Scala analysis: 525_M33
Miscellaneous tetrachord 64/63 * 16/15 * 315/256
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: 1024/945 138.995377 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 315/256 359.0496 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 16/15 111.7313 minor diatonic semitone 3: 315/256 359.0496
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 315/256 359.050 cents 2: 1 1024/945 138.995 cents 2: 1 5/4 386.314 cents major 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 : 27.3 139.0 498.0 27.3 : 111.7 470.8 498.0 139.0: 359.0 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 359.0496 cents 19845/16384, 331.7855 cents 64/63, 27.2641 cents 2: 138.9954 .. 470.7809 cents 19845/16384, 331.7855 cents 262144/297675,-220.0542 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 : 315/256, 359.0496 cents Average / Smallest step : 6.089145 Largest / Average step : 2.162754 Largest / Smallest step : 13.169323 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 128.52785 cents, oct.: 385.58354 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1315-tone equal temperament with octave 4/3 degrees: 72 367 1315 Least number of segments generator : 658 of 249.212 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 984 of 372.682 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 : 0.556053 Lumma stability : 0.109484 Lumma impropriety factor : 0.441836 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 : 7 Odd number limit : 945 (O: 315 U: 945) Highest odd numerator or denominator: 945 Scale harmonicity : 0.028830 Average absolute harmonicity : 0.096457 Specific harmonicity : 0.132221 Fundamental : 1/945, -9.8842 octaves, 0.2769 Hz. Guide tone : 1024, 10.0000 octaves, 267904.579 Hz. Exponens Consonantiae : 9.676800E+05, 19.88417 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 1051.5, average 350.50000 Mersenne's string divisions : 1750441 Sum of van Prooijen's expressibility: 5.25189, average 1.75063 Sum of Tenney's harmonic distance : 10.67043, average 3.55681 Vogel's harmonic complexity : 14.66667 Wille's k value : 157 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 36.02673, average 6.00445 Lattice compactness (without 2's) : 11.83061, average 1.97177 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 10 6.00000 18 3: -3 ..-1 -2.00000 6 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-9 / 3 =-3.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 17 20| Scale is weakly epimorphic with val: <7 10 19 19| Scale is weakly epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <8 12 15 21| Scale is weakly epimorphic with val: <8 12 18 21| Scale is weakly epimorphic with val: <8 12 19 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 22.1615 c. M: 27.2641 c. 4: 0 1 3 N G T3 SD: 17.8243 c. M: 27.2641 c. 7: 0 2 5 N G T3 SD: 15.8560 c. M: 27.2641 c. 10: 1 2 7 N T3 SD: 14.3365 c. M:-22.5404 c. 11: 1 2 8 N T3 SD: 10.5590 c. M:-18.0127 c. 12: 1 2 9 N T3 SD: 11.7269 c. M: 14.4841 c. 13: 1 3 9 N T3 SD: 10.4096 c. M:-14.2492 c. 14: 1 3 10 N T3 SD: 5.1632 c. M:-8.3106 c. 15: 1 3 11 N T3 SD: 4.9499 c. M: 6.1834 c. 17: 1 4 12 N T3 SD: 4.4799 c. M:-7.4884 c. 18: 1 4 13 N T3 SD: 0.4420 c. M: 0.6495 c. 93: 5 21 67 N T3 SD: 0.3145 c. M: 0.4875 c. 111: 6 25 80 N T3 SD: 0.2059 c. M: 0.3427 c. 129: 7 29 93 N T3 SD: 0.1377 c. M: 0.2384 c. 147: 8 33 106 N T3 SD: 0.1044 c. M: 0.1596 c. 165: 9 37 119 N T3 SD: 0.1017 c. M: 0.1465 c. 312: 17 70 225 N T3 SD: 0.0999 c. M: 0.1270 c. 383: 21 86 276 N T3 SD: 0.0875 c. M:-0.1451 c. 401: 22 90 289 N T3 SD: 0.0721 c. M:-0.1095 c. 419: 23 94 302 N T3 SD: 0.0620 c. M:-0.0769 c. 437: 24 98 315 N T3 SD: 0.0578 c. M:-0.0885 c. 530: 29 119 382 N T3 SD: 0.0475 c. M:-0.0813 c. 548: 30 123 395 N T3 SD: 0.0331 c. M:-0.0573 c. 566: 31 127 408 N T3 SD: 0.0217 c. M:-0.0349 c. 584: 32 131 421 N T3 SD: 0.0170 c. M:-0.0260 c. 713: 39 160 514 N T3 SD: 0.0139 c. M: 0.0218 c. 731: 40 164 527 N T3 SD: 0.0074 c. M: 0.0113 c. 1297: 71 291 935 N T3 SD: 0.0068 c. M:-0.0118 c. 1315: 72 295 948 N T3 SD: 0.0034 c. M:-0.0053 c. 2046: 112 459 1475 N T3 SD: 0.0004 c. M: 0.0006 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: 97.9011 cents 6 x 7:8 S SD: 63.9378 cents 7 x 8:9 S SD: 55.8144 cents 8 x 9:11 SD: 41.9878 cents 9 x 10:12 S SD: 21.7042 cents 10 x 11:13 SD: 25.4834 cents 11 x 12:15 S SD: 20.3051 cents 12 x 13:16 SD: 0.2114 cents 13 x 14:17 SD: 17.6391 cents 14 x 15:19 SD: 18.1744 cents 15 x 16:20 S SD: 13.6320 cents 16 x 17:21 SD: 21.8062 cents 17 x 18:23 SD: 23.6751 cents 18 x 20:24 S SD: 21.7042 cents 19 x 21:25 SD: 20.6181 cents 20 x 22:27 SD: 16.8744 cents 23:24:25:31 SD: 16.7780 cents 24:25:26:32 SD: 14.4701 cents 26:27:28:35 S SD: 14.2924 cents 27:28:29:36 SD: 12.9436 cents 31:32:34:41 SD: 12.4795 cents 32:33:35:43 SD: 11.1485 cents 33:34:36:44 SD: 9.0172 cents 35:36:38:47 SD: 8.3384 cents 36:37:39:48 SD: 6.7248 cents 39:40:42:52 SD: 6.5735 cents 44:45:48:59 SD: 6.3881 cents 45:46:49:60 SD: 4.5639 cents 47:48:51:63 SD: 4.4033 cents 48:49:52:64 SD: 2.8144 cents 57:58:62:76 SD: 2.3872 cents 60:61:65:80 SD: 0.4722 cents 132:134:143:176 SD: 0.4335 cents 192:195:208:256 SD: 0.1993 cents 252:256:273:336 SD: 0.1409 cents 501:509:543:668 SD: 0.1360 cents 573:582:621:764 SD: 0.1315 cents