Scala analysis: 048_E1
Enharmonic tetrachord 60/59 * 118/115 * 23/18
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 24/23 73.680654 vicesimotertial minor semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/18 424.3643 vicesimotertial major third 1: 60/59 29.0971 2: 118/115 44.5836 3: 23/18 424.3643 vicesimotertial major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 118/115 44.584 cents 1: 1 23/18 424.364 cents vicesimotertial major third 2: 1 24/23 73.681 cents vicesimotertial minor semitone 2: 1 230/177 453.461 cents 2: 1 59/45 468.948 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 : 29.1 73.7 498.0 29.1 : 44.6 468.9 498.0 73.7 : 424.4 453.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 424.3643 cents 1357/1080, 395.2673 cents 60/59, 29.0971 cents 2: 73.6807 .. 468.9479 cents 1357/1080, 395.2673 cents 432/529,-350.6837 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/18, 424.3643 cents Average / Smallest step : 5.705560 Largest / Average step : 2.556181 Largest / Smallest step : 14.584443 Median interval of one step : 118/115, 44.5836 cents, amount: 1 Least squares average step : 119.32810 cents, oct.: 357.98429 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1318-tone equal temperament with octave 4/3 degrees: 77 195 1318 Least number of segments generator : 661 of 249.778 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 759 of 286.810 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 29.09706 cents Scale diversity : 0.220107 Lumma stability : 0.116845 Lumma impropriety factor : 0.704120 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 : 3481/3450, 15.4865 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% Limited inverse transpositions with margin 379.7807 cents: 2 -- Rational properties -- Prime limit : 59 Odd number limit : 177 (O: 115 U: 177) Highest odd numerator or denominator: 59 Scale harmonicity : 0.017599 Fundamental : 1/4071, -11.9912 octaves, 0.0643 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 4.885200E+05, 18.89806 octaves Euler's gradus suavitatis : 92 Sum of Mann's harmonic distance : 86.5, average 28.83333 Mersenne's string divisions : 5593 Sum of van Prooijen's expressibility: 3.60970, average 1.20323 Sum of Tenney's harmonic distance : 7.37012, average 2.45671 Vogel's harmonic complexity : 62.66667 Wille's k value : 678 Wilson's harmonic complexity : 93 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.41979, average 2.40330 Lattice compactness (without 2's) : 9.71478, average 1.61913 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.33333 1 23: -1 .. 0 -0.33333 1 1 59: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is weakly epimorphic with val: <7 11 15 31 44| Scale is weakly epimorphic with val: <7 11 15 33 42| Scale is weakly epimorphic with val: <7 11 15 34 44| Scale is weakly epimorphic with val: <7 11 15 36 42| Scale is weakly epimorphic with val: <7 11 16 30 43| Scale is weakly epimorphic with val: <7 11 16 31 42| Scale is weakly epimorphic with val: <7 11 16 33 43| Scale is weakly epimorphic with val: <7 11 16 34 42| Scale is weakly epimorphic with val: <7 11 16 36 43| Scale is weakly epimorphic with val: <7 11 17 30 44| Scale is weakly epimorphic with val: <7 11 17 31 43| Scale is weakly epimorphic with val: <7 11 17 33 44| Scale is weakly epimorphic with val: <7 11 17 34 43| Scale is weakly epimorphic with val: <7 11 17 36 44| Scale is JI-epimorphic with val: <7 11 18 30 42| Scale is weakly epimorphic with val: <7 11 18 31 44| Scale is weakly epimorphic with val: <7 11 18 33 42| Scale is weakly epimorphic with val: <7 11 18 34 44| Scale is weakly epimorphic with val: <7 11 18 36 42| Scale is JI-epimorphic with val: <7 11 19 30 43| Scale is weakly epimorphic with val: <7 11 19 31 42| Scale is weakly epimorphic with val: <7 11 19 33 43| Scale is weakly epimorphic with val: <7 11 19 34 42| Scale is weakly epimorphic with val: <7 11 19 36 43| Scale is weakly epimorphic with val: <7 12 15 30 43| Scale is weakly epimorphic with val: <7 12 16 30 44| Scale is weakly epimorphic with val: <7 12 17 30 42| Scale is weakly epimorphic with val: <7 12 18 30 43| Scale is weakly epimorphic with val: <7 12 19 30 44| Scale is weakly epimorphic with val: <7 12 19 32 42| Scale is weakly epimorphic with val: <7 12 19 35 42| Scale is weakly epimorphic with val: <8 11 15 32 44| Scale is weakly epimorphic with val: <8 11 16 32 42| Scale is weakly epimorphic with val: <8 11 17 32 43| Scale is weakly epimorphic with val: <8 11 18 31 42| Scale is weakly epimorphic with val: <8 11 18 32 44| Scale is weakly epimorphic with val: <8 11 18 34 42| Scale is weakly epimorphic with val: <8 11 19 31 43| Scale is weakly epimorphic with val: <8 11 19 32 42| Scale is weakly epimorphic with val: <8 11 19 34 43| Scale is weakly epimorphic with val: <8 12 15 33 44| Scale is weakly epimorphic with val: <8 12 16 33 42| Scale is weakly epimorphic with val: <8 12 17 31 42| Scale is weakly epimorphic with val: <8 12 17 33 43| Scale is weakly epimorphic with val: <8 12 17 34 42| Scale is weakly epimorphic with val: <8 12 18 31 43| Scale is weakly epimorphic with val: <8 12 18 33 44| Scale is weakly epimorphic with val: <8 12 18 34 43| Scale is weakly epimorphic with val: <8 12 19 31 44| Scale is weakly epimorphic with val: <8 12 19 33 42| Scale is weakly epimorphic with val: <8 12 19 34 44|
FIT/MODE
3: 0 0 3 N M DE S SD: 45.7365 c. M: 73.6807 c. 5: 0 1 4 N G T3 SD: 22.5012 c. M: 29.0971 c. 6: 0 1 5 N G T3 SD: 17.6411 c. M: 29.0971 c. 7: 0 1 6 N G T3 SD: 16.8626 c. M: 29.0971 c. 8: 0 1 7 N G T3 SD: 18.0478 c. M: 29.0971 c. 11: 1 1 9 N M DE S SD: 13.4967 c. M:-16.8730 c. 12: 1 1 10 N M DE S SD: 8.9613 c. M:-12.4067 c. 13: 1 1 11 N M DE S SD: 5.5843 c. M:-9.2141 c. 14: 1 1 12 N M DE S SD: 4.0153 c. M:-6.4776 c. 19: 1 2 16 N T3 SD: 3.3116 c. M:-4.9580 c. 20: 1 2 17 N T3 SD: 2.4933 c. M: 4.1948 c. 32: 2 3 27 N T3 SD: 2.6617 c. M:-4.1389 c. 33: 2 3 28 N T3 SD: 1.2047 c. M:-1.7807 c. 34: 2 3 29 N T3 SD: 0.2783 c. M: 0.4387 c. 101: 6 9 86 N T3 SD: 0.3276 c. M:-0.4898 c. 121: 7 11 103 N T3 SD: 0.2875 c. M:-0.4087 c. 135: 8 12 115 N T3 SD: 0.2479 c. M:-0.4167 c. 155: 9 14 132 N T3 SD: 0.1648 c. M:-0.2228 c. 189: 11 17 161 N T3 SD: 0.0874 c. M: 0.1103 c. 223: 13 20 190 N T3 SD: 0.0384 c. M: 0.0630 c. 257: 15 23 219 N T3 SD: 0.0282 c. M: 0.0398 c. 480: 28 43 409 N T3 SD: 0.0265 c. M: 0.0444 c. 737: 43 66 628 N T3 SD: 0.0256 c. M: 0.0388 c. 804: 47 72 685 N T3 SD: 0.0226 c. M:-0.0350 c. 838: 49 75 714 N T3 SD: 0.0170 c. M:-0.0249 c. 1061: 62 95 904 N T3 SD: 0.0104 c. M:-0.0169 c. 1095: 64 98 933 N T3 SD: 0.0073 c. M:-0.0124 c. 1318: 77 118 1123 N T3 SD: 0.0034 c. M:-0.0058 c. 1352: 79 121 1152 N T3 SD: 0.0041 c. M: 0.0054 c. 1575: 92 141 1342 N T3 SD: 0.0030 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: 96.5951 cents 7 x 8:9 S SD: 84.8060 cents 8 x 9:11 SD: 70.3521 cents 9 x 10:12 S SD: 54.3615 cents 10 x 11:13 SD: 50.6487 cents 11 x 12:15 S SD: 43.1160 cents 12 x 13:16 SD: 32.4460 cents 13 x 14:17 SD: 32.0671 cents 14 x 15:19 SD: 27.5369 cents 15 x 16:20 S SD: 19.0253 cents 16 x 17:21 SD: 20.7451 cents 17 x 18:23 SD: 17.8714 cents 18 x 19:24 SD: 9.9612 cents 19 x 20:25 S SD: 13.7334 cents 20 x 21:27 SD: 12.0299 cents 21 x 22:28 SD: 3.4282 cents 22 x 23:29 SD: 10.0275 cents 23 x 24:31 SD: 9.3581 cents 24 x 25:32 SD: 1.5041 cents 25 x 26:33 SD: 9.1673 cents 26 x 27:35 SD: 9.2746 cents 27 x 28:36 SD: 5.3599 cents 28 x 29:37 SD: 10.1026 cents 29 x 30:39 SD: 10.5535 cents 30 x 31:40 SD: 8.4569 cents 31 x 32:41 SD: 11.6919 cents 32 x 33:43 SD: 12.2269 cents 33 x 34:44 SD: 10.9991 cents 34:35 x 45 SD: 12.3279 cents 35:36:37:47 SD: 10.7816 cents 36:37:38:48 SD: 9.0256 cents 38:39:40:51 SD: 8.2289 cents 39:40:41:52 SD: 6.5275 cents 41:42:43:55 SD: 6.2098 cents 42:43:44:56 SD: 4.5030 cents 45:46:47:60 SD: 3.0319 cents 48:49:50:64 SD: 2.4177 cents 63:64:66:84 SD: 2.3657 cents 66:67:69:88 SD: 1.4949 cents 69:70:72:92 SD: 1.3956 cents 111:113:116:148 SD: 1.0570 cents 114:116:119:152 SD: 0.3979 cents 183:186:191:244 SD: 0.3417 cents 231:235:241:308 SD: 0.2327 cents 297:302:310:396 SD: 0.1744 cents 414:421:432:552 SD: 0.0232 cents