Scala analysis: 335_C26
Chromatic tetrachord 93/85 * 85/81 * 36/31
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93/85 155.721450 2: 31/27 239.170570 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 36/31 258.8744 1: 93/85 155.7214 2: 85/81 83.4491 3: 36/31 258.8744
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85/81 83.449 cents 1: 1 93/85 155.721 cents 1: 1 36/31 258.874 cents 2: 1 31/27 239.171 cents 2: 1 340/279 342.324 cents 2: 1 108/85 414.596 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 : 155.7 239.2 498.0 155.7: 83.4 342.3 498.0 239.2: 258.9 414.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.4491 .. 258.8744 cents 2916/2635, 175.4253 cents 85/81, 83.4491 cents 2: 239.1706 .. 414.5959 cents 2916/2635, 175.4253 cents 961/972,-19.7039 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 85/81, 83.4491 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 36/31, 258.8744 cents Average / Smallest step : 1.989416 Largest / Average step : 1.559344 Largest / Smallest step : 3.102183 Median interval of one step : 93/85, 155.7214 cents, amount: 1 Least squares average step : 152.01411 cents, oct.: 456.04234 cents Scale is not proper Scale has trivalence property Scale is a mode of a 758-tone equal temperament with octave 4/3 degrees: 237 364 758 Least number of segments generator : 381 of 250.337 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 571 of 375.176 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.70386 cents Scale diversity : 1.089454 Lumma stability : 0.335107 Lumma impropriety factor : 0.039562 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 : 972/961, 19.7039 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 31 Odd number limit : 279 (O: 93 U: 279) Highest odd numerator or denominator: 93 Scale harmonicity : 0.020332 Fundamental : 1/2295, -11.1643 octaves, 0.1140 Hz. Guide tone : 372, 8.5392 octaves, 97324.710 Hz. Exponens Consonantiae : 8.537400E+05, 19.70344 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 121.5, average 40.50000 Mersenne's string divisions : 36134 Sum of van Prooijen's expressibility: 3.93697, average 1.31232 Sum of Tenney's harmonic distance : 7.89981, average 2.63327 Vogel's harmonic complexity : 42.00000 Wille's k value : 1317 Wilson's harmonic complexity : 65 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 17.20146, average 2.86691 Lattice compactness (without 2's) : 14.42418, average 2.40403 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -3 .. 1 -1.00000 5 1 5: -1 .. 0 -0.33333 1 17: -1 .. 0 -0.33333 1 31: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 27 33| Scale is weakly epimorphic with val: <6 10 15 29 37| Scale is weakly epimorphic with val: <6 10 15 30 33| Scale is weakly epimorphic with val: <6 10 15 33 33| Scale is weakly epimorphic with val: <6 10 16 28 37| Scale is weakly epimorphic with val: <6 10 16 29 33| Scale is weakly epimorphic with val: <6 10 16 32 33| Scale is weakly epimorphic with val: <6 10 17 27 37| Scale is weakly epimorphic with val: <6 10 17 28 33| Scale is weakly epimorphic with val: <6 10 17 31 33| Scale is weakly epimorphic with val: <6 10 18 27 33| Scale is weakly epimorphic with val: <6 10 18 30 33| Scale is weakly epimorphic with val: <6 10 18 33 33| Scale is weakly epimorphic with val: <6 10 19 29 33| Scale is weakly epimorphic with val: <6 10 19 32 33| Scale is weakly epimorphic with val: <6 11 15 27 36| Scale is weakly epimorphic with val: <6 11 15 28 35| Scale is weakly epimorphic with val: <6 11 15 30 36| Scale is weakly epimorphic with val: <6 11 15 31 38| Scale is weakly epimorphic with val: <6 11 15 33 36| Scale is weakly epimorphic with val: <6 11 16 27 35| Scale is weakly epimorphic with val: <6 11 16 29 36| Scale is weakly epimorphic with val: <6 11 16 30 38| Scale is weakly epimorphic with val: <6 11 16 32 36| Scale is weakly epimorphic with val: <6 11 17 28 36| Scale is weakly epimorphic with val: <6 11 17 29 38| Scale is weakly epimorphic with val: <6 11 17 31 36| Scale is weakly epimorphic with val: <6 11 18 27 36| Scale is weakly epimorphic with val: <6 11 18 28 38| Scale is weakly epimorphic with val: <6 11 18 30 36| Scale is weakly epimorphic with val: <6 11 18 33 36| Scale is weakly epimorphic with val: <6 11 19 27 38| Scale is weakly epimorphic with val: <6 11 19 29 36| Scale is weakly epimorphic with val: <6 11 19 32 36| Scale is weakly epimorphic with val: <7 10 15 27 35| Scale is weakly epimorphic with val: <7 10 15 29 33| Scale is weakly epimorphic with val: <7 10 15 30 38| Scale is weakly epimorphic with val: <7 10 15 32 33| Scale is weakly epimorphic with val: <7 10 16 28 33| Scale is weakly epimorphic with val: <7 10 16 29 38| Scale is weakly epimorphic with val: <7 10 16 31 33| Scale is weakly epimorphic with val: <7 10 17 27 33| Scale is weakly epimorphic with val: <7 10 17 28 38| Scale is weakly epimorphic with val: <7 10 17 30 33| Scale is weakly epimorphic with val: <7 10 17 33 33| Scale is weakly epimorphic with val: <7 10 18 27 38| Scale is weakly epimorphic with val: <7 10 18 29 33| Scale is weakly epimorphic with val: <7 10 18 32 33| Scale is weakly epimorphic with val: <7 10 19 28 33| Scale is weakly epimorphic with val: <7 10 19 31 33| Scale is weakly epimorphic with val: <7 11 15 27 35| Scale is weakly epimorphic with val: <7 11 15 27 38| Scale is weakly epimorphic with val: <7 11 15 28 34| Scale is weakly epimorphic with val: <7 11 15 28 37| Scale is JI-epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 31 34| Scale is weakly epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 33 35| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is weakly epimorphic with val: <7 11 16 27 34| Scale is weakly epimorphic with val: <7 11 16 27 37| Scale is JI-epimorphic with val: <7 11 16 29 35| Scale is weakly epimorphic with val: <7 11 16 29 38| Scale is weakly epimorphic with val: <7 11 16 30 34| Scale is weakly epimorphic with val: <7 11 16 30 37| Scale is weakly epimorphic with val: <7 11 16 32 35| Scale is weakly epimorphic with val: <7 11 16 32 38| Scale is weakly epimorphic with val: <7 11 16 33 34| Scale is weakly epimorphic with val: <7 11 16 33 37| Scale is JI-epimorphic with val: <7 11 17 28 35| Scale is weakly epimorphic with val: <7 11 17 28 38| Scale is weakly epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 17 29 37| Scale is weakly epimorphic with val: <7 11 17 31 35| Scale is weakly epimorphic with val: <7 11 17 31 38| Scale is weakly epimorphic with val: <7 11 17 32 34| Scale is weakly epimorphic with val: <7 11 17 32 37| Scale is JI-epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 27 38| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 28 37| Scale is weakly epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 31 34| Scale is weakly epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 33 35| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 19 27 34| Scale is weakly epimorphic with val: <7 11 19 27 37| Scale is weakly epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 19 29 38| Scale is weakly epimorphic with val: <7 11 19 30 34| Scale is weakly epimorphic with val: <7 11 19 30 37| Scale is weakly epimorphic with val: <7 11 19 32 35| Scale is weakly epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 11 19 33 34| Scale is weakly epimorphic with val: <7 11 19 33 37| Scale is weakly epimorphic with val: <7 12 15 28 34| Scale is weakly epimorphic with val: <7 12 15 29 39| Scale is weakly epimorphic with val: <7 12 15 31 37| Scale is weakly epimorphic with val: <7 12 15 32 39| Scale is weakly epimorphic with val: <7 12 16 27 34| Scale is weakly epimorphic with val: <7 12 16 28 39| Scale is weakly epimorphic with val: <7 12 16 30 37| Scale is weakly epimorphic with val: <7 12 16 31 39| Scale is weakly epimorphic with val: <7 12 17 27 39| Scale is weakly epimorphic with val: <7 12 17 29 37| Scale is weakly epimorphic with val: <7 12 17 30 39| Scale is weakly epimorphic with val: <7 12 17 33 39| Scale is weakly epimorphic with val: <7 12 18 28 37| Scale is weakly epimorphic with val: <7 12 18 29 39| Scale is weakly epimorphic with val: <7 12 18 32 39| Scale is weakly epimorphic with val: <7 12 19 27 37| Scale is weakly epimorphic with val: <7 12 19 28 39| Scale is weakly epimorphic with val: <7 12 19 31 39| Scale is weakly epimorphic with val: <8 11 15 27 34| Scale is weakly epimorphic with val: <8 11 15 28 36| Scale is weakly epimorphic with val: <8 11 15 30 37| Scale is weakly epimorphic with val: <8 11 15 31 36| Scale is weakly epimorphic with val: <8 11 16 27 36| Scale is weakly epimorphic with val: <8 11 16 29 37| Scale is weakly epimorphic with val: <8 11 16 30 36| Scale is weakly epimorphic with val: <8 11 16 33 36| Scale is weakly epimorphic with val: <8 11 17 28 37| Scale is weakly epimorphic with val: <8 11 17 29 36| Scale is weakly epimorphic with val: <8 11 17 32 36| Scale is weakly epimorphic with val: <8 11 18 27 37| Scale is weakly epimorphic with val: <8 11 18 28 36| Scale is weakly epimorphic with val: <8 11 18 31 36| Scale is weakly epimorphic with val: <8 11 19 27 36| Scale is weakly epimorphic with val: <8 11 19 30 36| Scale is weakly epimorphic with val: <8 11 19 33 36| Scale is weakly epimorphic with val: <8 12 15 28 39| Scale is weakly epimorphic with val: <8 12 15 29 35| Scale is weakly epimorphic with val: <8 12 15 31 39| Scale is weakly epimorphic with val: <8 12 15 32 38| Scale is weakly epimorphic with val: <8 12 16 27 39| Scale is weakly epimorphic with val: <8 12 16 28 35| Scale is weakly epimorphic with val: <8 12 16 30 39| Scale is weakly epimorphic with val: <8 12 16 31 38| Scale is weakly epimorphic with val: <8 12 16 33 39| Scale is weakly epimorphic with val: <8 12 17 27 35| Scale is weakly epimorphic with val: <8 12 17 29 39| Scale is weakly epimorphic with val: <8 12 17 30 38| Scale is weakly epimorphic with val: <8 12 17 32 39| Scale is weakly epimorphic with val: <8 12 18 28 39| Scale is weakly epimorphic with val: <8 12 18 29 38| Scale is weakly epimorphic with val: <8 12 18 31 39| Scale is weakly epimorphic with val: <8 12 19 27 39| Scale is weakly epimorphic with val: <8 12 19 28 38| Scale is weakly epimorphic with val: <8 12 19 30 39| Scale is weakly epimorphic with val: <8 12 19 33 39|
FIT/MODE
3: 1 0 2 N G T3 SD: 42.6525 c. M: 73.1556 c. 4: 1 1 2 P M ME S SD: 18.8957 c. M: 31.2102 c. 6: 2 1 3 P T3 SD: 8.2263 c. M:-10.2935 c. 10: 3 2 5 P T3 SD: 6.7540 c. M:-9.8519 c. 13: 4 2 7 N T3 SD: 5.5586 c. M: 9.3036 c. 17: 5 3 9 N T3 SD: 6.0094 c. M: 9.2376 c. 19: 6 3 10 N T3 SD: 2.0827 c. M: 3.2545 c. 23: 7 4 12 N T3 SD: 2.4571 c. M: 4.1425 c. 25: 8 4 13 N T3 SD: 2.1100 c. M:-3.6529 c. 29: 9 5 15 N T3 SD: 0.9893 c. M:-1.2649 c. 48: 15 8 25 N T3 SD: 0.3063 c. M: 0.5240 c. 77: 24 13 40 N T3 SD: 0.2940 c. M: 0.4866 c. 125: 39 21 65 N T3 SD: 0.2014 c. M: 0.3314 c. 173: 54 29 90 N T3 SD: 0.1992 c. M: 0.2623 c. 179: 56 30 93 N T3 SD: 0.0842 c. M:-0.1136 c. 227: 71 38 118 N T3 SD: 0.0339 c. M:-0.0547 c. 531: 166 89 276 N T3 SD: 0.0139 c. M: 0.0238 c. 758: 237 127 394 N T3 SD: 0.0022 c. M: 0.0038 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: 56.9703 cents 6 x 7:8 S SD: 13.8502 cents 7 x 8:9 S SD: 31.7333 cents 8 x 9:11 SD: 31.9426 cents 9:10 x 12 S SD: 13.3411 cents 10:11 x 13 SD: 22.4016 cents 11:12:13:15 SD: 21.1960 cents 12:13:14:16 S SD: 10.8597 cents 16 x 18:21 S SD: 22.2859 cents 17:19:20:23 SD: 20.4816 cents 18:20:21:24 S SD: 12.8203 cents 19:21:22:25 SD: 10.7902 cents 20:22:23:27 SD: 7.8632 cents 21:23:24:28 SD: 2.7302 cents 33:36:38:44 SD: 2.3933 cents 54:59:62:72 SD: 0.8049 cents 129:141:148:172 SD: 0.7219 cents 168:184:193:224 SD: 0.6777 cents 189:207:217:252 SD: 0.5907 cents 222:243:255:296 SD: 0.3557 cents 243:266:279:324 SD: 0.2808 cents 276:302:317:368 SD: 0.2072 cents 297:325:341:396 SD: 0.0836 cents 351:384:403:468 SD: 0.0530 cents