Scala analysis: xen12-chalmers-tritriadic-dm-21-25-17
Tritriadic D->M scale built from 21:25:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 578/525 166.502484 2: 25/21 301.846520 BP second, quasi-equal minor third 3: 34/25 532.327982 4: 25/17 667.672018 5: 34/21 834.174502 supraminor sixth 6: 625/357 969.518539 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 714/625 230.4815 1: 578/525 166.5025 2: 625/578 135.3440 3: 714/625 230.4815 4: 625/578 135.3440 5: 578/525 166.5025 6: 625/578 135.3440 7: 714/625 230.4815
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 625/578 135.344 cents 1: 2 578/525 166.502 cents 1: 2 714/625 230.481 cents 2: 3 25/21 301.847 cents BP second, quasi-equal minor third 2: 3 21/17 365.825 cents submajor third 2: 1 19652/15625 396.984 cents 3: 1 15625/12138 437.191 cents 3: 1 13125/9826 501.170 cents 3: 5 34/25 532.328 cents 4: 5 25/17 667.672 cents 4: 1 19652/13125 698.830 cents 4: 1 24276/15625 762.809 cents 5: 1 15625/9826 803.016 cents 5: 3 34/21 834.175 cents supraminor sixth 5: 3 42/25 898.153 cents quasi-equal major sixth 6: 2 625/357 969.519 cents 6: 2 525/289 1033.498 cents 6: 3 1156/625 1064.656 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 : 166.5 301.8 532.3 667.7 834.2 969.5 1200.0 166.5 : 135.3 365.8 501.2 667.7 803.0 1033.5 1200.0 301.8 : 230.5 365.8 532.3 667.7 898.2 1064.7 1200.0 532.3 : 135.3 301.8 437.2 667.7 834.2 969.5 1200.0 667.7 : 166.5 301.8 532.3 698.8 834.2 1064.7 1200.0 834.2 : 135.3 365.8 532.3 667.7 898.2 1033.5 1200.0 969.5 : 230.5 397.0 532.3 762.8 898.2 1064.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 135.3440 .. 230.4815 cents 412692/390625, 95.1374 cents 625/578, 135.3440 cents 2: 301.8465 .. 396.9839 cents 412692/390625, 95.1374 cents 15625/14994, 71.3651 cents 3: 437.1906 .. 532.3280 cents 412692/390625, 95.1374 cents 244140625/238535976, 40.2066 cents 4: 667.6720 .. 762.8094 cents 412692/390625, 95.1374 cents 625/578, 135.3440 cents 5: 803.0161 .. 898.1535 cents 412692/390625, 95.1374 cents 244140625/238535976, 40.2066 cents 6: 969.5185 .. 1064.6560 cents 412692/390625, 95.1374 cents 15625/14994, 71.3651 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 625/578, 135.3440 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 714/625, 230.4815 cents Average / Smallest step : 1.266613 Largest / Average step : 1.344475 Largest / Smallest step : 1.702930 Median interval of one step : 578/525, 166.5025 cents, amount: 2 Most common interval of one step : 625/578, 135.3440 cents, amount: 3 Least squares average step : 167.32751 cents, oct.: 1171.29256 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1463-tone equal temperament with octave 2/1 degrees: 203 368 649 814 1017 1182 1463 Least number of segments generator : 732 of 600.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 872 of 715.243 cents and inv. generated superset size: 47 = 40 more = 671.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBABC Step pattern size order : MSLSMSL Scale is a Constant Structure, by a margin of 40.20661 cents Scale diversity : 1.377106 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.524313 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 : 334084/328125, 31.1584 cents Most common intervals : 34/25, 532.3280 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 365.825 667.672 cents Most common triad is 0.0 532.328 667.672 cents, amount: 3 Number of recognisable fifths : 1, average 698.8305 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 17 25 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 17 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.007007 Average absolute harmonicity : 0.161950 Specific harmonicity : 0.038040 Fundamental : 1/8925, -13.1236 octaves, 0.0293 Hz. Guide tone : 361250, 18.4626 octaves, 94512235.465 Hz. Exponens Consonantiae : 3.224156E+09, 31.58627 octaves Euler's gradus suavitatis : 82 Sum of Mann's harmonic distance : 1145.0, average 163.57143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.03208, average 1.57601 Sum of Tenney's harmonic distance : 22.26333, average 3.18048 Vogel's harmonic complexity : 39.57143 Wille's k value : 7812 Wilson's harmonic complexity : 91 Rectangular lattice diameter : 11 Triangular lattice diameter : 6 Lattice compactness : 89.96081, average 3.21289 Lattice compactness (without 2's) : 86.74367, average 3.09799 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.57143 4 1 3: -1 .. 0 -0.57143 4 5: -2 .. 4 0.57143 12 7: -1 .. 0 -0.57143 4 1 17: -1 .. 2 0.28571 6 5 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 26 / 7 = 3.71429 Scale is JI-epimorphic with val: <7 10 15 18 26| Scale is weakly epimorphic with val: <7 10 15 19 28| Scale is weakly epimorphic with val: <7 10 15 21 32| Scale is weakly epimorphic with val: <7 10 15 22 27| Scale is weakly epimorphic with val: <7 10 16 18 31| Scale is weakly epimorphic with val: <7 10 16 19 26| Scale is JI-epimorphic with val: <7 10 16 20 28| Scale is weakly epimorphic with val: <7 10 16 21 30| Scale is weakly epimorphic with val: <7 10 17 18 29| Scale is weakly epimorphic with val: <7 10 17 19 31| Scale is weakly epimorphic with val: <7 10 17 20 26| Scale is weakly epimorphic with val: <7 10 17 21 28| Scale is JI-epimorphic with val: <7 10 17 22 30| Scale is weakly epimorphic with val: <7 10 18 18 27| Scale is weakly epimorphic with val: <7 10 18 20 31| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 18 22 28| Scale is weakly epimorphic with val: <7 11 15 18 28| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 22 29| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is JI-epimorphic with val: <7 11 16 19 28| Scale is weakly epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 17 18 31| Scale is weakly epimorphic with val: <7 11 17 19 26| Scale is weakly epimorphic with val: <7 11 17 20 28| Scale is JI-epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 22 32| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 21 28| Scale is weakly epimorphic with val: <7 11 18 22 30| Scale is weakly epimorphic with val: <7 12 15 19 32| Scale is weakly epimorphic with val: <7 12 15 20 27| Scale is weakly epimorphic with val: <7 12 15 21 29| Scale is weakly epimorphic with val: <7 12 15 22 31| Scale is JI-epimorphic with val: <7 12 16 18 28| Scale is weakly epimorphic with val: <7 12 16 19 30| Scale is weakly epimorphic with val: <7 12 16 21 27| Scale is weakly epimorphic with val: <7 12 16 22 29| Scale is weakly epimorphic with val: <7 12 17 18 26| Scale is weakly epimorphic with val: <7 12 17 19 28| Scale is JI-epimorphic with val: <7 12 17 20 30| Scale is weakly epimorphic with val: <7 12 17 21 32| Scale is weakly epimorphic with val: <7 12 18 18 31| Scale is weakly epimorphic with val: <7 12 18 19 26| Scale is weakly epimorphic with val: <7 12 18 20 28| Scale is weakly epimorphic with val: <7 12 18 21 30| Scale is JI-epimorphic with val: <7 12 18 22 32|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 30.1709 c. M:-59.0529 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 26.2328 c. M: 36.1852 c. Pseudo Pelog, Pelogic-7, Antiionian 12: 2 1 2 2 1 2 2 P M ME S SD: 27.5492 c. M: 34.1745 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 13: 2 1 3 1 2 2 2 P D3 S SD: 23.8765 c. M:-45.8661 c. 14: 2 2 2 2 2 1 3 P T3 SD: 22.6639 c. M:-41.0106 c. 15: 2 2 3 1 2 2 3 P T3 SD: 21.2529 c. M: 34.1745 c. 16: 2 2 3 2 2 2 3 SP M ME S SD: 8.4292 c. M: 16.5025 c. Pseudo Pelog, Pelogic-7, Antiionian 20: 3 2 4 2 3 2 4 P T3 SD: 7.8180 c. M:-13.4975 c. 27: 4 3 5 3 4 3 5 SP T3 SD: 7.4515 c. M:-11.2753 c. 36: 5 4 7 4 5 4 7 SP T3 SD: 1.4292 c. M: 2.8519 c. 79: 11 9 15 9 11 9 15 SP T3 SD: 1.3951 c. M:-2.6334 c. 115: 16 13 22 13 16 13 22 SP T3 SD: 0.5403 c. M:-0.9162 c. 151: 21 17 29 17 21 17 29 SP T3 SD: 0.1953 c. M:-0.3849 c. 338: 47 38 65 38 47 38 65 SP T3 SD: 0.2182 c. M:-0.3614 c. 354: 49 40 68 40 49 40 68 SP T3 SD: 0.2041 c. M: 0.4008 c. 390: 54 44 75 44 54 44 75 SP T3 SD: 0.2414 c. M: 0.3486 c. 469: 65 53 90 53 65 53 90 SP T3 SD: 0.1319 c. M:-0.2043 c. 505: 70 57 97 57 70 57 97 SP T3 SD: 0.0847 c. M: 0.1659 c. 620: 86 70 119 70 86 70 119 SP T3 SD: 0.0810 c. M:-0.1589 c. 656: 91 74 126 74 91 74 126 SP T3 SD: 0.0203 c. M: 0.0391 c. 807: 112 91 155 91 112 91 155 SP T3 SD: 0.0202 c. M:-0.0403 c. 1463: 203 165 281 165 203 165 281 SP T3 SD: 0.0029 c. M:-0.0047 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: 17.1415 cents 3 x x 4 x 5 x 6 S SD: 20.2588 cents 4 x 5 x 6 x 7:8 S SD: 22.7905 cents 5 x 6:7 x 8:9:10 S SD: 14.7513 cents 6 x 7:8:9:10:11:12 S SD: 18.6097 cents 7:8 x x 10:11:12:14 S SD: 20.6844 cents 8:9:10:11:12:13:14:16 S SD: 14.3646 cents 9:10:11:12:13:15:16:18 SD: 12.5299 cents 10:11:12:14:15:16:18:20 S SD: 11.6212 cents 11:12:13:15:16:18:19:22 SD: 5.8494 cents 19:21:23:26:28:31:33:38 SD: 5.3007 cents 20:22:24:27:29:32:35:40 SD: 5.2911 cents 21:23:25:29:31:34:37:42 SD: 4.3963 cents 27:30:32:37:40:44:47:54 SD: 4.2216 cents 28:31:33:38:41:45:49:56 SD: 3.5835 cents 31:34:37:42:46:50:54:62 SD: 3.0896 cents 36:40:43:49:53:58:63:72 SD: 2.7277 cents 41:45:49:56:60:66:72:82 SD: 2.5897 cents 42:46:50:57:62:68:74:84 SD: 2.3023 cents 47:52:56:64:69:76:82:94 SD: 1.6186 cents 58:64:69:79:85:94:102:116 SD: 1.5884 cents 68:75:81:92:100:110:119:136 SD: 1.3901 cents 78:86:93:106:115:126:137:156 SD: 1.2937 cents 79:87:94:107:116:128:138:158 SD: 1.2348 cents 89:98:106:121:131:144:156:178 SD: 0.4304 cents 100:110:119:136:147:162:175:200 SD: 0.3104 cents 189:208:225:257:278:306:331:378 SD: 0.1449 cents 336:370:400:457:494:544:588:672 SD: 0.1288 cents 425:468:506:578:625:688:744:850 SD: 0.0671 cents 525:578:625:714:772:850:919:1050 SD: 0.0368 cents