: <7 12 18 19 29| Scale is weakly epimorphic with val: <7 12 18 20 35| Scale is JI-epimorphic with val: <7 12 18 21 34| Scale is weakly epimorphic with val: <7 12 18 22 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 47.0836 c. M:-82.1616 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 13.9728 c. M: 24.9812 c. 20: 3 2 3 2 3 4 3 P SD: 16.7713 c. M:-22.5066 c. 21: 3 3 2 3 3 4 3 SP T3 SD: 16.5704 c. M:-27.8703 c. 22: 3 3 2 3 3 5 3 P T3 SD: 13.1982 c. M: 23.6307 c. 23: 3 3 3 3 3 5 3 SP M DE S SD: 5.7245 c. M:-9.5708 c. 31: 4 4 4 4 4 7 4 SP M DE S SD: 3.0900 c. M: 5.3095 c. 60: 8 8 7 8 8 13 8 SP T3 SD: 3.1441 c. M:-5.0188 c. 68: 9 9 8 9 9 15 9 SP T3 SD: 1.4257 c. M:-2.6602 c. 76: 10 10 9 10 10 17 10 SP T3 SD: 1.1917 c. M: 2.0996 c. 99: 13 13 12 13 13 22 13 SP T3 SD: 0.4628 c. M:-0.7763 c. 175: 23 23 21 23 23 39 23 SP T3 SD: 0.3267 c. M: 0.5658 c. 206: 27 27 25 27 27 46 27 SP T3 SD: 0.2267 c. M: 0.4238 c. 274: 36 36 33 36 36 61 36 SP T3 SD: 0.1837 c. M:-0.3416 c. 305: 40 40 37 40 40 68 40 SP T3 SD: 0.1889 c. M:-0.3335 c. 373: 49 49 45 49 49 83 49 SP T3 SD: 0.2076 c. M:-0.3539 c. 381: 50 50 46 50 50 85 50 SP T3 SD: 0.1089 c. M: 0.1781 c. 480: 63 63 58 63 63 107 63 SP T3 SD: 0.0106 c. M:-0.0188 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 36.5131 cents 3 x x 4 x 5 x 6 S SD: 38.6024 cents 4 x 5 x x 6:7:8 S SD: 31.4734 cents 5 x 6 x 7:8:9:10 S SD: 11.5626 cents 6 x 7:8 x 9:11:12 SD: 19.1236 cents 7:8 x 9:10:11:13:14 SD: 13.9026 cents 8:9:10 x 11:13:15:16 SD: 22.3675 cents 9:10:11:12:13:14:16:18 S SD: 10.8244 cents 10:11:12:13:14:16:18:20 S SD: 8.3692 cents 14:15:17:18:20:22:26:28 SD: 8.3595 cents 16:18:19:21:23:25:29:32 SD: 7.6468 cents 19:21:23:25:27:30:35:38 SD: 5.1254 cents 21:23:25:27:30:33:38:42 SD: 4.7347 cents 23:25:28:30:33:36:42:46 SD: 4.2452 cents 29:32:35:38:41:45:53:58 SD: 4.2226 cents 30:33:36:39:43:47:55:60 SD: 1.8928 cents 62:68:74:81:89:97:113:124 SD: 1.8621 cents 63:69:76:82:90:99:115:126 SD: 1.8414 cents 65:71:78:85:93:102:119:130 SD: 1.3867 cents 75:82:90:98:107:117:137:150 SD: 1.0190 cents 96:105:115:125:137:150:175:192 SD: 0.8803 cents 105:115:126:137:150:164:192:210 SD: 0.5597 cents 115:126:138:150:164:180:210:230 SD: 0.4599 cents 191:209:229:249:273:299:349:382 SD: 0.3739 cents 200:219:240:261:286:313:365:400 SD: 0.3365 cents 276:302:331:360:394:432:504:552 SD: 0.3142 cents 282:309:338:368:403:441:515:564 SD: 0.3005 cents 292:320:350:381:417:457:533:584 SD: 0.2947 cents 296:324:355:386:423:463:541:592 SD: 0.2931 cents 305:334:366:398:436:477:557:610 SD: 0.2455 cents 306:335:367:399:437:479:559:612 SD: 0.2204 cents 315:345:378:411:450:493:575:630 SD: 0.1696 cents 420:460:504:548:600:657:767:840 SD: 0.1341 cents 441:483:529:575:630:690:805:882 SD: 0.1322 cents 546:598:655:712:780:854:997:1092 SD: 0.1046 cents