Scala analysis: 058_E4
Enharmonic tetrachord 88/87 * 29/28 * 14/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/87 19.785747 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: 88/87 19.7857 2: 29/28 60.7513 3: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88/87 19.786 cents 1: 1 29/28 60.751 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: 1 112/87 437.294 cents 2: 1 29/22 478.259 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 : 19.8 80.5 498.0 19.8 : 60.8 478.3 498.0 80.5 : 417.5 437.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.7857 .. 417.5080 cents 609/484, 397.7222 cents 88/87, 19.7857 cents 2: 80.5370 .. 478.2593 cents 609/484, 397.7222 cents 121/147,-336.9709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 88/87, 19.7857 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 8.390636 Largest / Average step : 2.514881 Largest / Smallest step : 21.101450 Median interval of one step : 29/28, 60.7513 cents, amount: 1 Least squares average step : 119.64249 cents, oct.: 358.92746 cents Scale is not proper Scale has trivalence property Scale is a mode of a 705-tone equal temperament with octave 4/3 degrees: 28 114 705 Least number of segments generator : 353 of 249.376 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 518 of 365.939 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.78575 cents Scale diversity : 0.233991 Lumma stability : 0.079454 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 : 88/87, 19.7857 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 29 Odd number limit : 87 (O: 29 U: 87) Highest odd numerator or denominator: 87 Scale harmonicity : 0.011337 Average absolute harmonicity : 0.086079 Specific harmonicity : 0.056379 Fundamental : 1/609, -9.2503 octaves, 0.4296 Hz. Guide tone : 88, 6.4594 octaves, 23023.050 Hz. Exponens Consonantiae : 5.359200E+04, 15.70973 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 112.5, average 37.50000 Mersenne's string divisions : 7525 Sum of van Prooijen's expressibility: 3.73886, average 1.24629 Sum of Tenney's harmonic distance : 7.62783, average 2.54261 Vogel's harmonic complexity : 33.33333 Wille's k value : 159 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 13.61376, average 2.26896 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 ..-1 -1.00000 3 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 25 32| Scale is weakly epimorphic with val: <6 10 18 25 35| Scale is weakly epimorphic with val: <6 10 18 25 38| Scale is weakly epimorphic with val: <6 10 19 26 33| Scale is weakly epimorphic with val: <6 10 19 26 36| Scale is weakly epimorphic with val: <6 10 19 27 32| Scale is weakly epimorphic with val: <6 10 20 27 34| Scale is weakly epimorphic with val: <6 10 20 27 37| Scale is weakly epimorphic with val: <6 10 22 27 32| Scale is weakly epimorphic with val: <6 11 18 26 34| Scale is weakly epimorphic with val: <6 11 18 26 37| Scale is weakly epimorphic with val: <6 11 19 27 32| Scale is weakly epimorphic with val: <6 11 19 27 35| Scale is weakly epimorphic with val: <6 11 19 27 38| Scale is weakly epimorphic with val: <7 10 18 24 33| Scale is weakly epimorphic with val: <7 10 18 24 36| Scale is weakly epimorphic with val: <7 10 18 26 34| Scale is weakly epimorphic with val: <7 10 19 24 32| Scale is weakly epimorphic with val: <7 10 19 25 34| Scale is weakly epimorphic with val: <7 10 19 25 37| Scale is weakly epimorphic with val: <7 10 19 27 35| Scale is weakly epimorphic with val: <7 10 20 25 33| Scale is weakly epimorphic with val: <7 10 20 26 32| Scale is weakly epimorphic with val: <7 10 20 26 35| Scale is weakly epimorphic with val: <7 10 20 26 38| Scale is weakly epimorphic with val: <7 10 21 26 34| Scale is weakly epimorphic with val: <7 10 21 27 33| Scale is weakly epimorphic with val: <7 10 21 27 36| Scale is weakly epimorphic with val: <7 10 22 24 32| Scale is weakly epimorphic with val: <7 10 22 27 35| Scale is weakly epimorphic with val: <7 11 18 23 34| Scale is weakly epimorphic with val: <7 11 18 23 37| Scale is JI-epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 24 36| Scale is weakly epimorphic with val: <7 11 18 26 34| Scale is weakly epimorphic with val: <7 11 18 26 37| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 27 36| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 24 35| Scale is weakly epimorphic with val: <7 11 19 24 38| Scale is JI-epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 25 37| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 27 35| Scale is weakly epimorphic with val: <7 11 19 27 38| Scale is weakly epimorphic with val: <7 11 20 23 32| Scale is weakly epimorphic with val: <7 11 20 23 35| Scale is weakly epimorphic with val: <7 11 20 23 38| Scale is weakly epimorphic with val: <7 11 20 25 33| Scale is weakly epimorphic with val: <7 11 20 25 36| Scale is weakly epimorphic with val: <7 11 20 26 32| Scale is JI-epimorphic with val: <7 11 20 26 35| Scale is weakly epimorphic with val: <7 11 20 26 38| Scale is weakly epimorphic with val: <7 11 21 23 34| Scale is weakly epimorphic with val: <7 11 21 23 37| Scale is weakly epimorphic with val: <7 11 21 24 33| Scale is weakly epimorphic with val: <7 11 21 24 36| Scale is weakly epimorphic with val: <7 11 21 26 34| Scale is weakly epimorphic with val: <7 11 21 26 37| Scale is weakly epimorphic with val: <7 11 21 27 33| Scale is JI-epimorphic with val: <7 11 21 27 36| Scale is weakly epimorphic with val: <7 11 22 24 32| Scale is weakly epimorphic with val: <7 11 22 24 35| Scale is weakly epimorphic with val: <7 11 22 24 38| Scale is weakly epimorphic with val: <7 11 22 25 34| Scale is weakly epimorphic with val: <7 11 22 25 37| Scale is weakly epimorphic with val: <7 11 22 27 32| Scale is weakly epimorphic with val: <7 11 22 27 35| Scale is weakly epimorphic with val: <7 11 22 27 38| Scale is weakly epimorphic with val: <7 12 18 26 34| Scale is weakly epimorphic with val: <7 12 18 26 37| Scale is weakly epimorphic with val: <7 12 18 27 33| Scale is weakly epimorphic with val: <7 12 19 27 32| Scale is weakly epimorphic with val: <7 12 19 27 35| Scale is weakly epimorphic with val: <7 12 19 27 38| Scale is weakly epimorphic with val: <7 12 20 26 32| Scale is weakly epimorphic with val: <7 12 21 27 33| Scale is weakly epimorphic with val: <8 11 18 24 33| Scale is weakly epimorphic with val: <8 11 18 24 36| Scale is weakly epimorphic with val: <8 11 18 25 35| Scale is weakly epimorphic with val: <8 11 19 23 33| Scale is weakly epimorphic with val: <8 11 19 25 34| Scale is weakly epimorphic with val: <8 11 19 25 37| Scale is weakly epimorphic with val: <8 11 19 26 36| Scale is weakly epimorphic with val: <8 11 20 24 34| Scale is weakly epimorphic with val: <8 11 20 26 32| Scale is weakly epimorphic with val: <8 11 20 26 35| Scale is weakly epimorphic with val: <8 11 20 26 38| Scale is weakly epimorphic with val: <8 11 20 27 37| Scale is weakly epimorphic with val: <8 11 21 25 35| Scale is weakly epimorphic with val: <8 11 21 27 33| Scale is weakly epimorphic with val: <8 11 21 27 36| Scale is weakly epimorphic with val: <8 11 22 23 33| Scale is weakly epimorphic with val: <8 11 22 26 36| Scale is weakly epimorphic with val: <8 12 18 24 33| Scale is weakly epimorphic with val: <8 12 18 25 32| Scale is weakly epimorphic with val: <8 12 18 25 35| Scale is weakly epimorphic with val: <8 12 18 25 38| Scale is weakly epimorphic with val: <8 12 18 27 36| Scale is weakly epimorphic with val: <8 12 19 25 34| Scale is weakly epimorphic with val: <8 12 19 26 33| Scale is weakly epimorphic with val: <8 12 19 26 36| Scale is weakly epimorphic with val: <8 12 20 23 32| Scale is weakly epimorphic with val: <8 12 20 26 35| Scale is weakly epimorphic with val: <8 12 20 27 34| Scale is weakly epimorphic with val: <8 12 20 27 37| Scale is weakly epimorphic with val: <8 12 21 24 33| Scale is weakly epimorphic with val: <8 12 21 27 36| Scale is weakly epimorphic with val: <8 12 22 25 34|
FIT/MODE
3: 0 0 3 N M DE S SD: 47.8807 c. M: 80.5370 c. 4: 0 1 3 N G T3 SD: 27.8401 c. M:-43.9742 c. 5: 0 1 4 N G T3 SD: 15.8663 c. M: 19.7857 c. 6: 0 1 5 N G T3 SD: 11.5120 c. M: 19.7857 c. 7: 0 1 6 N G T3 SD: 12.6439 c. M: 19.7857 c. 12: 0 2 10 N G T3 SD: 11.5120 c. M: 19.7857 c. 15: 1 1 13 N M DE S SD: 11.2503 c. M: 14.1310 c. 17: 1 2 14 N T3 SD: 6.9409 c. M:-9.5110 c. 18: 1 2 15 N T3 SD: 4.7697 c. M:-7.8834 c. 19: 1 2 16 N T3 SD: 3.8692 c. M:-6.4271 c. 20: 1 2 17 N T3 SD: 4.4785 c. M: 5.8303 c. 23: 1 3 19 N T3 SD: 3.6720 c. M:-6.0795 c. 24: 1 3 20 N T3 SD: 1.5315 c. M:-2.4705 c. 25: 1 3 21 N T3 SD: 0.4969 c. M: 0.8498 c. 49: 2 6 41 N T3 SD: 0.5469 c. M:-0.7764 c. 74: 3 9 62 N T3 SD: 0.2682 c. M:-0.4053 c. 99: 4 12 83 N T3 SD: 0.1964 c. M:-0.3373 c. 124: 5 15 104 N T3 SD: 0.2089 c. M:-0.2967 c. 173: 7 21 145 N T3 SD: 0.2155 c. M:-0.3664 c. 179: 7 22 150 N T3 SD: 0.1988 c. M: 0.3091 c. 204: 8 25 171 N T3 SD: 0.1479 c. M: 0.2546 c. 229: 9 28 192 N T3 SD: 0.1283 c. M: 0.2119 c. 253: 10 31 212 N T3 SD: 0.1158 c. M:-0.1738 c. 254: 10 31 213 N T3 SD: 0.1320 c. M: 0.1777 c. 278: 11 34 233 N T3 SD: 0.0656 c. M:-0.0818 c. 303: 12 37 254 N T3 SD: 0.0354 c. M: 0.0612 c. 328: 13 40 275 N T3 SD: 0.0438 c. M: 0.0603 c. 377: 15 46 316 N T3 SD: 0.0330 c. M:-0.0485 c. 402: 16 49 337 N T3 SD: 0.0217 c. M:-0.0369 c. 680: 27 83 570 N T3 SD: 0.0178 c. M:-0.0291 c. 705: 28 86 591 N T3 SD: 0.0033 c. M: 0.0052 c. 1812: 72 221 1519 N T3 SD: 0.0030 c. M:-0.0041 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 x 34:43 SD: 13.9443 cents 33 x 35:44 SD: 10.6648 cents 34 x 36:45 S SD: 11.2077 cents 36:37:38:48 SD: 10.1934 cents 38:39:40:51 SD: 9.6113 cents 39:40:41:52 SD: 8.2643 cents 41:42:43:55 SD: 8.1342 cents 42:43:44:56 SD: 6.9837 cents 45:46:47:60 SD: 6.3352 cents 48:49:50:64 SD: 6.2403 cents 54:55:57:72 SD: 5.9091 cents 56:57:59:75 SD: 5.5130 cents 57:58:60:76 SD: 4.4078 cents 59:60:62:79 SD: 4.3290 cents 60:61:63:80 SD: 3.2218 cents 63:64:66:84 SD: 2.4928 cents 66:67:69:88 SD: 2.4005 cents 78:79:82:104 SD: 2.1515 cents 81:82:85:108 SD: 1.0854 cents 84:85:88:112 SD: 0.2342 cents 357:361:374:476 SD: 0.1653 cents 441:446:462:588 SD: 0.0892 cents 525:531:550:700 SD: 0.0375 cents