Scala analysis: 200_C11
Chromatic tetrachord 40/39 * 91/85 * 17/14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 56/51 161.915496 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 40/39 43.8311 tridecimal minor diesis 2: 91/85 118.0844 3: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 91/85 118.084 cents 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 340/273 379.961 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 161.9 498.0 43.8 : 118.1 454.2 498.0 161.9: 336.1 380.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 336.1295 cents 663/560, 292.2985 cents 40/39, 43.8311 cents 2: 161.9155 .. 454.2139 cents 663/560, 292.2985 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 3.787612 Largest / Average step : 2.024694 Largest / Smallest step : 7.668753 Median interval of one step : 91/85, 118.0844 cents, amount: 1 Least squares average step : 132.98550 cents, oct.: 398.95651 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1375-tone equal temperament with octave 4/3 degrees: 121 447 1375 Least number of segments generator : 688 of 249.204 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1212 of 439.004 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 43.83105 cents Scale diversity : 0.753488 Lumma stability : 0.176012 Lumma impropriety factor : 0.349796 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 : 40/39, 43.8311 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% -- Rational properties -- Prime limit : 17 Odd number limit : 273 (O: 91 U: 273) Highest odd numerator or denominator: 51 Scale harmonicity : 0.013401 Average absolute harmonicity : 0.088404 Specific harmonicity : 0.071151 Fundamental : 1/663, -9.3729 octaves, 0.3946 Hz. Guide tone : 280, 8.1293 octaves, 73255.158 Hz. Exponens Consonantiae : 1.856400E+05, 17.50215 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 96.5, average 32.16667 Mersenne's string divisions : 59171 Sum of van Prooijen's expressibility: 3.77576, average 1.25859 Sum of Tenney's harmonic distance : 7.72806, average 2.57602 Vogel's harmonic complexity : 26.66667 Wille's k value : 110 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.62837, average 2.43806 Lattice compactness (without 2's) : 9.29253, average 1.54875 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.33333 1 13: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 16 19 27 31| Scale is weakly epimorphic with val: <7 11 16 19 28 30| Scale is weakly epimorphic with val: <7 11 16 20 27 29| Scale is weakly epimorphic with val: <7 11 16 20 28 31| Scale is weakly epimorphic with val: <7 11 16 21 27 30| Scale is weakly epimorphic with val: <7 11 16 21 28 29| Scale is weakly epimorphic with val: <7 11 17 19 26 30| Scale is weakly epimorphic with val: <7 11 17 19 28 31| Scale is weakly epimorphic with val: <7 11 17 20 26 31| Scale is weakly epimorphic with val: <7 11 17 20 28 29| Scale is JI-epimorphic with val: <7 11 17 21 26 29| Scale is weakly epimorphic with val: <7 11 17 21 28 30| Scale is weakly epimorphic with val: <7 11 18 19 26 31| Scale is weakly epimorphic with val: <7 11 18 19 27 30| Scale is weakly epimorphic with val: <7 11 18 20 26 29| Scale is weakly epimorphic with val: <7 11 18 20 27 31| Scale is weakly epimorphic with val: <7 11 18 21 26 30| Scale is JI-epimorphic with val: <7 11 18 21 27 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 25.4163 c. M: 43.8311 c. 6: 1 1 4 N M DE S SD: 22.7420 c. M:-39.1764 c. 8: 1 2 5 N T3 SD: 17.8611 c. M:-24.8514 c. 9: 1 2 6 N T3 SD: 7.0527 c. M:-11.5073 c. 12: 1 3 8 N T3 SD: 2.7217 c. M:-4.0995 c. 21: 2 5 14 N T3 SD: 3.1506 c. M:-4.0995 c. 22: 2 5 15 N T3 SD: 2.1579 c. M: 3.4466 c. 34: 3 8 23 N T3 SD: 0.4570 c. M: 0.7833 c. 46: 4 11 31 N T3 SD: 0.4139 c. M: 0.5228 c. 80: 7 19 54 N T3 SD: 0.1485 c. M: 0.2521 c. 194: 17 46 131 N T3 SD: 0.1499 c. M: 0.1879 c. 249: 22 59 168 N T3 SD: 0.1151 c. M:-0.1729 c. 283: 25 67 191 N T3 SD: 0.0958 c. M:-0.1659 c. 295: 26 70 199 N T3 SD: 0.0997 c. M:-0.1602 c. 329: 29 78 222 N T3 SD: 0.0541 c. M:-0.0696 c. 363: 32 86 245 N T3 SD: 0.0436 c. M:-0.0737 c. 409: 36 97 276 N T3 SD: 0.0237 c. M:-0.0405 c. 443: 39 105 299 N T3 SD: 0.0157 c. M: 0.0228 c. 852: 75 202 575 N T3 SD: 0.0077 c. M:-0.0109 c. 932: 82 221 629 N T3 SD: 0.0069 c. M: 0.0116 c. 1375: 121 326 928 N T3 SD: 0.0037 c. M: 0.0056 c. 1784: 157 423 1204 N T3 SD: 0.0029 c. M:-0.0050 c. 2227: 196 528 1503 N T3 SD: 0.0014 c. M:-0.0023 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: 87.7017 cents 6 x 7:8 S SD: 52.4777 cents 7 x 8:9 S SD: 46.7996 cents 8 x 9:11 SD: 33.9173 cents 9 x 10:12 S SD: 10.2441 cents 10 x 11:13 SD: 21.9699 cents 11 x 12:15 S SD: 20.2538 cents 12 x 13:16 SD: 11.6714 cents 13 x 14:17 SD: 23.7710 cents 14 x 15:19 SD: 26.1862 cents 15 x 16:20 S SD: 25.0921 cents 16 x 18:21 S SD: 25.0343 cents 17:18:19:23 SD: 22.6478 cents 18:19:20:24 S SD: 17.9413 cents 19:20:21:25 SD: 17.2464 cents 20:21:22:27 SD: 15.3600 cents 21:22:23:28 SD: 12.3238 cents 24:25:26:32 SD: 11.8572 cents 27:28:30:36 S SD: 9.3436 cents 28:29:31:37 SD: 9.0167 cents 29:30:32:39 SD: 7.5575 cents 30:31:33:40 SD: 4.4331 cents 39:40:43:52 SD: 2.3732 cents 42:43:46:56 SD: 1.7990 cents 72:74:79:96 SD: 1.2755 cents 81:83:89:108 SD: 0.6568 cents 153:157:168:204 SD: 0.2828 cents 234:240:257:312 SD: 0.1321 cents 429:440:471:572 SD: 0.0721 cents