Scala analysis: 460_D15
Diatonic tetrachord 9/8 * 11/10 * 320/297, Al-Farabi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 99/80 368.914230 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 320/297 129.1308 1: 9/8 203.9100 major whole tone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 320/297 129.1308
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 320/297 129.131 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 40/33 333.041 cents 2: 1 99/80 368.914 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 : 203.9 368.9 498.0 203.9: 165.0 294.1 498.0 368.9: 129.1 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 129.1308 .. 203.9100 cents 2673/2560, 74.7792 cents 320/297, 129.1308 cents 2: 294.1350 .. 368.9142 cents 2673/2560, 74.7792 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 320/297, 129.1308 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.285635 Largest / Average step : 1.228263 Largest / Smallest step : 1.579097 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 173.99096 cents, oct.: 521.97288 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1805-tone equal temperament with octave 4/3 degrees: 739 1337 1805 Least number of segments generator : 903 of 249.160 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1779 of 490.871 cents and inv. generated superset size: 42 = 39 more = 1400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.342936 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.699709 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 : 3267/3200, 35.8735 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly decreasing 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 : 11 Odd number limit : 297 (O: 99 U: 297) Highest odd numerator or denominator: 99 Scale harmonicity : 0.025919 Average absolute harmonicity : 0.121257 Specific harmonicity : 0.128950 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 9.504000E+04, 16.53625 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 101.5, average 33.83333 Mersenne's string divisions : 21301 Sum of van Prooijen's expressibility: 3.42700, average 1.14233 Sum of Tenney's harmonic distance : 6.83524, average 2.27841 Vogel's harmonic complexity : 15.33333 Wille's k value : 148 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 24.95069, average 4.15845 Lattice compactness (without 2's) : 13.18033, average 2.19672 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.66667 9 3: -1 .. 2 1.00000 5 2 5: -1 .. 0 -0.33333 1 11: 0 .. 1 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: <7 10 15 26| Scale is weakly epimorphic with val: <7 10 16 27| Scale is JI-epimorphic with val: <7 11 15 23| Scale is weakly epimorphic with val: <7 11 15 26| Scale is JI-epimorphic with val: <7 11 16 24| Scale is weakly epimorphic with val: <7 11 16 27| Scale is JI-epimorphic with val: <7 11 17 25| = patent Scale is weakly epimorphic with val: <7 11 18 23| Scale is JI-epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 19 24| Scale is JI-epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 12 15 23| Scale is weakly epimorphic with val: <7 12 15 26| Scale is weakly epimorphic with val: <7 12 16 24| Scale is weakly epimorphic with val: <7 12 16 27| Scale is weakly epimorphic with val: <7 12 17 25| Scale is weakly epimorphic with val: <7 12 18 23| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 19 24| Scale is weakly epimorphic with val: <7 12 19 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 30.5313 c. M: 37.8950 c. 4: 2 1 1 P M ME S SD: 26.1819 c. M:-45.1125 c. 5: 2 2 1 SP M ME S SD: 17.2583 c. M:-29.5218 c. 7: 3 2 2 SP M ME S SD: 9.3873 c. M: 13.1678 c. 12: 5 4 3 SP T3 SD: 3.3844 c. M:-4.6195 c. 27: 11 9 7 SP T3 SD: 0.5790 c. M: 1.0028 c. 66: 27 22 17 SP T3 SD: 0.4978 c. M:-0.8465 c. 73: 30 24 19 SP T3 SD: 0.5273 c. M:-0.7660 c. 93: 38 31 24 SP T3 SD: 0.4203 c. M:-0.6030 c. 100: 41 33 26 SP T3 SD: 0.2668 c. M: 0.3609 c. 127: 52 42 33 SP T3 SD: 0.1633 c. M: 0.2825 c. 154: 63 51 40 SP T3 SD: 0.1639 c. M: 0.2316 c. 166: 68 55 43 SP T3 SD: 0.0930 c. M:-0.1191 c. 193: 79 64 50 SP T3 SD: 0.0657 c. M:-0.1036 c. 293: 120 97 76 SP T3 SD: 0.0502 c. M:-0.0675 c. 320: 131 106 83 SP T3 SD: 0.0316 c. M: 0.0497 c. 486: 199 161 126 SP T3 SD: 0.0135 c. M:-0.0220 c. 806: 330 267 209 SP T3 SD: 0.0089 c. M: 0.0149 c. 999: 409 331 259 SP T3 SD: 0.0057 c. M:-0.0080 c. 1319: 540 437 342 SP T3 SD: 0.0067 c. M: 0.0099 c. 1485: 608 492 385 SP T3 SD: 0.0050 c. M:-0.0080 c. 1805: 739 598 468 SP T3 SD: 0.0015 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 5 x S SD: 17.3995 cents 5 x 6:7 S SD: 49.9317 cents 6:7 x 8 S SD: 31.4805 cents 7:8 x 9 S SD: 34.3053 cents 8:9:10:11 H SD: 18.6808 cents 9:10:11:12 H SD: 10.1382 cents 17:19:21:23 SD: 9.2927 cents 21:24:26:28 S SD: 9.0923 cents 24:27:30:32 S SD: 5.7998 cents 30:34:37:40 SD: 4.6826 cents 33:37:41:44 SD: 3.0067 cents 54:61:67:72 SD: 2.8097 cents 63:71:78:84 SD: 1.0541 cents 72:81:89:96 SD: 0.6480 cents 135:152:167:180 SD: 0.5216 cents 168:189:208:224 SD: 0.2775 cents 240:270:297:320 SD: 0.0000 cents