Scala analysis: xen03-wilson-positive-05
Positive, 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: 32/27 294.134997 Pythagorean minor third 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 16/9 996.089998 Pythagorean minor seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 32/27 294.1350 Pythagorean minor third 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 32/27 294.1350 Pythagorean minor third 5: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean major third 2: 4 4/3 498.045 cents perfect fourth 3: 4 3/2 701.955 cents perfect fifth 3: 1 128/81 792.180 cents Pythagorean minor sixth 4: 2 27/16 905.865 cents Pythagorean major sixth 4: 3 16/9 996.090 cents Pythagorean minor seventh Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 294.1 498.0 702.0 996.1 1200.0 294.1 : 203.9 407.8 702.0 905.9 1200.0 498.0 : 203.9 498.0 702.0 996.1 1200.0 702.0 : 294.1 498.0 792.2 996.1 1200.0 996.1 : 203.9 498.0 702.0 905.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 203.9100 .. 294.1350 cents 256/243, 90.2250 cents 9/8, 203.9100 cents 2: 407.8200 .. 498.0450 cents 256/243, 90.2250 cents 2187/2048, 113.6850 cents 3: 701.9550 .. 792.1800 cents 256/243, 90.2250 cents 9/8, 203.9100 cents 4: 905.8650 .. 996.0900 cents 256/243, 90.2250 cents 2187/2048, 113.6850 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 9/8, 203.9100 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.176990 Largest / Average step : 1.225562 Largest / Smallest step : 1.442475 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 243.28091 cents, oct.: 1216.40454 cents Scale is strictly proper Scale has Myhill's property chromas: 256/243, 90.2250 cents and 2187/2048, 113.6850 cents, ratio: 1.260017 generators: 2 of 498.04500 cents and 3 of 701.95500 cents ET pair of linear temperament : 12&41 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 163 276 389 552 665 generators: 276 and 389 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBAB Step pattern size order : LSSLS Scale is a Constant Structure, by a margin of 113.68501 cents Ratio Whole / Half tone : 2.260017 Scale diversity : 1.281255 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.699250 Rothenberg efficiency : 0.800000 redundancy: 0.200000 Efficiency x scale size : 4.000000 Number of different interval sizes : 8 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 256/243, 90.2250 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Scale is a chain of 2 triads 0.0 498.045 996.090 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Scale is a complete genus musicum : 2^m 3^4 Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 60.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 4-5 -- Rational properties -- Prime limit : 3 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.060000 Average absolute harmonicity : 0.334215 Specific harmonicity : 0.313043 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 96, 6.5850 octaves, 25116.054 Hz. Exponens Consonantiae : 5.184000E+03, 12.33985 octaves Euler's gradus suavitatis : 15 Sum of Mann's harmonic distance : 49.5, average 9.90000 Mersenne's string divisions : 30975 Sum of van Prooijen's expressibility: 3.33985, average 0.66797 Sum of Tenney's harmonic distance : 7.25324, average 1.45065 Vogel's harmonic complexity : 9.20000 Wille's k value : 40 Wilson's harmonic complexity : 12 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 51.11264, average 3.40751 Lattice compactness (without 2's) : 27.00000, average 1.80000 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 2.20000 13 1 3: -3 .. 1 -1.00000 7 4 Average exponent except 2's :-5 / 5 =-1.00000 Average absolute exponent except 2's: 7 / 5 = 1.40000 Scale is weakly epimorphic with val: <5 7| Scale is JI-epimorphic with val: <5 8| = patent Scale is weakly epimorphic with val: <5 9|
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 31.2549 c. M: 54.1350 c. 7: 2 1 1 2 1 P M ME S SD: 28.1297 c. M:-48.7221 c. Thai mode 6 12: 3 2 2 3 2 SP M ME S SD: 3.3862 c. M:-5.8650 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 29: 7 5 5 7 5 SP M DE S SD: 2.5864 c. M: 4.4798 c. 41: 10 7 7 10 7 SP M DE S SD: 0.8384 c. M: 1.4521 c. 53: 13 9 9 13 9 SP M DE S SD: 0.1181 c. M:-0.2046 c. 200: 49 34 34 49 34 SP M DE S SD: 0.0779 c. M: 0.1350 c. 253: 62 43 43 62 43 SP M DE S SD: 0.0369 c. M: 0.0639 c. 306: 75 52 52 75 52 SP M DE S SD: 0.0100 c. M: 0.0174 c. 359: 88 61 61 88 61 SP M DE S SD: 0.0089 c. M:-0.0154 c. 665: 163 113 113 163 113 SP M DE S SD: 0.0002 c. M:-0.0003 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: 37.2438 cents 4:5 x 6:7:8 S SD: 24.0316 cents 6:7:8:9:11:12 SD: 11.9689 cents 10:12:13:15:18:20 SD: 10.6700 cents 12:14:16:18:21:24 S SD: 7.7114 cents 18:21:24:27:32:36 SD: 5.4528 cents 22:26:29:33:39:44 SD: 4.1952 cents 28:33:37:42:50:56 SD: 3.9719 cents 32:38:43:48:57:64 SD: 2.8589 cents 36:43:48:54:64:72 SD: 2.6945 cents 42:50:56:63:75:84 SD: 2.1811 cents 48:57:64:72:85:96 SD: 1.5142 cents 54:64:72:81:96:108 SD: 0.0000 cents