Scala analysis: 066_E6
Enharmonic tetrachord 312/307 * 307/297 * 33/26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 312/307 27.968848 2: 104/99 85.299718 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/26 412.7453 tridecimal major third 1: 312/307 27.9688 2: 307/297 57.3309 3: 33/26 412.7453 tridecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 312/307 27.969 cents 1: 1 307/297 57.331 cents 1: 1 33/26 412.745 cents tridecimal major third 2: 1 104/99 85.300 cents 2: 1 396/307 440.714 cents 2: 1 307/234 470.076 cents 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 : 28.0 85.3 498.0 28.0 : 57.3 470.1 498.0 85.3 : 412.7 440.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.9688 .. 412.7453 cents 3377/2704, 384.7764 cents 312/307, 27.9688 cents 2: 85.2997 .. 470.0762 cents 3377/2704, 384.7764 cents 2704/3267,-327.4456 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 312/307, 27.9688 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/26, 412.7453 cents Average / Smallest step : 5.935711 Largest / Average step : 2.486193 Largest / Smallest step : 14.757321 Median interval of one step : 307/297, 57.3309 cents, amount: 1 Least squares average step : 120.90738 cents, oct.: 362.72213 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2137-tone equal temperament with octave 4/3 degrees: 120 366 2137 Least number of segments generator : 1069 of 249.139 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2076 of 483.828 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 27.96885 cents Scale diversity : 0.288580 Lumma stability : 0.112315 Lumma impropriety factor : 0.657462 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 : 312/307, 27.9688 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 307 Odd number limit : 307 (O: 307 U: 307) Highest odd numerator or denominator: 307 Scale harmonicity : 0.019480 Fundamental : 1/30393, -14.8915 octaves, 0.0086 Hz. Guide tone : 312, 8.2854 octaves, 81627.176 Hz. Exponens Consonantiae : 9.482616E+06, 23.17685 octaves Euler's gradus suavitatis : 338 Sum of Mann's harmonic distance : 414.5, average 138.16667 Mersenne's string divisions : 125657 Sum of van Prooijen's expressibility: 4.95989, average 1.65330 Sum of Tenney's harmonic distance : 10.07314, average 3.35771 Vogel's harmonic complexity : 227.33333 Wille's k value : 5065 Wilson's harmonic complexity : 340 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 17.03744, average 2.83957 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -2 .. 1 -0.66667 4 1 11: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 307: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 23 28 61| Scale is weakly epimorphic with val: <6 10 24 29 59| Scale is weakly epimorphic with val: <6 10 25 30 60| Scale is weakly epimorphic with val: <6 11 23 30 60| Scale is weakly epimorphic with val: <7 10 23 25 60| Scale is weakly epimorphic with val: <7 10 24 26 61| Scale is weakly epimorphic with val: <7 10 25 27 59| Scale is weakly epimorphic with val: <7 10 26 28 60| Scale is weakly epimorphic with val: <7 10 27 29 61| Scale is weakly epimorphic with val: <7 11 23 25 61| Scale is weakly epimorphic with val: <7 11 23 26 60| Scale is weakly epimorphic with val: <7 11 23 28 61| Scale is weakly epimorphic with val: <7 11 23 29 60| Scale is weakly epimorphic with val: <7 11 24 26 59| Scale is weakly epimorphic with val: <7 11 24 27 61| Scale is weakly epimorphic with val: <7 11 24 29 59| Scale is weakly epimorphic with val: <7 11 24 30 61| Scale is weakly epimorphic with val: <7 11 25 25 59| Scale is weakly epimorphic with val: <7 11 25 27 60| = patent Scale is JI-epimorphic with val: <7 11 25 28 59| Scale is weakly epimorphic with val: <7 11 25 30 60| Scale is weakly epimorphic with val: <7 11 26 26 60| Scale is weakly epimorphic with val: <7 11 26 28 61| Scale is JI-epimorphic with val: <7 11 26 29 60| Scale is weakly epimorphic with val: <7 11 27 27 61| Scale is weakly epimorphic with val: <7 11 27 29 59| Scale is JI-epimorphic with val: <7 11 27 30 61| Scale is weakly epimorphic with val: <7 12 23 29 61| Scale is weakly epimorphic with val: <7 12 23 30 60| Scale is weakly epimorphic with val: <7 12 24 30 59| Scale is weakly epimorphic with val: <7 12 25 29 59| Scale is weakly epimorphic with val: <7 12 26 30 60| Scale is weakly epimorphic with val: <8 11 23 28 60| Scale is weakly epimorphic with val: <8 11 24 25 59| Scale is weakly epimorphic with val: <8 11 24 29 61| Scale is weakly epimorphic with val: <8 11 25 26 60| Scale is weakly epimorphic with val: <8 11 25 27 59| Scale is weakly epimorphic with val: <8 11 26 27 61| Scale is weakly epimorphic with val: <8 11 26 28 60| Scale is weakly epimorphic with val: <8 11 27 28 59| Scale is weakly epimorphic with val: <8 11 27 29 61| Scale is weakly epimorphic with val: <8 12 23 26 60| Scale is weakly epimorphic with val: <8 12 23 28 61| Scale is weakly epimorphic with val: <8 12 24 26 59| Scale is weakly epimorphic with val: <8 12 24 27 61| Scale is weakly epimorphic with val: <8 12 25 27 60| Scale is weakly epimorphic with val: <8 12 25 28 59| Scale is weakly epimorphic with val: <8 12 26 28 61| Scale is weakly epimorphic with val: <8 12 26 29 60| Scale is weakly epimorphic with val: <8 12 27 30 61|
FIT/MODE
3: 0 0 3 N M DE S SD: 51.8276 c. M: 85.2997 c. 4: 0 1 3 N G T3 SD: 27.8077 c. M:-39.2115 c. 5: 0 1 4 N G T3 SD: 18.1385 c. M: 27.9688 c. 6: 0 1 5 N G T3 SD: 16.2020 c. M: 27.9688 c. 7: 0 1 6 N G T3 SD: 18.0969 c. M: 27.9688 c. 10: 1 1 8 N M DE S SD: 15.0726 c. M:-21.8357 c. 11: 1 1 9 N M DE S SD: 10.4430 c. M:-17.3080 c. 12: 1 1 10 N M DE S SD: 7.9257 c. M:-13.5349 c. 13: 1 1 11 N M DE S SD: 7.7945 c. M:-10.3423 c. 15: 1 2 12 N T3 SD: 8.7968 c. M:-14.3093 c. 16: 1 2 13 N T3 SD: 5.0108 c. M:-8.0837 c. 17: 1 2 14 N T3 SD: 1.6807 c. M:-2.5906 c. 18: 1 2 15 N T3 SD: 1.3347 c. M: 2.2922 c. 35: 2 4 29 N T3 SD: 0.2871 c. M:-0.4909 c. 88: 5 10 73 N T3 SD: 0.3016 c. M: 0.4057 c. 123: 7 14 102 N T3 SD: 0.2661 c. M:-0.3752 c. 158: 9 18 131 N T3 SD: 0.2563 c. M:-0.4008 c. 181: 10 21 150 N T3 SD: 0.2613 c. M: 0.4525 c. 193: 11 22 160 N T3 SD: 0.2544 c. M:-0.4171 c. 198: 11 23 164 N T3 SD: 0.2157 c. M: 0.2997 c. 216: 12 25 179 N T3 SD: 0.1732 c. M: 0.2997 c. 233: 13 27 193 N T3 SD: 0.1564 c. M:-0.2016 c. 251: 14 29 208 N T3 SD: 0.1102 c. M: 0.1894 c. 268: 15 31 222 N T3 SD: 0.1199 c. M:-0.1856 c. 269: 15 31 223 N T3 SD: 0.1369 c. M: 0.1968 c. 286: 16 33 237 N T3 SD: 0.0637 c. M: 0.1062 c. 321: 18 37 266 N T3 SD: 0.0312 c. M: 0.0411 c. 356: 20 41 295 N T3 SD: 0.0237 c. M:-0.0395 c. 677: 38 78 561 N T3 SD: 0.0230 c. M:-0.0374 c. 695: 39 80 576 N T3 SD: 0.0180 c. M: 0.0229 c. 730: 41 84 605 N T3 SD: 0.0106 c. M: 0.0180 c. 1051: 59 121 871 N T3 SD: 0.0059 c. M: 0.0101 c. 1086: 61 125 900 N T3 SD: 0.0035 c. M:-0.0061 c. 2137: 120 246 1771 N T3 SD: 0.0011 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 90.7856 cents 7 x 8:9 S SD: 79.4409 cents 8 x 9:11 SD: 65.0123 cents 9 x 10:12 S SD: 48.5520 cents 10 x 11:13 SD: 45.4807 cents 11 x 12:15 S SD: 38.0218 cents 12 x 13:16 SD: 26.6365 cents 13 x 14:17 SD: 27.2901 cents 14 x 15:19 SD: 22.9384 cents 15 x 16:20 S SD: 13.2158 cents 16 x 17:21 SD: 16.8053 cents 17 x 18:23 SD: 14.3634 cents 18 x 19:24 SD: 4.1516 cents 19 x 20:25 S SD: 11.5982 cents 20 x 21:27 SD: 10.7612 cents 21 x 22:28 SD: 2.3813 cents 22 x 23:29 SD: 10.7365 cents 23 x 24:31 SD: 11.0148 cents 24 x 25:32 SD: 7.3136 cents 25 x 26:33 SD: 12.3033 cents 26 x 27:35 SD: 12.9707 cents 27 x 28:36 SD: 11.1694 cents 28 x 29:37 SD: 14.5233 cents 29 x 30:39 SD: 15.2384 cents 30 x 32:40 S SD: 13.2158 cents 31:32:33:41 SD: 12.6991 cents 32:33:34:43 SD: 11.5862 cents 33:34:35:44 SD: 9.6425 cents 35:36:37:47 SD: 8.8409 cents 36:37:38:48 SD: 7.0541 cents 38:39:40:51 SD: 6.9134 cents 39:40:41:52 SD: 5.3046 cents 42:43:44:56 SD: 4.5424 cents 54:55:57:72 SD: 3.0435 cents 57:58:60:76 SD: 1.3678 cents 60:61:63:80 SD: 0.3515 cents 237:241:249:316 SD: 0.3428 cents 297:302:312:396 SD: 0.3113 cents 315:320:331:420 SD: 0.2834 cents 375:381:394:500 SD: 0.1854 cents 435:442:457:580 SD: 0.1170 cents 495:503:520:660 SD: 0.0710 cents 555:564:583:740 SD: 0.0500 cents