Scala analysis: xen12-chalmers-tritriadic-dm-19-25-7
Tritriadic D->M scale built from 19:25:7
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: 625/532 278.915933 3: 25/19 475.114412 4: 28/19 671.312890 5: 784/475 867.511369 6: 25/14 1003.801521 middle minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 28/25 196.1985 middle second 2: 15625/14896 82.7175 3: 28/25 196.1985 middle second 4: 28/25 196.1985 middle second 5: 28/25 196.1985 middle second 6: 11875/10976 136.2902 7: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15625/14896 82.717 cents 1: 1 11875/10976 136.290 cents 1: 5 28/25 196.198 cents middle second 2: 2 625/532 278.916 cents 2: 2 475/392 332.489 cents 2: 3 784/625 392.397 cents two (middle second) 3: 3 25/19 475.114 cents 3: 3 19/14 528.687 cents 3: 1 21952/15625 588.595 cents 4: 1 15625/10976 611.405 cents 4: 3 28/19 671.313 cents 4: 3 38/25 724.886 cents 5: 3 625/392 807.603 cents 5: 2 784/475 867.511 cents 5: 2 1064/625 921.084 cents 6: 5 25/14 1003.802 cents middle minor seventh 6: 1 21952/11875 1063.710 cents 6: 1 29792/15625 1117.283 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 : 196.2 278.9 475.1 671.3 867.5 1003.8 1200.0 196.2 : 82.7 278.9 475.1 671.3 807.6 1003.8 1200.0 278.9 : 196.2 392.4 588.6 724.9 921.1 1117.3 1200.0 475.1 : 196.2 392.4 528.7 724.9 921.1 1003.8 1200.0 671.3 : 196.2 332.5 528.7 724.9 807.6 1003.8 1200.0 867.5 : 136.3 332.5 528.7 611.4 807.6 1003.8 1200.0 1003.8: 196.2 392.4 475.1 671.3 867.5 1063.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.7175 .. 196.1985 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents 2: 278.9159 .. 392.3970 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents 3: 475.1144 .. 588.5954 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents 4: 611.4046 .. 724.8856 cents 417088/390625, 113.4810 cents 244140625/240945152, 22.8091 cents 5: 807.6030 .. 921.0841 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents 6: 1003.8015 .. 1117.2825 cents 417088/390625, 113.4810 cents 15625/14896, 82.7175 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 15625/14896, 82.7175 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 2.072459 Largest / Average step : 1.144491 Largest / Smallest step : 2.371911 Median interval of one step : 28/25, 196.1985 cents, amount: 5 Most common interval of one step : 28/25, 196.1985 cents, amount: 5 Least squares average step : 168.74994 cents, oct.: 1181.24956 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : LSLLLML Scale is a Constant Structure, by a margin of 22.80913 cents Scale diversity : 1.483257 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.432595 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 : 244140625/240945152, 22.8091 cents Most common intervals : 28/25, 196.1985 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 528.687 1003.802 cents Most common triad is 0.0 196.198 1003.802 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 : 7 25 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.009144 Average absolute harmonicity : 0.164591 Specific harmonicity : 0.045891 Fundamental : 1/13300, -13.6991 octaves, 0.0197 Hz. Guide tone : 490000, 18.9024 octaves, 128196526.997 Hz. Exponens Consonantiae : 6.517000E+09, 32.60156 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 1301.0, average 185.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.94515, average 1.56359 Sum of Tenney's harmonic distance : 22.18560, average 3.16937 Vogel's harmonic complexity : 32.85714 Wille's k value : 7812 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 107.77187, average 3.84900 Lattice compactness (without 2's) : 83.60828, average 2.98601 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.85714 12 1 5: -2 .. 4 0.57143 12 7: -1 .. 2 0.28571 6 2 19: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 15 18 31| Scale is weakly epimorphic with val: <7 15 19 28| Scale is weakly epimorphic with val: <7 15 20 32| Scale is weakly epimorphic with val: <7 15 21 29| Scale is weakly epimorphic with val: <7 15 22 33| Scale is JI-epimorphic with val: <7 16 19 29| Scale is weakly epimorphic with val: <7 16 20 33| Scale is weakly epimorphic with val: <7 16 21 30| Scale is weakly epimorphic with val: <7 16 22 27| Scale is weakly epimorphic with val: <7 17 18 33| Scale is weakly epimorphic with val: <7 17 19 30| Scale is JI-epimorphic with val: <7 17 21 31| Scale is weakly epimorphic with val: <7 17 22 28| Scale is weakly epimorphic with val: <7 18 18 27| Scale is weakly epimorphic with val: <7 18 19 31| Scale is weakly epimorphic with val: <7 18 20 28| Scale is weakly epimorphic with val: <7 18 21 32|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 31.9930 c. M:-63.9412 c. Lebeng 10: 2 0 2 2 1 1 2 P D3 S SD: 34.8523 c. M:-48.6871 c. 11: 2 1 1 2 2 1 2 P D3 S SD: 27.0314 c. M:-48.3568 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 20.6023 c. M:-32.4886 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 13: 2 1 2 2 2 2 2 SP M ME S SD: 18.6684 c. M: 36.7421 c. Tamashian 18: 3 1 3 3 3 2 3 P T3 SD: 6.2406 c. M: 12.2493 c. 25: 4 2 4 4 4 3 4 SP T3 SD: 4.6972 c. M:-9.0841 c. 43: 7 3 7 7 7 5 7 SP T3 SD: 1.1998 c. M: 2.3951 c. 104: 17 7 17 17 17 12 17 SP T3 SD: 1.5577 c. M: 2.1268 c. 116: 19 8 19 19 19 13 19 SP T3 SD: 0.7829 c. M:-1.4541 c. 134: 22 9 22 22 22 15 22 SP T3 SD: 0.8186 c. M: 1.3040 c. 159: 26 11 26 26 26 18 26 SP T3 SD: 0.2820 c. M:-0.4132 c. 202: 33 14 33 33 33 23 33 SP T3 SD: 0.1640 c. M:-0.2920 c. 361: 59 25 59 59 59 41 59 SP T3 SD: 0.1651 c. M:-0.3084 c. 379: 62 26 62 62 62 43 62 SP T3 SD: 0.1440 c. M: 0.2880 c. 422: 69 29 69 69 69 48 69 SP T3 SD: 0.1725 c. M: 0.2429 c. 538: 88 37 88 88 88 61 88 SP T3 SD: 0.0855 c. M:-0.1466 c. 581: 95 40 95 95 95 66 95 SP T3 SD: 0.0506 c. M: 0.0863 c. 740: 121 51 121 121 121 84 121 SP T3 SD: 0.0285 c. M:-0.0562 c. 1321: 216 91 216 216 216 150 216 SP T3 SD: 0.0187 c. M: 0.0363 c. 1523: 249 105 249 249 249 173 249 SP T3 SD: 0.0071 c. M: 0.0130 c. 2263: 370 156 370 370 370 257 370 SP T3 SD: 0.0060 c. M:-0.0096 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: 15.3211 cents 3 x x 4 x 5 x 6 S SD: 9.4848 cents 4 x x 5:6 x 7:8 S SD: 25.0597 cents 5 x 6 x 7:8:9:10 S SD: 22.2007 cents 6 x 7:8:9:10:11:12 S SD: 10.5007 cents 7:8 x 9:10:12:13:14 S SD: 20.1653 cents 8:9 x 11:12:13:14:16 SD: 15.5963 cents 9:10:11:12:13:15:16:18 SD: 11.9132 cents 10:11:12:13:15:17:18:20 SD: 11.5195 cents 12:13:14:16:18:20:21:24 S SD: 11.4622 cents 13 x 15:17:19:21:23:26 SD: 9.0328 cents 14:16 x 18:21:23:25:28 SD: 10.3141 cents 15:17:18:20:22:25:27:30 SD: 7.6087 cents 16:18:19:21:24:26:29:32 SD: 7.4990 cents 17:19:20:22:25:28:30:34 SD: 5.1353 cents 23:26:27:30:34:38:41:46 SD: 3.2858 cents 32:36:38:42:47:53:57:64 SD: 3.2341 cents 34:38:40:45:50:56:61:68 SD: 2.0942 cents 51:57:60:67:75:84:91:102 SD: 1.0591 cents 57:64:67:75:84:94:102:114 SD: 0.8458 cents 108:121:127:142:159:178:193:216 SD: 0.5623 cents 149:167:175:196:220:246:266:298 SD: 0.5239 cents 177:198:208:233:261:292:316:354 SD: 0.3838 cents 200:224:235:263:295:330:357:400 SD: 0.2972 cents 234:262:275:308:345:386:418:468 SD: 0.2457 cents 275:308:323:362:405:454:491:550 SD: 0.2126 cents 332:372:390:437:489:548:593:664 SD: 0.2031 cents 383:429:450:504:564:632:684:766 SD: 0.2003 cents 418:468:491:550:616:690:746:836 SD: 0.1716 cents 424:475:498:558:625:700:757:848 SD: 0.1401 cents 475:532:558:625:700:784:848:950 SD: 0.0645 cents