Scala analysis: 047_E1
Enharmonic tetrachord 30/29 * 116/115 * 23/18, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 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: 30/29 58.6915 2: 116/115 14.9891 3: 23/18 424.3643 vicesimotertial major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 116/115 14.989 cents 1: 1 30/29 58.692 cents 1: 1 23/18 424.364 cents vicesimotertial major third 2: 1 24/23 73.681 cents vicesimotertial minor semitone 2: 1 58/45 439.353 cents 2: 1 115/87 483.056 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 : 58.7 73.7 498.0 58.7 : 15.0 439.4 498.0 73.7 : 424.4 483.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.9891 .. 424.3643 cents 2645/2088, 409.3752 cents 116/115, 14.9891 cents 2: 73.6807 .. 483.0559 cents 2645/2088, 409.3752 cents 432/529,-350.6837 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 116/115, 14.9891 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/18, 424.3643 cents Average / Smallest step : 11.075691 Largest / Average step : 2.556181 Largest / Smallest step : 28.311467 Median interval of one step : 30/29, 58.6915 cents, amount: 1 Least squares average step : 121.44199 cents, oct.: 364.32596 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1994-tone equal temperament with octave 4/3 degrees: 235 295 1994 Least number of segments generator : 999 of 249.522 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1699 of 424.362 cents and inv. generated superset size: 35 = 32 more = 1166.667% 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 14.98913 cents Scale diversity : 0.178665 Lumma stability : 0.060192 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 : 116/115, 14.9891 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 483.0559 cents Number of appreciable fourths : 0 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 29 Odd number limit : 115 (O: 115 U: 115) Highest odd numerator or denominator: 29 Scale harmonicity : 0.009018 Average absolute harmonicity : 0.083606 Specific harmonicity : 0.047571 Fundamental : 1/2001, -10.9665 octaves, 0.1307 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 2.401200E+05, 17.87340 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 56.5, average 18.83333 Mersenne's string divisions : 19411 Sum of van Prooijen's expressibility: 3.30125, average 1.10042 Sum of Tenney's harmonic distance : 6.76064, average 2.25355 Vogel's harmonic complexity : 42.33333 Wille's k value : 517 Wilson's harmonic complexity : 63 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.29369, average 2.54895 Lattice compactness (without 2's) : 10.56387, average 1.76065 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.33333 1 23: -1 .. 0 -0.33333 1 1 29: -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: <6 10 19 30 32| Scale is weakly epimorphic with val: <6 11 18 30 32| Scale is weakly epimorphic with val: <6 11 19 30 33| Scale is weakly epimorphic with val: <6 11 19 33 33| Scale is weakly epimorphic with val: <7 10 18 32 32| Scale is weakly epimorphic with val: <7 10 19 32 33| Scale is JI-epimorphic with val: <7 11 15 30 32| Scale is weakly epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 31 34| Scale is weakly epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 33 35| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is weakly epimorphic with val: <7 11 15 34 34| Scale is weakly epimorphic with val: <7 11 15 34 37| Scale is weakly epimorphic with val: <7 11 15 36 38| Scale is JI-epimorphic with val: <7 11 16 30 33| Scale is weakly epimorphic with val: <7 11 16 30 36| Scale is weakly epimorphic with val: <7 11 16 31 32| Scale is weakly epimorphic with val: <7 11 16 31 35| Scale is weakly epimorphic with val: <7 11 16 31 38| Scale is weakly epimorphic with val: <7 11 16 33 33| Scale is weakly epimorphic with val: <7 11 16 33 36| Scale is weakly epimorphic with val: <7 11 16 34 35| Scale is weakly epimorphic with val: <7 11 16 34 38| Scale is weakly epimorphic with val: <7 11 16 36 36| Scale is JI-epimorphic with val: <7 11 17 30 34| Scale is weakly epimorphic with val: <7 11 17 30 37| Scale is weakly epimorphic with val: <7 11 17 31 33| Scale is weakly epimorphic with val: <7 11 17 31 36| Scale is weakly epimorphic with val: <7 11 17 33 34| Scale is weakly epimorphic with val: <7 11 17 33 37| Scale is weakly epimorphic with val: <7 11 17 34 36| Scale is weakly epimorphic with val: <7 11 17 36 37| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is JI-epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 31 34| Scale is weakly epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 33 35| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 18 34 34| Scale is weakly epimorphic with val: <7 11 18 34 37| Scale is weakly epimorphic with val: <7 11 18 36 38| Scale is weakly epimorphic with val: <7 11 19 30 33| Scale is JI-epimorphic with val: <7 11 19 30 36| Scale is weakly epimorphic with val: <7 11 19 31 32| Scale is weakly epimorphic with val: <7 11 19 31 35| Scale is weakly epimorphic with val: <7 11 19 31 38| Scale is weakly epimorphic with val: <7 11 19 33 33| Scale is weakly epimorphic with val: <7 11 19 33 36| Scale is weakly epimorphic with val: <7 11 19 34 35| Scale is weakly epimorphic with val: <7 11 19 34 38| Scale is weakly epimorphic with val: <7 11 19 36 36| Scale is weakly epimorphic with val: <7 12 15 30 33| Scale is weakly epimorphic with val: <7 12 15 30 36| Scale is weakly epimorphic with val: <7 12 16 30 34| Scale is weakly epimorphic with val: <7 12 16 30 37| Scale is weakly epimorphic with val: <7 12 16 32 32| Scale is weakly epimorphic with val: <7 12 17 30 32| Scale is weakly epimorphic with val: <7 12 17 30 35| Scale is weakly epimorphic with val: <7 12 17 30 38| Scale is weakly epimorphic with val: <7 12 17 32 33| Scale is weakly epimorphic with val: <7 12 18 30 33| Scale is weakly epimorphic with val: <7 12 18 30 36| Scale is weakly epimorphic with val: <7 12 18 32 34| Scale is weakly epimorphic with val: <7 12 19 30 34| Scale is weakly epimorphic with val: <7 12 19 30 37| Scale is weakly epimorphic with val: <7 12 19 32 35| Scale is weakly epimorphic with val: <7 12 19 35 35| Scale is weakly epimorphic with val: <8 11 15 32 33| Scale is weakly epimorphic with val: <8 11 15 32 36| Scale is weakly epimorphic with val: <8 11 16 31 32| Scale is weakly epimorphic with val: <8 11 16 32 34| Scale is weakly epimorphic with val: <8 11 16 32 37| Scale is weakly epimorphic with val: <8 11 17 31 33| Scale is weakly epimorphic with val: <8 11 17 32 32| Scale is weakly epimorphic with val: <8 11 17 32 35| Scale is weakly epimorphic with val: <8 11 17 32 38| Scale is weakly epimorphic with val: <8 11 18 31 34| Scale is weakly epimorphic with val: <8 11 18 32 33| Scale is weakly epimorphic with val: <8 11 18 32 36| Scale is weakly epimorphic with val: <8 11 18 34 34| Scale is weakly epimorphic with val: <8 11 19 31 35| Scale is weakly epimorphic with val: <8 11 19 32 34| Scale is weakly epimorphic with val: <8 11 19 32 37| Scale is weakly epimorphic with val: <8 11 19 34 35| Scale is weakly epimorphic with val: <8 12 15 31 32| Scale is weakly epimorphic with val: <8 12 15 33 33| Scale is weakly epimorphic with val: <8 12 15 33 36| Scale is weakly epimorphic with val: <8 12 16 31 33| Scale is weakly epimorphic with val: <8 12 16 33 34| Scale is weakly epimorphic with val: <8 12 16 33 37| Scale is weakly epimorphic with val: <8 12 17 31 34| Scale is weakly epimorphic with val: <8 12 17 33 35| Scale is weakly epimorphic with val: <8 12 17 33 38| Scale is weakly epimorphic with val: <8 12 17 34 34| Scale is weakly epimorphic with val: <8 12 18 31 35| Scale is weakly epimorphic with val: <8 12 18 33 33| Scale is weakly epimorphic with val: <8 12 18 33 36| Scale is weakly epimorphic with val: <8 12 18 34 35| Scale is weakly epimorphic with val: <8 12 19 31 36| Scale is weakly epimorphic with val: <8 12 19 33 34| Scale is weakly epimorphic with val: <8 12 19 33 37| Scale is weakly epimorphic with val: <8 12 19 34 36|
FIT/MODE
3: 0 0 3 N M DE S SD: 54.3861 c. M: 73.6807 c. 5: 1 0 4 N G T3 SD: 27.9674 c. M:-40.9175 c. 6: 1 0 5 N G T3 SD: 15.0361 c. M:-24.3160 c. 7: 1 0 6 N G T3 SD: 7.3395 c. M:-12.4578 c. 8: 1 0 7 N G T3 SD: 6.9098 c. M: 11.4250 c. 15: 2 0 13 N G T3 SD: 6.1219 c. M:-7.7145 c. 18: 2 1 15 N T3 SD: 5.7223 c. M:-9.3268 c. 19: 2 1 16 N T3 SD: 4.6131 c. M: 6.2657 c. 20: 2 1 17 N T3 SD: 5.1650 c. M: 8.8870 c. 24: 3 1 20 N T3 SD: 5.7646 c. M:-9.3268 c. 25: 3 1 21 N T3 SD: 3.5229 c. M:-6.0065 c. 26: 3 1 22 N T3 SD: 1.8397 c. M:-2.9417 c. 27: 3 1 23 N T3 SD: 1.9369 c. M: 3.3532 c. 33: 4 1 28 N T3 SD: 1.4125 c. M:-1.7807 c. 34: 4 1 29 N T3 SD: 0.2595 c. M: 0.4387 c. 128: 15 4 109 N T3 SD: 0.2369 c. M: 0.3269 c. 135: 16 4 115 N T3 SD: 0.2031 c. M:-0.3360 c. 162: 19 5 138 N T3 SD: 0.1718 c. M: 0.2788 c. 169: 20 5 144 N T3 SD: 0.1436 c. M:-0.2487 c. 196: 23 6 167 N T3 SD: 0.1430 c. M: 0.2475 c. 203: 24 6 173 N T3 SD: 0.1189 c. M:-0.1906 c. 230: 27 7 196 N T3 SD: 0.1342 c. M: 0.2254 c. 237: 28 7 202 N T3 SD: 0.1142 c. M:-0.1492 c. 263: 31 8 224 N T3 SD: 0.1007 c. M:-0.1739 c. 297: 35 9 253 N T3 SD: 0.0599 c. M:-0.1038 c. 331: 39 10 282 N T3 SD: 0.0283 c. M:-0.0481 c. 365: 43 11 311 N T3 SD: 0.0104 c. M: 0.0177 c. 1061: 125 32 904 N T3 SD: 0.0131 c. M:-0.0169 c. 1129: 133 34 962 N T3 SD: 0.0131 c. M: 0.0201 c. 1264: 149 38 1077 N T3 SD: 0.0104 c. M:-0.0179 c. 1298: 153 39 1106 N T3 SD: 0.0103 c. M:-0.0149 c. 1494: 176 45 1273 N T3 SD: 0.0121 c. M: 0.0196 c. 1595: 188 48 1359 N T3 SD: 0.0096 c. M:-0.0122 c. 1629: 192 49 1388 N T3 SD: 0.0058 c. M:-0.0099 c. 1663: 196 50 1417 N T3 SD: 0.0061 c. M:-0.0077 c. 1960: 231 59 1670 N T3 SD: 0.0068 c. M:-0.0097 c. 1994: 235 60 1699 N T3 SD: 0.0030 c. M:-0.0049 c. 2359: 278 71 2010 N T3 SD: 0.0015 c. M:-0.0021 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 26:27 x 35 SD: 8.9251 cents 27:28 x 36 SD: 2.1347 cents 28:29 x 37 SD: 7.8314 cents 29:30 x 39 SD: 7.4302 cents 30:31 x 40 SD: 0.9623 cents 31:32 x 41 SD: 7.2526 cents 32:33 x 43 SD: 7.2608 cents 33:34 x 44 SD: 3.5045 cents 34:35 x 45 SD: 7.6749 cents 36:37:38:48 SD: 7.6277 cents 39:40:41:52 SD: 6.5593 cents 42:43:44:56 SD: 6.4064 cents 44 x 46:59 SD: 5.1706 cents 45 x 47:60 SD: 0.8011 cents 46 x 48:61 SD: 4.7173 cents 47 x 49:63 SD: 4.6559 cents 48 x 50:64 SD: 1.5041 cents 49 x 51:65 SD: 4.9491 cents 50 x 52:67 SD: 5.1954 cents 51 x 53:68 SD: 3.5433 cents 52:54 x 69 SD: 5.3333 cents 53:55 x 71 SD: 4.8969 cents 54:56 x 72 SD: 2.1347 cents 55:57 x 73 SD: 4.2455 cents 56:58 x 75 SD: 3.9909 cents 57:59 x 76 SD: 0.5061 cents 73 x 76:97 SD: 3.5683 cents 74 x 77:99 SD: 3.8051 cents 75 x 78:100 SD: 2.8902 cents 76 x 79:101 SD: 4.3832 cents 77:80 x 103 SD: 4.6749 cents 78:81 x 104 SD: 3.3229 cents 79:82 x 105 SD: 4.0045 cents 80:83 x 107 SD: 3.6946 cents 81:84:85:108 SD: 3.5536 cents 83:86:87:111 SD: 3.2615 cents 84:87:88:112 SD: 2.3864 cents 86:89:90:115 SD: 2.3795 cents 87:90:91:116 SD: 1.3802 cents 90:93:94:120 SD: 0.8348 cents 102 x 106:136 SD: 3.5433 cents 103:107 x 137 SD: 4.1990 cents 104:108:109:139 SD: 3.6423 cents 105:109:110:140 SD: 3.0447 cents 107:111:112:143 SD: 2.7652 cents 108:112:113:144 SD: 2.1089 cents 110:114:115:147 SD: 2.0019 cents 111:115:116:148 SD: 1.2245 cents 114:118:119:152 SD: 0.3979 cents 204:211:213:272 SD: 0.3659 cents 231:239:241:308 SD: 0.1333 cents 435:450:454:580 SD: 0.1105 cents 552:571:576:736 SD: 0.0348 cents