Scala analysis: 468_D15
Diatonic tetrachord 32/29 * 9/8 * 29/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/29 170.422806 29th subharmonic 2: 36/29 374.332808 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 29/27 123.7122 1: 32/29 170.4228 29th subharmonic 2: 9/8 203.9100 major whole tone 3: 29/27 123.7122
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 29/27 123.712 cents 1: 1 32/29 170.423 cents 29th subharmonic 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 29/24 327.622 cents 2: 1 36/29 374.333 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 : 170.4 374.3 498.0 170.4: 203.9 327.6 498.0 374.3: 123.7 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 123.7122 .. 203.9100 cents 243/232, 80.1978 cents 29/27, 123.7122 cents 2: 294.1350 .. 374.3328 cents 243/232, 80.1978 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 29/27, 123.7122 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.341945 Largest / Average step : 1.228263 Largest / Smallest step : 1.648261 Median interval of one step : 32/29, 170.4228 cents, amount: 1 Least squares average step : 172.37310 cents, oct.: 517.11930 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2186-tone equal temperament with octave 4/3 degrees: 748 1643 2186 Least number of segments generator : 1095 of 249.478 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1115 of 254.035 cents and inv. generated superset size: 35 = 32 more = 1166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.320391 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.677950 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 : 261/256, 33.4872 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 29 Odd number limit : 29 (O: 29 U: 29) Highest odd numerator or denominator: 29 Scale harmonicity : 0.014910 Average absolute harmonicity : 0.082500 Specific harmonicity : 0.062677 Fundamental : 1/87, -6.4429 octaves, 3.0072 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 2.505600E+04, 14.61287 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 66.5, average 22.16667 Mersenne's string divisions : 27755 Sum of van Prooijen's expressibility: 3.40192, average 1.13397 Sum of Tenney's harmonic distance : 7.06543, average 2.35514 Vogel's harmonic complexity : 16.66667 Wille's k value : 14 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 20.41954, average 3.40326 Lattice compactness (without 2's) : 10.81256, average 1.80209 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.00000 9 3: -1 .. 2 0.33333 3 1 29: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 32| Scale is JI-epimorphic with val: <7 11 34| Scale is weakly epimorphic with val: <7 11 37| Scale is weakly epimorphic with val: <8 11 37|
FIT/MODE
3: 1 1 1 SP B ME I SD: 24.5558 c. M: 42.3028 c. 5: 2 2 1 SP M ME S SD: 21.6805 c. M:-28.7952 c. 7: 2 3 2 SP M ME I SD: 19.4630 c. M: 28.1242 c. 8: 3 3 2 SP M ME S SD: 9.4475 c. M:-16.3441 c. 9: 3 4 2 SP T3 SD: 7.9447 c. M:-13.0355 c. 11: 4 4 3 SP M ME S SD: 9.3276 c. M: 12.1183 c. 12: 4 5 3 SP T3 SD: 2.5863 c. M: 4.4078 c. Raga Bilwadala 20: 7 8 5 SP T3 SD: 2.2945 c. M:-3.8929 c. 29: 10 12 7 SP T3 SD: 2.1560 c. M:-3.4944 c. 32: 11 13 8 SP T3 SD: 0.6448 c. M: 0.7991 c. 44: 15 18 11 SP T3 SD: 0.5892 c. M: 0.7991 c. 73: 25 30 18 SP T3 SD: 0.5297 c. M:-0.9066 c. 76: 26 31 19 SP T3 SD: 0.4619 c. M: 0.7991 c. 85: 29 35 21 SP T3 SD: 0.4813 c. M:-0.6658 c. 105: 36 43 26 SP T3 SD: 0.2956 c. M:-0.3868 c. 117: 40 48 29 SP T3 SD: 0.1762 c. M:-0.2651 c. 149: 51 61 37 SP T3 SD: 0.0353 c. M:-0.0490 c. 491: 168 201 122 SP T3 SD: 0.0232 c. M: 0.0383 c. 640: 219 262 159 SP T3 SD: 0.0121 c. M: 0.0209 c. 789: 270 323 196 SP T3 SD: 0.0085 c. M:-0.0108 c. 1397: 478 572 347 SP T3 SD: 0.0065 c. M: 0.0108 c. 1546: 529 633 384 SP T3 SD: 0.0047 c. M:-0.0063 c. 1695: 580 694 421 SP T3 SD: 0.0052 c. M:-0.0090 c. 2037: 697 834 506 SP T3 SD: 0.0047 c. M: 0.0068 c. 2186: 748 895 543 SP T3 SD: 0.0020 c. M: 0.0030 c. 2335: 799 956 580 SP T3 SD: 0.0005 c. M:-0.0008 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: 11.9809 cents 5 x 6:7 S SD: 51.4281 cents 6:7 x 8 S SD: 48.2240 cents 7:8:9 x S SD: 42.9576 cents 8:9:10:11 H SD: 21.3514 cents 9:10:11:12 H SD: 9.8234 cents 20:22:25:27 SD: 8.4025 cents 21:23:26:28 SD: 4.5729 cents 30:33:37:40 SD: 4.1646 cents 48:53:60:64 SD: 4.0113 cents 49:54:61:65 SD: 3.4531 cents 57:63:71:76 SD: 2.1821 cents 66:73:82:88 SD: 1.4484 cents 78:86:97:104 SD: 1.1261 cents 87:96:108:116 SD: 0.0000 cents