Scala analysis: 046_E1
Enharmonic tetrachord 72/71 * 71/69 * 23/18
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 72/71 24.213458 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: 72/71 24.2135 2: 71/69 49.4672 3: 23/18 424.3643 vicesimotertial major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 72/71 24.213 cents 1: 1 71/69 49.467 cents 1: 1 23/18 424.364 cents vicesimotertial major third 2: 1 24/23 73.681 cents vicesimotertial minor semitone 2: 1 92/71 448.578 cents 2: 1 71/54 473.832 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 : 24.2 73.7 498.0 24.2 : 49.5 473.8 498.0 73.7 : 424.4 448.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.2135 .. 424.3643 cents 1633/1296, 400.1509 cents 72/71, 24.2135 cents 2: 73.6807 .. 473.8315 cents 1633/1296, 400.1509 cents 432/529,-350.6837 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 72/71, 24.2135 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/18, 424.3643 cents Average / Smallest step : 6.856311 Largest / Average step : 2.556181 Largest / Smallest step : 17.525970 Median interval of one step : 71/69, 49.4672 cents, amount: 1 Least squares average step : 118.97927 cents, oct.: 356.93781 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1913-tone equal temperament with octave 4/3 degrees: 93 283 1913 Least number of segments generator : 957 of 249.153 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1288 of 335.328 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 24.21346 cents Scale diversity : 0.208037 Lumma stability : 0.097234 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 : 72/71, 24.2135 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 374.8972 cents: 2 -- Rational properties -- Prime limit : 71 Odd number limit : 71 (O: 71 U: 71) Highest odd numerator or denominator: 71 Scale harmonicity : 0.018837 Fundamental : 1/4899, -12.2583 octaves, 0.0534 Hz. Guide tone : 72, 6.1699 octaves, 18837.041 Hz. Exponens Consonantiae : 3.527280E+05, 18.42820 octaves Euler's gradus suavitatis : 102 Sum of Mann's harmonic distance : 98.5, average 32.83333 Mersenne's string divisions : 47047 Sum of van Prooijen's expressibility: 3.69011, average 1.23004 Sum of Tenney's harmonic distance : 7.52971, average 2.50990 Vogel's harmonic complexity : 70.33333 Wille's k value : 816 Wilson's harmonic complexity : 103 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.18423, average 2.69737 Lattice compactness (without 2's) : 11.06450, average 1.84408 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 2 0.66667 4 1 23: -1 .. 0 -0.33333 1 1 71: -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 30 45| Scale is weakly epimorphic with val: <7 11 31 44| Scale is weakly epimorphic with val: <7 11 33 45| Scale is weakly epimorphic with val: <7 11 34 44| Scale is weakly epimorphic with val: <7 11 36 45| Scale is weakly epimorphic with val: <7 12 30 44| Scale is weakly epimorphic with val: <8 11 31 43| Scale is weakly epimorphic with val: <8 11 32 45| Scale is weakly epimorphic with val: <8 11 34 43| Scale is weakly epimorphic with val: <8 12 31 45| Scale is weakly epimorphic with val: <8 12 33 43| Scale is weakly epimorphic with val: <8 12 34 45|
FIT/MODE
3: 0 0 3 N M DE S SD: 44.7777 c. M: 73.6807 c. 5: 0 1 4 N G T3 SD: 20.4823 c. M:-25.9283 c. 6: 0 1 5 N G T3 SD: 14.9809 c. M: 24.2135 c. 7: 0 1 6 N G T3 SD: 14.0558 c. M: 24.2135 c. 8: 0 1 7 N G T3 SD: 15.4577 c. M: 24.2135 c. 12: 1 1 10 N M DE S SD: 11.3423 c. M:-17.2903 c. 13: 1 1 11 N M DE S SD: 8.3146 c. M:-14.0977 c. 14: 1 1 12 N M DE S SD: 6.7202 c. M:-11.3612 c. 15: 1 1 13 N M DE S SD: 6.6766 c. M:-8.9895 c. 18: 1 2 15 N T3 SD: 5.7426 c. M:-9.3268 c. 19: 1 2 16 N T3 SD: 3.0865 c. M:-4.9580 c. 20: 1 2 17 N T3 SD: 0.7135 c. M:-1.0261 c. 41: 2 4 35 N T3 SD: 0.4620 c. M: 0.7960 c. 61: 3 6 52 N T3 SD: 0.1985 c. M:-0.2806 c. 81: 4 8 69 N T3 SD: 0.2282 c. M:-0.3814 c. 142: 7 14 121 N T3 SD: 0.1958 c. M:-0.3381 c. 203: 10 20 173 N T3 SD: 0.1906 c. M:-0.3208 c. 250: 12 25 213 N T3 SD: 0.1783 c. M: 0.3073 c. 270: 13 27 230 N T3 SD: 0.1475 c. M: 0.2335 c. 290: 14 29 247 N T3 SD: 0.1377 c. M: 0.1699 c. 291: 14 29 248 N T3 SD: 0.1541 c. M: 0.2525 c. 310: 15 31 264 N T3 SD: 0.1446 c. M:-0.2228 c. 311: 15 31 265 N T3 SD: 0.1112 c. M: 0.1920 c. 331: 16 33 282 N T3 SD: 0.0848 c. M: 0.1388 c. 351: 17 35 299 N T3 SD: 0.0799 c. M:-0.1038 c. 372: 18 37 317 N T3 SD: 0.0710 c. M: 0.1145 c. 392: 19 39 334 N T3 SD: 0.0428 c. M: 0.0735 c. 412: 20 41 351 N T3 SD: 0.0401 c. M:-0.0590 c. 453: 22 45 386 N T3 SD: 0.0183 c. M: 0.0258 c. 473: 23 47 403 N T3 SD: 0.0151 c. M:-0.0258 c. 926: 45 92 789 N T3 SD: 0.0065 c. M: 0.0104 c. 987: 48 98 841 N T3 SD: 0.0065 c. M: 0.0083 c. 1440: 70 143 1227 N T3 SD: 0.0069 c. M: 0.0115 c. 1460: 71 145 1244 N T3 SD: 0.0041 c. M:-0.0065 c. 1913: 93 190 1630 N T3 SD: 0.0015 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 x 32:41 SD: 11.6919 cents 32 x 33:43 SD: 12.2269 cents 33 x 34:44 SD: 10.9991 cents 34 x 35:45 SD: 13.3728 cents 35:36:37:47 SD: 11.8425 cents 36:37:38:48 SD: 10.1986 cents 37:38:39:49 SD: 10.1357 cents 38:39:40:51 SD: 9.3590 cents 39:40:41:52 SD: 7.8261 cents 41:42:43:55 SD: 7.4101 cents 42:43:44:56 SD: 5.9631 cents 45:46:47:60 SD: 4.6432 cents 48:49:50:64 SD: 3.9569 cents 51:52:53:68 SD: 3.9250 cents 60:61:63:80 SD: 3.8835 cents 62:63:65:83 SD: 3.7522 cents 63:64:66:84 SD: 2.5015 cents 66:67:69:88 SD: 1.2492 cents 69:70:72:92 SD: 0.2323 cents 435:441:454:580 SD: 0.1993 cents 504:511:526:672 SD: 0.1466 cents 573:581:598:764 SD: 0.1092 cents