Scala analysis: 057_E4
Enharmonic tetrachord 66/65 * 65/63 * 14/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66/65 26.431568 Winmeanma 2: 22/21 80.537035 undecimal minor semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 14/11 417.5080 undecimal diminished fourth or major third 1: 66/65 26.4316 Winmeanma 2: 65/63 54.1055 3: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66/65 26.432 cents Winmeanma 1: 1 65/63 54.105 cents 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 22/21 80.537 cents undecimal minor semitone 2: 1 84/65 443.940 cents 2: 1 130/99 471.613 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 : 26.4 80.5 498.0 26.4 : 54.1 471.6 498.0 80.5 : 417.5 443.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.4316 .. 417.5080 cents 455/363, 391.0764 cents 66/65, 26.4316 cents 2: 80.5370 .. 471.6134 cents 455/363, 391.0764 cents 121/147,-336.9709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66/65, 26.4316 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 6.280937 Largest / Average step : 2.514881 Largest / Smallest step : 15.795808 Median interval of one step : 65/63, 54.1055 cents, amount: 1 Least squares average step : 120.11719 cents, oct.: 360.35156 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1583-tone equal temperament with octave 4/3 degrees: 84 256 1583 Least number of segments generator : 792 of 249.180 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1198 of 376.916 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 26.43157 cents Scale diversity : 0.255445 Lumma stability : 0.106141 Lumma impropriety factor : 0.676587 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 : 66/65, 26.4316 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% -- Rational properties -- Prime limit : 13 Odd number limit : 99 (O: 65 U: 99) Highest odd numerator or denominator: 65 Scale harmonicity : 0.015539 Average absolute harmonicity : 0.088415 Specific harmonicity : 0.074796 Fundamental : 1/1365, -10.4147 octaves, 0.1917 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 1.801800E+05, 17.45908 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 90.5, average 30.16667 Mersenne's string divisions : 39431 Sum of van Prooijen's expressibility: 3.61225, average 1.20408 Sum of Tenney's harmonic distance : 7.37628, average 2.45876 Vogel's harmonic complexity : 27.33333 Wille's k value : 357 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 13.67837, average 2.27973 Lattice compactness (without 2's) : 11.43777, average 1.90629 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 16 19 24 27| Scale is JI-epimorphic with val: <7 11 16 19 25 26| Scale is weakly epimorphic with val: <7 11 16 20 25 28| Scale is JI-epimorphic with val: <7 11 16 20 26 27| Scale is weakly epimorphic with val: <7 11 16 21 24 28| Scale is weakly epimorphic with val: <7 11 16 21 26 26| Scale is weakly epimorphic with val: <7 11 17 19 24 26| Scale is weakly epimorphic with val: <7 11 17 19 25 28| Scale is weakly epimorphic with val: <7 11 17 20 25 27| = patent Scale is JI-epimorphic with val: <7 11 17 20 26 26| Scale is weakly epimorphic with val: <7 11 17 21 24 27| Scale is weakly epimorphic with val: <7 11 17 21 26 28| Scale is weakly epimorphic with val: <7 11 18 19 24 28| Scale is weakly epimorphic with val: <7 11 18 19 25 27| Scale is weakly epimorphic with val: <7 11 18 20 25 26| Scale is weakly epimorphic with val: <7 11 18 20 26 28| Scale is weakly epimorphic with val: <7 11 18 21 24 26| Scale is weakly epimorphic with val: <7 11 18 21 26 27| Scale is weakly epimorphic with val: <7 12 16 20 26 26|
FIT/MODE
3: 0 0 3 N M DE S SD: 48.9382 c. M: 80.5370 c. 4: 0 1 3 N G T3 SD: 29.6218 c. M:-43.9742 c. 5: 0 1 4 N G T3 SD: 18.8181 c. M: 26.4316 c. 6: 0 1 5 N G T3 SD: 15.3268 c. M: 26.4316 c. 7: 0 1 6 N G T3 SD: 16.1942 c. M: 26.4316 c. 11: 1 1 9 N M DE S SD: 12.3217 c. M:-18.8453 c. 12: 1 1 10 N M DE S SD: 8.8180 c. M:-15.0722 c. 13: 1 1 11 N M DE S SD: 7.2215 c. M:-11.8796 c. 14: 1 1 12 N M DE S SD: 7.5658 c. M: 9.3877 c. 16: 1 2 13 N T3 SD: 7.8969 c. M:-12.8464 c. 17: 1 2 14 N T3 SD: 4.5563 c. M:-7.3533 c. 18: 1 2 15 N T3 SD: 1.5953 c. M:-2.4705 c. 19: 1 2 16 N T3 SD: 1.1033 c. M: 1.8984 c. 37: 2 4 31 N T3 SD: 0.3117 c. M:-0.4898 c. 93: 5 10 78 N T3 SD: 0.2324 c. M:-0.3450 c. 130: 7 14 109 N T3 SD: 0.2282 c. M:-0.3862 c. 149: 8 16 125 N T3 SD: 0.2548 c. M: 0.3150 c. 167: 9 18 140 N T3 SD: 0.2364 c. M:-0.4092 c. 204: 11 22 171 N T3 SD: 0.2453 c. M:-0.4238 c. 210: 11 23 176 N T3 SD: 0.2064 c. M: 0.3435 c. 228: 12 25 191 N T3 SD: 0.2079 c. M:-0.2861 c. 229: 12 25 192 N T3 SD: 0.1962 c. M: 0.3331 c. 247: 13 27 207 N T3 SD: 0.1435 c. M: 0.2187 c. 266: 14 29 223 N T3 SD: 0.1271 c. M: 0.2187 c. 284: 15 31 238 N T3 SD: 0.1056 c. M:-0.1322 c. 303: 16 33 254 N T3 SD: 0.0764 c. M: 0.1322 c. 340: 18 37 285 N T3 SD: 0.0408 c. M: 0.0645 c. 377: 20 41 316 N T3 SD: 0.0286 c. M:-0.0485 c. 396: 21 43 332 N T3 SD: 0.0284 c. M: 0.0449 c. 433: 23 47 363 N T3 SD: 0.0184 c. M:-0.0235 c. 773: 41 84 648 N T3 SD: 0.0088 c. M: 0.0152 c. 810: 43 88 679 N T3 SD: 0.0078 c. M:-0.0110 c. 1206: 64 131 1011 N T3 SD: 0.0043 c. M: 0.0074 c. 1583: 84 172 1327 N T3 SD: 0.0040 c. M:-0.0059 c. 1979: 105 215 1659 N T3 SD: 0.0046 c. M: 0.0067 c. 2016: 107 219 1690 N T3 SD: 0.0014 c. M:-0.0024 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: 93.1669 cents 7 x 8:9 S SD: 81.6327 cents 8 x 9:11 SD: 67.1917 cents 9 x 10:12 S SD: 50.9333 cents 10 x 11:13 SD: 47.5812 cents 11 x 12:15 S SD: 40.0864 cents 12 x 13:16 SD: 29.0178 cents 13 x 14:17 SD: 29.2030 cents 14 x 15:19 SD: 24.7619 cents 15 x 16:20 S SD: 15.5971 cents 16 x 17:21 SD: 18.3002 cents 17 x 18:23 SD: 15.6363 cents 18 x 19:24 SD: 6.5330 cents 19 x 20:25 S SD: 12.1871 cents 20 x 21:27 SD: 10.9312 cents 21 x 22:28 SD: 0.0000 cents 22 x 23:29 SD: 10.0536 cents 23 x 24:31 SD: 9.9663 cents 24 x 25:32 SD: 4.9323 cents 25 x 26:33 SD: 10.7521 cents 26 x 27:35 SD: 11.2416 cents 27 x 28:36 SD: 8.7881 cents 28 x 29:37 SD: 12.5754 cents 29 x 30:39 SD: 13.2104 cents 30 x 31:40 SD: 11.8851 cents 31 x 32:41 SD: 14.5814 cents 32:33:34:43 SD: 12.9023 cents 33:34:35:44 SD: 11.0180 cents 34:35:36:45 S SD: 10.8865 cents 35:36:37:47 SD: 9.9795 cents 36:37:38:48 SD: 8.2450 cents 38:39:40:51 SD: 7.7519 cents 39:40:41:52 SD: 6.1396 cents 42:43:44:56 SD: 4.7684 cents 45:46:47:60 SD: 4.2506 cents 57:58:60:76 SD: 3.0150 cents 60:61:63:80 SD: 1.4988 cents 63:64:66:84 SD: 0.2775 cents 396:402:415:528 SD: 0.2388 cents 399:405:418:532 SD: 0.1973 cents 459:466:481:612 SD: 0.1876 cents 462:469:484:616 SD: 0.1325 cents 525:533:550:700 SD: 0.0833 cents 588:597:616:784 SD: 0.0446 cents