Scala analysis: 302_C22
Chromatic tetrachord 46/45 * 10/9 * 27/23
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: 92/81 220.454344 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 46/45 38.0506 23rd-partial chroma 2: 10/9 182.4037 minor whole tone 3: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 10/9 182.404 cents minor whole tone 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 92/81 220.454 cents 2: 1 6/5 315.641 cents minor third 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 : 38.1 220.5 498.0 38.1 : 182.4 460.0 498.0 220.5: 277.6 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 277.5907 cents 1215/1058, 239.5400 cents 46/45, 38.0506 cents 2: 220.4543 .. 459.9944 cents 1215/1058, 239.5400 cents 2116/2187,-57.1363 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 : 27/23, 277.5907 cents Average / Smallest step : 4.363002 Largest / Average step : 1.672082 Largest / Smallest step : 7.295297 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 140.93531 cents, oct.: 422.80593 cents Scale is not proper Scale has trivalence property 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 38.05063 cents Scale diversity : 0.712143 Lumma stability : 0.152800 Lumma impropriety factor : 0.114721 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 : 46/45, 38.0506 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 : 81 (O: 27 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.016352 Average absolute harmonicity : 0.083596 Specific harmonicity : 0.069803 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 3.726000E+04, 15.18534 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 135.5, average 45.16667 Mersenne's string divisions : 15743 Sum of van Prooijen's expressibility: 4.03882, average 1.34627 Sum of Tenney's harmonic distance : 8.26742, average 2.75581 Vogel's harmonic complexity : 25.33333 Wille's k value : 103 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.07616, average 2.84603 Lattice compactness (without 2's) : 14.70299, average 2.45050 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -4 ..-1 -2.33333 7 1 5: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 15 32| Scale is weakly epimorphic with val: <6 10 16 31| Scale is weakly epimorphic with val: <6 10 18 35| Scale is weakly epimorphic with val: <6 10 19 31| Scale is weakly epimorphic with val: <6 11 15 34| Scale is weakly epimorphic with val: <6 11 17 35| Scale is weakly epimorphic with val: <7 10 15 31| Scale is weakly epimorphic with val: <7 10 18 34| Scale is JI-epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 16 35| Scale is weakly epimorphic with val: <7 11 17 31| Scale is weakly epimorphic with val: <7 11 17 34| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 19 35| Scale is weakly epimorphic with val: <7 12 15 35| Scale is weakly epimorphic with val: <8 11 15 32| Scale is weakly epimorphic with val: <8 11 16 31| Scale is weakly epimorphic with val: <8 11 18 35| Scale is weakly epimorphic with val: <8 11 19 31| Scale is weakly epimorphic with val: <8 12 15 34| Scale is weakly epimorphic with val: <8 12 17 35|
FIT/MODE
3: 0 1 2 N G T3 SD: 38.3471 c. M: 54.4393 c. 4: 0 2 2 P M DE S SD: 27.4711 c. M: 38.0506 c. 5: 0 2 3 N G T3 SD: 25.1584 c. M: 38.0506 c. 7: 0 3 4 N G T3 SD: 22.3379 c. M: 38.0506 c. 9: 1 3 5 N T3 SD: 9.9945 c. M:-17.2877 c. 11: 1 4 6 N T3 SD: 5.3969 c. M:-7.2262 c. 14: 1 5 8 N T3 SD: 4.2904 c. M: 7.0065 c. 16: 1 6 9 N T3 SD: 4.2613 c. M: 6.9228 c. 23: 2 8 13 N T3 SD: 3.7839 c. M:-5.2576 c. 25: 2 9 14 N T3 SD: 1.2836 c. M:-1.7930 c. 27: 2 10 15 N T3 SD: 0.8466 c. M: 1.1584 c. 52: 4 19 29 N T3 SD: 0.1781 c. M:-0.2605 c. 79: 6 29 44 N T3 SD: 0.1730 c. M: 0.2244 c. 131: 10 48 73 N T3 SD: 0.0363 c. M:-0.0541 c. 183: 14 67 102 N T3 SD: 0.0299 c. M:-0.0512 c. 314: 24 115 175 N T3 SD: 0.0140 c. M:-0.0178 c. 1701: 130 623 948 N T3 SD: 0.0140 c. M:-0.0206 c. 2015: 154 738 1123 N T3 SD: 0.0140 c. M:-0.0202 c. 2108: 161 772 1175 N T3 SD: 0.0134 c. M: 0.0198 c. 2187: 167 801 1219 N T3 SD: 0.0133 c. M: 0.0198 c. 2239: 171 820 1248 N T3 SD: 0.0118 c. M: 0.0155 c. 2291: 175 839 1277 N T3 SD: 0.0116 c. M: 0.0189 c. 2370: 181 868 1321 N T3 SD: 0.0106 c. M: 0.0143 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: 63.6303 cents 6 x 7:8 S SD: 23.2083 cents 7 x 8:9 S SD: 31.9335 cents 8 x 9:11 SD: 27.8914 cents 9 x 10:12 S SD: 19.0253 cents 10 x 11:13 SD: 35.3408 cents 11 x 13:15 SD: 39.4999 cents 12 x 14:16 S SD: 23.2083 cents 18:19:20:24 S SD: 22.4448 cents 19:20:22:25 SD: 21.6375 cents 20:21:23:27 SD: 18.4979 cents 21:22:24:28 S SD: 14.6060 cents 22:23:25:29 SD: 14.5521 cents 23:24:26:31 SD: 13.6912 cents 24:25:27:32 SD: 12.1924 cents 27:28:31:36 SD: 10.3860 cents 28:29:32:37 SD: 9.8394 cents 29:30:33:39 SD: 8.5465 cents 30:31:34:40 SD: 6.3639 cents 36:37:41:48 SD: 3.4979 cents 44:45:50:59 SD: 3.2943 cents 45:46:51:60 SD: 1.2559 cents 87:89:99:116 SD: 1.1638 cents 96:98:109:128 SD: 0.8087 cents 132:135:150:176 SD: 0.4031 cents 177:181:201:236 SD: 0.2377 cents 228:233:259:304 SD: 0.1846 cents 360:368:409:480 SD: 0.1568 cents 405:414:460:540 SD: 0.0000 cents