Scala analysis: xen09-chalmers-tritriadic-3-5-7
Tritriadic scale built from 3:5:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 49/36 533.741811 Arabic lute acute fourth 3: 10/7 617.487807 Euler's tritone 4: 5/3 884.358713 major sixth, BP sixth 5: 12/7 933.129094 septimal major sixth 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 7/6 266.8709 septimal minor third 2: 7/6 266.8709 septimal minor third 3: 360/343 83.7460 4: 7/6 266.8709 septimal minor third 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 245/216 218.1005 7: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 360/343 83.746 cents 1: 1 245/216 218.101 cents 1: 3 7/6 266.871 cents septimal minor third 2: 2 7/6 266.871 cents septimal minor third 2: 2 6/5 315.641 cents minor third 2: 2 60/49 350.617 cents smaller approximation to neutral third 2: 1 49/36 533.742 cents Arabic lute acute fourth 3: 1 6/5 315.641 cents minor third 3: 1 432/343 399.387 cents 3: 2 49/36 533.742 cents Arabic lute acute fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 2 10/7 617.488 cents Euler's tritone 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 4: 2 72/49 666.258 cents Arabic lute grave fifth 4: 1 343/216 800.613 cents 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 72/49 666.258 cents Arabic lute grave fifth 5: 2 49/30 849.383 cents larger approximation to neutral sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 2 12/7 933.129 cents septimal major sixth 6: 3 12/7 933.129 cents septimal major sixth 6: 1 432/245 981.899 cents 6: 1 343/180 1116.254 cents 6: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 266.9 533.7 617.5 884.4 933.1 1151.2 1200.0 266.9 : 266.9 350.6 617.5 666.3 884.4 933.1 1200.0 533.7 : 83.7 350.6 399.4 617.5 666.3 933.1 1200.0 617.5 : 266.9 315.6 533.7 582.5 849.4 1116.3 1200.0 884.4 : 48.8 266.9 315.6 582.5 849.4 933.1 1200.0 933.1 : 218.1 266.9 533.7 800.6 884.4 1151.2 1200.0 1151.2: 48.8 315.6 582.5 666.3 933.1 981.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 266.8709 cents 245/216, 218.1005 cents 36/35, 48.7704 cents 2: 266.8709 .. 533.7418 cents 7/6, 266.8709 cents 1/1, 0.0000 cents 3: 315.6413 .. 617.4878 cents 25/21, 301.8465 cents 216/245,-218.1005 cents 4: 582.5122 .. 884.3587 cents 25/21, 301.8465 cents 49/50,-34.9756 cents 5: 666.2582 .. 933.1291 cents 7/6, 266.8709 cents 216/245,-218.1005 cents 6: 933.1291 .. 1151.2296 cents 245/216, 218.1005 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 3.515014 Largest / Average step : 1.556747 Largest / Smallest step : 5.471987 Median interval of one step : 245/216, 218.1005 cents, amount: 1 Most common interval of one step : 7/6, 266.8709 cents, amount: 3 Least squares average step : 190.69483 cents, oct.: 1334.86380 cents Scale is not proper Scale is a mode of a 1304-tone equal temperament with octave 2/1 degrees: 290 580 671 961 1014 1251 1304 Least number of segments generator : 653 of 600.920 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1077 of 991.104 cents and inv. generated superset size: 104 = 97 more = 1485.714% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABACDC Step pattern size order : DDBDACA Scale is not a Constant Structure Scale diversity : 1.359971 Lumma stability : 0.081284 Lumma impropriety factor : 0.392647 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 : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 50/49, 34.9756 cents Most common intervals : 7/6, 266.8709 cents & inv., amount: 5 Most common triad is 0.0 266.871 933.129 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 3 7 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.020302 Average absolute harmonicity : 0.197809 Specific harmonicity : 0.109768 Fundamental : 1/252, -7.9773 octaves, 1.0382 Hz. Guide tone : 2940, 11.5216 octaves, 769179.162 Hz. Exponens Consonantiae : 7.408800E+05, 19.49888 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 99.0, average 14.14286 Mersenne's string divisions : 26705640 Sum of van Prooijen's expressibility: 6.46853, average 0.92408 Sum of Tenney's harmonic distance : 12.91559, average 1.84508 Vogel's harmonic complexity : 17.00000 Wille's k value : 171 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 73.35402, average 2.61979 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 8 1 3: -2 .. 1 -0.71429 7 5: 0 .. 1 0.42857 3 1 7: -1 .. 2 0.28571 6 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 15 20| Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 18 19| Scale is weakly epimorphic with val: <7 11 15 19| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 12 15 18| Scale is weakly epimorphic with val: <7 12 16 20| Scale is weakly epimorphic with val: <7 12 17 22|
FIT/MODE
7: 1 2 0 2 0 1 1 N T3 SD: 77.1808 c. M: 122.6582 c. 8: 2 2 0 2 0 2 0 N M DE S SD: 36.8670 c. M:-66.2582 c. 9: 2 2 1 2 0 2 0 N SD: 32.0622 c. M:-49.1789 c. 13: 3 3 1 3 0 3 0 N SD: 27.5309 c. M:-48.7704 c. 14: 3 3 1 3 1 2 1 N SD: 20.6300 c. M: 36.9439 c. 18: 4 4 1 4 1 3 1 N SD: 11.5842 c. M: 17.8963 c. 22: 5 5 1 5 1 4 1 N SD: 9.8579 c. M: 17.4878 c. 23: 5 5 2 5 1 4 1 N SD: 6.6373 c. M: 12.0027 c. 27: 6 6 2 6 1 5 1 N SD: 2.9737 c. M:-4.7344 c. 45: 10 10 3 10 2 8 2 N SD: 2.8618 c. M: 4.5630 c. 68: 15 15 5 15 3 12 3 N SD: 2.6610 c. M: 4.3300 c. 72: 16 16 5 16 3 13 3 N SD: 0.7059 c. M: 1.2296 c. 99: 22 22 7 22 4 18 4 N SD: 0.3879 c. M:-0.6940 c. 171: 38 38 12 38 7 31 7 N SD: 0.2389 c. M: 0.4085 c. 270: 60 60 19 60 11 49 11 N SD: 0.2254 c. M: 0.4085 c. 346: 77 77 24 77 14 63 14 N SD: 0.1949 c. M:-0.3622 c. 418: 93 93 29 93 17 76 17 N SD: 0.1564 c. M: 0.2629 c. 445: 99 99 31 99 18 81 18 N SD: 0.1352 c. M:-0.2311 c. 517: 115 115 36 115 21 94 21 N SD: 0.0598 c. M:-0.1073 c. 616: 137 137 43 137 25 112 25 N SD: 0.0395 c. M:-0.0691 c. 688: 153 153 48 153 28 125 28 N SD: 0.0386 c. M: 0.0668 c. 787: 175 175 55 175 32 143 32 N SD: 0.0381 c. M: 0.0696 c. 1133: 252 252 79 252 46 206 46 N SD: 0.0355 c. M:-0.0622 c. 1205: 268 268 84 268 49 219 49 N SD: 0.0337 c. M: 0.0604 c. 1304: 290 290 91 290 53 237 53 N SD: 0.0019 c. M: 0.0031 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 42.2336 cents 3 x 4 x 5 x x 6 S SD: 11.8989 cents 4:5 x 6 x 7 x 8 S SD: 37.6460 cents 5:6 x 7:8:9 x 10 S SD: 25.0848 cents 6:7:8:9:10 x x 12 S SD: 18.3401 cents 7:8 x 10 x 12 x 14 S SD: 8.9242 cents 8:9:11 x 13:14 x 16 SD: 17.2840 cents 9:11:12:13:15 x x 18 SD: 18.0293 cents 10:12 x 14 x 17:19:20 SD: 14.7162 cents 11:13:15:16:18:19:21:22 SD: 8.6560 cents 12:14:16:17:20:21:23:24 SD: 8.3041 cents 13:15:18:19 x 22:25:26 SD: 10.0961 cents 14:16:19:20:23:24:27:28 SD: 6.5803 cents 16:19:22:23:27 x 31:32 SD: 7.1978 cents 17:20:23:24:28:29:33:34 SD: 5.0283 cents 19:22:26:27:32:33:37:38 SD: 4.9233 cents 23:27:31:33:38:39:45:46 SD: 4.8680 cents 24:28:33:34:40:41:47:48 SD: 3.7982 cents 25:29:34:36:42:43:49:50 SD: 3.7918 cents 28:33:38:40:47:48:54:56 SD: 3.7462 cents 30:35:41:43:50:51:58:60 SD: 2.8257 cents 35:41:48:50:58:60:68:70 SD: 2.5598 cents 36:42:49:51:60:62:70:72 SD: 2.3640 cents 42:49:57:60:70:72:82:84 SD: 1.2395 cents 66:77:90:94:110:113:128:132 SD: 1.1335 cents 72:84:98:103:120:123:140:144 SD: 0.9262 cents 84:98:114:120:140:144:163:168 SD: 0.8813 cents 91:106:124:130:152:156:177:182 SD: 0.7271 cents 108:126:147:154:180:185:210:216 SD: 0.4966 cents 144:168:196:206:240:247:280:288 SD: 0.3719 cents 180:210:245:257:300:309:350:360 SD: 0.3698 cents 210:245:286:300:350:360:408:420 SD: 0.2481 cents 252:294:343:360:420:432:490:504 SD: 0.0000 cents