Scala analysis: 305_C23
Chromatic tetrachord 384/353 * 706/675 * 75/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 384/353 145.725753 2: 256/225 223.462571 Neapolitan diminished third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 75/64 274.5824 classic augmented second 1: 384/353 145.7258 2: 706/675 77.7368 3: 75/64 274.5824 classic augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 706/675 77.737 cents 1: 1 384/353 145.726 cents 1: 1 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 353/288 352.319 cents 2: 1 450/353 420.308 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 : 145.7 223.5 498.0 145.7: 77.7 352.3 498.0 223.5: 274.6 420.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.7368 .. 274.5824 cents 50625/45184, 196.8456 cents 706/675, 77.7368 cents 2: 223.4626 .. 420.3082 cents 50625/45184, 196.8456 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 706/675, 77.7368 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 2.135603 Largest / Average step : 1.653962 Largest / Smallest step : 3.532206 Median interval of one step : 384/353, 145.7258 cents, amount: 1 Least squares average step : 149.05614 cents, oct.: 447.16841 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1890-tone equal temperament with octave 4/3 degrees: 553 848 1890 Least number of segments generator : 947 of 249.550 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1541 of 406.078 cents and inv. generated superset size: 63 = 60 more = 2100.000% 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 51.11986 cents Scale diversity : 1.081367 Lumma stability : 0.312168 Lumma impropriety factor : 0.102641 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 : 16875/16384, 51.1199 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% -- Rational properties -- Prime limit : 353 Odd number limit : 675 (O: 353 U: 675) Highest odd numerator or denominator: 353 Scale harmonicity : 0.034722 Fundamental : 1/79425, -16.2773 octaves, 0.0033 Hz. Guide tone : 768, 9.5850 octaves, 200928.434 Hz. Exponens Consonantiae : 6.099840E+07, 25.86227 octaves Euler's gradus suavitatis : 375 Sum of Mann's harmonic distance : 612.5, average 204.16667 Mersenne's string divisions : 2481479 Sum of van Prooijen's expressibility: 5.37708, average 1.79236 Sum of Tenney's harmonic distance : 10.97171, average 3.65724 Vogel's harmonic complexity : 251.66667 Wille's k value : 13237 Wilson's harmonic complexity : 372 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 33.32236, average 5.55373 Lattice compactness (without 2's) : 12.67005, average 2.11167 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 5.66667 17 3: -2 .. 1 -0.66667 4 1 5: -2 .. 0 -0.66667 2 1 353: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 15 61| Scale is weakly epimorphic with val: <7 11 16 62| Scale is weakly epimorphic with val: <7 11 18 61| Scale is weakly epimorphic with val: <7 11 19 62|
FIT/MODE
3: 1 0 2 N G T3 SD: 35.1752 c. M: 57.4476 c. 4: 1 1 2 P M ME S SD: 19.1778 c. M:-25.5599 c. 6: 2 1 3 P T3 SD: 18.8411 c. M:-25.5599 c. 7: 2 1 4 N T3 SD: 6.1112 c. M: 10.0147 c. 11: 3 2 6 N T3 SD: 5.9569 c. M: 9.8953 c. 13: 4 2 7 N T3 SD: 5.7023 c. M:-7.5189 c. 18: 5 3 10 N T3 SD: 4.4314 c. M: 7.3799 c. 20: 6 3 11 N T3 SD: 2.1627 c. M:-3.6877 c. 27: 8 4 15 N T3 SD: 1.6172 c. M: 2.1092 c. 31: 9 5 17 N T3 SD: 1.0671 c. M:-1.4610 c. 38: 11 6 21 N T3 SD: 0.9736 c. M: 1.5548 c. 51: 15 8 28 N T3 SD: 0.7933 c. M:-1.1460 c. 58: 17 9 32 N T3 SD: 0.1865 c. M:-0.2530 c. 147: 43 23 81 N T3 SD: 0.0892 c. M:-0.1495 c. 205: 60 32 113 N T3 SD: 0.0384 c. M:-0.0503 c. 506: 148 79 279 N T3 SD: 0.0353 c. M: 0.0525 c. 564: 165 88 311 N T3 SD: 0.0307 c. M: 0.0488 c. 653: 191 102 360 N T3 SD: 0.0291 c. M: 0.0495 c. 711: 208 111 392 N T3 SD: 0.0150 c. M: 0.0248 c. 769: 225 120 424 N T3 SD: 0.0131 c. M: 0.0224 c. 916: 268 143 505 N T3 SD: 0.0063 c. M: 0.0095 c. 974: 285 152 537 N T3 SD: 0.0054 c. M: 0.0071 c. 1685: 493 263 929 N T3 SD: 0.0058 c. M: 0.0074 c. 1890: 553 295 1042 N T3 SD: 0.0011 c. M: 0.0015 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 6:7 S SD: 62.5132 cents 6 x 7:8 S SD: 21.7042 cents 7 x 8:9 S SD: 31.7157 cents 8 x 9:11 SD: 28.3739 cents 9:10 x 12 S SD: 18.3390 cents 10:11 x 13 SD: 23.9417 cents 12:13:14:16 S SD: 14.6646 cents 14:15:16:19 SD: 13.7000 cents 15:16:17:20 SD: 11.5544 cents 18:20 x 24 S SD: 18.3390 cents 19:21:22:25 SD: 15.6526 cents 20:22:23:27 SD: 11.4327 cents 21:23:24:28 SD: 4.6898 cents 36:39:41:48 SD: 2.4500 cents 45:49:51:60 SD: 2.3288 cents 57:62:65:76 SD: 1.3047 cents 81:88:92:108 SD: 1.2478 cents 102:111:116:136 SD: 0.3452 cents 159:173:181:212 SD: 0.3220 cents 240:261:273:320 SD: 0.2201 cents 261:284:297:348 SD: 0.1790 cents 399:434:454:532 SD: 0.0627 cents 501:545:570:668 SD: 0.0272 cents