Scala analysis: xen03-wilson-negative-07
Negative, linear-mapped intonational system, 7 notes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 3/2 701.955 cents perfect fifth 5: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh 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 4 5 6 7 0.0 : 111.7 315.6 498.0 702.0 813.7 1017.6 1200.0 111.7 : 203.9 386.3 590.2 702.0 905.9 1088.3 1200.0 315.6 : 182.4 386.3 498.0 702.0 884.4 996.1 1200.0 498.0 : 203.9 315.6 519.6 702.0 813.7 1017.6 1200.0 702.0 : 111.7 315.6 498.0 609.8 813.7 996.1 1200.0 813.7 : 203.9 386.3 498.0 702.0 884.4 1088.3 1200.0 1017.6: 182.4 294.1 498.0 680.4 884.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 168.70699 cents, oct.: 1180.94890 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : SLMLSLM Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.374079 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.539106 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 386.314 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 Limited inverse transpositions with margin 92.1787 cents: 5 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.051546 Average absolute harmonicity : 0.264927 Specific harmonicity : 0.256959 Fundamental : 1/30, -4.9069 octaves, 8.7209 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 4.320000E+03, 12.07682 octaves Euler's gradus suavitatis : 16 Sum of Mann's harmonic distance : 42.0, average 6.00000 Mersenne's string divisions : 930930 Sum of van Prooijen's expressibility: 4.48252, average 0.64036 Sum of Tenney's harmonic distance : 9.27097, average 1.32442 Vogel's harmonic complexity : 8.42857 Wille's k value : 22 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 73.81840, average 2.63637 Lattice compactness (without 2's) : 42.00604, average 1.50022 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.42857 12 1 3: -1 .. 2 0.28571 6 2 5: -1 .. 0 -0.57143 4 4 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 31.2614 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 33.7023 c. M:-49.0704 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 32.2356 c. M:-62.4037 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 11.2559 c. M: 17.5963 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 19: 2 3 3 3 2 3 3 SP M ME S SD: 7.7568 c. M:-14.5845 c. Nineteen-tone Phrygian 31: 3 5 5 5 3 5 5 SP M DE S SD: 5.7744 c. M: 11.1447 c. Intense Diatonic Dorian, M.Phrygian 34: 3 6 5 6 3 6 5 P T3 SD: 3.9275 c. M:-5.9331 c. 41: 4 7 6 7 4 7 6 SP T3 SD: 4.6124 c. M:-6.7940 c. 46: 4 8 7 8 4 8 7 P T3 SD: 3.7352 c. M: 7.3835 c. 53: 5 9 8 9 5 9 8 SP T3 SD: 1.0408 c. M:-1.4763 c. 118: 11 20 18 20 11 20 18 SP T3 SD: 0.3246 c. M: 0.6471 c. 171: 16 29 26 29 16 29 26 SP T3 SD: 0.2748 c. M:-0.5494 c. 289: 27 49 44 49 27 49 44 SP T3 SD: 0.2271 c. M:-0.3794 c. 323: 30 55 49 55 30 55 49 SP T3 SD: 0.2146 c. M:-0.3604 c. 376: 35 64 57 64 35 64 57 SP T3 SD: 0.2449 c. M:-0.4888 c. 388: 36 66 59 66 36 66 59 SP T3 SD: 0.2046 c. M: 0.3911 c. 441: 41 75 67 75 41 75 67 SP T3 SD: 0.0905 c. M: 0.1667 c. 559: 52 95 85 95 52 95 85 SP T3 SD: 0.0649 c. M: 0.1034 c. 612: 57 104 93 104 57 104 93 SP T3 SD: 0.0323 c. M:-0.0508 c. 1171: 109 199 178 199 109 199 178 SP T3 SD: 0.0165 c. M: 0.0319 c. 1783: 166 303 271 303 166 303 271 SP T3 SD: 0.0082 c. M:-0.0145 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 16.8934 cents 6 x 7:8:9:10:11:12 S SD: 15.2591 cents 7 x 8:9 x 11:13:14 SD: 24.4943 cents 8:9:10:11:12:13:14:16 S SD: 19.9123 cents 9:10:11:12 x 14:16:18 S SD: 15.6745 cents 10:11:12:13:15:16:18:20 SD: 9.8552 cents 12:13:14:16:18:19:22:24 SD: 9.5156 cents 14:15:17:19:21:22:25:28 SD: 7.2584 cents 15:16:18:20:23:24:27:30 SD: 5.4358 cents 20:21:24:27:30:32:36:40 S SD: 4.9608 cents 26:28:31:35:39:42:47:52 SD: 4.5217 cents 28:30:34:37:42:45:50:56 SD: 4.4494 cents 30:32:36:40:45:48:54:60 S SD: 0.0000 cents