Scala analysis: xen03-wilson-negative-05
Negative, linear-mapped intonational system, 5 notes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 9/5 1017.596288 just minor seventh, BP seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 6/5 315.6413 minor third 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 6/5 315.6413 minor third 5: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 2 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 3 4/3 498.045 cents perfect fourth 2: 1 27/20 519.551 cents acute fourth 3: 1 40/27 680.449 cents grave fifth 3: 3 3/2 701.955 cents perfect fifth 3: 1 8/5 813.686 cents minor sixth 4: 2 5/3 884.359 cents major sixth, BP sixth 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 2 9/5 1017.596 cents just minor seventh, BP 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 0.0 : 315.6 498.0 702.0 1017.6 1200.0 315.6 : 182.4 386.3 702.0 884.4 1200.0 498.0 : 203.9 519.6 702.0 1017.6 1200.0 702.0 : 315.6 498.0 813.7 996.1 1200.0 1017.6: 182.4 498.0 680.4 884.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 182.4037 .. 315.6413 cents 27/25, 133.2376 cents 10/9, 182.4037 cents 2: 386.3137 .. 519.5513 cents 27/25, 133.2376 cents 25/24, 70.6724 cents 3: 680.4487 .. 813.6863 cents 27/25, 133.2376 cents 800/729, 160.8974 cents 4: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 10/9, 182.4037 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 1.315763 Largest / Average step : 1.315172 Largest / Smallest step : 1.730454 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 245.23603 cents, oct.: 1226.18013 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCAB Step pattern size order : LSMLS Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 1.388134 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.555875 Rothenberg efficiency : 0.580000 redundancy: 0.420000 Efficiency x scale size : 2.900000 Number of different interval sizes : 12 = 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 : 81/80, 21.5063 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 315.641 498.045 cents Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 3 = 60.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Limited inverse transpositions with margin 133.2376 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 9 Scale harmonicity : 0.057471 Average absolute harmonicity : 0.334315 Specific harmonicity : 0.297848 Fundamental : 1/30, -4.9069 octaves, 8.7209 Hz. Guide tone : 36, 5.1699 octaves, 9418.520 Hz. Exponens Consonantiae : 1.080000E+03, 10.07682 octaves Euler's gradus suavitatis : 14 Sum of Mann's harmonic distance : 20.0, average 4.00000 Mersenne's string divisions : 2310 Sum of van Prooijen's expressibility: 2.60746, average 0.52149 Sum of Tenney's harmonic distance : 5.28870, average 1.05774 Vogel's harmonic complexity : 9.40000 Wille's k value : 22 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 31.31142, average 2.08743 Lattice compactness (without 2's) : 22.11312, average 1.47421 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.60000 5 1 3: -1 .. 2 0.60000 5 2 5: -1 .. 0 -0.40000 2 2 Average exponent except 2's : 1 / 5 = 0.20000 Average absolute exponent except 2's: 7 / 5 = 1.40000 Scale is weakly epimorphic with val: <5 7 13| Scale is JI-epimorphic with val: <5 8 12| = patent Scale is weakly epimorphic with val: <5 9 11|
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 44.0231 c. M: 75.6413 c. 7: 2 1 1 2 1 P M ME S SD: 16.6654 c. M:-27.2159 c. Thai mode 6 12: 3 2 2 3 2 SP M ME S SD: 10.6012 c. M: 17.5963 c. Minor Pentatonic, Blues Pentatonic, Raga Dhani (Suddha Dhanyasi), Abheri, Udhayaravi Chandrika, Qing Shang, Gu Xian, Jia Zhong, Yu: China, P'yongjo-kyemyonjo: Korea, Minyo: Japan, Lai Yai, Lai Noi: Laos, Nam, Northern Sa mac: Vietnam, Peruvian Pentatonic 2, Batti Minor: Ethiopia 19: 5 3 3 5 3 SP M DE S SD: 5.5536 c. M:-7.2182 c. Nineteen-tone Minor Pentatonic 34: 9 5 6 9 5 SP T3 SD: 3.7436 c. M:-5.9331 c. 41: 11 6 7 11 6 SP T3 SD: 4.1579 c. M:-6.7940 c. 46: 12 7 8 12 7 SP T3 SD: 1.9101 c. M: 2.5978 c. 53: 14 8 9 14 8 SP T3 SD: 0.8272 c. M:-1.3398 c. 99: 26 15 17 26 15 SP T3 SD: 0.7610 c. M:-1.0753 c. 118: 31 18 20 31 18 SP T3 SD: 0.3752 c. M: 0.6471 c. 171: 45 26 29 45 26 SP T3 SD: 0.1451 c. M:-0.2006 c. 388: 102 59 66 102 59 SP T3 SD: 0.1089 c. M: 0.1774 c. 441: 116 67 75 116 67 SP T3 SD: 0.0678 c. M:-0.0908 c. 559: 147 85 95 147 85 SP T3 SD: 0.0460 c. M: 0.0778 c. 612: 161 93 104 161 93 SP T3 SD: 0.0306 c. M:-0.0508 c. 1000: 263 152 170 263 152 SP T3 SD: 0.0340 c. M:-0.0450 c. 1171: 308 178 199 308 178 SP T3 SD: 0.0086 c. M: 0.0136 c. 1783: 469 271 303 469 271 SP T3 SD: 0.0087 c. M:-0.0145 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.0000 cents 3 x 4 x 5:6 S SD: 44.4125 cents 4:5 x 6:7:8 S SD: 21.4668 cents 6:7:8:9:11:12 SD: 11.6407 cents 10:12:13:15:18:20 SD: 8.7662 cents 14:17:19:21:25:28 SD: 7.8715 cents 15:18:20:23:27:30 SD: 7.6101 cents 16:19:21:24:29:32 SD: 6.9728 cents 20:24:27:30:36:40 S SD: 4.3013 cents 24:29:32:36:43:48 SD: 2.8850 cents 30:36:40:45:54:60 S SD: 0.0000 cents