Scala analysis: 319_C24
Chromatic tetrachord 46/45 * 180/161 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 46/45 38.0506 23rd-partial chroma 2: 180/161 193.1235 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 180/161 193.123 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 161/135 304.922 cents 2: 1 30/23 459.994 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 0.0 : 38.1 231.2 498.0 38.1 : 193.1 460.0 498.0 231.2: 266.9 304.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 266.8709 cents 105/92, 228.8203 cents 46/45, 38.0506 cents 2: 231.1741 .. 459.9944 cents 105/92, 228.8203 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 4.363002 Largest / Average step : 1.607511 Largest / Smallest step : 7.013574 Median interval of one step : 180/161, 193.1235 cents, amount: 1 Least squares average step : 142.46670 cents, oct.: 427.40010 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1898-tone equal temperament with octave 4/3 degrees: 145 881 1898 Least number of segments generator : 951 of 249.547 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1133 of 297.305 cents and inv. generated superset size: 26 = 23 more = 866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 0.677278 Lumma stability : 0.152800 Lumma impropriety factor : 0.071674 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 23 Odd number limit : 161 (O: 161 U: 161) Highest odd numerator or denominator: 45 Scale harmonicity : 0.014902 Average absolute harmonicity : 0.102598 Specific harmonicity : 0.078054 Fundamental : 1/315, -8.2992 octaves, 0.8306 Hz. Guide tone : 184, 7.5236 octaves, 48139.104 Hz. Exponens Consonantiae : 5.796000E+04, 15.82277 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 56.5, average 18.83333 Mersenne's string divisions : 1365 Sum of van Prooijen's expressibility: 2.97543, average 0.99181 Sum of Tenney's harmonic distance : 6.14334, average 2.04778 Vogel's harmonic complexity : 20.66667 Wille's k value : 80 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.09277, average 2.51546 Lattice compactness (without 2's) : 10.24151, average 1.70692 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -2 .. 0 -1.00000 3 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 23: 0 .. 1 0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 20 32| Scale is weakly epimorphic with val: <6 10 16 20 33| Scale is weakly epimorphic with val: <6 10 17 20 34| Scale is weakly epimorphic with val: <6 10 18 20 35| Scale is weakly epimorphic with val: <6 10 19 20 36| Scale is weakly epimorphic with val: <6 11 15 19 34| Scale is weakly epimorphic with val: <6 11 15 22 34| Scale is weakly epimorphic with val: <6 11 16 19 35| Scale is weakly epimorphic with val: <6 11 16 22 35| Scale is weakly epimorphic with val: <6 11 17 19 36| Scale is weakly epimorphic with val: <6 11 17 22 36| Scale is weakly epimorphic with val: <7 10 15 18 30| Scale is weakly epimorphic with val: <7 10 15 18 33| Scale is weakly epimorphic with val: <7 10 15 18 36| Scale is weakly epimorphic with val: <7 10 15 19 31| Scale is weakly epimorphic with val: <7 10 15 22 31| Scale is weakly epimorphic with val: <7 10 16 18 31| Scale is weakly epimorphic with val: <7 10 16 18 34| Scale is weakly epimorphic with val: <7 10 16 19 32| Scale is weakly epimorphic with val: <7 10 16 22 32| Scale is weakly epimorphic with val: <7 10 17 18 32| Scale is weakly epimorphic with val: <7 10 17 18 35| Scale is weakly epimorphic with val: <7 10 17 19 33| Scale is weakly epimorphic with val: <7 10 17 22 33| Scale is weakly epimorphic with val: <7 10 18 18 30| Scale is weakly epimorphic with val: <7 10 18 18 33| Scale is weakly epimorphic with val: <7 10 18 18 36| Scale is weakly epimorphic with val: <7 10 18 19 34| Scale is weakly epimorphic with val: <7 10 18 22 34| Scale is weakly epimorphic with val: <7 10 19 19 35| Scale is weakly epimorphic with val: <7 10 19 22 35| Scale is JI-epimorphic with val: <7 11 15 19 31| Scale is weakly epimorphic with val: <7 11 15 19 34| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 20 35| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 15 22 34| Scale is JI-epimorphic with val: <7 11 16 19 32| Scale is weakly epimorphic with val: <7 11 16 19 35| Scale is weakly epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 20 33| Scale is weakly epimorphic with val: <7 11 16 20 36| Scale is weakly epimorphic with val: <7 11 16 22 32| Scale is weakly epimorphic with val: <7 11 16 22 35| Scale is weakly epimorphic with val: <7 11 17 19 30| Scale is JI-epimorphic with val: <7 11 17 19 33| Scale is weakly epimorphic with val: <7 11 17 19 36| Scale is weakly epimorphic with val: <7 11 17 20 31| Scale is weakly epimorphic with val: <7 11 17 20 34| Scale is weakly epimorphic with val: <7 11 17 22 30| Scale is weakly epimorphic with val: <7 11 17 22 33| Scale is weakly epimorphic with val: <7 11 17 22 36| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is JI-epimorphic with val: <7 11 18 19 34| Scale is weakly epimorphic with val: <7 11 18 20 32| Scale is weakly epimorphic with val: <7 11 18 20 35| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 18 22 34| Scale is weakly epimorphic with val: <7 11 19 19 32| Scale is JI-epimorphic with val: <7 11 19 19 35| Scale is weakly epimorphic with val: <7 11 19 20 30| Scale is weakly epimorphic with val: <7 11 19 20 33| Scale is weakly epimorphic with val: <7 11 19 20 36| Scale is weakly epimorphic with val: <7 11 19 22 32| Scale is weakly epimorphic with val: <7 11 19 22 35| Scale is weakly epimorphic with val: <7 12 15 18 30| Scale is weakly epimorphic with val: <7 12 15 18 33| Scale is weakly epimorphic with val: <7 12 15 18 36| Scale is weakly epimorphic with val: <7 12 15 20 35| Scale is weakly epimorphic with val: <7 12 16 18 31| Scale is weakly epimorphic with val: <7 12 16 18 34| Scale is weakly epimorphic with val: <7 12 16 20 36| Scale is weakly epimorphic with val: <7 12 17 18 32| Scale is weakly epimorphic with val: <7 12 17 18 35| Scale is weakly epimorphic with val: <7 12 18 18 30| Scale is weakly epimorphic with val: <7 12 18 18 33| Scale is weakly epimorphic with val: <7 12 18 18 36| Scale is weakly epimorphic with val: <8 11 15 20 32| Scale is weakly epimorphic with val: <8 11 15 21 30| Scale is weakly epimorphic with val: <8 11 15 21 33| Scale is weakly epimorphic with val: <8 11 15 21 36| Scale is weakly epimorphic with val: <8 11 16 20 33| Scale is weakly epimorphic with val: <8 11 16 21 31| Scale is weakly epimorphic with val: <8 11 16 21 34| Scale is weakly epimorphic with val: <8 11 17 20 34| Scale is weakly epimorphic with val: <8 11 17 21 32| Scale is weakly epimorphic with val: <8 11 17 21 35| Scale is weakly epimorphic with val: <8 11 18 20 35| Scale is weakly epimorphic with val: <8 11 18 21 30| Scale is weakly epimorphic with val: <8 11 18 21 33| Scale is weakly epimorphic with val: <8 11 18 21 36| Scale is weakly epimorphic with val: <8 11 19 20 36| Scale is weakly epimorphic with val: <8 11 19 21 31| Scale is weakly epimorphic with val: <8 11 19 21 34| Scale is weakly epimorphic with val: <8 12 15 19 34| Scale is weakly epimorphic with val: <8 12 15 21 30| Scale is weakly epimorphic with val: <8 12 15 21 33| Scale is weakly epimorphic with val: <8 12 15 21 36| Scale is weakly epimorphic with val: <8 12 15 22 34| Scale is weakly epimorphic with val: <8 12 16 19 35| Scale is weakly epimorphic with val: <8 12 16 21 31| Scale is weakly epimorphic with val: <8 12 16 21 34| Scale is weakly epimorphic with val: <8 12 16 22 35| Scale is weakly epimorphic with val: <8 12 17 19 36| Scale is weakly epimorphic with val: <8 12 17 21 32| Scale is weakly epimorphic with val: <8 12 17 21 35| Scale is weakly epimorphic with val: <8 12 17 22 36| Scale is weakly epimorphic with val: <8 12 18 21 30| Scale is weakly epimorphic with val: <8 12 18 21 33| Scale is weakly epimorphic with val: <8 12 18 21 36| Scale is weakly epimorphic with val: <8 12 19 21 31| Scale is weakly epimorphic with val: <8 12 19 21 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 43.5644 c. M: 65.1591 c. 4: 0 2 2 P M DE S SD: 24.2653 c. M: 38.0506 c. 5: 0 2 3 N G T3 SD: 28.6882 c. M: 38.0506 c. 6: 0 3 3 P M DE S SD: 24.2653 c. M: 38.0506 c. 7: 0 3 4 N G T3 SD: 24.2354 c. M: 38.0506 c. 8: 1 3 4 P T3 SD: 17.3632 c. M:-24.2050 c. 9: 1 3 5 N T3 SD: 11.4791 c. M:-17.2877 c. 10: 1 4 5 P T3 SD: 12.3385 c. M:-17.8484 c. 11: 1 4 6 N T3 SD: 5.0054 c. M:-7.2262 c. 13: 1 5 7 N T3 SD: 0.7695 c. M: 1.3072 c. 54: 4 21 29 N T3 SD: 0.7526 c. M: 1.1584 c. 67: 5 26 36 N T3 SD: 0.6635 c. M: 0.8831 c. 80: 6 31 43 N T3 SD: 0.6251 c. M: 0.8283 c. 93: 7 36 50 N T3 SD: 0.6107 c. M: 0.8952 c. 106: 8 41 57 N T3 SD: 0.6078 c. M: 0.9457 c. 116: 9 45 62 N T3 SD: 0.5177 c. M:-0.6744 c. 129: 10 50 69 N T3 SD: 0.4228 c. M:-0.5575 c. 142: 11 55 76 N T3 SD: 0.3551 c. M:-0.5303 c. 144: 11 56 77 N T3 SD: 0.3205 c. M:-0.5552 c. 155: 12 60 83 N T3 SD: 0.3102 c. M:-0.5077 c. 157: 12 61 84 N T3 SD: 0.2317 c. M:-0.4010 c. 170: 13 66 91 N T3 SD: 0.1574 c. M:-0.2703 c. 183: 14 71 98 N T3 SD: 0.0960 c. M:-0.1583 c. 196: 15 76 105 N T3 SD: 0.0515 c. M:-0.0651 c. 209: 16 81 112 N T3 SD: 0.0467 c. M:-0.0772 c. 405: 31 157 217 N T3 SD: 0.0424 c. M:-0.0713 c. 601: 46 233 322 N T3 SD: 0.0439 c. M:-0.0693 c. 614: 47 238 329 N T3 SD: 0.0424 c. M:-0.0733 c. 616: 47 239 330 N T3 SD: 0.0457 c. M:-0.0611 c. 629: 48 244 337 N T3 SD: 0.0317 c. M: 0.0440 c. 642: 49 249 344 N T3 SD: 0.0221 c. M: 0.0379 c. 655: 50 254 351 N T3 SD: 0.0219 c. M: 0.0319 c. 838: 64 325 449 N T3 SD: 0.0134 c. M:-0.0186 c. 851: 65 330 456 N T3 SD: 0.0056 c. M: 0.0096 c. 1047: 80 406 561 N T3 SD: 0.0064 c. M:-0.0101 c. 1060: 81 411 568 N T3 SD: 0.0056 c. M:-0.0075 c. 1898: 145 736 1017 N T3 SD: 0.0030 c. M:-0.0049 c. 1911: 146 741 1024 N T3 SD: 0.0024 c. M: 0.0041 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11 x 13:15 SD: 34.9349 cents 12 x 14:16 S SD: 17.8484 cents 20:21:23:27 SD: 17.4272 cents 21:22:24:28 S SD: 14.1621 cents 26:27:30:35 S SD: 11.9884 cents 27:28:31:36 SD: 8.7208 cents 30:31:34:40 SD: 7.8894 cents 33:34:38:44 SD: 6.2941 cents 34:35:39:45 SD: 6.2435 cents 35:36:40:47 SD: 5.4441 cents 36:37:41:48 SD: 3.7165 cents 42:43:48:56 SD: 0.8954 cents 90:92:103:120 SD: 0.8009 cents 132:135:151:176 SD: 0.6161 cents 174:178:199:232 SD: 0.5989 cents 183:187:209:244 SD: 0.4447 cents 225:230:257:300 SD: 0.3207 cents 267:273:305:356 SD: 0.3048 cents 273:279:312:364 SD: 0.1379 cents 315:322:360:420 SD: 0.0000 cents