Scala analysis: 359_D1
Diatonic tetrachord 104/97 * 97/90 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 104/97 120.632251 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 104/97 120.6323 2: 97/90 129.6717 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 104/97 120.632 cents 1: 1 97/90 129.672 cents 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 120/97 368.373 cents 2: 1 97/78 377.413 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 : 120.6 250.3 498.0 120.6: 129.7 377.4 498.0 250.3: 247.7 368.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 120.6323 .. 247.7411 cents 1455/1352, 127.1088 cents 104/97, 120.6323 cents 2: 250.3039 .. 377.4127 cents 1455/1352, 127.1088 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 104/97, 120.6323 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.376207 Largest / Average step : 1.492281 Largest / Smallest step : 2.053688 Median interval of one step : 97/90, 129.6717 cents, amount: 1 Least squares average step : 151.09822 cents, oct.: 453.29467 cents Scale is strictly proper Scale has trivalence property 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 2.56289 cents Scale diversity : 1.129181 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.489569 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 : 676/675, 2.5629 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% Limited inverse transpositions with margin 118.0694 cents: 2 -- Rational properties -- Prime limit : 97 Odd number limit : 97 (O: 97 U: 97) Highest odd numerator or denominator: 97 Scale harmonicity : 0.027110 Fundamental : 1/4365, -12.0918 octaves, 0.0599 Hz. Guide tone : 104, 6.7004 octaves, 27209.059 Hz. Exponens Consonantiae : 4.539600E+05, 18.79221 octaves Euler's gradus suavitatis : 120 Sum of Mann's harmonic distance : 152.5, average 50.83333 Mersenne's string divisions : 136479 Sum of van Prooijen's expressibility: 4.11711, average 1.37237 Sum of Tenney's harmonic distance : 8.45220, average 2.81740 Vogel's harmonic complexity : 82.00000 Wille's k value : 727 Wilson's harmonic complexity : 121 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.47421, average 2.41237 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 .. 0 -1.00000 3 1 5: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 97: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 26 49| Scale is weakly epimorphic with val: <6 10 16 27 47| Scale is weakly epimorphic with val: <6 10 17 28 48| Scale is weakly epimorphic with val: <6 10 18 29 49| Scale is weakly epimorphic with val: <6 10 19 30 47| Scale is weakly epimorphic with val: <6 11 15 28 47| Scale is weakly epimorphic with val: <6 11 16 29 48| Scale is weakly epimorphic with val: <6 11 17 30 49| Scale is weakly epimorphic with val: <7 10 15 29 47| Scale is weakly epimorphic with val: <7 10 16 25 47| Scale is weakly epimorphic with val: <7 10 16 30 48| Scale is weakly epimorphic with val: <7 10 17 26 48| Scale is weakly epimorphic with val: <7 10 18 27 49| Scale is weakly epimorphic with val: <7 10 18 29 47| Scale is weakly epimorphic with val: <7 10 19 28 47| Scale is weakly epimorphic with val: <7 10 19 30 48| Scale is weakly epimorphic with val: <7 11 15 25 48| Scale is weakly epimorphic with val: <7 11 15 27 49| Scale is weakly epimorphic with val: <7 11 15 28 48| Scale is weakly epimorphic with val: <7 11 15 30 49| Scale is weakly epimorphic with val: <7 11 16 25 47| Scale is weakly epimorphic with val: <7 11 16 26 49| Scale is weakly epimorphic with val: <7 11 16 28 47| Scale is weakly epimorphic with val: <7 11 16 29 49| Scale is weakly epimorphic with val: <7 11 17 26 48| Scale is JI-epimorphic with val: <7 11 17 27 47| Scale is weakly epimorphic with val: <7 11 17 29 48| Scale is weakly epimorphic with val: <7 11 17 30 47| Scale is weakly epimorphic with val: <7 11 18 25 48| Scale is weakly epimorphic with val: <7 11 18 27 49| Scale is JI-epimorphic with val: <7 11 18 28 48| Scale is weakly epimorphic with val: <7 11 18 30 49| Scale is weakly epimorphic with val: <7 11 19 25 47| Scale is weakly epimorphic with val: <7 11 19 26 49| Scale is weakly epimorphic with val: <7 11 19 28 47| Scale is JI-epimorphic with val: <7 11 19 29 49| Scale is weakly epimorphic with val: <7 12 15 28 48| Scale is weakly epimorphic with val: <7 12 15 29 47| Scale is weakly epimorphic with val: <7 12 16 29 49| Scale is weakly epimorphic with val: <7 12 16 30 48| Scale is weakly epimorphic with val: <7 12 17 30 47| Scale is weakly epimorphic with val: <7 12 18 29 47| Scale is weakly epimorphic with val: <7 12 19 30 48| Scale is weakly epimorphic with val: <8 11 15 28 49| Scale is weakly epimorphic with val: <8 11 16 25 48| Scale is weakly epimorphic with val: <8 11 16 26 47| Scale is weakly epimorphic with val: <8 11 17 26 49| Scale is weakly epimorphic with val: <8 11 17 27 48| Scale is weakly epimorphic with val: <8 11 18 27 47| Scale is weakly epimorphic with val: <8 11 18 28 49| Scale is weakly epimorphic with val: <8 11 19 26 47| Scale is weakly epimorphic with val: <8 11 19 28 48| Scale is weakly epimorphic with val: <8 12 15 26 48| Scale is weakly epimorphic with val: <8 12 15 28 49| Scale is weakly epimorphic with val: <8 12 16 26 47| Scale is weakly epimorphic with val: <8 12 16 27 49| Scale is weakly epimorphic with val: <8 12 17 27 48| Scale is weakly epimorphic with val: <8 12 17 28 47| Scale is weakly epimorphic with val: <8 12 18 28 49| Scale is weakly epimorphic with val: <8 12 18 29 48| Scale is weakly epimorphic with val: <8 12 19 26 47| Scale is weakly epimorphic with val: <8 12 19 30 49|
FIT/MODE
3: 0 1 2 N G T3 SD: 84.9642 c. M: 120.6323 c. 4: 1 1 2 P M ME S SD: 2.3586 c. M:-3.8790 c. 30: 7 8 15 P T3 SD: 2.6579 c. M: 4.4218 c. 34: 8 9 17 P T3 SD: 2.1222 c. M: 3.4452 c. 38: 9 10 19 P T3 SD: 1.7121 c. M: 2.6742 c. 42: 10 11 21 P T3 SD: 1.3958 c. M: 2.0501 c. 46: 11 12 23 P T3 SD: 1.1543 c. M: 1.5345 c. 50: 12 13 25 P T3 SD: 0.9756 c. M: 1.2814 c. 54: 13 14 27 P T3 SD: 0.8522 c. M: 1.2814 c. 58: 14 15 29 P T3 SD: 0.7776 c. M: 1.2814 c. 62: 15 16 31 P T3 SD: 0.7441 c. M: 1.2814 c. 66: 16 17 33 P T3 SD: 0.7424 c. M: 1.2814 c. 78: 19 20 39 P T3 SD: 0.8393 c. M: 1.2814 c. 95: 23 25 47 SP T3 SD: 0.7742 c. M:-1.3398 c. 99: 24 26 49 SP T3 SD: 0.7150 c. M:-1.2339 c. 103: 25 27 51 SP T3 SD: 0.6720 c. M:-1.1362 c. 107: 26 28 53 SP T3 SD: 0.6441 c. M:-1.0459 c. 111: 27 29 55 SP T3 SD: 0.6297 c. M:-0.9620 c. 115: 28 30 57 SP T3 SD: 0.6270 c. M:-0.8840 c. 119: 29 31 59 SP T3 SD: 0.6340 c. M:-0.8112 c. 133: 32 35 66 SP T3 SD: 0.5751 c. M: 0.8019 c. 137: 33 36 68 SP T3 SD: 0.4933 c. M: 0.6652 c. 141: 34 37 70 SP T3 SD: 0.4173 c. M: 0.5363 c. 145: 35 38 72 SP T3 SD: 0.3473 c. M:-0.4359 c. 149: 36 39 74 SP T3 SD: 0.2837 c. M:-0.3898 c. 153: 37 40 76 SP T3 SD: 0.2280 c. M:-0.3462 c. 157: 38 41 78 SP T3 SD: 0.1828 c. M:-0.3047 c. 161: 39 42 80 SP T3 SD: 0.1533 c. M:-0.2653 c. 165: 40 43 82 SP T3 SD: 0.1450 c. M:-0.2278 c. 169: 41 44 84 SP T3 SD: 0.1581 c. M:-0.1952 c. 211: 51 55 105 SP T3 SD: 0.1566 c. M: 0.2517 c. 215: 52 56 107 SP T3 SD: 0.1235 c. M: 0.1749 c. 219: 53 57 109 SP T3 SD: 0.1017 c. M: 0.1444 c. 223: 54 58 111 SP T3 SD: 0.0966 c. M: 0.1648 c. 372: 90 97 185 SP T3 SD: 0.0860 c. M: 0.1375 c. 376: 91 98 187 SP T3 SD: 0.0601 c. M: 0.0948 c. 380: 92 99 189 SP T3 SD: 0.0349 c. M: 0.0529 c. 384: 93 100 191 SP T3 SD: 0.0113 c. M:-0.0155 c. 772: 187 201 384 SP T3 SD: 0.0069 c. M:-0.0088 c. 1156: 280 301 575 SP T3 SD: 0.0064 c. M:-0.0111 c. 1928: 467 502 959 SP T3 SD: 0.0063 c. M:-0.0102 c. 2147: 520 559 1068 SP T3 SD: 0.0050 c. M: 0.0065 c. 2151: 521 560 1070 SP T3 SD: 0.0046 c. M: 0.0080 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: 53.3940 cents 6 x 7:8 S SD: 8.2835 cents 7 x 8:9 S SD: 32.9015 cents 8 x 9:11 SD: 35.3214 cents 9:10 x 12 S SD: 30.8857 cents 10:11:12:13 H SD: 30.1091 cents 11:12:13:15 SD: 20.8902 cents 12:13:14:16 S SD: 8.1399 cents 25:27:29:33 SD: 7.4967 cents 26:28:30:35 S SD: 6.1446 cents 27:29:31:36 SD: 3.8505 cents 39:42:45:52 SD: 2.6944 cents 57:61:66:76 SD: 1.5845 cents 84:90:97:112 SD: 0.5607 cents 96:103:111:128 SD: 0.5327 cents 180:193:208:240 SD: 0.0308 cents