Scala analysis: 337_C27
Chromatic tetrachord 23/21 * 21/20 * 80/69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/21 157.493440 2: 23/20 241.960633 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 80/69 256.0844 1: 23/21 157.4934 2: 21/20 84.4672 minor semitone 3: 80/69 256.0844
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 23/21 157.493 cents 1: 1 80/69 256.084 cents 2: 1 23/20 241.961 cents 2: 1 28/23 340.552 cents 2: 1 80/63 413.578 cents wide major third 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 : 157.5 242.0 498.0 157.5: 84.5 340.6 498.0 242.0: 256.1 413.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 256.0844 cents 1600/1449, 171.6172 cents 21/20, 84.4672 cents 2: 241.9606 .. 413.5778 cents 1600/1449, 171.6172 cents 1587/1600,-14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 80/69, 256.0844 cents Average / Smallest step : 1.965438 Largest / Average step : 1.542538 Largest / Smallest step : 3.031761 Median interval of one step : 23/21, 157.4934 cents, amount: 1 Least squares average step : 152.53926 cents, oct.: 457.61779 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1480-tone equal temperament with octave 4/3 degrees: 468 719 1480 Least number of segments generator : 741 of 249.359 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1149 of 386.658 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 14.12373 cents Scale diversity : 1.087987 Lumma stability : 0.339195 Lumma impropriety factor : 0.028358 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 : 1600/1587, 14.1237 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 : 23 Odd number limit : 69 (O: 23 U: 69) Highest odd numerator or denominator: 23 Scale harmonicity : 0.015281 Average absolute harmonicity : 0.084087 Specific harmonicity : 0.066370 Fundamental : 1/420, -8.7142 octaves, 0.6229 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 3.864000E+04, 15.23781 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 47.0, average 15.66667 Mersenne's string divisions : 13244 Sum of van Prooijen's expressibility: 3.20058, average 1.06686 Sum of Tenney's harmonic distance : 6.42589, average 2.14196 Vogel's harmonic complexity : 26.33333 Wille's k value : 241 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 15.87175, average 2.64529 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 18 31| Scale is weakly epimorphic with val: <6 10 15 19 30| Scale is weakly epimorphic with val: <6 10 15 21 34| Scale is weakly epimorphic with val: <6 10 15 22 30| Scale is weakly epimorphic with val: <6 10 16 19 32| Scale is weakly epimorphic with val: <6 10 16 20 31| Scale is weakly epimorphic with val: <6 10 16 22 35| Scale is weakly epimorphic with val: <6 10 17 18 32| Scale is weakly epimorphic with val: <6 10 17 20 33| Scale is weakly epimorphic with val: <6 10 17 21 32| Scale is weakly epimorphic with val: <6 10 18 18 31| Scale is weakly epimorphic with val: <6 10 18 19 33| Scale is weakly epimorphic with val: <6 10 18 21 34| Scale is weakly epimorphic with val: <6 10 18 22 33| Scale is weakly epimorphic with val: <6 10 19 19 32| Scale is weakly epimorphic with val: <6 10 19 20 34| Scale is weakly epimorphic with val: <6 10 19 22 35| Scale is weakly epimorphic with val: <6 11 15 18 32| Scale is weakly epimorphic with val: <6 11 15 20 30| Scale is weakly epimorphic with val: <6 11 15 21 35| Scale is weakly epimorphic with val: <6 11 16 18 31| Scale is weakly epimorphic with val: <6 11 16 19 33| Scale is weakly epimorphic with val: <6 11 16 21 31| Scale is weakly epimorphic with val: <6 11 16 22 36| Scale is weakly epimorphic with val: <6 11 17 19 32| Scale is weakly epimorphic with val: <6 11 17 20 34| Scale is weakly epimorphic with val: <6 11 17 22 32| Scale is weakly epimorphic with val: <6 11 18 18 32| Scale is weakly epimorphic with val: <6 11 18 20 33| Scale is weakly epimorphic with val: <6 11 18 21 35| Scale is weakly epimorphic with val: <6 11 19 19 33| Scale is weakly epimorphic with val: <6 11 19 21 34| Scale is weakly epimorphic with val: <6 11 19 22 36| Scale is weakly epimorphic with val: <7 10 15 18 31| Scale is weakly epimorphic with val: <7 10 15 20 32| Scale is weakly epimorphic with val: <7 10 15 21 34| Scale is weakly epimorphic with val: <7 10 16 18 33| Scale is weakly epimorphic with val: <7 10 16 19 32| Scale is weakly epimorphic with val: <7 10 16 21 33| Scale is weakly epimorphic with val: <7 10 16 22 35| Scale is weakly epimorphic with val: <7 10 17 19 34| Scale is weakly epimorphic with val: <7 10 17 20 33| Scale is weakly epimorphic with val: <7 10 17 22 34| Scale is weakly epimorphic with val: <7 10 18 18 31| Scale is weakly epimorphic with val: <7 10 18 20 35| Scale is weakly epimorphic with val: <7 10 18 21 34| Scale is weakly epimorphic with val: <7 10 19 19 32| Scale is weakly epimorphic with val: <7 10 19 21 36| 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 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 20 36| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 15 22 34| Scale is weakly epimorphic with val: <7 11 16 18 31| Scale is weakly epimorphic with val: <7 11 16 18 34| Scale is JI-epimorphic with val: <7 11 16 20 32| Scale is weakly epimorphic with val: <7 11 16 20 35| Scale is weakly epimorphic with val: <7 11 16 21 31| Scale is weakly epimorphic with val: <7 11 16 21 34| Scale is weakly epimorphic with val: <7 11 17 18 30| Scale is weakly epimorphic with val: <7 11 17 18 33| Scale is weakly epimorphic with val: <7 11 17 18 36| Scale is weakly epimorphic with val: <7 11 17 19 32| Scale is weakly epimorphic with val: <7 11 17 19 35| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is JI-epimorphic with val: <7 11 17 21 33| Scale is weakly epimorphic with val: <7 11 17 21 36| Scale is weakly epimorphic with val: <7 11 17 22 32| Scale is weakly epimorphic with val: <7 11 17 22 35| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 19 34| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 20 36| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is JI-epimorphic with val: <7 11 18 22 34| Scale is weakly epimorphic with val: <7 11 19 20 32| Scale is weakly epimorphic with val: <7 11 19 20 35| Scale is weakly epimorphic with val: <7 11 19 21 31| Scale is weakly epimorphic with val: <7 11 19 21 34| Scale is weakly epimorphic with val: <7 12 15 18 33| Scale is weakly epimorphic with val: <7 12 15 19 32| Scale is weakly epimorphic with val: <7 12 15 21 36| Scale is weakly epimorphic with val: <7 12 15 22 32| Scale is weakly epimorphic with val: <7 12 16 19 34| Scale is weakly epimorphic with val: <7 12 16 20 33| Scale is weakly epimorphic with val: <7 12 17 18 34| Scale is weakly epimorphic with val: <7 12 17 20 35| Scale is weakly epimorphic with val: <7 12 17 21 34| Scale is weakly epimorphic with val: <7 12 18 18 33| Scale is weakly epimorphic with val: <7 12 18 19 35| Scale is weakly epimorphic with val: <7 12 18 21 36| Scale is weakly epimorphic with val: <7 12 18 22 35| Scale is weakly epimorphic with val: <7 12 19 19 34| Scale is weakly epimorphic with val: <7 12 19 20 36| Scale is weakly epimorphic with val: <8 11 15 18 32| Scale is weakly epimorphic with val: <8 11 15 19 34| Scale is weakly epimorphic with val: <8 11 15 21 35| Scale is weakly epimorphic with val: <8 11 15 22 34| Scale is weakly epimorphic with val: <8 11 16 19 33| Scale is weakly epimorphic with val: <8 11 16 20 35| Scale is weakly epimorphic with val: <8 11 16 22 36| Scale is weakly epimorphic with val: <8 11 17 18 36| Scale is weakly epimorphic with val: <8 11 17 20 34| Scale is weakly epimorphic with val: <8 11 17 21 36| Scale is weakly epimorphic with val: <8 11 18 18 32| Scale is weakly epimorphic with val: <8 11 18 21 35| Scale is weakly epimorphic with val: <8 11 19 19 33| Scale is weakly epimorphic with val: <8 11 19 22 36| Scale is weakly epimorphic with val: <8 12 15 18 33| Scale is weakly epimorphic with val: <8 12 15 20 34| Scale is weakly epimorphic with val: <8 12 15 21 36| Scale is weakly epimorphic with val: <8 12 16 18 35| Scale is weakly epimorphic with val: <8 12 16 19 34| Scale is weakly epimorphic with val: <8 12 16 21 35| Scale is weakly epimorphic with val: <8 12 17 19 36| Scale is weakly epimorphic with val: <8 12 17 20 35| Scale is weakly epimorphic with val: <8 12 17 22 36| Scale is weakly epimorphic with val: <8 12 18 18 33| Scale is weakly epimorphic with val: <8 12 18 21 36| Scale is weakly epimorphic with val: <8 12 19 19 34|
FIT/MODE
3: 1 0 2 N G T3 SD: 44.1224 c. M: 75.9456 c. 4: 1 1 2 P M ME S SD: 19.4739 c. M: 32.9822 c. 6: 2 1 3 P T3 SD: 6.3898 c. M:-8.5216 c. 10: 3 2 5 P T3 SD: 6.1956 c. M: 8.0799 c. 16: 5 3 8 P T3 SD: 4.2154 c. M:-7.0619 c. 19: 6 3 10 N T3 SD: 3.4921 c. M: 6.0446 c. 23: 7 4 12 N T3 SD: 4.0480 c. M: 5.9145 c. 25: 8 4 13 N T3 SD: 1.9952 c. M: 2.8990 c. 29: 9 5 15 N T3 SD: 1.9059 c. M: 2.9278 c. 35: 11 6 18 N T3 SD: 0.5580 c. M: 0.9650 c. 41: 13 7 21 N T3 SD: 0.6206 c. M:-0.9881 c. 76: 24 13 39 N T3 SD: 0.3191 c. M:-0.5086 c. 101: 32 17 52 N T3 SD: 0.2607 c. M: 0.3348 c. 136: 43 23 70 N T3 SD: 0.1521 c. M: 0.2623 c. 171: 54 29 88 N T3 SD: 0.1778 c. M: 0.2195 c. 177: 56 30 91 N T3 SD: 0.0489 c. M:-0.0801 c. 389: 123 66 200 N T3 SD: 0.0141 c. M:-0.0201 c. 566: 179 96 291 N T3 SD: 0.0157 c. M:-0.0224 c. 914: 289 155 470 N T3 SD: 0.0154 c. M: 0.0219 c. 955: 302 162 491 N T3 SD: 0.0125 c. M:-0.0214 c. 1091: 345 185 561 N T3 SD: 0.0080 c. M: 0.0139 c. 1268: 401 215 652 N T3 SD: 0.0081 c. M:-0.0113 c. 1480: 468 251 761 N T3 SD: 0.0035 c. M: 0.0050 c. 1657: 524 281 852 N T3 SD: 0.0032 c. M:-0.0054 c. 2046: 647 347 1052 N T3 SD: 0.0018 c. M:-0.0026 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: 56.0436 cents 6 x 7:8 S SD: 12.4551 cents 7 x 8:9 S SD: 31.9391 cents 8 x 9:11 SD: 32.7332 cents 9:10 x 12 S SD: 12.4551 cents 12:13:14:16 S SD: 10.4271 cents 16 x 18:21 S SD: 23.4050 cents 17:19:20:23 SD: 19.4949 cents 18:20:21:24 S SD: 11.7428 cents 19:21:22:25 SD: 10.0826 cents 20:22:23:27 SD: 7.5934 cents 21:23:24:28 SD: 3.5955 cents 33:36:38:44 SD: 2.4085 cents 54:59:62:72 SD: 1.6771 cents 93:102:107:124 SD: 0.8526 cents 114:125:131:152 SD: 0.7933 cents 126:138:145:168 SD: 0.3981 cents 147:161:169:196 SD: 0.1707 cents 273:299:314:364 SD: 0.0919 cents 420:460:483:560 SD: 0.0000 cents