Scala analysis: 304_C23
Chromatic tetrachord 768/737 * 737/675 * 75/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 768/737 71.330030 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: 768/737 71.3300 2: 737/675 152.1325 3: 75/64 274.5824 classic augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 768/737 71.330 cents 1: 1 737/675 152.133 cents 1: 1 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 900/737 345.912 cents 2: 1 737/576 426.715 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 : 71.3 223.5 498.0 71.3 : 152.1 426.7 498.0 223.5: 274.6 345.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.3300 .. 274.5824 cents 18425/16384, 203.2524 cents 768/737, 71.3300 cents 2: 223.4626 .. 426.7150 cents 18425/16384, 203.2524 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 768/737, 71.3300 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 2.327421 Largest / Average step : 1.653962 Largest / Smallest step : 3.849465 Median interval of one step : 737/675, 152.1325 cents, amount: 1 Least squares average step : 143.74215 cents, oct.: 431.22646 cents Scale is not proper Scale has trivalence property Scale is a mode of a 789-tone equal temperament with octave 4/3 degrees: 113 354 789 Least number of segments generator : 395 of 249.338 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 467 of 294.787 cents and inv. generated superset size: 14 = 11 more = 466.667% 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 51.11986 cents Scale diversity : 1.037582 Lumma stability : 0.286440 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 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 67 Odd number limit : 737 (O: 737 U: 737) Highest odd numerator or denominator: 737 Scale harmonicity : 0.021285 Fundamental : 1/165825, -17.3393 octaves, 0.0016 Hz. Guide tone : 768, 9.5850 octaves, 200928.434 Hz. Exponens Consonantiae : 1.273536E+08, 26.92426 octaves Euler's gradus suavitatis : 99 Sum of Mann's harmonic distance : 996.5, average 332.16667 Mersenne's string divisions : 723905 Sum of van Prooijen's expressibility: 5.69677, average 1.89892 Sum of Tenney's harmonic distance : 11.59243, average 3.86414 Vogel's harmonic complexity : 68.66667 Wille's k value : 27637 Wilson's harmonic complexity : 97 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 35.39329, average 5.89888 Lattice compactness (without 2's) : 13.45643, average 2.24274 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 6.00000 18 3: -2 .. 1 -0.66667 4 1 5: -2 .. 0 -0.66667 2 1 11: -1 .. 0 -0.33333 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 15 23 45| Scale is weakly epimorphic with val: <7 11 15 24 44| Scale is weakly epimorphic with val: <7 11 15 25 43| Scale is weakly epimorphic with val: <7 11 15 26 45| Scale is weakly epimorphic with val: <7 11 15 27 44| Scale is JI-epimorphic with val: <7 11 16 23 43| Scale is weakly epimorphic with val: <7 11 16 24 45| Scale is weakly epimorphic with val: <7 11 16 25 44| Scale is weakly epimorphic with val: <7 11 16 26 43| Scale is weakly epimorphic with val: <7 11 16 27 45| Scale is weakly epimorphic with val: <7 11 18 23 45| Scale is weakly epimorphic with val: <7 11 18 24 44| Scale is weakly epimorphic with val: <7 11 18 25 43| Scale is weakly epimorphic with val: <7 11 18 26 45| Scale is weakly epimorphic with val: <7 11 18 27 44| Scale is weakly epimorphic with val: <7 11 19 23 43| Scale is weakly epimorphic with val: <7 11 19 24 45| Scale is weakly epimorphic with val: <7 11 19 25 44| Scale is weakly epimorphic with val: <7 11 19 26 43| Scale is weakly epimorphic with val: <7 11 19 27 45| Scale is weakly epimorphic with val: <8 11 16 27 45| Scale is weakly epimorphic with val: <8 11 19 27 45|
FIT/MODE
3: 0 1 2 N G T3 SD: 52.8778 c. M: 71.3300 c. 4: 1 1 2 P M ME S SD: 34.0664 c. M:-53.1812 c. 5: 1 1 3 N M DE S SD: 21.5058 c. M:-28.2790 c. 6: 1 2 3 P T3 SD: 16.2242 c. M:-25.5599 c. 7: 1 2 4 N T3 SD: 5.7829 c. M: 10.0147 c. 13: 2 4 7 N T3 SD: 4.7967 c. M:-6.4044 c. 20: 3 6 11 N T3 SD: 1.9862 c. M:-3.3767 c. 27: 4 8 15 N T3 SD: 1.8684 c. M:-2.4544 c. 29: 4 9 16 N T3 SD: 1.5253 c. M: 2.6342 c. 36: 5 11 20 N T3 SD: 1.7418 c. M: 2.1571 c. 42: 6 13 23 N T3 SD: 1.0694 c. M:-1.8435 c. 49: 7 15 27 N T3 SD: 0.1354 c. M: 0.1807 c. 203: 29 62 112 N T3 SD: 0.1561 c. M: 0.2010 c. 216: 31 66 119 N T3 SD: 0.1423 c. M:-0.1965 c. 223: 32 68 123 N T3 SD: 0.1072 c. M:-0.1383 c. 272: 39 83 150 N T3 SD: 0.0636 c. M:-0.0808 c. 321: 46 98 177 N T3 SD: 0.0332 c. M:-0.0409 c. 370: 53 113 204 N T3 SD: 0.0111 c. M: 0.0154 c. 419: 60 128 231 N T3 SD: 0.0067 c. M: 0.0109 c. 789: 113 241 435 N T3 SD: 0.0030 c. M: 0.0051 c. 1208: 173 369 666 N T3 SD: 0.0026 c. M: 0.0040 c. 1997: 286 610 1101 N T3 SD: 0.0024 c. M: 0.0032 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 x 10:12 S SD: 20.5294 cents 10 x 11:13 SD: 36.5327 cents 11 x 13:15 SD: 38.1980 cents 12:13:14:16 S SD: 26.6789 cents 13:14:15:17 SD: 23.4874 cents 14:15:16:19 SD: 19.1869 cents 15:16:17:20 SD: 13.6552 cents 20:21:23:27 SD: 10.4205 cents 21:22:24:28 S SD: 4.0033 cents 44:46:50:59 SD: 3.8370 cents 45:47:51:60 SD: 2.6149 cents 51:53:58:68 SD: 1.6008 cents 72:75:82:96 SD: 0.6044 cents 168:175:191:224 SD: 0.4942 cents 189:197:215:252 SD: 0.1821 cents 261:272:297:348 SD: 0.0903 cents 450:469:512:600 SD: 0.0885 cents 501:522:570:668 SD: 0.0854 cents