Scala analysis: 526_M34
Miscellaneous tetrachord 64/63 * 2187/2048 * 896/729
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: 243/224 140.949098 Archytas' 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 896/729 357.0959 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 2187/2048 113.6850 apotome 3: 896/729 357.0959
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 2187/2048 113.685 cents apotome 1: 1 896/729 357.096 cents 2: 1 243/224 140.949 cents Archytas' 2/3-tone 2: 1 8192/6561 384.360 cents Pythagorean diminished fourth 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 : 27.3 140.9 498.0 27.3 : 113.7 470.8 498.0 140.9: 357.1 384.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 357.0959 cents 98/81, 329.8318 cents 64/63, 27.2641 cents 2: 140.9491 .. 470.7809 cents 98/81, 329.8318 cents 177147/200704,-216.1468 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 : 896/729, 357.0959 cents Average / Smallest step : 6.089145 Largest / Average step : 2.150986 Largest / Smallest step : 13.097664 Median interval of one step : 2187/2048, 113.6850 cents, amount: 1 Least squares average step : 128.80695 cents, oct.: 386.42085 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2265-tone equal temperament with octave 4/3 degrees: 124 641 2265 Least number of segments generator : 1133 of 249.132 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1879 of 413.168 cents and inv. generated superset size: 60 = 57 more = 2000.000% 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 : 0.563088 Lumma stability : 0.109484 Lumma impropriety factor : 0.433991 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 : 7 Odd number limit : 6561 (O: 2187 U: 6561) Highest odd numerator or denominator: 243 Scale harmonicity : 0.025030 Average absolute harmonicity : 0.098494 Specific harmonicity : 0.118686 Fundamental : 1/2016, -10.9773 octaves, 0.1298 Hz. Guide tone : 15552, 13.9248 octaves, 4068800.792 Hz. Exponens Consonantiae : 3.135283E+07, 24.90209 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 300.5, average 100.16667 Mersenne's string divisions : 415163 Sum of van Prooijen's expressibility: 4.66207, average 1.55402 Sum of Tenney's harmonic distance : 9.42056, average 3.14019 Vogel's harmonic complexity : 16.33333 Wille's k value : 1093 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 8 Triangular lattice diameter : 7 Lattice compactness : 42.33528, average 7.05588 Lattice compactness (without 2's) : 22.83206, average 3.80534 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 1.00000 13 3: -2 .. 5 0.66667 8 1 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <7 10 19| Scale is weakly epimorphic with val: <8 12 21|
FIT/MODE
3: 0 1 2 N G T3 SD: 21.3825 c. M: 27.2641 c. 4: 0 1 3 N G T3 SD: 18.3805 c. M: 27.2641 c. 7: 0 2 5 N G T3 SD: 15.7602 c. M: 27.2641 c. 10: 1 2 7 N T3 SD: 13.9010 c. M:-22.5404 c. 11: 1 2 8 N T3 SD: 10.8114 c. M:-18.0127 c. 12: 1 2 9 N T3 SD: 12.5562 c. M: 16.4378 c. 13: 1 3 9 N T3 SD: 9.5432 c. M:-12.2955 c. 14: 1 3 10 N T3 SD: 4.8609 c. M:-8.3106 c. 15: 1 3 11 N T3 SD: 5.8162 c. M: 8.1371 c. 17: 1 4 12 N T3 SD: 3.4042 c. M:-5.5347 c. 18: 1 4 13 N T3 SD: 1.5211 c. M: 2.6033 c. 35: 2 8 25 N T3 SD: 1.0409 c. M:-1.3495 c. 39: 2 9 28 N T3 SD: 1.0320 c. M: 1.7233 c. 53: 3 12 38 N T3 SD: 0.5353 c. M:-0.9271 c. 71: 4 16 51 N T3 SD: 0.5945 c. M:-0.7948 c. 74: 4 17 53 N T3 SD: 0.2989 c. M:-0.3880 c. 92: 5 21 66 N T3 SD: 0.1607 c. M: 0.1973 c. 145: 8 33 104 N T3 SD: 0.1425 c. M:-0.2143 c. 219: 12 50 157 N T3 SD: 0.0325 c. M:-0.0499 c. 311: 17 71 223 N T3 SD: 0.0266 c. M: 0.0398 c. 530: 29 121 380 N T3 SD: 0.0083 c. M: 0.0126 c. 1424: 78 325 1021 N T3 SD: 0.0095 c. M:-0.0165 c. 1516: 83 346 1087 N T3 SD: 0.0070 c. M: 0.0116 c. 1735: 95 396 1244 N T3 SD: 0.0043 c. M:-0.0064 c. 1954: 107 446 1401 N T3 SD: 0.0051 c. M:-0.0086 c. 2046: 112 467 1467 N T3 SD: 0.0039 c. M: 0.0067 c. 2265: 124 517 1624 N T3 SD: 0.0013 c. M:-0.0019 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: 97.0207 cents 6 x 7:8 S SD: 62.9609 cents 7 x 8:9 S SD: 55.0105 cents 8 x 9:11 SD: 41.2374 cents 9 x 10:12 S SD: 20.7273 cents 10 x 11:13 SD: 24.9991 cents 11 x 12:15 S SD: 20.0469 cents 12 x 13:16 SD: 1.1882 cents 13 x 14:17 SD: 17.9594 cents 14 x 15:19 SD: 18.7180 cents 15 x 16:20 S SD: 14.6089 cents 16 x 17:21 SD: 22.5770 cents 17 x 18:23 SD: 24.5067 cents 18 x 20:24 S SD: 20.7273 cents 19 x 21:25 SD: 19.8136 cents 20 x 22:27 SD: 16.1336 cents 24:25:26:32 SD: 14.4911 cents 26:27:28:35 S SD: 14.4687 cents 27:28:29:36 SD: 13.2135 cents 30:31:33:40 SD: 12.6889 cents 31:32:34:41 SD: 12.1276 cents 32:33:35:43 SD: 10.8492 cents 33:34:36:44 SD: 8.7567 cents 35:36:38:47 SD: 8.2757 cents 36:37:39:48 SD: 6.7698 cents 44:45:48:59 SD: 6.0148 cents 45:46:49:60 SD: 4.1943 cents 48:49:52:64 SD: 2.9204 cents 57:58:62:76 SD: 1.8082 cents 60:61:65:80 SD: 0.9114 cents 117:119:127:156 SD: 0.7743 cents 129:131:140:172 SD: 0.3182 cents 189:192:205:252 SD: 0.0880 cents 507:515:550:676 SD: 0.0536 cents