Scala analysis: 140_C3
Chromatic tetrachord 102/97 * 194/189 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 102/97 87.015000 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 102/97 87.0150 2: 194/189 45.2045 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 194/189 45.205 cents 1: 1 102/97 87.015 cents 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 194/153 411.030 cents 2: 1 126/97 452.840 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 : 87.0 132.2 498.0 87.0 : 45.2 411.0 498.0 132.2: 365.8 452.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 45.2045 .. 365.8255 cents 3969/3298, 320.6210 cents 194/189, 45.2045 cents 2: 132.2195 .. 452.8405 cents 3969/3298, 320.6210 cents 1156/1323,-233.6060 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 194/189, 45.2045 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/17, 365.8255 cents Average / Smallest step : 3.672532 Largest / Average step : 2.203569 Largest / Smallest step : 8.092678 Median interval of one step : 102/97, 87.0150 cents, amount: 1 Least squares average step : 131.82779 cents, oct.: 395.48336 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1179-tone equal temperament with octave 4/3 degrees: 206 313 1179 Least number of segments generator : 590 of 249.234 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 806 of 340.479 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 45.20450 cents Scale diversity : 0.625402 Lumma stability : 0.181528 Lumma impropriety factor : 0.469046 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 : 9639/9409, 41.8105 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 : 97 Odd number limit : 189 (O: 97 U: 189) Highest odd numerator or denominator: 97 Scale harmonicity : 0.019840 Fundamental : 1/6111, -12.5772 octaves, 0.0428 Hz. Guide tone : 204, 7.6724 octaves, 53371.615 Hz. Exponens Consonantiae : 1.246644E+06, 20.24962 octaves Euler's gradus suavitatis : 127 Sum of Mann's harmonic distance : 168.5, average 56.16667 Mersenne's string divisions : 182483 Sum of van Prooijen's expressibility: 4.26323, average 1.42108 Sum of Tenney's harmonic distance : 8.70640, average 2.90213 Vogel's harmonic complexity : 86.33333 Wille's k value : 1606 Wilson's harmonic complexity : 130 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.62856, average 2.43809 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 .. 1 -0.66667 4 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 97: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 18 29 47| Scale is weakly epimorphic with val: <6 10 19 30 48| Scale is weakly epimorphic with val: <6 10 20 31 49| Scale is weakly epimorphic with val: <6 10 21 32 47| Scale is weakly epimorphic with val: <6 10 22 33 48| Scale is weakly epimorphic with val: <6 11 18 31 49| Scale is weakly epimorphic with val: <6 11 18 33 47| Scale is weakly epimorphic with val: <6 11 19 32 47| Scale is weakly epimorphic with val: <6 11 20 33 48| Scale is weakly epimorphic with val: <6 11 21 33 47| Scale is weakly epimorphic with val: <7 10 18 27 48| Scale is weakly epimorphic with val: <7 10 19 28 49| Scale is weakly epimorphic with val: <7 10 19 33 47| Scale is weakly epimorphic with val: <7 10 20 29 47| Scale is weakly epimorphic with val: <7 10 21 30 48| Scale is weakly epimorphic with val: <7 10 22 31 49| Scale is weakly epimorphic with val: <7 10 22 33 47| Scale is weakly epimorphic with val: <7 11 18 27 49| Scale is weakly epimorphic with val: <7 11 18 28 48| Scale is weakly epimorphic with val: <7 11 18 30 49| Scale is weakly epimorphic with val: <7 11 18 31 48| Scale is weakly epimorphic with val: <7 11 18 33 49| Scale is weakly epimorphic with val: <7 11 19 28 47| Scale is weakly epimorphic with val: <7 11 19 29 49| Scale is weakly epimorphic with val: <7 11 19 31 47| Scale is weakly epimorphic with val: <7 11 19 32 49| Scale is weakly epimorphic with val: <7 11 20 27 47| Scale is weakly epimorphic with val: <7 11 20 29 48| Scale is JI-epimorphic with val: <7 11 20 30 47| Scale is weakly epimorphic with val: <7 11 20 32 48| Scale is weakly epimorphic with val: <7 11 20 33 47| Scale is weakly epimorphic with val: <7 11 21 27 49| Scale is weakly epimorphic with val: <7 11 21 28 48| Scale is weakly epimorphic with val: <7 11 21 30 49| Scale is JI-epimorphic with val: <7 11 21 31 48| Scale is weakly epimorphic with val: <7 11 21 33 49| Scale is weakly epimorphic with val: <7 11 22 28 47| Scale is weakly epimorphic with val: <7 11 22 29 49| Scale is weakly epimorphic with val: <7 11 22 31 47| Scale is JI-epimorphic with val: <7 11 22 32 49| Scale is weakly epimorphic with val: <7 12 18 31 49| Scale is weakly epimorphic with val: <7 12 18 32 48| Scale is weakly epimorphic with val: <7 12 19 32 47| Scale is weakly epimorphic with val: <7 12 19 33 49| Scale is weakly epimorphic with val: <7 12 20 31 47| Scale is weakly epimorphic with val: <7 12 20 33 48| Scale is weakly epimorphic with val: <7 12 21 32 48| Scale is weakly epimorphic with val: <7 12 22 33 49| Scale is weakly epimorphic with val: <8 11 18 27 48| Scale is weakly epimorphic with val: <8 11 18 31 47| Scale is weakly epimorphic with val: <8 11 19 28 49| Scale is weakly epimorphic with val: <8 11 19 32 48| Scale is weakly epimorphic with val: <8 11 20 29 47| Scale is weakly epimorphic with val: <8 11 20 33 49| Scale is weakly epimorphic with val: <8 11 21 30 48| Scale is weakly epimorphic with val: <8 11 21 31 47| Scale is weakly epimorphic with val: <8 11 22 31 49| Scale is weakly epimorphic with val: <8 11 22 32 48| Scale is weakly epimorphic with val: <8 12 18 29 47| Scale is weakly epimorphic with val: <8 12 18 31 48| Scale is weakly epimorphic with val: <8 12 19 30 48| Scale is weakly epimorphic with val: <8 12 19 32 49| Scale is weakly epimorphic with val: <8 12 20 30 47| Scale is weakly epimorphic with val: <8 12 20 31 49| Scale is weakly epimorphic with val: <8 12 21 31 48| Scale is weakly epimorphic with val: <8 12 21 32 47| Scale is weakly epimorphic with val: <8 12 22 32 49| Scale is weakly epimorphic with val: <8 12 22 33 48|
FIT/MODE
3: 1 0 2 N G T3 SD: 49.6089 c. M:-79.0000 c. 4: 1 0 3 N G T3 SD: 22.1012 c. M:-37.4963 c. 5: 1 0 4 N G T3 SD: 20.1829 c. M: 32.6105 c. 6: 1 1 4 N M DE S SD: 19.6485 c. M:-33.7955 c. 7: 1 1 5 N M DE S SD: 10.8522 c. M: 15.8657 c. 10: 2 1 7 N T3 SD: 12.3050 c. M:-17.1940 c. 11: 2 1 8 N T3 SD: 2.9190 c. M:-3.6110 c. 23: 4 2 17 N T3 SD: 1.3447 c. M: 2.2947 c. 34: 6 3 25 N T3 SD: 0.5519 c. M:-0.8753 c. 75: 13 7 55 N T3 SD: 0.5239 c. M: 0.6872 c. 86: 15 8 63 N T3 SD: 0.5713 c. M:-0.9786 c. 98: 17 9 72 N T3 SD: 0.3610 c. M: 0.6194 c. 109: 19 10 80 N T3 SD: 0.2023 c. M:-0.2879 c. 132: 23 12 97 N T3 SD: 0.1646 c. M: 0.2344 c. 143: 25 13 105 N T3 SD: 0.0807 c. M:-0.1281 c. 275: 48 25 202 N T3 SD: 0.0486 c. M: 0.0835 c. 309: 54 28 227 N T3 SD: 0.0327 c. M: 0.0522 c. 418: 73 38 307 N T3 SD: 0.0295 c. M:-0.0365 c. 452: 79 41 332 N T3 SD: 0.0191 c. M:-0.0327 c. 727: 127 66 534 N T3 SD: 0.0065 c. M: 0.0113 c. 1179: 206 107 866 N T3 SD: 0.0033 c. M:-0.0056 c. 1906: 333 173 1400 N T3 SD: 0.0005 c. M: 0.0008 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 67.3257 cents 7 x 8:9 S SD: 58.6432 cents 8 x 9:11 SD: 44.6585 cents 9 x 10:12 S SD: 25.0921 cents 10 x 11:13 SD: 27.3679 cents 11 x 12:15 S SD: 21.5225 cents 12 x 13:16 SD: 3.1766 cents 13 x 14:17 SD: 16.9226 cents 14 x 15:19 SD: 16.5996 cents 15 x 16:20 S SD: 10.2441 cents 16:17 x 21 SD: 16.3186 cents 17:18 x 23 SD: 13.9761 cents 18:19 x 24 SD: 3.2940 cents 30 x 32:40 S SD: 10.2441 cents 31:33 x 41 SD: 12.7171 cents 32:34:35:43 SD: 10.6911 cents 33:35:36:44 SD: 7.8865 cents 34:36:37:45 SD: 7.5023 cents 35:37:38:47 SD: 6.1407 cents 36:38:39:48 SD: 3.0508 cents 39:41:42:52 SD: 1.3151 cents 75:79:81:100 SD: 1.0369 cents 99:104:107:132 SD: 0.9599 cents 114:120:123:152 SD: 0.6358 cents 138:145:149:184 SD: 0.4874 cents 177:186:191:236 SD: 0.4098 cents 213:224:230:284 SD: 0.2448 cents 252:265:272:336 SD: 0.0225 cents