Scala analysis: xen12-chalmers-tritriadic-mt-9-25-7
Tritriadic M->T 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: 175/162 133.633331 2: 28/25 196.198479 middle second 3: 25/18 568.717426 classic augmented fourth 4: 36/25 631.282574 classic diminished fifth 5: 14/9 764.915905 septimal minor sixth 6: 625/324 1137.434852 octave - major diesis 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 648/625 62.5651 major diesis 1: 175/162 133.6333 2: 648/625 62.5651 major diesis 3: 625/504 372.5189 4: 648/625 62.5651 major diesis 5: 175/162 133.6333 6: 625/504 372.5189 7: 648/625 62.5651 major diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 648/625 62.565 cents major diesis 1: 2 175/162 133.633 cents 1: 2 625/504 372.519 cents 2: 3 28/25 196.198 cents middle second 2: 3 9/7 435.084 cents septimal major third, BP third 2: 1 15625/11664 506.152 cents two (semi-augmented whole tone) 3: 1 18144/15625 258.764 cents 3: 1 5832/4375 497.649 cents 3: 5 25/18 568.717 cents classic augmented fourth 4: 5 36/25 631.283 cents classic diminished fifth 4: 1 4375/2916 702.351 cents 4: 1 15625/9072 941.236 cents 5: 1 23328/15625 693.848 cents 5: 3 14/9 764.916 cents septimal minor sixth 5: 3 25/14 1003.802 cents middle minor seventh 6: 2 1008/625 827.481 cents 6: 2 324/175 1066.367 cents 6: 3 625/324 1137.435 cents octave - major diesis 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 : 133.6 196.2 568.7 631.3 764.9 1137.4 1200.0 133.6 : 62.6 435.1 497.6 631.3 1003.8 1066.4 1200.0 196.2 : 372.5 435.1 568.7 941.2 1003.8 1137.4 1200.0 568.7 : 62.6 196.2 568.7 631.3 764.9 827.5 1200.0 631.3 : 133.6 506.2 568.7 702.4 764.9 1137.4 1200.0 764.9 : 372.5 435.1 568.7 631.3 1003.8 1066.4 1200.0 1137.4: 62.6 196.2 258.8 631.3 693.8 827.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.5651 .. 372.5189 cents 390625/326592, 309.9538 cents 648/625, 62.5651 cents 2: 196.1985 .. 506.1523 cents 390625/326592, 309.9538 cents 14112/15625,-176.3205 cents 3: 258.7636 .. 568.7174 cents 390625/326592, 309.9538 cents 211631616/244140625,-247.3887 cents 4: 631.2826 .. 941.2364 cents 390625/326592, 309.9538 cents 648/625, 62.5651 cents 5: 693.8477 .. 1003.8015 cents 390625/326592, 309.9538 cents 211631616/244140625,-247.3887 cents 6: 827.4811 .. 1137.4349 cents 390625/326592, 309.9538 cents 14112/15625,-176.3205 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 648/625, 62.5651 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 625/504, 372.5189 cents Average / Smallest step : 2.740001 Largest / Average step : 2.173027 Largest / Smallest step : 5.954097 Median interval of one step : 175/162, 133.6333 cents, amount: 2 Most common interval of one step : 648/625, 62.5651 cents, amount: 3 Least squares average step : 170.04644 cents, oct.: 1190.32507 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : MSLSMLS Scale is a Constant Structure, by a margin of 8.50303 cents Scale diversity : 1.442170 Lumma stability : 0.156413 Lumma impropriety factor : 0.516590 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 : 68359375/68024448, 8.5030 cents Most common intervals : 25/18, 568.7174 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 196.198 631.283 cents Most common triad is 0.0 568.717 631.283 cents, amount: 3 Number of recognisable fifths : 2, average 698.0992 cents Scale contains a complete diamond : 9 25 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 7 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.014559 Average absolute harmonicity : 0.179553 Specific harmonicity : 0.077467 Fundamental : 1/8100, -12.9837 octaves, 0.0323 Hz. Guide tone : 157500, 17.2650 octaves, 41206026.535 Hz. Exponens Consonantiae : 1.275750E+09, 30.24870 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 734.5, average 104.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.18698, average 1.45528 Sum of Tenney's harmonic distance : 20.61293, average 2.94470 Vogel's harmonic complexity : 25.85714 Wille's k value : 7812 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 13 Triangular lattice diameter : 6 Lattice compactness : 119.55510, average 4.26982 Lattice compactness (without 2's) : 106.27333, average 3.79548 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.28571 10 1 3: -4 .. 2 -1.42857 14 5: -2 .. 4 0.57143 12 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 29 / 7 = 4.14286 Scale is JI-epimorphic with val: <7 10 15 18| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 18 21| Scale is weakly epimorphic with val: <7 11 15 19| Scale is JI-epimorphic with val: <7 11 16 20| = patent Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <7 12 16 21| Scale is JI-epimorphic with val: <7 12 17 22|
FIT/MODE
7: 1 0 2 1 0 3 0 N SD: 50.9270 c. M: 79.2016 c. 8: 1 0 3 0 1 3 0 N T3 SD: 34.8389 c. M:-62.5651 c. 10: 1 1 3 0 1 3 1 N SD: 36.6018 c. M: 57.4349 c. 11: 1 1 3 1 1 3 1 N M DE S SD: 24.8832 c. M: 46.5258 c. 13: 1 1 4 1 1 4 1 N M DE S SD: 23.5091 c. M: 41.3256 c. 14: 2 0 5 0 2 4 1 N SD: 25.5721 c. M:-37.7952 c. 15: 2 0 5 1 2 4 1 N SD: 22.9670 c. M: 36.1985 c. 17: 2 1 5 1 2 5 1 N T3 SD: 8.6954 c. M:-15.5662 c. 19: 2 1 6 1 2 6 1 N T3 SD: 4.6073 c. M: 7.3175 c. 36: 4 2 11 2 4 11 2 N T3 SD: 2.4739 c. M: 4.1015 c. 55: 6 3 17 3 6 17 3 N T3 SD: 1.7570 c. M: 2.8894 c. 80: 9 4 25 4 9 25 4 N T3 SD: 1.3722 c. M:-2.5651 c. 97: 11 5 30 5 11 30 5 N T3 SD: 1.4226 c. M:-2.4491 c. 99: 11 5 31 5 11 31 5 N T3 SD: 1.3410 c. M: 2.2591 c. 116: 13 6 36 6 13 36 6 N T3 SD: 0.4747 c. M:-0.8494 c. 135: 15 7 42 7 15 42 7 N T3 SD: 0.3590 c. M: 0.6429 c. 171: 19 9 53 9 19 53 9 N T3 SD: 0.3168 c. M: 0.5927 c. 251: 28 13 78 13 28 78 13 N T3 SD: 0.2217 c. M:-0.4138 c. 287: 32 15 89 15 32 89 15 N T3 SD: 0.1776 c. M:-0.3172 c. 306: 34 16 95 16 34 95 16 N T3 SD: 0.1678 c. M: 0.3000 c. 422: 47 22 131 22 47 131 22 N T3 SD: 0.0091 c. M:-0.0160 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 46.2615 cents 4 x x x x 6 x 8 S SD: 31.4805 cents 5 x 6:7 x 8 x 10 S SD: 32.4379 cents 6 x 7:8 x 9 x 12 S SD: 29.5310 cents 7 x 8 x 10:11 x 14 SD: 10.3758 cents 8 x 9:11 x 12:15:16 SD: 16.4239 cents 9 x 10 x 13:14:17:18 SD: 7.8561 cents 10 x 11:14 x 16:19:20 SD: 13.0080 cents 11:12 x 15:16:17:21:22 SD: 7.5483 cents 12:13 x x 17:19:23:24 SD: 8.6874 cents 14:15:16:19:20:22:27:28 SD: 8.4834 cents 15:16:17:21:22:23:29:30 SD: 7.4702 cents 16:17:18:22:23:25:31:32 SD: 5.1724 cents 17:18:19:24 x 26:33:34 SD: 9.1215 cents 18:19:20:25:26:28:35:36 S SD: 6.4071 cents 19 x 21:26:27:30:37:38 SD: 8.5777 cents 20 x 22:28:29:31:39:40 SD: 6.8643 cents 22:24:25:31:32:34:42:44 SD: 6.8477 cents 23:25:26:32:33:36:44:46 SD: 3.8946 cents 25:27:28:35:36:39:48:50 SD: 2.3929 cents 41:44:46:57:59:64:79:82 SD: 1.9318 cents 52:56:58:72:75:81:100:104 SD: 1.7486 cents 59:64:66:82:85:92:114:118 SD: 1.3087 cents 75:81:84:104:108:117:145:150 SD: 0.9819 cents 100:108:112:139:144:156:193:200 SD: 0.7458 cents 126:136:141:175:181:196:243:252 SD: 0.6700 cents 139:150:156:193:200:216:268:278 SD: 0.6682 cents 150:162:168:208:216:233:289:300 SD: 0.6129 cents 159:172:178:221:229:247:307:318 SD: 0.5778 cents 173:187:194:240:249:269:334:346 SD: 0.5173 cents 175:189:196:243:252:272:338:350 SD: 0.3782 cents 198:214:222:275:285:308:382:396 SD: 0.3165 cents 200:216:224:278:288:311:386:400 SD: 0.2572 cents 250:270:280:347:360:389:482:500 SD: 0.2239 cents 375:405:420:521:540:583:723:750 SD: 0.2152 cents 398:430:446:553:573:619:768:796 SD: 0.2004 cents 409:442:458:568:589:636:789:818 SD: 0.1426 cents 450:486:504:625:648:700:868:900 SD: 0.0587 cents