Scala analysis: 063_E5
Enharmonic tetrachord 63/61 * 61/60 * 80/63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63/61 55.851103 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: 63/61 55.8511 2: 61/60 28.6161 3: 80/63 413.5778 wide major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 61/60 28.616 cents 1: 1 63/61 55.851 cents 1: 1 80/63 413.578 cents wide major third 2: 1 21/20 84.467 cents minor semitone 2: 1 244/189 442.194 cents 2: 1 80/61 469.429 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 : 55.9 84.5 498.0 55.9 : 28.6 442.2 498.0 84.5 : 413.6 469.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 28.6161 .. 413.5778 cents 1600/1281, 384.9617 cents 61/60, 28.6161 cents 2: 84.4672 .. 469.4289 cents 1600/1281, 384.9617 cents 1323/1600,-329.1106 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 61/60, 28.6161 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 80/63, 413.5778 cents Average / Smallest step : 5.801456 Largest / Average step : 2.491207 Largest / Smallest step : 14.452631 Median interval of one step : 63/61, 55.8511 cents, amount: 1 Least squares average step : 122.78003 cents, oct.: 368.34010 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1079-tone equal temperament with octave 4/3 degrees: 121 183 1079 Least number of segments generator : 540 of 249.253 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 555 of 256.177 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 28.61609 cents Scale diversity : 0.285453 Lumma stability : 0.114914 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 : 3780/3721, 27.2350 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 384.9617 cents: 2 -- Rational properties -- Prime limit : 61 Odd number limit : 189 (O: 63 U: 189) Highest odd numerator or denominator: 63 Scale harmonicity : 0.034861 Fundamental : 1/3660, -11.8376 octaves, 0.0715 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 9.223200E+05, 19.81491 octaves Euler's gradus suavitatis : 81 Sum of Mann's harmonic distance : 86.0, average 28.66667 Mersenne's string divisions : 35588 Sum of van Prooijen's expressibility: 3.59868, average 1.19956 Sum of Tenney's harmonic distance : 7.28710, average 2.42903 Vogel's harmonic complexity : 55.66667 Wille's k value : 1921 Wilson's harmonic complexity : 82 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 17.99945, average 2.99991 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 0.00000 4 3: -1 .. 2 0.66667 4 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 1 61: -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 42| Scale is weakly epimorphic with val: <6 10 16 21 43| Scale is weakly epimorphic with val: <6 10 17 22 44| Scale is weakly epimorphic with val: <6 11 15 19 42| Scale is weakly epimorphic with val: <6 11 16 20 43| Scale is weakly epimorphic with val: <6 11 17 21 44| Scale is weakly epimorphic with val: <6 11 18 22 42| Scale is weakly epimorphic with val: <7 10 15 22 43| Scale is weakly epimorphic with val: <7 11 15 19 42| Scale is weakly epimorphic with val: <7 11 15 20 44| Scale is weakly epimorphic with val: <7 11 15 22 42| Scale is weakly epimorphic with val: <7 11 16 18 42| Scale is weakly epimorphic with val: <7 11 16 20 43| Scale is JI-epimorphic with val: <7 11 16 21 42| Scale is weakly epimorphic with val: <7 11 17 18 44| Scale is weakly epimorphic with val: <7 11 17 19 43| Scale is weakly epimorphic with val: <7 11 17 21 44| Scale is JI-epimorphic with val: <7 11 17 22 43| Scale is weakly epimorphic with val: <7 11 18 19 42| Scale is weakly epimorphic with val: <7 11 18 20 44| Scale is weakly epimorphic with val: <7 11 18 22 42| Scale is weakly epimorphic with val: <7 11 19 20 43| Scale is weakly epimorphic with val: <7 11 19 21 42| Scale is weakly epimorphic with val: <7 12 15 20 43| Scale is weakly epimorphic with val: <7 12 15 21 42| Scale is weakly epimorphic with val: <7 12 16 21 44| Scale is weakly epimorphic with val: <7 12 16 22 43| Scale is weakly epimorphic with val: <7 12 17 22 42| Scale is weakly epimorphic with val: <7 12 18 21 42| Scale is weakly epimorphic with val: <7 12 19 22 43| Scale is weakly epimorphic with val: <8 12 15 21 42| Scale is weakly epimorphic with val: <8 12 15 22 44| Scale is weakly epimorphic with val: <8 12 16 22 43| Scale is weakly epimorphic with val: <8 12 18 21 42| Scale is weakly epimorphic with val: <8 12 19 22 43|
FIT/MODE
3: 0 0 3 N M DE S SD: 58.4638 c. M: 84.4672 c. 4: 0 1 3 N G T3 SD: 39.6773 c. M: 55.8511 c. 5: 1 0 4 N G T3 SD: 26.7334 c. M:-43.7579 c. 6: 1 0 5 N G T3 SD: 15.7014 c. M:-27.1564 c. 7: 1 0 6 N G T3 SD: 11.7104 c. M:-15.2982 c. 10: 1 1 8 N M DE S SD: 9.4134 c. M:-15.1418 c. 11: 1 1 9 N M DE S SD: 7.0442 c. M: 10.5743 c. 12: 1 1 10 N M DE S SD: 8.3262 c. M: 14.3474 c. 16: 2 1 13 N T3 SD: 6.3382 c. M:-8.9162 c. 17: 2 1 14 N T3 SD: 2.5324 c. M:-3.4231 c. 18: 2 1 15 N T3 SD: 0.8932 c. M: 1.4597 c. 35: 4 2 29 N T3 SD: 0.8110 c. M:-1.0683 c. 53: 6 3 44 N T3 SD: 0.3129 c. M:-0.5313 c. 71: 8 4 59 N T3 SD: 0.2277 c. M: 0.2906 c. 124: 14 7 103 N T3 SD: 0.2301 c. M:-0.3798 c. 188: 21 11 156 N T3 SD: 0.2173 c. M:-0.3064 c. 206: 23 12 171 N T3 SD: 0.1661 c. M: 0.2441 c. 224: 25 13 186 N T3 SD: 0.1540 c. M: 0.2657 c. 242: 27 14 201 N T3 SD: 0.1717 c. M: 0.2841 c. 259: 29 15 215 N T3 SD: 0.0961 c. M:-0.1428 c. 277: 31 16 230 N T3 SD: 0.0691 c. M: 0.1132 c. 330: 37 19 274 N T3 SD: 0.0291 c. M:-0.0495 c. 348: 39 20 289 N T3 SD: 0.0264 c. M: 0.0357 c. 401: 45 23 333 N T3 SD: 0.0235 c. M:-0.0392 c. 678: 76 39 563 N T3 SD: 0.0144 c. M: 0.0231 c. 731: 82 42 607 N T3 SD: 0.0137 c. M:-0.0171 c. 749: 84 43 622 N T3 SD: 0.0112 c. M: 0.0190 c. 1079: 121 62 896 N T3 SD: 0.0011 c. M:-0.0020 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 25:26 x 33 SD: 10.5821 cents 26:27 x 35 SD: 9.5453 cents 27:28 x 36 SD: 3.5549 cents 28:29 x 37 SD: 8.1409 cents 29:30 x 39 SD: 7.5647 cents 33:34:35:44 SD: 5.9640 cents 36:37:38:48 SD: 4.1407 cents 39:40:41:52 SD: 4.0681 cents 46 x 48:61 SD: 7.1652 cents 47 x 49:63 SD: 7.6841 cents 48 x 50:64 SD: 6.8974 cents 49:51 x 65 SD: 8.0340 cents 50:52:53:67 SD: 7.3713 cents 51:53:54:68 SD: 6.0120 cents 52:54:55:69 SD: 5.9562 cents 53:55:56:71 SD: 5.2986 cents 54:56:57:72 SD: 3.8588 cents 56:58:59:75 SD: 3.6215 cents 57:59:60:76 SD: 1.9328 cents 60:62:63:80 SD: 0.3053 cents 303:313:318:404 SD: 0.2978 cents 339:350:356:452 SD: 0.2058 cents 399:412:419:532 SD: 0.1339 cents 459:474:482:612 SD: 0.0847 cents 519:536:545:692 SD: 0.0558 cents 579:598:608:772 SD: 0.0500 cents