Scala analysis: xen12-chalmers-tritriadic-dm-15-21-23
Tritriadic D->M scale built from 15:21:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/21 157.493440 2: 147/115 425.018753 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 23/15 740.005633 5: 529/315 897.499072 6: 42/23 1042.506560 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/21 157.4934 1: 23/21 157.4934 2: 3087/2645 267.5253 3: 23/21 157.4934 4: 23/21 157.4934 5: 23/21 157.4934 6: 13230/12167 145.0075 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 : 157.5 425.0 582.5 740.0 897.5 1042.5 1200.0 157.5 : 267.5 425.0 582.5 740.0 885.0 1042.5 1200.0 425.0 : 157.5 315.0 472.5 617.5 775.0 932.5 1200.0 582.5 : 157.5 315.0 460.0 617.5 775.0 1042.5 1200.0 740.0 : 157.5 302.5 460.0 617.5 885.0 1042.5 1200.0 897.5 : 145.0 302.5 460.0 727.5 885.0 1042.5 1200.0 1042.5: 157.5 315.0 582.5 740.0 897.5 1055.0 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 : 177.55446 cents, oct.: 1242.88124 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : MLMMMSM 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: 3 -- 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 : 0.162693 Specific harmonicity : 0.032229 Fundamental : 1/7245, -12.8228 octaves, 0.0361 Hz. Guide tone : 155526, 17.2468 octaves, 40689577.669 Hz. Exponens Consonantiae : 1.126786E+09, 30.06957 octaves Euler's gradus suavitatis : 96 Sum of Mann's harmonic distance : 634.0, average 90.57143 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 : 19.50162, average 2.78595 Vogel's harmonic complexity : 46.14286 Wille's k value : 6083 Wilson's harmonic complexity : 104 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 70.20387, average 2.50728 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 0.28571 2 1 3: -2 .. 1 -0.28571 6 5: -1 .. 0 -0.57143 4 7: -1 .. 2 0.28571 6 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: 48.3587 c. M: 82.1616 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 12.8081 c. M:-24.9812 c. 20: 3 4 3 2 3 2 3 P SD: 15.8140 c. M:-22.5066 c. 21: 3 4 3 3 3 2 3 SP T3 SD: 14.2783 c. M: 25.0188 c. 23: 3 5 3 3 3 3 3 SP M DE S SD: 6.9360 c. M: 10.5426 c. 31: 4 7 4 4 4 4 4 SP M DE S SD: 3.5887 c. M: 7.1765 c. 39: 5 9 5 5 5 5 5 SP M DE S SD: 3.6534 c. M:-5.7505 c. 60: 8 13 8 8 8 7 8 SP T3 SD: 2.6811 c. M: 5.0188 c. 68: 9 15 9 9 9 8 9 SP T3 SD: 1.3840 c. M:-2.5009 c. 76: 10 17 10 10 10 9 10 SP T3 SD: 1.4905 c. M:-2.5009 c. 99: 13 22 13 13 13 12 13 SP T3 SD: 0.5003 c. M: 0.7763 c. 175: 23 39 23 23 23 21 23 SP T3 SD: 0.4090 c. M:-0.7866 c. 206: 27 46 27 27 27 25 27 SP T3 SD: 0.2235 c. M: 0.4117 c. 274: 36 61 36 36 36 33 36 SP T3 SD: 0.1758 c. M:-0.3111 c. 373: 49 83 49 49 49 45 49 SP T3 SD: 0.1783 c. M: 0.3539 c. 381: 50 85 50 50 50 46 50 SP T3 SD: 0.1205 c. M:-0.1781 c. 480: 63 107 63 63 63 58 63 SP T3 SD: 0.0094 c. M: 0.0188 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: 19.0253 cents 3 x 4 x x 5 x 6 S SD: 24.7330 cents 4 x 5 x 6:7 x 8 S SD: 22.4074 cents 5 x 6:7:8 x 9:10 S SD: 26.8423 cents 6:7:8 x 9:10:11:12 S SD: 22.9515 cents 7:8:9:10:11:12:13:14 H SD: 14.7637 cents 10:11:13:14:15:17:18:20 SD: 8.3595 cents 13:14:17:18:20:22:24:26 SD: 8.2554 cents 15:16:19:21:23:25:27:30 SD: 8.0003 cents 17:19:22:24:26:29:31:34 SD: 7.3625 cents 18:20:23:25:28:30:33:36 SD: 5.8054 cents 21:23:27:29:32:35:38:42 SD: 4.9520 cents 22:24:28:31:34:37:40:44 SD: 3.1220 cents 32:35:41:45:49:54:58:64 SD: 2.5717 cents 40:44:51:56:61:67:73:80 SD: 1.9501 cents 43:47:55:60:66:72:79:86 SD: 1.9500 cents 50:55:64:70:77:84:91:100 SD: 1.7625 cents 53:58:68:74:81:89:97:106 SD: 1.5166 cents 62:68:79:87:95:104:113:124 SD: 1.1848 cents 75:82:96:105:115:126:137:150 SD: 0.5597 cents 115:126:147:161:176:193:210:230 SD: 0.5042 cents 137:150:175:192:210:230:250:274 SD: 0.3796 cents 190:208:243:266:291:319:347:380 SD: 0.3396 cents 212:232:271:297:325:356:387:424 SD: 0.2808 cents 240:263:307:336:368:403:438:480 SD: 0.2670 cents 305:334:390:427:468:512:557:610 SD: 0.2224 cents 345:378:441:483:529:579:630:690 SD: 0.1876 cents 420:460:537:588:644:705:767:840 SD: 0.1322 cents 493:540:630:690:756:828:900:986 SD: 0.1298 cents 525:575:671:735:805:882:959:1050 SD: 0.1262 cents 568:622:726:795:871:954:1037:1136 SD: 0.0982 cents