Scala analysis: pygmie
Pygmie scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 21/16 470.780907 narrow fourth 3: 3/2 701.955001 perfect fifth 4: 7/4 968.825906 harmonic seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 8/7 231.1741 septimal whole tone 2: 147/128 239.6068 3: 8/7 231.1741 septimal whole tone 4: 7/6 266.8709 septimal minor third 5: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 8/7 231.174 cents septimal whole tone 1: 1 147/128 239.607 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 2: 2 21/16 470.781 cents narrow fourth 2: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 3: 2 32/21 729.219 cents wide fifth 3: 1 49/32 737.652 cents 4: 1 12/7 933.129 cents septimal major sixth 4: 1 256/147 960.393 cents 4: 3 7/4 968.826 cents harmonic seventh 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 4 5 0.0 : 231.2 470.8 702.0 968.8 1200.0 231.2 : 239.6 470.8 737.7 968.8 1200.0 470.8 : 231.2 498.0 729.2 960.4 1200.0 702.0 : 266.9 498.0 729.2 968.8 1200.0 968.8 : 231.2 462.3 702.0 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 231.1741 .. 266.8709 cents 49/48, 35.6968 cents 8/7, 231.1741 cents 2: 462.3482 .. 498.0450 cents 49/48, 35.6968 cents 384/343, 195.4773 cents 3: 701.9550 .. 737.6518 cents 49/48, 35.6968 cents 9/8, 203.9100 cents 4: 933.1291 .. 968.8259 cents 49/48, 35.6968 cents 384/343, 195.4773 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 8/7, 231.1741 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.038179 Largest / Average step : 1.111962 Largest / Smallest step : 1.154415 Median interval of one step : 8/7, 231.1741 cents, amount: 3 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 239.16190 cents, oct.: 1195.80950 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACA Step pattern size order : SMSLS Scale is a Constant Structure, by a margin of 195.47728 cents Scale diversity : 1.144764 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.881011 Rothenberg efficiency : 0.580000 redundancy: 0.420000 Efficiency x scale size : 2.900000 Number of different interval sizes : 12 = 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 : 1029/1024, 8.4327 cents Most common intervals : 8/7, 231.1741 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 470.781 968.826 cents Number of recognisable fifths : 2, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 7 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 3 = 60.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Limited transpositions with margin 35.6968 cents: 1 2 3 4 Limited inverse transpositions with margin 35.6968 cents: 1 2 3 4 -- Rational properties -- Prime limit : 7 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 21 Scale harmonicity : 0.033071 Average absolute harmonicity : 0.297676 Specific harmonicity : 0.179957 Fundamental : 1/112, -6.8074 octaves, 2.3359 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 1.881600E+04, 14.19967 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 35.5, average 7.10000 Mersenne's string divisions : 6105 Sum of van Prooijen's expressibility: 3.48954, average 0.69791 Sum of Tenney's harmonic distance : 6.80087, average 1.36017 Vogel's harmonic complexity : 13.00000 Wille's k value : 73 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 3 Triangular lattice diameter : 3 Lattice compactness : 48.99244, average 3.26616 Lattice compactness (without 2's) : 17.89292, average 1.19286 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.60000 11 1 3: 0 .. 1 0.40000 2 1 7: -1 .. 1 0.20000 3 3 Average exponent except 2's : 3 / 5 = 0.60000 Average absolute exponent except 2's: 5 / 5 = 1.00000 Scale is JI-epimorphic with val: <5 8 14| = patent
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 10.6434 c. M:-18.0450 c. 21: 4 4 4 5 4 SP M ME S SD: 9.6261 c. M: 16.2407 c. 26: 5 5 5 6 5 SP M ME S SD: 5.9803 c. M: 9.6473 c. 31: 6 6 6 7 6 SP M ME S SD: 3.6997 c. M: 6.2648 c. Slendric-5 36: 7 7 7 8 7 SP M ME S SD: 2.4525 c. M: 4.1142 c. Slendric-5 41: 8 8 8 9 8 SP M ME S SD: 2.1952 c. M:-2.9722 c. Rodan-5 77: 15 15 15 17 15 SP M DE S SD: 2.2100 c. M: 3.2484 c. Slendric-5 84: 16 17 16 19 16 SP T3 SD: 1.8862 c. M:-2.6027 c. 89: 17 18 17 20 17 SP T3 SD: 1.3896 c. M:-1.9606 c. 94: 18 19 18 21 18 SP T3 SD: 1.1233 c. M:-1.5595 c. 99: 19 20 19 22 19 SP T3 SD: 1.1368 c. M:-1.9464 c. 125: 24 25 24 28 24 SP T3 SD: 0.7318 c. M: 1.1550 c. 130: 25 26 25 29 25 SP T3 SD: 0.3167 c. M: 0.4165 c. 135: 26 27 26 30 26 SP T3 SD: 0.1941 c. M:-0.3302 c. 265: 51 53 51 59 51 SP T3 SD: 0.1658 c. M:-0.2307 c. 306: 59 61 59 68 59 SP T3 SD: 0.1523 c. M:-0.1985 c. 400: 77 80 77 89 77 SP T3 SD: 0.1488 c. M:-0.2191 c. 436: 84 87 84 97 84 SP T3 SD: 0.0829 c. M: 0.1387 c. 441: 85 88 85 98 85 SP T3 SD: 0.0854 c. M:-0.1184 c. 571: 110 114 110 127 110 SP T3 SD: 0.0178 c. M: 0.0286 c. 1277: 246 255 246 284 246 SP T3 SD: 0.0065 c. M:-0.0100 c. 1848: 356 369 356 411 356 SP T3 SD: 0.0046 c. M: 0.0069 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.0000 cents 3 x 4 x 5:6 S SD: 29.5861 cents 4 x 5:6:7:8 S SD: 21.1168 cents 6:7:8:9:11:12 SD: 18.4432 cents 8:9:11:12:14:16 SD: 17.0053 cents 10:11:13:15:18:20 SD: 16.7708 cents 12:14:16:18:21:24 S SD: 8.9835 cents 16:18:21:24:28:32 S SD: 5.4528 cents 20:23:26:30:35:40 SD: 3.9538 cents 28:32:37:42:49:56 SD: 2.3474 cents 36:41:47:54:63:72 SD: 2.1965 cents 48:55:63:72:84:96 SD: 0.9005 cents 64:73:84:96:112:128 SD: 0.6769 cents 112:128:147:168:196:224 SD: 0.0000 cents