Scala analysis: xen12-chalmers-tritriadic-mt-27-5-1
Tritriadic M->T scale built from 27:5:1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 800/729 160.897423 grave whole tone 2: 32/27 294.134997 Pythagorean minor third 3: 27/20 519.551289 acute fourth 4: 40/27 680.448711 grave fifth 5: 8/5 813.686286 minor sixth 6: 1280/729 974.583709 grave minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 729/640 225.4163 acute major second 1: 800/729 160.8974 grave whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 729/640 225.4163 acute major second 4: 800/729 160.8974 grave whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 800/729 160.8974 grave whole tone 7: 729/640 225.4163 acute major second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 800/729 160.897 cents grave whole tone 1: 2 729/640 225.416 cents acute major second 2: 3 32/27 294.135 cents Pythagorean minor third 2: 1 19683/16000 358.654 cents 2: 3 5/4 386.314 cents major third 3: 1 25600/19683 455.032 cents 3: 5 27/20 519.551 cents acute fourth 3: 1 1000/729 547.211 cents 4: 1 729/500 652.789 cents 4: 5 40/27 680.449 cents grave fifth 4: 1 19683/12800 744.968 cents 5: 3 8/5 813.686 cents minor sixth 5: 1 32000/19683 841.346 cents 5: 3 27/16 905.865 cents Pythagorean major sixth 6: 2 1280/729 974.584 cents grave minor seventh 6: 3 729/400 1039.103 cents acute minor seventh 6: 2 50/27 1066.762 cents grave major seventh 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 : 160.9 294.1 519.6 680.4 813.7 974.6 1200.0 160.9 : 133.2 358.7 519.6 652.8 813.7 1039.1 1200.0 294.1 : 225.4 386.3 519.6 680.4 905.9 1066.8 1200.0 519.6 : 160.9 294.1 455.0 680.4 841.3 974.6 1200.0 680.4 : 133.2 294.1 519.6 680.4 813.7 1039.1 1200.0 813.7 : 160.9 386.3 547.2 680.4 905.9 1066.8 1200.0 974.6 : 225.4 386.3 519.6 745.0 905.9 1039.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 225.4163 cents 135/128, 92.1787 cents 27/25, 133.2376 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 20480/19683, 68.7187 cents 3: 455.0324 .. 547.2111 cents 135/128, 92.1787 cents 20480/19683, 68.7187 cents 4: 652.7889 .. 744.9676 cents 135/128, 92.1787 cents 531441/500000, 105.5777 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 20480/19683, 68.7187 cents 6: 974.5837 .. 1066.7624 cents 135/128, 92.1787 cents 20480/19683, 68.7187 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 729/640, 225.4163 cents Average / Smallest step : 1.286638 Largest / Average step : 1.314928 Largest / Smallest step : 1.691837 Median interval of one step : 800/729, 160.8974 cents, amount: 3 Most common interval of one step : 800/729, 160.8974 cents, amount: 3 Least squares average step : 166.75393 cents, oct.: 1167.27749 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1432-tone equal temperament with octave 2/1 degrees: 192 351 620 812 971 1163 1432 Least number of segments generator : 717 of 600.838 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1229 of 1029.888 cents and inv. generated superset size: 46 = 39 more = 657.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABAC Step pattern size order : MSLMSML Scale is a Constant Structure, by a margin of 68.71871 cents Scale diversity : 1.396467 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.539106 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 : 20000/19683, 27.6598 cents Most common intervals : 27/20, 519.5513 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 294.135 680.449 cents Most common triad is 0.0 519.551 680.449 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 5 27 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions with margin 92.1787 cents: 2 -- Rational properties -- Prime limit : 5 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.018797 Average absolute harmonicity : 0.194890 Specific harmonicity : 0.105855 Fundamental : 1/14580, -13.8317 octaves, 0.0179 Hz. Guide tone : 172800, 17.3987 octaves, 45208897.684 Hz. Exponens Consonantiae : 2.519424E+09, 31.23045 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 1863.5, average 266.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.71852, average 1.53122 Sum of Tenney's harmonic distance : 22.34118, average 3.19160 Vogel's harmonic complexity : 23.28571 Wille's k value : 9841 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 12 Triangular lattice diameter : 9 Lattice compactness : 162.20247, average 5.79295 Lattice compactness (without 2's) : 114.30814, average 4.08243 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 8 3.28571 27 1 3: -6 .. 3 -2.14286 21 1 5: -1 .. 2 0.28571 6 5 Average exponent except 2's :-13 / 7 =-1.85714 Average absolute exponent except 2's: 27 / 7 = 3.85714 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.3890 c. M:-53.9877 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 23.2474 c. M: 41.2504 c. Pseudo Pelog, Pelogic-7, Antiionian 12: 2 1 2 2 1 2 2 P M ME S SD: 21.2509 c. M:-39.1026 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 16: 2 2 3 2 2 2 3 SP M ME S SD: 6.9765 c. M:-11.3137 c. Pseudo Pelog, Pelogic-7, Antiionian 28: 4 3 5 4 3 4 5 SP T3 SD: 6.8139 c. M:-11.1306 c. 37: 5 4 7 5 4 5 7 SP T3 SD: 1.6166 c. M: 2.8755 c. 53: 7 6 10 7 6 7 10 SP T3 SD: 1.2935 c. M: 2.4069 c. 90: 12 10 17 12 10 12 17 SP T3 SD: 0.7110 c. M: 1.2504 c. 171: 23 19 32 23 19 23 32 SP T3 SD: 0.4779 c. M:-0.8549 c. 208: 28 23 39 28 23 28 39 SP T3 SD: 0.3483 c. M:-0.6410 c. 224: 30 25 42 30 25 30 42 SP T3 SD: 0.3466 c. M:-0.5994 c. 261: 35 29 49 35 29 35 49 SP T3 SD: 0.0781 c. M:-0.1289 c. 559: 75 62 105 75 62 75 105 SP T3 SD: 0.0612 c. M:-0.1044 c. 820: 110 91 154 110 91 110 154 SP T3 SD: 0.0424 c. M:-0.0782 c. 873: 117 97 164 117 97 117 164 SP T3 SD: 0.0417 c. M: 0.0727 c. 910: 122 101 171 122 101 122 171 SP T3 SD: 0.0463 c. M: 0.0782 c. 1081: 145 120 203 145 120 145 203 SP T3 SD: 0.0422 c. M:-0.0694 c. 1134: 152 126 213 152 126 152 213 SP T3 SD: 0.0400 c. M:-0.0703 c. 1171: 157 130 220 157 130 157 220 SP T3 SD: 0.0186 c. M: 0.0320 c. 1432: 192 159 269 192 159 192 269 SP T3 SD: 0.0020 c. M: 0.0036 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: 10.7531 cents 3 x x 4 x 5 x 6 S SD: 24.6241 cents 4 x 5 x 6 x 7:8 S SD: 23.7073 cents 5 x 6:7 x 8:9:10 S SD: 15.8451 cents 6 x 7:8:9:10:11:12 S SD: 18.4503 cents 7 x 8:9:10:11:12:14 S SD: 22.2076 cents 8:9 x 11:12:13:14:16 SD: 10.6397 cents 11:12:13:15:16:18:19:22 SD: 8.7610 cents 12:13:14:16:18:19:21:24 SD: 7.1835 cents 17:19:20:23:25:27:30:34 SD: 5.6829 cents 20:22:24:27:30:32:35:40 SD: 4.4608 cents 23:25:27:31:34:37:40:46 SD: 4.3593 cents 28:31:33:38:41:45:49:56 SD: 4.3164 cents 29:32:34:39:43:46:51:58 SD: 3.8364 cents 31:34:37:42:46:50:54:62 SD: 3.4341 cents 32:35:38:43:47:51:56:64 SD: 2.8977 cents 37:41:44:50:55:59:65:74 SD: 2.8186 cents 40:44:47:54:59:64:70:80 SD: 2.5987 cents 42:46:50:57:62:67:74:84 SD: 2.2824 cents 48:53:57:65:71:77:84:96 SD: 2.0903 cents 52:57:62:70:77:83:91:104 SD: 1.9537 cents 54:59:64:73:80:86:95:108 SD: 1.6855 cents 60:66:71:81:89:96:105:120 SD: 1.1251 cents 91:100:108:123:135:146:160:182 SD: 1.0062 cents 102:112:121:138:151:163:179:204 SD: 0.7104 cents 114:125:135:154:169:182:200:228 SD: 0.6865 cents 123:135:146:166:182:197:216:246 SD: 0.5518 cents 135:148:160:182:200:216:237:270 SD: 0.4219 cents 183:201:217:247:271:293:321:366 SD: 0.4054 cents 195:214:231:263:289:312:342:390 SD: 0.3958 cents 205:225:243:277:304:328:360:410 SD: 0.3351 cents 237:260:281:320:351:379:416:474 SD: 0.2156 cents 340:373:403:459:504:544:597:680 SD: 0.1656 cents 443:486:525:598:656:709:778:886 SD: 0.1624 cents 463:508:549:625:686:741:813:926 SD: 0.1467 cents 480:527:569:648:711:768:843:960 SD: 0.1456 cents 492:540:583:664:729:787:864:984 SD: 0.1264 cents 503:552:596:679:745:805:883:1006 SD: 0.1196 cents