Scala analysis: 044_E1
Enharmonic tetrachord 48/47 * 47/46 * 23/18, Schlesinger
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 48/47 36.448379 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: 48/47 36.4484 2: 47/46 37.2323 3: 23/18 424.3643 vicesimotertial major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 48/47 36.448 cents 1: 1 47/46 37.232 cents 1: 1 23/18 424.364 cents vicesimotertial major third 2: 1 24/23 73.681 cents vicesimotertial minor semitone 2: 1 184/141 460.813 cents 2: 1 47/36 461.597 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 : 36.4 73.7 498.0 36.4 : 37.2 461.6 498.0 73.7 : 424.4 460.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.4484 .. 424.3643 cents 1081/864, 387.9160 cents 48/47, 36.4484 cents 2: 73.6807 .. 461.5966 cents 1081/864, 387.9160 cents 432/529,-350.6837 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 48/47, 36.4484 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/18, 424.3643 cents Average / Smallest step : 4.554798 Largest / Average step : 2.556181 Largest / Smallest step : 11.642887 Median interval of one step : 47/46, 37.2323 cents, amount: 1 Least squares average step : 119.85319 cents, oct.: 359.55958 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1913-tone equal temperament with octave 4/3 degrees: 140 283 1913 Least number of segments generator : 957 of 249.153 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1417 of 368.913 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 36.44838 cents Scale diversity : 0.233451 Lumma stability : 0.146366 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 : 2209/2208, 0.7839 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 : 2 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 Limited inverse transpositions with margin 387.1321 cents: 2 -- Rational properties -- Prime limit : 47 Odd number limit : 141 (O: 47 U: 141) Highest odd numerator or denominator: 47 Scale harmonicity : 0.019448 Fundamental : 1/3243, -11.6631 octaves, 0.0807 Hz. Guide tone : 48, 5.5850 octaves, 12558.027 Hz. Exponens Consonantiae : 1.556640E+05, 17.24808 octaves Euler's gradus suavitatis : 77 Sum of Mann's harmonic distance : 74.5, average 24.83333 Mersenne's string divisions : 31255 Sum of van Prooijen's expressibility: 3.51095, average 1.17032 Sum of Tenney's harmonic distance : 7.17446, average 2.39149 Vogel's harmonic complexity : 53.66667 Wille's k value : 540 Wilson's harmonic complexity : 76 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.36793, average 2.72799 Lattice compactness (without 2's) : 8.65028, average 1.44171 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 1 0.33333 3 1 23: -1 .. 0 -0.33333 1 1 47: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is JI-epimorphic with val: <7 11 30 38| Scale is weakly epimorphic with val: <7 11 30 41| Scale is weakly epimorphic with val: <7 11 31 37| Scale is weakly epimorphic with val: <7 11 31 40| Scale is weakly epimorphic with val: <7 11 31 43| Scale is weakly epimorphic with val: <7 11 33 38| Scale is weakly epimorphic with val: <7 11 33 41| Scale is weakly epimorphic with val: <7 11 34 37| Scale is weakly epimorphic with val: <7 11 34 40| Scale is weakly epimorphic with val: <7 11 34 43| Scale is weakly epimorphic with val: <7 11 36 38| Scale is weakly epimorphic with val: <7 11 36 41| Scale is weakly epimorphic with val: <7 12 30 39| Scale is weakly epimorphic with val: <7 12 30 42| Scale is weakly epimorphic with val: <7 12 32 37| Scale is weakly epimorphic with val: <7 12 35 37| Scale is weakly epimorphic with val: <8 11 31 40| Scale is weakly epimorphic with val: <8 11 32 39| Scale is weakly epimorphic with val: <8 11 32 42| Scale is weakly epimorphic with val: <8 11 34 40| Scale is weakly epimorphic with val: <8 12 31 41| Scale is weakly epimorphic with val: <8 12 33 39| Scale is weakly epimorphic with val: <8 12 33 42| Scale is weakly epimorphic with val: <8 12 34 41|
FIT/MODE
3: 0 0 3 N M DE S SD: 47.4599 c. M: 73.6807 c. 5: 0 1 4 N G T3 SD: 25.8248 c. M: 36.4484 c. 6: 0 1 5 N G T3 SD: 21.7215 c. M: 36.4484 c. 7: 0 1 6 N G T3 SD: 21.0942 c. M: 36.4484 c. 8: 0 1 7 N G T3 SD: 22.0531 c. M: 36.4484 c. 9: 0 1 8 N G T3 SD: 23.5579 c. M: 36.4484 c. 10: 1 1 8 N M DE S SD: 16.8391 c. M:-25.9283 c. 11: 1 1 9 N M DE S SD: 10.9945 c. M:-16.8730 c. 12: 1 1 10 N M DE S SD: 6.1250 c. M:-9.3268 c. 13: 1 1 11 N M DE S SD: 2.0102 c. M:-2.9417 c. 14: 1 1 12 N M DE S SD: 1.5461 c. M: 2.5314 c. 27: 2 2 23 N M DE S SD: 0.2632 c. M:-0.4438 c. 68: 5 5 58 N M DE S SD: 0.2722 c. M: 0.4387 c. 95: 7 7 81 N M DE S SD: 0.2186 c. M: 0.2845 c. 122: 9 9 104 N M DE S SD: 0.2042 c. M:-0.2926 c. 149: 11 11 127 N M DE S SD: 0.2026 c. M:-0.3200 c. 203: 15 15 173 N M DE S SD: 0.2087 c. M:-0.3530 c. 217: 16 16 185 N M DE S SD: 0.2088 c. M:-0.2738 c. 230: 17 17 196 N M DE S SD: 0.2125 c. M:-0.3636 c. 257: 19 19 219 N M DE S SD: 0.2160 c. M:-0.3721 c. 271: 20 20 231 N M DE S SD: 0.2025 c. M:-0.3077 c. 284: 21 21 242 N M DE S SD: 0.2193 c. M:-0.3789 c. 311: 23 23 265 N M DE S SD: 0.2222 c. M:-0.3845 c. 312: 23 23 266 N M DE S SD: 0.2113 c. M:-0.2665 c. 317: 23 24 270 N T3 SD: 0.2033 c. M: 0.3126 c. 331: 24 25 282 N T3 SD: 0.1962 c. M: 0.3364 c. 344: 25 26 293 N T3 SD: 0.1722 c. M: 0.2532 c. 358: 26 27 305 N T3 SD: 0.1630 c. M: 0.2775 c. 371: 27 28 316 N T3 SD: 0.1467 c. M: 0.2025 c. 372: 27 28 317 N T3 SD: 0.1751 c. M: 0.3000 c. 384: 28 29 327 N T3 SD: 0.1623 c. M:-0.2479 c. 385: 28 29 328 N T3 SD: 0.1349 c. M: 0.2269 c. 398: 29 30 339 N T3 SD: 0.1261 c. M: 0.1587 c. 399: 29 30 340 N T3 SD: 0.1455 c. M: 0.2496 c. 412: 30 31 351 N T3 SD: 0.1110 c. M: 0.1830 c. 425: 31 32 362 N T3 SD: 0.1098 c. M:-0.1472 c. 426: 31 32 363 N T3 SD: 0.1197 c. M: 0.2057 c. 439: 32 33 374 N T3 SD: 0.0907 c. M: 0.1444 c. 453: 33 34 386 N T3 SD: 0.0970 c. M: 0.1670 c. 466: 34 35 397 N T3 SD: 0.0737 c. M: 0.1103 c. 480: 35 36 409 N T3 SD: 0.0768 c. M: 0.1326 c. 493: 36 37 420 N T3 SD: 0.0600 c. M: 0.0800 c. 507: 37 38 432 N T3 SD: 0.0589 c. M: 0.1019 c. 520: 38 39 443 N T3 SD: 0.0498 c. M:-0.0683 c. 534: 39 40 455 N T3 SD: 0.0429 c. M: 0.0743 c. 561: 41 42 478 N T3 SD: 0.0287 c. M: 0.0494 c. 588: 43 44 501 N T3 SD: 0.0164 c. M: 0.0267 c. 615: 45 46 524 N T3 SD: 0.0087 c. M:-0.0138 c. 1257: 92 94 1071 N T3 SD: 0.0093 c. M:-0.0157 c. 1271: 93 95 1083 N T3 SD: 0.0079 c. M: 0.0123 c. 1298: 95 97 1106 N T3 SD: 0.0060 c. M: 0.0099 c. 1886: 138 141 1607 N T3 SD: 0.0041 c. M: 0.0061 c. 1913: 140 143 1630 N T3 SD: 0.0013 c. M: 0.0023 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 31:32 x 41 SD: 11.6120 cents 32:33 x 43 SD: 10.7771 cents 33:34 x 44 SD: 7.6170 cents 34:35 x 45 SD: 9.3797 cents 36:37:38:48 SD: 7.5835 cents 38:39:40:51 SD: 6.9130 cents 39:40:41:52 SD: 4.9541 cents 41:42:43:55 SD: 4.8936 cents 42:43:44:56 SD: 2.6957 cents 45:46:47:60 SD: 0.7553 cents 93:95:97:124 SD: 0.2891 cents 138:141:144:184 SD: 0.2613 cents 231:236:241:308 SD: 0.2327 cents 573:585:598:764 SD: 0.2067 cents