Scala analysis: 312_C24
Chromatic tetrachord 64/63 * 9/8 * 7/6, Barbour
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: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 9/8 203.9100 major whole tone 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 9/8 203.910 cents major whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 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 : 27.3 231.2 498.0 27.3 : 203.9 470.8 498.0 231.2: 266.9 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 266.8709 cents 147/128, 239.6068 cents 64/63, 27.2641 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 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 : 7/6, 266.8709 cents Average / Smallest step : 6.089145 Largest / Average step : 1.607511 Largest / Smallest step : 9.788366 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 141.69623 cents, oct.: 425.08870 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2247-tone equal temperament with octave 4/3 degrees: 123 1043 2247 Least number of segments generator : 1124 of 249.133 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1327 of 294.128 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 : 0.549395 Lumma stability : 0.109484 Lumma impropriety factor : 0.071674 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 All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 63 Scale harmonicity : 0.046256 Average absolute harmonicity : 0.111936 Specific harmonicity : 0.203021 Fundamental : 1/63, -5.9773 octaves, 4.1528 Hz. Guide tone : 64, 6.0000 octaves, 16744.036 Hz. Exponens Consonantiae : 4.032000E+03, 11.97728 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 74.5, average 24.83333 Mersenne's string divisions : 13335 Sum of van Prooijen's expressibility: 3.12156, average 1.04052 Sum of Tenney's harmonic distance : 6.43289, average 2.14430 Vogel's harmonic complexity : 9.00000 Wille's k value : 10 Wilson's harmonic complexity : 13 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 21.38171, average 3.56362 Lattice compactness (without 2's) : 9.06450, average 1.51075 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 3.66667 11 3: -2 .. 0 -1.00000 3 1 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 19| Scale is JI-epimorphic with val: <7 11 19| Scale is weakly epimorphic with val: <7 11 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 40.7801 c. M: 65.1591 c. 4: 0 2 2 P M DE S SD: 18.8140 c. M: 27.2641 c. 7: 0 3 4 N G T3 SD: 18.7754 c. M: 27.2641 c. 9: 0 4 5 N G T3 SD: 16.7310 c. M: 27.2641 c. 11: 1 4 6 N T3 SD: 10.7611 c. M:-18.0127 c. 13: 1 5 7 N T3 SD: 6.4225 c. M:-11.0471 c. 15: 1 6 8 N T3 SD: 3.5036 c. M:-5.9389 c. 17: 1 7 9 N T3 SD: 2.1888 c. M:-3.2000 c. 35: 2 14 19 N T3 SD: 2.1334 c. M: 3.4964 c. 37: 2 15 20 N T3 SD: 1.3669 c. M: 2.3426 c. 39: 2 16 21 N T3 SD: 1.2488 c. M: 1.7233 c. 52: 3 21 28 N T3 SD: 1.1354 c. M:-1.4693 c. 54: 3 22 29 N T3 SD: 0.4169 c. M: 0.5977 c. 56: 3 23 30 N T3 SD: 0.3385 c. M: 0.5831 c. 110: 6 45 59 N T3 SD: 0.1617 c. M: 0.2623 c. 127: 7 52 68 N T3 SD: 0.1586 c. M:-0.2011 c. 181: 10 74 97 N T3 SD: 0.1472 c. M:-0.2522 c. 183: 10 75 98 N T3 SD: 0.0956 c. M:-0.1583 c. 237: 13 97 127 N T3 SD: 0.0327 c. M:-0.0548 c. 420: 23 172 225 N T3 SD: 0.0357 c. M:-0.0611 c. 530: 29 217 284 N T3 SD: 0.0081 c. M: 0.0126 c. 767: 42 314 411 N T3 SD: 0.0068 c. M: 0.0085 c. 1297: 71 531 695 N T3 SD: 0.0043 c. M: 0.0075 c. 1827: 100 748 979 N T3 SD: 0.0046 c. M: 0.0071 c. 2247: 123 920 1204 N T3 SD: 0.0034 c. M:-0.0057 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11 x 13:15 SD: 34.9349 cents 12 x 14:16 S SD: 17.8484 cents 21:22:24:28 S SD: 17.7576 cents 24:25:27:32 SD: 17.0868 cents 25:26:29:33 SD: 17.0568 cents 26:27:30:35 S SD: 14.9015 cents 27:28:31:36 SD: 12.1938 cents 29:30:33:39 SD: 11.8530 cents 30:31:34:40 SD: 10.9560 cents 33:34:38:44 SD: 9.2314 cents 34:35:39:45 SD: 8.9996 cents 35:36:40:47 SD: 8.2620 cents 36:37:41:48 SD: 7.0165 cents 41:42:47:55 SD: 6.2135 cents 42:43:48:56 SD: 4.4909 cents 48:49:55:64 SD: 3.1865 cents 54:55:62:72 SD: 3.0590 cents 56:57:64:75 SD: 2.8063 cents 57:58:65:76 SD: 1.5825 cents 63:64:72:84 S SD: 0.0000 cents