Scala analysis: xen12-chalmers-tritriadic-dm-25-23-7
Tritriadic D->M scale built from 25:23:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/25 196.198479 middle second 2: 28/23 340.551559 3: 784/575 536.750038 4: 529/350 715.095360 5: 23/14 859.448441 6: 46/25 1055.646920 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/23 144.3531 1: 28/25 196.1985 middle second 2: 25/23 144.3531 3: 28/25 196.1985 middle second 4: 12167/10976 178.3453 5: 25/23 144.3531 6: 28/25 196.1985 middle second 7: 25/23 144.3531
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 : 196.2 340.6 536.8 715.1 859.4 1055.6 1200.0 196.2 : 144.4 340.6 518.9 663.2 859.4 1003.8 1200.0 340.6 : 196.2 374.5 518.9 715.1 859.4 1055.6 1200.0 536.8 : 178.3 322.7 518.9 663.2 859.4 1003.8 1200.0 715.1 : 144.4 340.6 484.9 681.1 825.5 1021.7 1200.0 859.4 : 196.2 340.6 536.8 681.1 877.3 1055.6 1200.0 1055.6: 144.4 340.6 484.9 681.1 859.4 1003.8 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 : 174.13612 cents, oct.: 1218.95284 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : LSLMSLS 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: 6 -- 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 : 0.159529 Specific harmonicity : 0.031349 Fundamental : 1/8050, -12.9748 octaves, 0.0325 Hz. Guide tone : 414736, 18.6618 octaves, 108505540.451 Hz. Exponens Consonantiae : 3.338625E+09, 31.63661 octaves Euler's gradus suavitatis : 98 Sum of Mann's harmonic distance : 1226.5, average 175.21429 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 : 22.44508, average 3.20644 Vogel's harmonic complexity : 45.00000 Wille's k value : 6612 Wilson's harmonic complexity : 100 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 90.52320, average 3.23297 Lattice compactness (without 2's) : 66.76217, average 2.38436 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.14286 12 1 5: -2 .. 0 -1.14286 8 7: -1 .. 2 0.28571 6 1 23: -1 .. 2 0.28571 6 5 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 20 / 7 = 2.85714 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: 19.7309 c. M: 29.3811 c. Lebeng 17: 3 2 3 2 2 3 2 SP M ME S SD: 14.2719 c. M:-27.9558 c. 18: 3 2 3 3 2 3 2 SP M ME S SD: 9.1370 c. M:-18.2380 c. 24: 4 3 4 3 3 4 3 SP M ME S SD: 9.4742 c. M: 15.0954 c. Neutral Hypodorian, Iced Dark Lydian 25: 4 3 4 4 3 4 3 SP M ME S SD: 4.7780 c. M: 8.7500 c. 42: 7 5 7 6 5 7 5 SP T3 SD: 3.0536 c. M:-6.1071 c. 49: 8 6 8 7 6 8 6 SP T3 SD: 2.5473 c. M: 4.8913 c. 67: 11 8 11 10 8 11 8 SP T3 SD: 0.7564 c. M:-1.3226 c. 116: 19 14 19 17 14 19 14 SP T3 SD: 0.8290 c. M: 1.3023 c. 141: 23 17 23 21 17 23 17 SP T3 SD: 0.3212 c. M: 0.5798 c. 208: 34 25 34 31 25 34 25 SP T3 SD: 0.1695 c. M:-0.2893 c. 324: 53 39 53 48 39 53 39 SP T3 SD: 0.1892 c. M:-0.2870 c. 349: 57 42 57 52 42 57 42 SP T3 SD: 0.1817 c. M: 0.3604 c. 391: 64 47 64 58 47 64 47 SP T3 SD: 0.1682 c. M:-0.3344 c. 465: 76 56 76 69 56 76 56 SP T3 SD: 0.1284 c. M: 0.2567 c. 532: 87 64 87 79 64 87 64 SP T3 SD: 0.0516 c. M:-0.0921 c. 673: 110 81 110 100 81 110 81 SP T3 SD: 0.0533 c. M: 0.0879 c. 740: 121 89 121 110 89 121 89 SP T3 SD: 0.0207 c. M:-0.0398 c. 1413: 231 170 231 210 170 231 170 SP T3 SD: 0.0154 c. M: 0.0211 c. 2153: 352 259 352 320 259 352 259 SP T3 SD: 0.0054 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: 6.5702 cents 3 x x 4 x 5 x 6 S SD: 15.3428 cents 4 x 5 x 6 x 7:8 S SD: 24.7547 cents 5 x 6:7 x 8:9:10 S SD: 15.8199 cents 6:7 x 8:9:10:11:12 S SD: 14.2647 cents 8:9:10:11:12:13:15:16 SD: 8.9906 cents 14:16:17:19:21:23:26:28 SD: 5.9561 cents 17:19:21:23:26:28:31:34 SD: 5.5579 cents 19:21:23:26:29:31:35:38 SD: 4.7272 cents 23:26:28:31:35:38:42:46 SD: 4.6606 cents 24:27:29:33:36:39:44:48 SD: 4.5379 cents 25:28:30:34:38:41:46:50 SD: 3.8993 cents 27:30:33:37:41:44:50:54 SD: 3.7758 cents 31:35:38:42:47:51:57:62 SD: 3.1718 cents 33:37:40:45:50:54:61:66 SD: 1.9616 cents 50:56:61:68:76:82:92:100 SD: 1.6795 cents 64:72:78:87:97:105:118:128 SD: 1.6377 cents 68:76:83:93:103:112:125:136 SD: 1.4155 cents 69:77:84:94:104:113:127:138 SD: 1.3910 cents 74:83:90:101:112:122:136:148 SD: 1.0984 cents 82:92:100:112:124:135:151:164 SD: 0.9407 cents 101:113:123:138:153:166:186:202 SD: 0.8452 cents 107:120:130:146:162:176:197:214 SD: 0.8252 cents 115:129:140:157:174:189:212:230 SD: 0.7371 cents 124:139:151:169:187:204:228:248 SD: 0.7180 cents 143:160:174:195:216:235:263:286 SD: 0.3453 cents 207:232:252:282:313:340:381:414 SD: 0.3056 cents 258:289:314:352:390:424:475:516 SD: 0.2442 cents 317:355:386:432:479:521:583:634 SD: 0.2204 cents 350:392:426:477:529:575:644:700 SD: 0.1235 cents 501:561:610:683:757:823:922:1002 SD: 0.1147 cents 575:644:700:784:869:945:1058:1150 SD: 0.0957 cents