Scala analysis: 243_C16
Chromatic tetrachord 64/63 * 21/19 * 19/16
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/63 27.264092 septimal comma, Archytas' comma 2: 64/57 200.531983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 21/19 173.2679 3: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 21/19 173.268 cents 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 76/63 324.777 cents 2: 1 21/16 470.781 cents narrow 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 : 27.3 200.5 498.0 27.3 : 173.3 470.8 498.0 200.5: 297.5 324.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 297.5130 cents 1197/1024, 270.2489 cents 64/63, 27.2641 cents 2: 200.5320 .. 470.7809 cents 1197/1024, 270.2489 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 6.089145 Largest / Average step : 1.792085 Largest / Smallest step : 10.912266 Median interval of one step : 21/19, 173.2679 cents, amount: 1 Least squares average step : 137.31879 cents, oct.: 411.95637 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1443-tone equal temperament with octave 4/3 degrees: 79 581 1443 Least number of segments generator : 722 of 249.195 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 982 of 338.933 cents and inv. generated superset size: 29 = 26 more = 966.667% 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 27.26409 cents Scale diversity : 0.631077 Lumma stability : 0.109484 Lumma impropriety factor : 0.194723 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 : 64/63, 27.2641 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 : 19 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 63 Scale harmonicity : 0.017945 Average absolute harmonicity : 0.094640 Specific harmonicity : 0.093472 Fundamental : 1/1197, -10.2252 octaves, 0.2186 Hz. Guide tone : 64, 6.0000 octaves, 16744.036 Hz. Exponens Consonantiae : 7.660800E+04, 16.22521 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 127.5, average 42.50000 Mersenne's string divisions : 107569 Sum of van Prooijen's expressibility: 4.03234, average 1.34411 Sum of Tenney's harmonic distance : 8.24676, average 2.74892 Vogel's harmonic complexity : 24.00000 Wille's k value : 199 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 24.90140, average 4.15023 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 4.66667 14 3: -2 ..-1 -1.33333 4 1 7: -1 .. 0 -0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 10 19 33| Scale is weakly epimorphic with val: <7 10 20 29| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is JI-epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 21 33| Scale is weakly epimorphic with val: <7 11 22 29| Scale is weakly epimorphic with val: <7 11 22 32| Scale is weakly epimorphic with val: <8 11 19 34| Scale is weakly epimorphic with val: <8 11 22 34| Scale is weakly epimorphic with val: <8 12 19 33| Scale is weakly epimorphic with val: <8 12 21 28| Scale is weakly epimorphic with val: <8 12 21 31| Scale is weakly epimorphic with val: <8 12 21 34| Scale is weakly epimorphic with val: <8 12 22 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 25.3952 c. M: 34.5170 c. 5: 0 2 3 N G T3 SD: 15.7592 c. M: 27.2641 c. 8: 0 3 5 N G T3 SD: 17.6334 c. M: 27.2641 c. 10: 1 3 6 N T3 SD: 13.0358 c. M:-22.5404 c. 11: 1 3 7 N T3 SD: 15.2946 c. M: 19.4247 c. 12: 1 4 7 N T3 SD: 9.1576 c. M:-14.2397 c. 13: 1 4 8 N T3 SD: 8.2181 c. M:-11.0471 c. 14: 1 5 8 N T3 SD: 8.8673 c. M:-12.9159 c. 15: 1 5 9 N T3 SD: 3.5118 c. M:-5.9389 c. 17: 1 6 10 N T3 SD: 2.8747 c. M:-4.5454 c. 20: 1 7 12 N T3 SD: 1.5604 c. M: 2.3618 c. 35: 2 12 21 N T3 SD: 1.0257 c. M: 1.3140 c. 37: 2 13 22 N T3 SD: 0.8199 c. M:-1.3782 c. 52: 3 18 31 N T3 SD: 0.9166 c. M:-1.4693 c. 55: 3 19 33 N T3 SD: 0.7607 c. M: 1.3140 c. 57: 3 20 34 N T3 SD: 0.6565 c. M: 1.0512 c. 72: 4 25 43 N T3 SD: 0.2373 c. M:-0.4051 c. 92: 5 32 55 N T3 SD: 0.1752 c. M: 0.2313 c. 164: 9 57 98 N T3 SD: 0.0693 c. M: 0.0992 c. 293: 16 102 175 N T3 SD: 0.0469 c. M: 0.0671 c. 365: 20 127 218 N T3 SD: 0.0328 c. M:-0.0505 c. 457: 25 159 273 N T3 SD: 0.0114 c. M: 0.0187 c. 822: 45 286 491 N T3 SD: 0.0110 c. M:-0.0190 c. 986: 54 343 589 N T3 SD: 0.0071 c. M:-0.0122 c. 1279: 70 445 764 N T3 SD: 0.0067 c. M:-0.0100 c. 1443: 79 502 862 N T3 SD: 0.0020 c. M: 0.0024 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: 71.3878 cents 6 x 7:8 S SD: 33.1695 cents 7 x 8:9 S SD: 35.0108 cents 8 x 9:11 SD: 26.6900 cents 9 x 10:12 S SD: 9.0641 cents 10 x 11:13 SD: 28.2107 cents 11 x 12:15 S SD: 31.6353 cents 12 x 13:16 SD: 30.9797 cents 13 x 15:17 SD: 28.9776 cents 14 x 16:19 SD: 21.6672 cents 21:22:24:28 S SD: 20.4856 cents 22:23:25:29 SD: 19.1268 cents 23:24:26:31 SD: 17.1341 cents 24:25:27:32 SD: 14.5132 cents 26:27:29:35 SD: 14.3600 cents 27:28:30:36 S SD: 13.3454 cents 30:31:34:40 SD: 11.2120 cents 31:32:35:41 SD: 10.8292 cents 32:33:36:43 SD: 9.8284 cents 33:34:37:44 SD: 8.1807 cents 39:40:44:52 SD: 6.1771 cents 41:42:46:55 SD: 5.9762 cents 42:43:47:56 SD: 4.8902 cents 48:49:54:64 SD: 3.0281 cents 56:57:63:75 SD: 3.0238 cents 57:58:64:76 SD: 0.9484 cents 66:67:74:88 SD: 0.9171 cents 123:125:138:164 SD: 0.4919 cents 186:189:209:248 SD: 0.4597 cents 195:198:219:260 SD: 0.3102 cents 252:256:283:336 SD: 0.1073 cents 375:381:421:500 SD: 0.1020 cents 570:579:640:760 SD: 0.0475 cents