Scala analysis: 473_D16
Diatonic tetrachord 11/10 * 13/12 * 160/143, Al-Farabi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 143/120 303.576889 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 160/143 194.4681 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 160/143 194.4681
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 160/143 194.468 cents 2: 1 143/120 303.577 cents 2: 1 40/33 333.041 cents 2: 1 16/13 359.472 cents tridecimal neutral third 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 : 165.0 303.6 498.0 165.0: 138.6 333.0 498.0 303.6: 194.5 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 194.4681 cents 1920/1859, 55.8954 cents 13/12, 138.5727 cents 2: 303.5769 .. 359.4723 cents 1920/1859, 55.8954 cents 20449/19200, 109.1088 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 160/143, 194.4681 cents Average / Smallest step : 1.198036 Largest / Average step : 1.171389 Largest / Smallest step : 1.403366 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 161.87807 cents, oct.: 485.63422 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 109.10878 cents Scale diversity : 1.329395 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.775541 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 : 66/65, 26.4316 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 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 Limited inverse transpositions with margin 55.8954 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 143 (O: 143 U: 143) Highest odd numerator or denominator: 143 Scale harmonicity : 0.018382 Average absolute harmonicity : 0.090819 Specific harmonicity : 0.083570 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 572, 9.1599 octaves, 149649.823 Hz. Exponens Consonantiae : 6.864000E+04, 16.06676 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 145.5, average 48.50000 Mersenne's string divisions : 5523 Sum of van Prooijen's expressibility: 3.67385, average 1.22462 Sum of Tenney's harmonic distance : 7.35509, average 2.45170 Vogel's harmonic complexity : 16.66667 Wille's k value : 71 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 18.77876, average 3.12979 Lattice compactness (without 2's) : 9.29253, average 1.54875 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.66667 6 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.66667 2 11: 0 .. 1 0.66667 2 1 13: 0 .. 1 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 24 26| Scale is weakly epimorphic with val: <6 10 15 24 29| Scale is weakly epimorphic with val: <6 10 16 25 26| Scale is weakly epimorphic with val: <6 10 16 25 29| Scale is weakly epimorphic with val: <6 10 17 26 26| Scale is weakly epimorphic with val: <6 10 17 26 29| Scale is weakly epimorphic with val: <6 10 18 27 29| Scale is weakly epimorphic with val: <6 10 19 23 27| Scale is weakly epimorphic with val: <6 11 15 24 25| Scale is weakly epimorphic with val: <6 11 15 24 28| Scale is weakly epimorphic with val: <6 11 16 25 25| Scale is weakly epimorphic with val: <6 11 16 25 28| Scale is weakly epimorphic with val: <6 11 17 26 28| Scale is weakly epimorphic with val: <6 11 18 23 27| Scale is weakly epimorphic with val: <6 11 18 27 28| Scale is weakly epimorphic with val: <6 11 19 24 27| Scale is weakly epimorphic with val: <7 10 15 24 25| Scale is weakly epimorphic with val: <7 10 15 25 26| Scale is weakly epimorphic with val: <7 10 15 25 29| Scale is weakly epimorphic with val: <7 10 16 25 25| Scale is weakly epimorphic with val: <7 10 16 26 26| Scale is weakly epimorphic with val: <7 10 16 26 29| Scale is weakly epimorphic with val: <7 10 17 23 28| Scale is weakly epimorphic with val: <7 10 17 27 29| Scale is weakly epimorphic with val: <7 10 18 24 28| Scale is weakly epimorphic with val: <7 10 19 25 28| Scale is JI-epimorphic with val: <7 11 15 23 26| Scale is weakly epimorphic with val: <7 11 15 23 29| Scale is weakly epimorphic with val: <7 11 15 24 27| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 26 26| Scale is weakly epimorphic with val: <7 11 15 26 29| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is JI-epimorphic with val: <7 11 16 24 26| Scale is weakly epimorphic with val: <7 11 16 24 29| Scale is weakly epimorphic with val: <7 11 16 25 27| Scale is weakly epimorphic with val: <7 11 16 25 30| Scale is weakly epimorphic with val: <7 11 16 27 29| Scale is weakly epimorphic with val: <7 11 17 23 27| Scale is weakly epimorphic with val: <7 11 17 23 30| Scale is JI-epimorphic with val: <7 11 17 25 26| Scale is weakly epimorphic with val: <7 11 17 25 29| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 18 23 26| Scale is weakly epimorphic with val: <7 11 18 23 29| Scale is weakly epimorphic with val: <7 11 18 24 27| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is JI-epimorphic with val: <7 11 18 26 26| Scale is weakly epimorphic with val: <7 11 18 26 29| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 19 24 26| Scale is weakly epimorphic with val: <7 11 19 24 29| Scale is weakly epimorphic with val: <7 11 19 25 27| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is weakly epimorphic with val: <7 12 15 23 28| Scale is weakly epimorphic with val: <7 12 15 25 27| Scale is weakly epimorphic with val: <7 12 15 25 30| Scale is weakly epimorphic with val: <7 12 16 24 28| Scale is weakly epimorphic with val: <7 12 16 26 27| Scale is weakly epimorphic with val: <7 12 16 26 30| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 17 27 27| Scale is weakly epimorphic with val: <7 12 17 27 30| Scale is weakly epimorphic with val: <7 12 18 26 28| Scale is weakly epimorphic with val: <7 12 19 27 28| Scale is weakly epimorphic with val: <8 11 15 24 29| Scale is weakly epimorphic with val: <8 11 15 26 28| Scale is weakly epimorphic with val: <8 11 16 25 29| Scale is weakly epimorphic with val: <8 11 16 27 28| Scale is weakly epimorphic with val: <8 11 17 26 29| Scale is weakly epimorphic with val: <8 11 18 27 29| Scale is weakly epimorphic with val: <8 12 15 25 29| Scale is weakly epimorphic with val: <8 12 15 26 27| Scale is weakly epimorphic with val: <8 12 15 26 30| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 27 27| Scale is weakly epimorphic with val: <8 12 16 27 30| Scale is weakly epimorphic with val: <8 12 17 27 29|
FIT/MODE
3: 1 1 1 SP B ME I SD: 16.4378 c. M:-28.4531 c. 7: 2 2 3 SP M ME S SD: 17.0858 c. M: 22.7057 c. 8: 3 2 3 SP M ME I SD: 13.3282 c. M:-21.7626 c. 10: 3 3 4 SP M ME S SD: 9.4098 c. M: 15.5907 c. 12: 4 3 5 SP T3 SD: 7.5574 c. M: 13.0506 c. Raga Malasri, Peruvian tritonic 1 13: 4 4 5 SP M ME S SD: 6.9945 c. M: 11.7596 c. 15: 5 4 6 SP T3 SD: 2.8038 c. M: 4.7499 c. 18: 6 5 7 SP T3 SD: 0.7385 c. M:-1.0108 c. 69: 23 19 27 SP T3 SD: 0.6317 c. M:-1.0108 c. 82: 27 23 32 SP T3 SD: 0.5887 c. M: 1.0138 c. 97: 32 27 38 SP T3 SD: 0.5488 c. M: 0.7007 c. 100: 33 28 39 SP T3 SD: 0.3978 c. M: 0.6494 c. 115: 38 32 45 SP T3 SD: 0.3478 c. M: 0.4328 c. 118: 39 33 46 SP T3 SD: 0.2922 c. M: 0.3961 c. 133: 44 37 52 SP T3 SD: 0.2017 c. M: 0.2563 c. 151: 50 42 59 SP T3 SD: 0.0919 c. M: 0.1323 c. 169: 56 47 66 SP T3 SD: 0.0259 c. M: 0.0347 c. 794: 263 221 310 SP T3 SD: 0.0224 c. M: 0.0347 c. 812: 269 226 317 SP T3 SD: 0.0209 c. M:-0.0343 c. 963: 319 268 376 SP T3 SD: 0.0144 c. M: 0.0236 c. 981: 325 273 383 SP T3 SD: 0.0132 c. M:-0.0224 c. 1132: 375 315 442 SP T3 SD: 0.0092 c. M: 0.0158 c. 1150: 381 320 449 SP T3 SD: 0.0081 c. M:-0.0140 c. 1301: 431 362 508 SP T3 SD: 0.0061 c. M: 0.0101 c. 1319: 437 367 515 SP T3 SD: 0.0050 c. M:-0.0078 c. 1470: 487 409 574 SP T3 SD: 0.0050 c. M: 0.0066 c. 1488: 493 414 581 SP T3 SD: 0.0042 c. M:-0.0066 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: 82.7368 cents 5 x 6:7 S SD: 42.6622 cents 6 x 7:8 S SD: 18.3530 cents 7:8 x 9 S SD: 45.6687 cents 8:9:10:11 H SD: 35.2720 cents 9:10:11:12 H SD: 15.7194 cents 10:11:12:13 H SD: 15.1537 cents 11:12:13:15 SD: 14.6306 cents 17:19:20:23 SD: 14.4976 cents 18:20:21:24 S SD: 13.5404 cents 19:21:23:25 SD: 12.1705 cents 20:22:24:27 S SD: 8.2197 cents 21:23:25:28 SD: 2.5692 cents 51:56:61:68 SD: 2.3680 cents 69:76:82:92 SD: 1.7544 cents 78:86:93:104 SD: 1.3790 cents 90:99:107:120 SD: 1.3467 cents 99:109:118:132 SD: 0.5436 cents 120:132:143:160 SD: 0.0000 cents