Scala analysis: xen12-chalmers-tritriadic-dm-25-27-11
Tritriadic D->M scale built from 25:27:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 729/550 487.784635 4: 968/675 624.143454 5: 44/27 845.452940 neutral sixth 6: 44/25 978.690515 undecimal grave minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/22 221.3095 undecimal acute whole tone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 25/22 221.3095 undecimal acute whole tone 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 21296/19683 136.3588 5: 25/22 221.3095 undecimal acute whole tone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 25/22 221.3095 undecimal acute whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 21296/19683 136.359 cents 1: 3 25/22 221.309 cents undecimal acute whole tone 2: 1 21296/18225 269.596 cents 2: 5 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 24200/19683 357.668 cents 3: 2 729/550 487.785 cents 3: 3 968/729 490.906 cents 3: 2 675/484 575.857 cents 4: 2 968/675 624.143 cents 4: 3 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 4: 2 1100/729 712.215 cents 5: 1 19683/12100 842.332 cents 5: 5 44/27 845.453 cents neutral sixth 5: 1 18225/10648 930.404 cents 6: 3 44/25 978.691 cents undecimal grave minor seventh 6: 1 19683/10648 1063.641 cents 6: 3 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 : 133.2 354.5 487.8 624.1 845.5 978.7 1200.0 133.2 : 221.3 354.5 490.9 712.2 845.5 1066.8 1200.0 354.5 : 133.2 269.6 490.9 624.1 845.5 978.7 1200.0 487.8 : 136.4 357.7 490.9 712.2 845.5 1066.8 1200.0 624.1 : 221.3 354.5 575.9 709.1 930.4 1063.6 1200.0 845.5 : 133.2 354.5 487.8 709.1 842.3 978.7 1200.0 978.7 : 221.3 354.5 575.9 709.1 845.5 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 221.3095 cents 625/594, 88.0719 cents 27/25, 133.2376 cents 2: 269.5964 .. 357.6683 cents 625/594, 88.0719 cents 468512/455625, 48.2869 cents 3: 487.7846 .. 575.8565 cents 625/594, 88.0719 cents 14348907/13310000, 130.1163 cents 4: 624.1435 .. 712.2154 cents 625/594, 88.0719 cents 468512/455625, 48.2869 cents 5: 842.3317 .. 930.4036 cents 625/594, 88.0719 cents 14348907/13310000, 130.1163 cents 6: 978.6905 .. 1066.7624 cents 625/594, 88.0719 cents 468512/455625, 48.2869 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 : 25/22, 221.3095 cents Average / Smallest step : 1.286638 Largest / Average step : 1.290972 Largest / Smallest step : 1.661014 Median interval of one step : 21296/19683, 136.3588 cents, amount: 1 Least squares average step : 166.44048 cents, oct.: 1165.08336 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : SLSMLSL Scale is a Constant Structure, by a margin of 48.28691 cents Scale diversity : 1.278198 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.559640 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 : 532400/531441, 3.1212 cents Most common intervals : 27/22, 354.5471 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 221.309 354.547 cents Most common triad is 0.0 354.547 845.453 cents, amount: 3 Number of recognisable fifths : 5, average 710.3426 cents Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 11 27 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 88.0719 cents: 6 -- Rational properties -- Prime limit : 11 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.010488 Average absolute harmonicity : 0.169733 Specific harmonicity : 0.055896 Fundamental : 1/14850, -13.8582 octaves, 0.0176 Hz. Guide tone : 705672, 19.4286 octaves, 184621835.917 Hz. Exponens Consonantiae : 1.047923E+10, 33.28681 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 1583.0, average 226.14286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.38406, average 1.62629 Sum of Tenney's harmonic distance : 23.43860, average 3.34837 Vogel's harmonic complexity : 31.85714 Wille's k value : 9841 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 14 Triangular lattice diameter : 9 Lattice compactness : 134.33340, average 4.79762 Lattice compactness (without 2's) : 121.97559, average 4.35627 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.85714 10 1 3: -3 .. 6 0.85714 18 5: -2 .. 0 -1.14286 8 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 32 / 7 = 4.57143 Scale is weakly epimorphic with val: <7 10 17 24| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 18 25| Scale is weakly epimorphic with val: <7 12 15 24| Scale is weakly epimorphic with val: <7 12 17 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 35.2810 c. M:-61.5708 c. Lebeng 9: 1 2 1 1 1 1 2 N D3 S SD: 37.9325 c. M:-45.5487 c. 10: 1 2 1 1 2 1 2 P M ME S SD: 13.2425 c. M: 24.1435 c. 17: 2 3 2 2 3 2 3 SP M ME S SD: 6.8005 c. M:-11.1507 c. 27: 3 5 3 3 5 3 5 SP M DE S SD: 1.0547 c. M: 1.9212 c. 98: 11 18 11 11 18 11 18 SP M DE S SD: 1.0498 c. M:-2.0113 c. 125: 14 23 14 14 23 14 23 SP M DE S SD: 0.9087 c. M:-1.8154 c. 152: 17 28 17 17 28 17 28 SP M DE S SD: 0.8537 c. M:-1.6890 c. 179: 20 33 20 20 33 20 33 SP M DE S SD: 0.8361 c. M:-1.6008 c. 190: 21 35 21 22 35 21 35 SP T3 SD: 0.8729 c. M: 1.4688 c. 200: 22 37 22 23 37 22 37 SP T3 SD: 0.9112 c. M: 1.7846 c. 206: 23 38 23 23 38 23 38 SP M DE S SD: 0.8349 c. M:-1.5358 c. 217: 24 40 24 25 40 24 40 SP T3 SD: 0.6486 c. M: 1.1487 c. 227: 25 42 25 26 42 25 42 SP T3 SD: 0.7693 c. M: 1.4410 c. 244: 27 45 27 28 45 27 45 SP T3 SD: 0.4802 c. M: 0.8994 c. 271: 30 50 30 31 50 30 50 SP T3 SD: 0.3554 c. M: 0.6998 c. 298: 33 55 33 34 55 33 55 SP T3 SD: 0.2693 c. M: 0.5363 c. 325: 36 60 36 37 60 36 60 SP T3 SD: 0.2225 c. M: 0.4000 c. 342: 38 63 38 39 63 38 63 SP T3 SD: 0.2091 c. M:-0.4179 c. 352: 39 65 39 40 65 39 65 SP T3 SD: 0.2133 c. M: 0.2846 c. 369: 41 68 41 42 68 41 68 SP T3 SD: 0.1261 c. M:-0.2468 c. 396: 44 73 44 45 73 44 73 SP T3 SD: 0.0730 c. M:-0.0990 c. 721: 80 133 80 82 133 80 133 SP T3 SD: 0.0657 c. M: 0.1286 c. 748: 83 138 83 85 138 83 138 SP T3 SD: 0.0618 c. M: 0.0841 c. 1090: 121 201 121 124 201 121 201 SP T3 SD: 0.0517 c. M: 0.0782 c. 1117: 124 206 124 127 206 124 206 SP T3 SD: 0.0272 c. M: 0.0496 c. 1144: 127 211 127 130 211 127 211 SP T3 SD: 0.0152 c. M: 0.0224 c. 1540: 171 284 171 175 284 171 284 SP T3 SD: 0.0077 c. M:-0.0124 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: 38.9058 cents 3 x x 4 x 5 x 6 S SD: 13.4120 cents 4 x 5 x 6 x 7:8 S SD: 21.1558 cents 5 x 6 x 7:8:9:10 S SD: 15.1916 cents 6 x 7:8:9:10:11:12 S SD: 23.7786 cents 7:8 x 9:10:11:12:14 S SD: 22.6404 cents 8:9:10:11 x 13:14:16 SD: 16.8009 cents 9:10:11:12:13:15:16:18 SD: 9.6315 cents 12:13:15:16:17:20:21:24 SD: 8.0823 cents 13:14:16:17:19:21:23:26 SD: 6.3661 cents 21:23:26:28:30:34:37:42 SD: 4.7373 cents 25:27:31:33:36:41:44:50 SD: 3.3245 cents 35:38:43:46:50:57:62:70 SD: 3.1055 cents 37:40:45:49:53:60:65:74 SD: 2.6245 cents 40:43:49:53:57:65:70:80 SD: 2.5456 cents 48:52:59:64:69:78:84:96 SD: 2.3883 cents 49:53:60:65:70:80:86:98 SD: 1.4437 cents 62:67:76:82:89:101:109:124 SD: 0.7340 cents 113:122:139:150:162:184:199:226 SD: 0.7292 cents 136:147:167:180:195:222:239:272 SD: 0.7065 cents 138:149:169:183:198:225:243:276 SD: 0.5879 cents 150:162:184:199:215:244:264:300 SD: 0.5338 cents 154:166:189:204:221:251:271:308 SD: 0.5290 cents 163:176:200:216:234:266:287:326 SD: 0.4545 cents 175:189:215:232:251:285:308:350 SD: 0.3129 cents 224:242:275:297:321:365:394:448 SD: 0.2747 cents 237:256:291:314:340:386:417:474 SD: 0.2437 cents 286:309:351:379:410:466:503:572 SD: 0.2291 cents 313:338:384:415:449:510:551:626 SD: 0.1566 cents 387:418:475:513:555:631:681:774 SD: 0.1439 cents 488:527:599:647:700:795:859:976 SD: 0.1334 cents 537:580:659:712:770:875:945:1074 SD: 0.0999 cents 599:647:735:794:859:976:1054:1198 SD: 0.0889 cents