Scala analysis: 514_M22
Miscellaneous tetrachord 87/85 * 85/84 * 112/87
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 87/85 40.263072 2: 29/28 60.751288 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/87 437.2937 1: 87/85 40.2631 2: 85/84 20.4882 3: 112/87 437.2937
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85/84 20.488 cents 1: 1 87/85 40.263 cents 1: 1 112/87 437.294 cents 2: 1 29/28 60.751 cents 2: 1 340/261 457.782 cents 2: 1 112/85 477.557 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 : 40.3 60.8 498.0 40.3 : 20.5 457.8 498.0 60.8 : 437.3 477.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.4882 .. 437.2937 cents 3136/2465, 416.8055 cents 85/84, 20.4882 cents 2: 60.7513 .. 477.5568 cents 3136/2465, 416.8055 cents 2523/3136,-376.5424 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 85/84, 20.4882 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/87, 437.2937 cents Average / Smallest step : 8.102950 Largest / Average step : 2.634061 Largest / Smallest step : 21.343669 Median interval of one step : 87/85, 40.2631 cents, amount: 1 Least squares average step : 118.27862 cents, oct.: 354.83585 cents Scale is not proper Scale has trivalence property Scale is a mode of a 705-tone equal temperament with octave 4/3 degrees: 57 86 705 Least number of segments generator : 353 of 249.376 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 446 of 315.075 cents and inv. generated superset size: 28 = 25 more = 933.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 20.48822 cents Scale diversity : 0.120949 Lumma stability : 0.082275 Lumma impropriety factor : 0.756041 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 : 7308/7225, 19.7749 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 416.8055 cents: 2 -- Rational properties -- Prime limit : 29 Odd number limit : 261 (O: 87 U: 261) Highest odd numerator or denominator: 87 Scale harmonicity : 0.009074 Average absolute harmonicity : 0.080026 Specific harmonicity : 0.041592 Fundamental : 1/7140, -12.8017 octaves, 0.0366 Hz. Guide tone : 348, 8.4429 octaves, 91045.697 Hz. Exponens Consonantiae : 2.484720E+06, 21.24465 octaves Euler's gradus suavitatis : 63 Sum of Mann's harmonic distance : 118.0, average 39.33333 Mersenne's string divisions : 68628 Sum of van Prooijen's expressibility: 3.87904, average 1.29301 Sum of Tenney's harmonic distance : 7.85768, average 2.61923 Vogel's harmonic complexity : 43.66667 Wille's k value : 3697 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.18951, average 2.86492 Lattice compactness (without 2's) : 10.79202, average 1.79867 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 17: -1 .. 0 -0.33333 1 29: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is JI-epimorphic with val: <7 11 16 19 29 35| Scale is weakly epimorphic with val: <7 11 16 19 30 34| Scale is weakly epimorphic with val: <7 11 16 19 30 37| Scale is weakly epimorphic with val: <7 11 16 20 30 33| Scale is JI-epimorphic with val: <7 11 16 20 30 36| Scale is weakly epimorphic with val: <7 11 16 20 31 35| Scale is weakly epimorphic with val: <7 11 16 21 29 33| Scale is weakly epimorphic with val: <7 11 16 21 29 36| Scale is weakly epimorphic with val: <7 11 16 21 31 34| Scale is JI-epimorphic with val: <7 11 16 21 31 37| Scale is weakly epimorphic with val: <7 11 17 19 29 34| Scale is weakly epimorphic with val: <7 11 17 19 29 37| Scale is weakly epimorphic with val: <7 11 17 19 31 35| Scale is weakly epimorphic with val: <7 11 17 20 29 33| Scale is JI-epimorphic with val: <7 11 17 20 29 36| Scale is weakly epimorphic with val: <7 11 17 20 30 35| = patent Scale is weakly epimorphic with val: <7 11 17 21 30 34| Scale is JI-epimorphic with val: <7 11 17 21 30 37| Scale is weakly epimorphic with val: <7 11 17 21 31 33| Scale is weakly epimorphic with val: <7 11 17 21 31 36| Scale is weakly epimorphic with val: <7 11 18 19 30 35| Scale is weakly epimorphic with val: <7 11 18 19 31 34| Scale is weakly epimorphic with val: <7 11 18 19 31 37| Scale is weakly epimorphic with val: <7 11 18 20 29 35| Scale is weakly epimorphic with val: <7 11 18 20 31 33| Scale is weakly epimorphic with val: <7 11 18 20 31 36| Scale is weakly epimorphic with val: <7 11 18 21 29 34| Scale is JI-epimorphic with val: <7 11 18 21 29 37| Scale is weakly epimorphic with val: <7 11 18 21 30 33| Scale is weakly epimorphic with val: <7 11 18 21 30 36| Scale is weakly epimorphic with val: <7 12 16 19 30 37| Scale is weakly epimorphic with val: <7 12 16 19 31 36| Scale is weakly epimorphic with val: <7 12 16 20 29 37| Scale is weakly epimorphic with val: <7 12 16 21 29 36| Scale is weakly epimorphic with val: <7 12 17 19 29 37| Scale is weakly epimorphic with val: <7 12 17 19 30 36| Scale is weakly epimorphic with val: <7 12 17 20 31 37| Scale is weakly epimorphic with val: <7 12 18 19 29 36| Scale is weakly epimorphic with val: <7 12 18 20 30 37|
FIT/MODE
3: 0 0 3 N M DE S SD: 42.0786 c. M: 60.7513 c. 5: 0 1 4 N G T3 SD: 32.3060 c. M: 40.2631 c. 6: 1 0 5 N G T3 SD: 27.8234 c. M:-42.7444 c. 7: 1 0 6 N G T3 SD: 18.8156 c. M:-30.8862 c. 8: 1 0 7 N G T3 SD: 12.7271 c. M:-21.9926 c. 9: 1 0 8 N G T3 SD: 9.2478 c. M:-15.0753 c. 10: 1 0 9 N G T3 SD: 8.3839 c. M: 10.9468 c. 13: 1 1 11 N M DE S SD: 9.2322 c. M:-15.8710 c. 14: 1 1 12 N M DE S SD: 6.5853 c. M:-10.3980 c. 15: 1 1 13 N M DE S SD: 5.2224 c. M: 7.0601 c. 16: 1 1 14 N M DE S SD: 5.3453 c. M: 9.1353 c. 22: 2 1 19 N T3 SD: 5.0484 c. M:-7.1639 c. 23: 2 1 20 N T3 SD: 3.0004 c. M:-4.2111 c. 24: 2 1 21 N T3 SD: 1.1258 c. M:-1.5043 c. 25: 2 1 22 N T3 SD: 0.6186 c. M: 0.9859 c. 49: 4 2 43 N T3 SD: 0.2643 c. M:-0.3937 c. 74: 6 3 65 N T3 SD: 0.1237 c. M: 0.1782 c. 123: 10 5 108 N T3 SD: 0.1321 c. M:-0.2284 c. 197: 16 8 173 N T3 SD: 0.1166 c. M:-0.1873 c. 271: 22 11 238 N T3 SD: 0.1143 c. M:-0.1686 c. 320: 26 13 281 N T3 SD: 0.1210 c. M:-0.2031 c. 345: 28 14 303 N T3 SD: 0.1144 c. M:-0.1580 c. 360: 29 15 316 N T3 SD: 0.1080 c. M: 0.1428 c. 385: 31 16 338 N T3 SD: 0.0970 c. M: 0.1607 c. 409: 33 17 359 N T3 SD: 0.0899 c. M:-0.1344 c. 410: 33 17 360 N T3 SD: 0.1022 c. M: 0.1765 c. 434: 35 18 381 N T3 SD: 0.0696 c. M: 0.0982 c. 459: 37 19 403 N T3 SD: 0.0672 c. M: 0.1157 c. 483: 39 20 424 N T3 SD: 0.0572 c. M:-0.0865 c. 508: 41 21 446 N T3 SD: 0.0431 c. M: 0.0665 c. 533: 43 22 468 N T3 SD: 0.0487 c. M: 0.0831 c. 557: 45 23 489 N T3 SD: 0.0332 c. M:-0.0513 c. 582: 47 24 511 N T3 SD: 0.0251 c. M: 0.0429 c. 631: 51 26 554 N T3 SD: 0.0150 c. M:-0.0244 c. 656: 53 27 576 N T3 SD: 0.0164 c. M: 0.0247 c. 705: 57 29 619 N T3 SD: 0.0031 c. M:-0.0044 c. 2066: 167 85 1814 N T3 SD: 0.0031 c. M: 0.0048 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: 103.0598 cents 7 x 8:9 S SD: 90.8405 cents 8 x 9:11 SD: 76.3748 cents 9 x 10:12 S SD: 60.8262 cents 10 x 11:13 SD: 56.5461 cents 11 x 12:15 S SD: 48.9722 cents 12 x 13:16 SD: 38.9107 cents 13 x 14:17 SD: 37.7250 cents 14 x 15:19 SD: 33.1045 cents 15 x 16:20 S SD: 25.4900 cents 16 x 17:21 SD: 25.9679 cents 17 x 18:23 SD: 22.9034 cents 18 x 19:24 SD: 16.4259 cents 19 x 20:25 S SD: 18.1148 cents 20 x 21:27 SD: 16.0075 cents 21 x 22:28 SD: 9.8929 cents 22 x 23:29 SD: 12.7875 cents 23 x 24:31 SD: 11.3739 cents 24 x 25:32 SD: 4.9606 cents 25 x 26:33 SD: 9.4054 cents 26 x 27:35 SD: 8.5950 cents 27 x 28:36 SD: 1.1048 cents 28 x 29:37 SD: 7.7634 cents 29 x 30:39 SD: 7.5013 cents 30 x 31:40 SD: 1.9922 cents 31 x 32:41 SD: 7.5828 cents 32 x 33:43 SD: 7.7045 cents 33 x 34:44 SD: 4.5344 cents 34:35 x 45 SD: 8.0882 cents 35:36 x 47 SD: 7.4868 cents 36:37 x 48 SD: 3.5855 cents 37:38 x 49 SD: 6.5697 cents 38:39 x 51 SD: 6.1447 cents 39:40 x 52 SD: 1.7840 cents 40:41 x 53 SD: 5.5676 cents 41:42 x 55 SD: 5.3122 cents 45:46:47:60 SD: 4.8997 cents 48:49:50:64 SD: 3.6405 cents 51:52:53:68 SD: 2.9497 cents 54:55:56:72 SD: 2.9263 cents 64 x 66:85 SD: 5.0457 cents 65 x 67:87 SD: 5.3108 cents 66 x 68:88 SD: 4.5344 cents 67 x 69:89 SD: 5.8842 cents 68:70 x 91 SD: 5.8905 cents 69:71 x 92 SD: 4.6021 cents 72:74:75:96 SD: 4.0805 cents 74:76:77:99 SD: 3.8550 cents 75:77:78:100 SD: 2.9661 cents 77:79:80:103 SD: 2.9422 cents 78:80:81:104 SD: 1.9368 cents 81:83:84:108 SD: 0.9855 cents 84:86:87:112 SD: 0.1579 cents 423:433:438:564 SD: 0.1545 cents 507:519:525:676 SD: 0.1415 cents 591:605:612:788 SD: 0.1352 cents