Scala analysis: 053_E3
Enharmonic tetrachord 480/473 * 473/459 * 51/40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 480/473 25.433067 2: 160/153 77.448303 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 51/40 420.5967 septendecimal diminished fourth 1: 480/473 25.4331 2: 473/459 52.0152 3: 51/40 420.5967 septendecimal diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 480/473 25.433 cents 1: 1 473/459 52.015 cents 1: 1 51/40 420.597 cents septendecimal diminished fourth 2: 1 160/153 77.448 cents 2: 1 612/473 446.030 cents 2: 1 473/360 472.612 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 : 25.4 77.4 498.0 25.4 : 52.0 472.6 498.0 77.4 : 420.6 446.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.4331 .. 420.5967 cents 8041/6400, 395.1636 cents 480/473, 25.4331 cents 2: 77.4483 .. 472.6119 cents 8041/6400, 395.1636 cents 6400/7803,-343.1484 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 480/473, 25.4331 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 51/40, 420.5967 cents Average / Smallest step : 6.527526 Largest / Average step : 2.533486 Largest / Smallest step : 16.537396 Median interval of one step : 473/459, 52.0152 cents, amount: 1 Least squares average step : 119.60462 cents, oct.: 358.81386 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1704-tone equal temperament with octave 4/3 degrees: 87 265 1704 Least number of segments generator : 853 of 249.315 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 937 of 273.866 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 25.43307 cents Scale diversity : 0.234042 Lumma stability : 0.102132 Lumma impropriety factor : 0.688991 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 : 480/473, 25.4331 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% Limited inverse transpositions with margin 368.5815 cents: 2 -- Rational properties -- Prime limit : 43 Odd number limit : 473 (O: 473 U: 473) Highest odd numerator or denominator: 473 Scale harmonicity : 0.014771 Fundamental : 1/72369, -16.1431 octaves, 0.0036 Hz. Guide tone : 480, 8.9069 octaves, 125580.271 Hz. Exponens Consonantiae : 3.473712E+07, 25.04997 octaves Euler's gradus suavitatis : 84 Sum of Mann's harmonic distance : 636.5, average 212.16667 Mersenne's string divisions : 2088023 Sum of van Prooijen's expressibility: 5.33667, average 1.77889 Sum of Tenney's harmonic distance : 10.82410, average 3.60803 Vogel's harmonic complexity : 58.66667 Wille's k value : 12061 Wilson's harmonic complexity : 85 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 23.74904, average 3.95817 Lattice compactness (without 2's) : 12.67971, average 2.11328 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 4.00000 12 3: -2 .. 1 -0.66667 4 1 5: 0 .. 1 0.66667 2 11: -1 .. 0 -0.33333 1 17: -1 .. 0 -0.33333 1 1 43: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <7 11 16 24 30 37| Scale is weakly epimorphic with val: <7 11 16 24 30 40| Scale is weakly epimorphic with val: <7 11 16 24 31 39| Scale is weakly epimorphic with val: <7 11 16 25 30 39| Scale is weakly epimorphic with val: <7 11 16 25 31 38| Scale is weakly epimorphic with val: <7 11 16 25 31 41| Scale is weakly epimorphic with val: <7 11 16 26 30 38| Scale is weakly epimorphic with val: <7 11 16 26 30 41| Scale is weakly epimorphic with val: <7 11 16 26 31 37| Scale is weakly epimorphic with val: <7 11 16 26 31 40| Scale is weakly epimorphic with val: <7 11 17 24 29 37| Scale is weakly epimorphic with val: <7 11 17 24 29 40| Scale is weakly epimorphic with val: <7 11 17 24 31 38| Scale is weakly epimorphic with val: <7 11 17 24 31 41| Scale is weakly epimorphic with val: <7 11 17 25 29 39| Scale is weakly epimorphic with val: <7 11 17 25 31 37| Scale is weakly epimorphic with val: <7 11 17 25 31 40| Scale is weakly epimorphic with val: <7 11 17 26 29 38| Scale is weakly epimorphic with val: <7 11 17 26 29 41| Scale is weakly epimorphic with val: <7 11 17 26 31 39| Scale is JI-epimorphic with val: <7 11 18 24 29 39| Scale is weakly epimorphic with val: <7 11 18 24 30 38| Scale is weakly epimorphic with val: <7 11 18 24 30 41| Scale is JI-epimorphic with val: <7 11 18 25 29 38| Scale is weakly epimorphic with val: <7 11 18 25 29 41| Scale is weakly epimorphic with val: <7 11 18 25 30 37| Scale is weakly epimorphic with val: <7 11 18 25 30 40| Scale is JI-epimorphic with val: <7 11 18 26 29 37| Scale is weakly epimorphic with val: <7 11 18 26 29 40| Scale is weakly epimorphic with val: <7 11 18 26 30 39| Scale is weakly epimorphic with val: <7 12 17 24 30 37| Scale is weakly epimorphic with val: <7 12 18 24 31 38| Scale is weakly epimorphic with val: <7 12 18 25 31 37|
FIT/MODE
3: 0 0 3 N M DE S SD: 47.0641 c. M: 77.4483 c. 4: 0 1 3 N G T3 SD: 30.8856 c. M:-47.0629 c. 5: 0 1 4 N G T3 SD: 19.4759 c. M: 25.4331 c. 6: 0 1 5 N G T3 SD: 15.0305 c. M: 25.4331 c. 7: 0 1 6 N G T3 SD: 15.1274 c. M: 25.4331 c. 8: 0 1 7 N G T3 SD: 17.1042 c. M: 25.4331 c. 11: 1 1 9 N M DE S SD: 13.7298 c. M:-19.8438 c. 12: 1 1 10 N M DE S SD: 9.8179 c. M:-16.0707 c. 13: 1 1 11 N M DE S SD: 7.4504 c. M:-12.8781 c. 14: 1 1 12 N M DE S SD: 6.8927 c. M:-10.1416 c. 17: 1 2 14 N T3 SD: 6.4282 c. M:-10.4420 c. 18: 1 2 15 N T3 SD: 3.4595 c. M:-5.5592 c. 19: 1 2 16 N T3 SD: 0.8216 c. M:-1.1904 c. 39: 2 4 33 N T3 SD: 0.4809 c. M: 0.8260 c. 58: 3 6 49 N T3 SD: 0.2120 c. M:-0.3279 c. 135: 7 14 114 N T3 SD: 0.2265 c. M:-0.3915 c. 193: 10 20 163 N T3 SD: 0.2158 c. M:-0.3724 c. 212: 11 22 179 N T3 SD: 0.2403 c. M:-0.4089 c. 213: 11 22 180 N T3 SD: 0.2343 c. M:-0.2876 c. 218: 11 23 184 N T3 SD: 0.2188 c. M: 0.3024 c. 219: 11 23 185 N T3 SD: 0.2516 c. M: 0.4171 c. 237: 12 25 200 N T3 SD: 0.2159 c. M:-0.3056 c. 238: 12 25 201 N T3 SD: 0.1861 c. M: 0.3216 c. 257: 13 27 217 N T3 SD: 0.1442 c. M: 0.2401 c. 276: 14 29 233 N T3 SD: 0.1292 c. M: 0.1699 c. 296: 15 31 250 N T3 SD: 0.1158 c. M: 0.1943 c. 315: 16 33 266 N T3 SD: 0.0796 c. M: 0.1355 c. 334: 17 35 282 N T3 SD: 0.0716 c. M:-0.0916 c. 354: 18 37 299 N T3 SD: 0.0742 c. M: 0.1087 c. 373: 19 39 315 N T3 SD: 0.0367 c. M: 0.0635 c. 392: 20 41 331 N T3 SD: 0.0336 c. M:-0.0536 c. 431: 22 45 364 N T3 SD: 0.0163 c. M: 0.0260 c. 450: 23 47 380 N T3 SD: 0.0196 c. M:-0.0254 c. 823: 42 86 695 N T3 SD: 0.0117 c. M: 0.0164 c. 881: 45 92 744 N T3 SD: 0.0036 c. M:-0.0062 c. 1704: 87 178 1439 N T3 SD: 0.0044 c. M:-0.0059 c. 2135: 109 223 1803 N T3 SD: 0.0034 c. M: 0.0059 c. 2193: 112 229 1852 N T3 SD: 0.0033 c. M: 0.0049 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: 94.7113 cents 7 x 8:9 S SD: 83.0598 cents 8 x 9:11 SD: 68.6123 cents 9 x 10:12 S SD: 52.4777 cents 10 x 11:13 SD: 48.9571 cents 11 x 12:15 S SD: 41.4435 cents 12 x 13:16 SD: 30.5622 cents 13 x 14:17 SD: 30.4788 cents 14 x 15:19 SD: 25.9927 cents 15 x 16:20 S SD: 17.1415 cents 16 x 17:21 SD: 19.3647 cents 17 x 18:23 SD: 16.5929 cents 18 x 19:24 SD: 8.0774 cents 19 x 20:25 S SD: 12.7934 cents 20 x 21:27 SD: 11.3113 cents 21 x 22:28 SD: 1.5444 cents 22 x 23:29 SD: 9.8959 cents 23 x 24:31 SD: 9.5458 cents 24 x 25:32 SD: 3.3879 cents 25 x 26:33 SD: 9.9236 cents 26 x 27:35 SD: 10.2608 cents 27 x 28:36 SD: 7.2437 cents 28 x 29:37 SD: 11.4004 cents 29 x 30:39 SD: 11.9651 cents 30 x 31:40 SD: 10.3407 cents 31 x 32:41 SD: 13.2480 cents 32 x 33:43 SD: 13.8380 cents 33 x 35:44 SD: 12.2092 cents 34:35:36:45 S SD: 11.7302 cents 35:36:37:47 SD: 10.7922 cents 36:37:38:48 SD: 9.0983 cents 38:39:40:51 SD: 8.4290 cents 39:40:41:52 SD: 6.8465 cents 41:42:43:55 SD: 6.6754 cents 42:43:44:56 SD: 5.2041 cents 45:46:47:60 SD: 4.2673 cents 48:49:50:64 SD: 4.0996 cents 57:58:60:76 SD: 4.0926 cents 59:60:62:79 SD: 3.9134 cents 60:61:63:80 SD: 2.5690 cents 63:64:66:84 SD: 1.1969 cents 66:67:69:88 SD: 0.2589 cents 414:420:433:552 SD: 0.1911 cents 480:487:502:640 SD: 0.1308 cents 546:554:571:728 SD: 0.0860 cents