Scala analysis: 064_E5
Enharmonic tetrachord 63/62 * 31/30 * 80/63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63/62 27.700336 2: 21/20 84.467193 minor semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 80/63 413.5778 wide major third 1: 63/62 27.7003 2: 31/30 56.7669 31st-partial chroma 3: 80/63 413.5778 wide major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 63/62 27.700 cents 1: 1 31/30 56.767 cents 31st-partial chroma 1: 1 80/63 413.578 cents wide major third 2: 1 21/20 84.467 cents minor semitone 2: 1 40/31 441.278 cents 2: 1 248/189 470.345 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 : 27.7 84.5 498.0 27.7 : 56.8 470.3 498.0 84.5 : 413.6 441.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.7003 .. 413.5778 cents 4960/3969, 385.8775 cents 63/62, 27.7003 cents 2: 84.4672 .. 470.3447 cents 4960/3969, 385.8775 cents 1323/1600,-329.1106 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 63/62, 27.7003 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 80/63, 413.5778 cents Average / Smallest step : 5.993249 Largest / Average step : 2.491207 Largest / Smallest step : 14.930426 Median interval of one step : 31/30, 56.7669 cents, amount: 1 Least squares average step : 120.76927 cents, oct.: 362.30780 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1079-tone equal temperament with octave 4/3 degrees: 60 183 1079 Least number of segments generator : 540 of 249.253 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 855 of 394.651 cents and inv. generated superset size: 20 = 17 more = 666.667% 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 27.70034 cents Scale diversity : 0.282778 Lumma stability : 0.111236 Lumma impropriety factor : 0.660805 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 : 63/62, 27.7003 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 : 31 Odd number limit : 189 (O: 63 U: 189) Highest odd numerator or denominator: 63 Scale harmonicity : 0.034861 Fundamental : 1/1860, -10.8611 octaves, 0.1407 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 4.687200E+05, 18.83837 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 86.5, average 28.83333 Mersenne's string divisions : 35875 Sum of van Prooijen's expressibility: 3.59868, average 1.19956 Sum of Tenney's harmonic distance : 7.29416, average 2.43139 Vogel's harmonic complexity : 35.33333 Wille's k value : 976 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 18.11267, average 3.01878 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 2 0.66667 4 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 1 31: -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: <6 10 15 20 33| Scale is weakly epimorphic with val: <6 10 15 20 36| Scale is weakly epimorphic with val: <6 10 15 20 39| Scale is weakly epimorphic with val: <6 10 16 21 34| Scale is weakly epimorphic with val: <6 10 16 21 37| Scale is weakly epimorphic with val: <6 10 16 22 33| Scale is weakly epimorphic with val: <6 10 17 22 35| Scale is weakly epimorphic with val: <6 10 17 22 38| Scale is weakly epimorphic with val: <6 10 19 22 33| Scale is weakly epimorphic with val: <6 11 15 19 33| Scale is weakly epimorphic with val: <6 11 15 19 36| Scale is weakly epimorphic with val: <6 11 15 19 39| Scale is weakly epimorphic with val: <6 11 15 21 34| Scale is weakly epimorphic with val: <6 11 16 20 34| Scale is weakly epimorphic with val: <6 11 16 20 37| Scale is weakly epimorphic with val: <6 11 16 22 35| Scale is weakly epimorphic with val: <6 11 17 20 33| Scale is weakly epimorphic with val: <6 11 17 21 35| Scale is weakly epimorphic with val: <6 11 17 21 38| Scale is weakly epimorphic with val: <6 11 18 21 34| Scale is weakly epimorphic with val: <6 11 18 22 33| Scale is weakly epimorphic with val: <6 11 18 22 36| Scale is weakly epimorphic with val: <6 11 18 22 39| Scale is weakly epimorphic with val: <6 11 19 22 35| Scale is weakly epimorphic with val: <7 10 15 22 33| Scale is weakly epimorphic with val: <7 10 15 22 36| Scale is weakly epimorphic with val: <7 10 15 22 39| Scale is weakly epimorphic with val: <7 11 15 19 35| Scale is weakly epimorphic with val: <7 11 15 19 38| Scale is JI-epimorphic with val: <7 11 15 20 34| Scale is weakly epimorphic with val: <7 11 15 20 37| Scale is weakly epimorphic with val: <7 11 15 22 35| Scale is weakly epimorphic with val: <7 11 15 22 38| Scale is weakly epimorphic with val: <7 11 16 18 35| Scale is weakly epimorphic with val: <7 11 16 18 38| Scale is weakly epimorphic with val: <7 11 16 20 33| Scale is weakly epimorphic with val: <7 11 16 20 36| Scale is weakly epimorphic with val: <7 11 16 20 39| Scale is JI-epimorphic with val: <7 11 16 21 35| Scale is weakly epimorphic with val: <7 11 16 21 38| Scale is weakly epimorphic with val: <7 11 17 18 34| Scale is weakly epimorphic with val: <7 11 17 18 37| Scale is weakly epimorphic with val: <7 11 17 19 33| Scale is weakly epimorphic with val: <7 11 17 19 36| Scale is weakly epimorphic with val: <7 11 17 19 39| Scale is weakly epimorphic with val: <7 11 17 21 34| Scale is weakly epimorphic with val: <7 11 17 21 37| Scale is weakly epimorphic with val: <7 11 17 22 33| Scale is JI-epimorphic with val: <7 11 17 22 36| Scale is weakly epimorphic with val: <7 11 17 22 39| Scale is weakly epimorphic with val: <7 11 18 19 35| Scale is weakly epimorphic with val: <7 11 18 19 38| Scale is weakly epimorphic with val: <7 11 18 20 34| Scale is weakly epimorphic with val: <7 11 18 20 37| Scale is weakly epimorphic with val: <7 11 18 22 35| Scale is weakly epimorphic with val: <7 11 18 22 38| Scale is weakly epimorphic with val: <7 11 19 20 33| Scale is weakly epimorphic with val: <7 11 19 20 36| Scale is weakly epimorphic with val: <7 11 19 20 39| Scale is weakly epimorphic with val: <7 11 19 21 35| Scale is weakly epimorphic with val: <7 11 19 21 38| Scale is weakly epimorphic with val: <7 12 15 20 33| Scale is weakly epimorphic with val: <7 12 15 20 36| Scale is weakly epimorphic with val: <7 12 15 20 39| Scale is weakly epimorphic with val: <7 12 15 21 35| Scale is weakly epimorphic with val: <7 12 16 19 33| Scale is weakly epimorphic with val: <7 12 16 21 34| Scale is weakly epimorphic with val: <7 12 16 21 37| Scale is weakly epimorphic with val: <7 12 16 22 36| Scale is weakly epimorphic with val: <7 12 17 20 34| Scale is weakly epimorphic with val: <7 12 17 22 35| Scale is weakly epimorphic with val: <7 12 17 22 38| Scale is weakly epimorphic with val: <7 12 18 21 35| Scale is weakly epimorphic with val: <7 12 19 19 33| Scale is weakly epimorphic with val: <7 12 19 22 36| Scale is weakly epimorphic with val: <8 11 16 22 33| Scale is weakly epimorphic with val: <8 11 19 22 33| Scale is weakly epimorphic with val: <8 12 15 21 34| Scale is weakly epimorphic with val: <8 12 15 22 33| Scale is weakly epimorphic with val: <8 12 15 22 36| Scale is weakly epimorphic with val: <8 12 15 22 39| Scale is weakly epimorphic with val: <8 12 16 22 35| Scale is weakly epimorphic with val: <8 12 17 20 33| Scale is weakly epimorphic with val: <8 12 18 21 34| Scale is weakly epimorphic with val: <8 12 19 22 35|
FIT/MODE
3: 0 0 3 N M DE S SD: 51.3226 c. M: 84.4672 c. 4: 0 1 3 N G T3 SD: 28.1119 c. M:-40.0441 c. 5: 0 1 4 N G T3 SD: 18.2262 c. M: 27.7003 c. 6: 0 1 5 N G T3 SD: 16.0150 c. M: 27.7003 c. 7: 0 1 6 N G T3 SD: 17.7452 c. M: 27.7003 c. 11: 1 1 9 N M DE S SD: 10.7390 c. M:-17.5765 c. 12: 1 1 10 N M DE S SD: 8.0138 c. M:-13.8034 c. 13: 1 1 11 N M DE S SD: 7.6187 c. M:-10.6108 c. 16: 1 2 13 N T3 SD: 5.5150 c. M:-8.9162 c. 17: 1 2 14 N T3 SD: 2.1807 c. M:-3.4231 c. 18: 1 2 15 N T3 SD: 0.8429 c. M: 1.4597 c. 35: 2 4 29 N T3 SD: 0.6852 c. M:-0.9119 c. 53: 3 6 44 N T3 SD: 0.2900 c. M:-0.4909 c. 71: 4 8 59 N T3 SD: 0.2664 c. M:-0.3585 c. 124: 7 14 103 N T3 SD: 0.2496 c. M:-0.4151 c. 183: 10 21 152 N T3 SD: 0.2856 c. M: 0.4848 c. 195: 11 22 162 N T3 SD: 0.2510 c. M:-0.3945 c. 200: 11 23 166 N T3 SD: 0.2121 c. M: 0.3079 c. 218: 12 25 181 N T3 SD: 0.1686 c. M: 0.2850 c. 236: 13 27 196 N T3 SD: 0.1564 c. M: 0.2657 c. 253: 14 29 210 N T3 SD: 0.1322 c. M:-0.1808 c. 271: 15 31 225 N T3 SD: 0.0874 c. M: 0.1333 c. 289: 16 33 240 N T3 SD: 0.0745 c. M: 0.1269 c. 307: 17 35 255 N T3 SD: 0.0937 c. M: 0.1213 c. 324: 18 37 269 N T3 SD: 0.0482 c. M:-0.0775 c. 342: 19 39 284 N T3 SD: 0.0181 c. M: 0.0312 c. 737: 41 84 612 N T3 SD: 0.0045 c. M:-0.0064 c. 1079: 60 123 896 N T3 SD: 0.0034 c. M: 0.0055 c. 1816: 101 207 1508 N T3 SD: 0.0018 c. M:-0.0030 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: 91.2019 cents 7 x 8:9 S SD: 79.8232 cents 8 x 9:11 SD: 65.3923 cents 9 x 10:12 S SD: 48.9683 cents 10 x 11:13 SD: 45.8459 cents 11 x 12:15 S SD: 38.3800 cents 12 x 13:16 SD: 27.0527 cents 13 x 14:17 SD: 27.6192 cents 14 x 15:19 SD: 23.2499 cents 15 x 16:20 S SD: 13.6320 cents 16 x 17:21 SD: 17.0521 cents 17 x 18:23 SD: 14.5659 cents 18 x 19:24 SD: 4.5679 cents 19 x 20:25 S SD: 11.6682 cents 20 x 21:27 SD: 10.7531 cents 21 x 22:28 SD: 1.9651 cents 22 x 23:29 SD: 10.5817 cents 23 x 24:31 SD: 10.8010 cents 24 x 25:32 SD: 6.8974 cents 25 x 26:33 SD: 12.0126 cents 26 x 27:35 SD: 12.6532 cents 27 x 28:36 SD: 10.7531 cents 28 x 29:37 SD: 14.1733 cents 29 x 30:39 SD: 14.8763 cents 30 x 32:40 S SD: 13.6320 cents 31:32:33:41 SD: 12.9308 cents 32:33:34:43 SD: 11.8098 cents 33:34:35:44 SD: 9.8764 cents 35:36:37:47 SD: 9.0280 cents 36:37:38:48 SD: 7.2486 cents 38:39:40:51 SD: 7.0387 cents 39:40:41:52 SD: 5.4228 cents 42:43:44:56 SD: 4.5387 cents 54:55:57:72 SD: 3.3333 cents 57:58:60:76 SD: 1.6527 cents 60:61:63:80 SD: 0.3053 cents 318:323:334:424 SD: 0.2881 cents 378:384:397:504 SD: 0.2056 cents 438:445:460:584 SD: 0.1508 cents 498:506:523:664 SD: 0.1163 cents 501:509:526:668 SD: 0.1066 cents 558:567:586:744 SD: 0.0985 cents 561:570:589:748 SD: 0.0693 cents