Scala analysis: 568_M76
Miscellaneous tetrachord 36/35 * 9/8 * 280/243
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 81/70 252.680383 Al-Hwarizmi's lute middle finger 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 280/243 245.3646 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 9/8 203.9100 major whole tone 3: 280/243 245.3646
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 1 280/243 245.365 cents 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 252.7 498.0 48.8 : 203.9 449.3 498.0 252.7: 245.4 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 245.3646 cents 2450/2187, 196.5942 cents 36/35, 48.7704 cents 2: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 19683/19600, 7.3158 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 280/243, 245.3646 cents Average / Smallest step : 3.404013 Largest / Average step : 1.477967 Largest / Smallest step : 5.031017 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 146.30472 cents, oct.: 438.91417 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1634-tone equal temperament with octave 4/3 degrees: 160 829 1634 Least number of segments generator : 819 of 249.632 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 821 of 250.242 cents and inv. generated superset size: 41 = 38 more = 1366.667% 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 7.31577 cents Scale diversity : 0.716918 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.210536 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 : 19683/19600, 7.3158 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 : 7 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.030286 Average absolute harmonicity : 0.097063 Specific harmonicity : 0.130000 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 6.804000E+04, 16.05410 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 114.5, average 38.16667 Mersenne's string divisions : 75047 Sum of van Prooijen's expressibility: 3.92967, average 1.30989 Sum of Tenney's harmonic distance : 7.93313, average 2.64438 Vogel's harmonic complexity : 14.00000 Wille's k value : 121 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 22.67942, average 3.77990 Lattice compactness (without 2's) : 18.20491, average 3.03415 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 4 1.66667 7 1 5: -1 .. 0 -0.66667 2 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 11 15 20| Scale is weakly epimorphic with val: <6 11 16 19| Scale is weakly epimorphic with val: <6 11 17 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is JI-epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <8 11 15 20| Scale is weakly epimorphic with val: <8 11 16 19| Scale is weakly epimorphic with val: <8 11 17 18|
FIT/MODE
3: 0 1 2 N G T3 SD: 57.4150 c. M: 86.6654 c. 4: 0 2 2 P M DE S SD: 28.2367 c. M: 48.7704 c. 6: 1 2 3 P T3 SD: 19.8793 c. M:-34.2371 c. 8: 1 3 4 P T3 SD: 8.0671 c. M:-13.4852 c. 10: 1 4 5 P T3 SD: 2.1947 c. M: 3.6579 c. 22: 2 9 11 P T3 SD: 2.9203 c. M: 3.6579 c. 31: 3 13 15 SP T3 SD: 2.5475 c. M:-4.3751 c. 32: 3 13 16 P T3 SD: 2.4291 c. M: 3.6579 c. 39: 4 16 19 SP T3 SD: 2.0639 c. M:-2.7273 c. 41: 4 17 20 SP T3 SD: 1.3987 c. M:-2.4158 c. 49: 5 20 24 SP T3 SD: 1.4414 c. M:-2.0505 c. 51: 5 21 25 SP T3 SD: 0.7080 c. M:-1.2249 c. 61: 6 25 30 SP T3 SD: 0.2754 c. M:-0.4245 c. 71: 7 29 35 SP T3 SD: 0.2108 c. M:-0.3326 c. 132: 13 54 65 SP T3 SD: 0.1745 c. M:-0.2795 c. 193: 19 79 95 SP T3 SD: 0.1940 c. M:-0.2600 c. 195: 19 80 96 SP T3 SD: 0.1723 c. M: 0.2429 c. 205: 20 84 101 SP T3 SD: 0.1046 c. M: 0.1806 c. 266: 26 109 131 SP T3 SD: 0.0719 c. M: 0.0893 c. 276: 27 113 136 SP T3 SD: 0.0398 c. M: 0.0489 c. 337: 33 138 166 SP T3 SD: 0.0213 c. M:-0.0368 c. 613: 60 251 302 SP T3 SD: 0.0128 c. M: 0.0221 c. 684: 67 280 337 SP T3 SD: 0.0131 c. M: 0.0172 c. 950: 93 389 468 SP T3 SD: 0.0108 c. M: 0.0144 c. 1021: 100 418 503 SP T3 SD: 0.0056 c. M:-0.0097 c. 1297: 127 531 639 SP T3 SD: 0.0059 c. M: 0.0099 c. 1358: 133 556 669 SP T3 SD: 0.0069 c. M:-0.0096 c. 1634: 160 669 805 SP T3 SD: 0.0013 c. M: 0.0022 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: 52.6754 cents 6 x 7:8 S SD: 7.0953 cents 7 x 8:9 S SD: 33.2663 cents 8 x 9:11 SD: 36.1129 cents 9 x 10:12 S SD: 35.1383 cents 10 x 12:13 S SD: 38.3576 cents 11:12:13:15 SD: 38.3331 cents 12:13:14:16 S SD: 30.3055 cents 13:14:15:17 SD: 28.8275 cents 14:15:16:19 SD: 26.6584 cents 15:16:17:20 SD: 24.1744 cents 17:18:20:23 SD: 21.0282 cents 18:19:21:24 SD: 15.6749 cents 19:20:22:25 SD: 15.3822 cents 20:21:23:27 SD: 14.3438 cents 21:22:24:28 S SD: 12.7873 cents 24:25:28:32 SD: 8.6991 cents 26:27:30:35 S SD: 7.9814 cents 27:28:31:36 SD: 6.5310 cents 30:31:35:40 SD: 5.4295 cents 32:33:37:43 SD: 4.7560 cents 33:34:38:44 SD: 2.9762 cents 39:40:45:52 SD: 2.3284 cents 63:65:73:84 SD: 1.9464 cents 69:71:80:92 SD: 1.1582 cents 102:105:118:136 SD: 0.4915 cents 108:111:125:144 SD: 0.4646 cents 210:216:243:280 SD: 0.0000 cents