Scala analysis: xen12-chalmers-tritriadic-dm-9-25-7
Tritriadic D->M scale built from 9:25:7
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: 625/504 372.518947 3: 25/18 568.717426 classic augmented fourth 4: 14/9 764.915905 septimal minor sixth 5: 392/225 961.114383 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: 15625/14112 176.3205 3: 28/25 196.1985 middle second 4: 28/25 196.1985 middle second 5: 28/25 196.1985 middle second 6: 5625/5488 42.6871 7: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 5625/5488 42.687 cents 1: 1 15625/14112 176.320 cents 1: 5 28/25 196.198 cents middle second 2: 2 225/196 238.886 cents two (major diatonic semitone) 2: 2 625/504 372.519 cents 2: 3 784/625 392.397 cents two (middle second) 3: 3 9/7 435.084 cents septimal major third, BP third 3: 3 25/18 568.717 cents classic augmented fourth 3: 1 21952/15625 588.595 cents 4: 1 15625/10976 611.405 cents 4: 3 36/25 631.283 cents classic diminished fifth 4: 3 14/9 764.916 cents septimal minor sixth 5: 3 625/392 807.603 cents 5: 2 1008/625 827.481 cents 5: 2 392/225 961.114 cents 6: 5 25/14 1003.802 cents middle minor seventh 6: 1 28224/15625 1023.680 cents 6: 1 10976/5625 1157.313 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 : 196.2 372.5 568.7 764.9 961.1 1003.8 1200.0 196.2 : 176.3 372.5 568.7 764.9 807.6 1003.8 1200.0 372.5 : 196.2 392.4 588.6 631.3 827.5 1023.7 1200.0 568.7 : 196.2 392.4 435.1 631.3 827.5 1003.8 1200.0 764.9 : 196.2 238.9 435.1 631.3 807.6 1003.8 1200.0 961.1 : 42.7 238.9 435.1 611.4 807.6 1003.8 1200.0 1003.8: 196.2 392.4 568.7 764.9 961.1 1157.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.6871 .. 196.1985 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents 2: 238.8856 .. 392.3970 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents 3: 435.0841 .. 588.5954 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents 4: 611.4046 .. 764.9159 cents 153664/140625, 153.5113 cents 244140625/240945152, 22.8091 cents 5: 807.6030 .. 961.1144 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents 6: 1003.8015 .. 1157.3129 cents 153664/140625, 153.5113 cents 5625/5488, 42.6871 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 5625/5488, 42.6871 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 4.015930 Largest / Average step : 1.144491 Largest / Smallest step : 4.596197 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 : 178.11024 cents, oct.: 1246.77167 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : LMLLLSL Scale is a Constant Structure, by a margin of 22.80913 cents Scale diversity : 1.272846 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.232443 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 : 395136/390625, 19.8780 cents Most common intervals : 28/25, 196.1985 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 435.084 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% Limited inverse transpositions with margin 153.5113 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.012408 Average absolute harmonicity : 0.177201 Specific harmonicity : 0.068504 Fundamental : 1/12600, -13.6211 octaves, 0.0208 Hz. Guide tone : 245000, 17.9024 octaves, 64098263.499 Hz. Exponens Consonantiae : 3.087000E+09, 31.52356 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 953.5, average 136.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.29613, average 1.47088 Sum of Tenney's harmonic distance : 20.88756, average 2.98394 Vogel's harmonic complexity : 27.71429 Wille's k value : 7812 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 11 Triangular lattice diameter : 6 Lattice compactness : 114.21808, average 4.07922 Lattice compactness (without 2's) : 92.19351, average 3.29263 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.28571 12 1 3: -2 .. 0 -1.14286 8 5: -2 .. 4 0.57143 12 1 7: -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 weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 18 18| Scale is weakly epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 12 15 18| Scale is JI-epimorphic with val: <7 12 17 21| Scale is weakly epimorphic with val: <7 12 18 19|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 56.2554 c. M: 103.9715 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 45.4559 c. M: 72.5189 c. 9: 1 2 1 2 1 1 1 N D3 S SD: 41.2553 c. M: 62.8651 c. 10: 2 1 2 1 2 0 2 N T3 SD: 31.6028 c. M: 44.9159 c. 11: 2 1 2 2 2 0 2 N T3 SD: 23.8603 c. M: 45.2462 c. 12: 2 2 2 2 2 0 2 P M DE S SD: 25.3707 c. M:-38.8856 c. 13: 2 2 2 2 2 1 2 SP M ME S SD: 19.4458 c. M: 38.0375 c. Karakalian 14: 2 2 3 2 2 1 2 P T3 SD: 22.2366 c. M:-31.2826 c. 16: 3 2 3 2 3 0 3 N SD: 20.9049 c. M:-31.2826 c. 17: 3 2 3 3 3 0 3 N T3 SD: 15.8252 c. M:-27.1209 c. 19: 3 3 3 3 3 1 3 SP M DE S SD: 7.2713 c. M: 13.7460 c. 25: 4 4 4 4 4 1 4 SP M DE S SD: 5.7428 c. M:-11.4811 c. 36: 6 5 6 6 6 1 6 P T3 SD: 3.8032 c. M: 5.8523 c. 49: 8 7 8 8 8 2 8 SP T3 SD: 4.2366 c. M: 6.0123 c. 55: 9 8 9 9 9 2 9 SP T3 SD: 1.0428 c. M: 1.6099 c. 116: 19 17 19 19 19 4 19 SP T3 SD: 0.4773 c. M:-0.9546 c. 171: 28 25 28 28 28 6 28 SP T3 SD: 0.3139 c. M: 0.5891 c. 251: 41 37 41 41 41 9 41 SP T3 SD: 0.2024 c. M:-0.3894 c. 306: 50 45 50 50 50 11 50 SP T3 SD: 0.1651 c. M: 0.3301 c. 367: 60 54 60 60 60 13 60 SP T3 SD: 0.1618 c. M:-0.2331 c. 422: 69 62 69 69 69 15 69 SP T3 SD: 0.0117 c. M:-0.0231 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: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 34.7787 cents 4 x 5 x 6:7 x 8 S SD: 16.2285 cents 5 x 6:7:8 x 9:10 S SD: 15.4845 cents 6:7 x 8:9:10:11:12 S SD: 24.6760 cents 7:8:9:10:11:12:13:14 H SD: 16.4247 cents 8:9:10:11:12:14 x 16 S SD: 11.2744 cents 9:10:11:13:14 x 16:18 SD: 12.3500 cents 11:12:14:15:17:19:20:22 SD: 11.4570 cents 12:13:15:17:19:21 x 24 SD: 12.5662 cents 13:15:16:18:20 x 23:26 SD: 9.8305 cents 15:17:19:21:23:26:27:30 SD: 7.6239 cents 16:18:20:22:25:28:29:32 SD: 5.2213 cents 17:19:21:24:26 x 30:34 SD: 7.7078 cents 18:20:22:25:28:31:32:36 SD: 5.1108 cents 23:26:29:32:36:40:41:46 SD: 5.0077 cents 24:27:30:33:37:42:43:48 SD: 4.2528 cents 25:28:31:35:39:44:45:50 SD: 3.8170 cents 32:36:40:44:50:56:57:64 SD: 3.7531 cents 33:37:41:46:51:57:59:66 SD: 2.8851 cents 34:38:42:47:53:59:61:68 SD: 2.2660 cents 41:46:51:57:64:71:73:82 SD: 2.0809 cents 42:47:52:58:65:73:75:84 SD: 2.0382 cents 50:56:62:69:78:87:89:100 SD: 1.9359 cents 51:57:63:71:79:89:91:102 SD: 1.6766 cents 59:66:73:82:92:103:105:118 SD: 1.3204 cents 67:75:83:93:104:117:120:134 SD: 1.1203 cents 74:83:92:103:115:129:132:148 SD: 0.9799 cents 92:103:114:128:143:160:164:184 SD: 0.8031 cents 108:121:134:150:168:188:193:216 SD: 0.3192 cents 167:187:207:232:260:291:298:334 SD: 0.3111 cents 234:262:290:325:364:408:418:468 SD: 0.2714 cents 275:308:341:382:428:479:491:550 SD: 0.1504 cents 342:383:424:475:532:596:611:684 SD: 0.1495 cents 383:429:475:532:596:667:684:766 SD: 0.1454 cents 450:504:558:625:700:784:804:900 SD: 0.1328 cents 466:522:578:647:725:812:832:932 SD: 0.1269 cents 542:607:672:753:843:944:968:1084 SD: 0.1249 cents 558:625:692:775:868:972:996:1116 SD: 0.1157 cents 574:643:712:797:893:1000:1025:1148 SD: 0.1117 cents