Scala analysis: 189_C9
Chromatic tetrachord 64/63 * 14/13 * 39/32
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: 128/117 155.562336 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 14/13 128.2982 2/3-tone 3: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 14/13 128.298 cents 2/3-tone 1: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 128/117 155.562 cents 2: 1 26/21 369.747 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 : 27.3 155.6 498.0 27.3 : 128.3 470.8 498.0 155.6: 342.5 369.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 342.4827 cents 2457/2048, 315.2186 cents 64/63, 27.2641 cents 2: 155.5623 .. 470.7809 cents 2457/2048, 315.2186 cents 4096/4563,-186.9203 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 : 39/32, 342.4827 cents Average / Smallest step : 6.089145 Largest / Average step : 2.062962 Largest / Smallest step : 12.561675 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 130.89455 cents, oct.: 392.68366 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2302-tone equal temperament with octave 4/3 degrees: 126 719 2302 Least number of segments generator : 1153 of 249.455 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1723 of 372.777 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 0.607060 Lumma stability : 0.109484 Lumma impropriety factor : 0.375308 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 117 Scale harmonicity : 0.022335 Average absolute harmonicity : 0.096512 Specific harmonicity : 0.113487 Fundamental : 1/819, -9.6777 octaves, 0.3194 Hz. Guide tone : 128, 7.0000 octaves, 33488.072 Hz. Exponens Consonantiae : 1.048320E+05, 16.67772 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 189.5, average 63.16667 Mersenne's string divisions : 31115 Sum of van Prooijen's expressibility: 4.34465, average 1.44822 Sum of Tenney's harmonic distance : 8.86010, average 2.95337 Vogel's harmonic complexity : 19.33333 Wille's k value : 136 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 27.15851, average 4.52642 Lattice compactness (without 2's) : 9.71478, average 1.61913 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 7 5.00000 15 3: -2 ..-1 -1.66667 5 1 7: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 10 20 26| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 18 29| Scale is JI-epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 21 29| Scale is weakly epimorphic with val: <7 11 22 25| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <8 12 19 29| Scale is weakly epimorphic with val: <8 12 21 27| Scale is weakly epimorphic with val: <8 12 21 30| Scale is weakly epimorphic with val: <8 12 22 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 16.8581 c. M: 27.2641 c. 7: 0 2 5 N G T3 SD: 17.5048 c. M: 27.2641 c. 9: 1 2 6 N T3 SD: 17.2957 c. M:-28.0742 c. 10: 0 3 7 N G T3 SD: 16.1363 c. M: 27.2641 c. 11: 1 2 8 N T3 SD: 15.4251 c. M: 19.7319 c. 12: 1 3 8 N T3 SD: 10.1985 c. M:-14.2397 c. 13: 1 3 9 N T3 SD: 6.5169 c. M:-11.0471 c. 15: 1 4 10 N T3 SD: 6.9409 c. M:-10.4527 c. 16: 1 4 11 N T3 SD: 2.2312 c. M:-3.8637 c. 19: 1 5 13 N T3 SD: 1.1614 c. M:-1.7150 c. 35: 2 9 24 N T3 SD: 0.8875 c. M:-1.1956 c. 54: 3 14 37 N T3 SD: 0.7474 c. M:-1.2296 c. 74: 4 19 51 N T3 SD: 0.4837 c. M: 0.7646 c. 90: 5 23 62 N T3 SD: 0.4252 c. M: 0.6150 c. 93: 5 24 64 N T3 SD: 0.3184 c. M: 0.4875 c. 109: 6 28 75 N T3 SD: 0.1489 c. M: 0.2089 c. 128: 7 33 88 N T3 SD: 0.0470 c. M:-0.0767 c. 237: 13 61 163 N T3 SD: 0.0447 c. M:-0.0548 c. 365: 20 94 251 N T3 SD: 0.0158 c. M:-0.0260 c. 493: 27 127 339 N T3 SD: 0.0105 c. M:-0.0136 c. 1351: 74 348 929 N T3 SD: 0.0102 c. M:-0.0159 c. 1572: 86 405 1081 N T3 SD: 0.0101 c. M: 0.0174 c. 1681: 92 433 1156 N T3 SD: 0.0099 c. M: 0.0159 c. 1809: 99 466 1244 N T3 SD: 0.0070 c. M: 0.0093 c. 1937: 106 499 1332 N T3 SD: 0.0057 c. M: 0.0092 c. 2174: 119 560 1495 N T3 SD: 0.0055 c. M: 0.0092 c. 2302: 126 593 1583 N T3 SD: 0.0033 c. M: 0.0044 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: 90.4986 cents 6 x 7:8 S SD: 55.6543 cents 7 x 8:9 S SD: 49.1966 cents 8 x 9:11 SD: 35.9705 cents 9 x 10:12 S SD: 13.4207 cents 10 x 11:13 SD: 22.4182 cents 11 x 12:15 S SD: 19.6081 cents 12 x 13:16 SD: 8.4948 cents 13 x 14:17 SD: 21.6417 cents 14 x 15:19 SD: 23.6831 cents 15 x 16:20 S SD: 21.9155 cents 16 x 18:21 S SD: 27.7526 cents 17 x 19:23 SD: 22.4021 cents 18 x 20:24 S SD: 13.4207 cents 29:30:32:39 SD: 12.6023 cents 30:31:33:40 SD: 10.3256 cents 32:33:35:43 SD: 9.7647 cents 33:34:36:44 SD: 8.3034 cents 39:40:43:52 SD: 7.1179 cents 40:41:44:53 SD: 7.0454 cents 41:42:45:55 SD: 6.2453 cents 42:43:46:56 SD: 4.5368 cents 45:46:49:60 SD: 4.5033 cents 51:52:56:68 SD: 2.9949 cents 54:55:59:72 SD: 1.6787 cents 63:64:69:84 SD: 0.6437 cents 129:131:141:172 SD: 0.5649 cents 180:183:197:240 SD: 0.5039 cents 192:195:210:256 SD: 0.1993 cents 255:259:279:340 SD: 0.1186 cents 564:573:617:752 SD: 0.0536 cents