Scala analysis: 395_D6
Diatonic tetrachord 35/33 * 11/10 * 8/7, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/33 101.866677 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 35/33 101.8667 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35/33 101.867 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 40/33 333.041 cents 2: 1 44/35 396.178 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 : 101.9 266.9 498.0 101.9: 165.0 396.2 498.0 266.9: 231.2 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.8667 .. 231.1741 cents 264/245, 129.3074 cents 35/33, 101.8667 cents 2: 266.8709 .. 396.1783 cents 264/245, 129.3074 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 35/33, 101.8667 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.629728 Largest / Average step : 1.392489 Largest / Smallest step : 2.269379 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 152.12453 cents, oct.: 456.37360 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 35.69681 cents Scale diversity : 1.229167 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.480740 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 : 49/48, 35.6968 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 35 Scale harmonicity : 0.024671 Average absolute harmonicity : 0.104200 Specific harmonicity : 0.121314 Fundamental : 1/66, -6.0444 octaves, 3.9640 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 9.240000E+03, 13.17368 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 44.0, average 14.66667 Mersenne's string divisions : 6188 Sum of van Prooijen's expressibility: 2.86629, average 0.95543 Sum of Tenney's harmonic distance : 5.76501, average 1.92167 Vogel's harmonic complexity : 15.00000 Wille's k value : 38 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.50820, average 2.25137 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.66667 2 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 19 23| Scale is weakly epimorphic with val: <6 10 15 19 26| Scale is weakly epimorphic with val: <6 10 16 19 24| Scale is weakly epimorphic with val: <6 10 16 19 27| Scale is weakly epimorphic with val: <6 10 16 20 23| Scale is weakly epimorphic with val: <6 10 17 19 25| Scale is weakly epimorphic with val: <6 10 17 20 24| Scale is weakly epimorphic with val: <6 10 18 19 23| Scale is weakly epimorphic with val: <6 10 18 19 26| Scale is weakly epimorphic with val: <6 10 18 20 25| Scale is weakly epimorphic with val: <6 10 19 19 24| Scale is weakly epimorphic with val: <6 10 19 19 27| Scale is weakly epimorphic with val: <6 10 19 20 26| Scale is weakly epimorphic with val: <6 11 15 20 25| Scale is weakly epimorphic with val: <6 11 15 22 23| Scale is weakly epimorphic with val: <6 11 16 20 23| Scale is weakly epimorphic with val: <6 11 16 20 26| Scale is weakly epimorphic with val: <6 11 16 22 24| Scale is weakly epimorphic with val: <6 11 17 20 24| Scale is weakly epimorphic with val: <6 11 17 20 27| Scale is weakly epimorphic with val: <6 11 17 22 25| Scale is weakly epimorphic with val: <6 11 18 19 23| Scale is weakly epimorphic with val: <6 11 18 20 25| Scale is weakly epimorphic with val: <6 11 18 22 26| Scale is weakly epimorphic with val: <6 11 19 19 24| Scale is weakly epimorphic with val: <6 11 19 20 23| Scale is weakly epimorphic with val: <6 11 19 20 26| Scale is weakly epimorphic with val: <6 11 19 22 27| Scale is weakly epimorphic with val: <7 10 15 20 23| Scale is weakly epimorphic with val: <7 10 15 20 26| Scale is weakly epimorphic with val: <7 10 15 22 24| Scale is weakly epimorphic with val: <7 10 16 20 24| Scale is weakly epimorphic with val: <7 10 16 20 27| Scale is weakly epimorphic with val: <7 10 16 22 25| Scale is weakly epimorphic with val: <7 10 17 19 23| Scale is weakly epimorphic with val: <7 10 17 20 25| Scale is weakly epimorphic with val: <7 10 17 22 26| Scale is weakly epimorphic with val: <7 10 18 19 24| Scale is weakly epimorphic with val: <7 10 18 20 23| Scale is weakly epimorphic with val: <7 10 18 20 26| Scale is weakly epimorphic with val: <7 10 18 22 27| Scale is weakly epimorphic with val: <7 10 19 19 25| Scale is weakly epimorphic with val: <7 10 19 20 24| Scale is weakly epimorphic with val: <7 10 19 20 27| Scale is weakly epimorphic with val: <7 11 15 19 24| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is JI-epimorphic with val: <7 11 15 20 23| Scale is weakly epimorphic with val: <7 11 15 20 26| Scale is weakly epimorphic with val: <7 11 15 22 24| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 16 19 25| Scale is JI-epimorphic with val: <7 11 16 20 24| Scale is weakly epimorphic with val: <7 11 16 20 27| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is weakly epimorphic with val: <7 11 17 19 23| Scale is weakly epimorphic with val: <7 11 17 19 26| Scale is JI-epimorphic with val: <7 11 17 20 25| = patent Scale is weakly epimorphic with val: <7 11 17 22 23| Scale is weakly epimorphic with val: <7 11 17 22 26| Scale is weakly epimorphic with val: <7 11 18 19 24| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 20 23| Scale is JI-epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 22 24| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 19 19 25| Scale is weakly epimorphic with val: <7 11 19 20 24| Scale is JI-epimorphic with val: <7 11 19 20 27| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is weakly epimorphic with val: <7 12 15 22 24| Scale is weakly epimorphic with val: <7 12 15 22 27| Scale is weakly epimorphic with val: <7 12 16 22 25| Scale is weakly epimorphic with val: <7 12 17 22 23| Scale is weakly epimorphic with val: <7 12 17 22 26| Scale is weakly epimorphic with val: <7 12 18 20 23| Scale is weakly epimorphic with val: <7 12 18 22 24| Scale is weakly epimorphic with val: <7 12 18 22 27| Scale is weakly epimorphic with val: <7 12 19 20 24| Scale is weakly epimorphic with val: <7 12 19 22 25| Scale is weakly epimorphic with val: <8 11 15 22 25| Scale is weakly epimorphic with val: <8 11 16 22 23| Scale is weakly epimorphic with val: <8 11 16 22 26| Scale is weakly epimorphic with val: <8 11 17 20 23| Scale is weakly epimorphic with val: <8 11 17 22 24| Scale is weakly epimorphic with val: <8 11 17 22 27| Scale is weakly epimorphic with val: <8 11 18 20 24| Scale is weakly epimorphic with val: <8 11 18 22 25| Scale is weakly epimorphic with val: <8 11 19 20 25| Scale is weakly epimorphic with val: <8 11 19 22 23| Scale is weakly epimorphic with val: <8 11 19 22 26| Scale is weakly epimorphic with val: <8 12 16 22 23| Scale is weakly epimorphic with val: <8 12 17 22 24| Scale is weakly epimorphic with val: <8 12 18 22 25| Scale is weakly epimorphic with val: <8 12 19 19 23| Scale is weakly epimorphic with val: <8 12 19 22 26|
FIT/MODE
3: 0 1 2 N G T3 SD: 82.7622 c. M: 101.8667 c. 4: 1 1 2 P M ME S SD: 16.6467 c. M:-22.6446 c. 5: 1 2 2 SP M ME S SD: 18.4958 c. M:-31.9561 c. 6: 1 2 3 P T3 SD: 14.9915 c. M: 18.8592 c. 9: 2 3 4 SP T3 SD: 7.6172 c. M:-9.8208 c. 11: 2 4 5 SP T3 SD: 7.0929 c. M: 11.3130 c. 15: 3 5 7 SP T3 SD: 1.4891 c. M: 2.2577 c. 39: 8 13 18 SP T3 SD: 0.7739 c. M:-1.3072 c. 54: 11 18 25 SP T3 SD: 0.4195 c. M:-0.5977 c. 88: 18 29 41 SP T3 SD: 0.5021 c. M: 0.8696 c. 97: 20 32 45 SP T3 SD: 0.4804 c. M:-0.8230 c. 112: 23 37 52 SP T3 SD: 0.2396 c. M:-0.4104 c. 127: 26 42 59 SP T3 SD: 0.1285 c. M: 0.2011 c. 166: 34 55 77 SP T3 SD: 0.1208 c. M:-0.1532 c. 181: 37 60 84 SP T3 SD: 0.0390 c. M: 0.0564 c. 308: 63 102 143 SP T3 SD: 0.0354 c. M: 0.0611 c. 474: 97 157 220 SP T3 SD: 0.0322 c. M:-0.0539 c. 489: 100 162 227 SP T3 SD: 0.0173 c. M: 0.0247 c. 655: 134 217 304 SP T3 SD: 0.0179 c. M:-0.0234 c. 670: 137 222 311 SP T3 SD: 0.0166 c. M: 0.0276 c. 836: 171 277 388 SP T3 SD: 0.0143 c. M:-0.0240 c. 963: 197 319 447 SP T3 SD: 0.0109 c. M:-0.0179 c. 1144: 234 379 531 SP T3 SD: 0.0036 c. M:-0.0062 c. 1325: 271 439 615 SP T3 SD: 0.0037 c. M:-0.0060 c. 1814: 371 601 842 SP T3 SD: 0.0039 c. M: 0.0063 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: 48.7680 cents 6 x 7:8 S SD: 0.0000 cents 7 x 8:9 S SD: 36.1882 cents 8 x 9:11 SD: 41.2374 cents 9:10:11:12 H SD: 37.9655 cents 10:11:12:13 H SD: 30.3426 cents 11:12:13:15 SD: 22.0888 cents 12:13:14:16 S SD: 12.2353 cents 17:18:20:23 SD: 9.7590 cents 18:19:21:24 SD: 2.7546 cents 48:51:56:64 SD: 1.0296 cents 66:70:77:88 SD: 0.0000 cents