Scala analysis: 474_D17
Diatonic tetrachord 12/11 * 11/10 * 10/9, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 2: 1 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 1 11/9 347.408 cents undecimal 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 : 150.6 315.6 498.0 150.6: 165.0 347.4 498.0 315.6: 182.4 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 182.4037 cents 55/54, 31.7667 cents 12/11, 150.6371 cents 2: 315.6413 .. 347.4079 cents 55/54, 31.7667 cents 27/25, 133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.102086 Largest / Average step : 1.098718 Largest / Smallest step : 1.210882 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 162.57533 cents, oct.: 487.72599 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 133.23757 cents Scale diversity : 1.272987 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.872435 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 : 121/120, 14.3672 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 All steps are superparticular (epimoric) Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Scale is subharmonic, base degree is: 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is differentially coherent in interval class 1 Limited inverse transpositions with margin 17.3995 cents: 1 2 -- Rational properties -- Prime limit : 11 Odd number limit : 33 (O: 11 U: 33) Highest odd numerator or denominator: 11 Scale harmonicity : 0.031333 Average absolute harmonicity : 0.119130 Specific harmonicity : 0.160946 Fundamental : 1/165, -7.3663 octaves, 1.5856 Hz. Guide tone : 12, 3.5850 octaves, 3139.507 Hz. Exponens Consonantiae : 1.980000E+03, 10.95128 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 20.5, average 6.83333 Mersenne's string divisions : 1771 Sum of van Prooijen's expressibility: 2.21748, average 0.73916 Sum of Tenney's harmonic distance : 4.67688, average 1.55896 Vogel's harmonic complexity : 16.33333 Wille's k value : 49 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.83522, average 2.13920 Lattice compactness (without 2's) : 9.71478, average 1.61913 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 0.33333 3 1 5: -1 .. 0 -0.33333 1 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is JI-epimorphic with val: <7 11 16 24| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 17 23| Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 19 24| Scale is weakly 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 16 25| Scale is weakly epimorphic with val: <7 12 18 23| Scale is weakly epimorphic with val: <8 11 15 24| Scale is weakly epimorphic with val: <8 11 16 23| Scale is weakly epimorphic with val: <8 11 16 26| Scale is weakly epimorphic with val: <8 11 18 24| Scale is weakly epimorphic with val: <8 12 15 25| Scale is weakly epimorphic with val: <8 12 17 23| Scale is weakly epimorphic with val: <8 12 17 26| Scale is weakly epimorphic with val: <8 12 18 25|
FIT/MODE
3: 1 1 1 SP B ME I SD: 12.9752 c. M:-16.3887 c. 10: 3 3 4 SP M ME S SD: 9.7334 c. M: 16.8143 c. 11: 3 4 4 SP M ME S SD: 8.5813 c. M: 14.8066 c. 13: 4 4 5 SP M ME S SD: 5.4942 c. M: 9.1521 c. 14: 4 5 5 SP M ME S SD: 5.4789 c. M: 8.3385 c. 16: 5 5 6 SP M ME S SD: 3.8322 c. M:-5.0020 c. 19: 6 6 7 SP M ME S SD: 3.8848 c. M:-6.6403 c. 24: 7 8 9 SP T3 SD: 3.9965 c. M: 5.3739 c. 27: 8 9 10 SP T3 SD: 2.1328 c. M: 3.0682 c. 30: 9 10 11 SP T3 SD: 0.7170 c. M: 1.2236 c. 63: 19 21 23 SP T3 SD: 0.4169 c. M:-0.5778 c. 109: 33 36 40 SP T3 SD: 0.2273 c. M: 0.3651 c. 139: 42 46 51 SP T3 SD: 0.2101 c. M: 0.3322 c. 142: 43 47 52 SP T3 SD: 0.1043 c. M:-0.1794 c. 172: 52 57 63 SP T3 SD: 0.0394 c. M: 0.0653 c. 314: 95 104 115 SP T3 SD: 0.0262 c. M:-0.0453 c. 486: 147 161 178 SP T3 SD: 0.0058 c. M: 0.0078 c. 1144: 346 379 419 SP T3 SD: 0.0061 c. M: 0.0096 c. 1630: 493 540 597 SP T3 SD: 0.0053 c. M: 0.0091 c. 2116: 640 701 775 SP T3 SD: 0.0051 c. M: 0.0088 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: 70.6724 cents 5 x 6:7 S SD: 42.2336 cents 6 x 7:8 S SD: 24.3852 cents 7:8 x 9 S SD: 51.1133 cents 8:9:10:11 H SD: 34.4329 cents 9:10:11:12 H SD: 14.9749 cents 15:16:18:20 S SD: 12.9686 cents 19:21:23:25 SD: 11.8630 cents 20:22:24:27 S SD: 8.6213 cents 21:23:25:28 SD: 5.1349 cents 30:33:36:40 S SD: 4.7891 cents 44:48:53:59 SD: 3.9307 cents 45:49:54:60 SD: 1.0697 cents 99:108:119:132 SD: 0.9707 cents 111:121:133:148 SD: 0.9694 cents 120:131:144:160 SD: 0.4006 cents 165:180:198:220 S SD: 0.0000 cents