Scala analysis: xen15-gilson-just-pentatonic
Just Intonation Pentatonic Scale (JIPS)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 5/3 884.358713 major sixth, BP sixth 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 9/8 203.9100 major whole tone 2: 32/27 294.1350 Pythagorean minor third 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 32/27 294.135 cents Pythagorean minor third 1: 1 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: 1 5/3 884.359 cents major sixth, BP sixth 4: 1 27/16 905.865 cents Pythagorean major sixth 4: 2 16/9 996.090 cents Pythagorean minor seventh 4: 1 9/5 1017.596 cents just minor seventh, BP seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.50000 = 7/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 203.9 498.0 702.0 884.4 1200.0 203.9 : 294.1 498.0 680.4 996.1 1200.0 498.0 : 203.9 386.3 702.0 905.9 1200.0 702.0 : 182.4 498.0 702.0 996.1 1200.0 884.4 : 315.6 519.6 813.7 1017.6 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: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 233.51454 cents, oct.: 1167.57271 cents Scale is strictly proper Step pattern alph. order: ABACD Step pattern size order : BCBAD Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 1.420222 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.555875 Rothenberg efficiency : 0.540000 redundancy: 0.460000 Efficiency x scale size : 2.700000 Number of different interval sizes : 14 = 3.50000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.50000 = 7/2 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 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 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: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 9 Scale harmonicity : 0.051546 Average absolute harmonicity : 0.343461 Specific harmonicity : 0.302521 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 4.320000E+03, 12.07682 octaves Euler's gradus suavitatis : 16 Sum of Mann's harmonic distance : 20.0, average 4.00000 Mersenne's string divisions : 14280 Sum of van Prooijen's expressibility: 2.60746, average 0.52149 Sum of Tenney's harmonic distance : 5.19179, average 1.03836 Vogel's harmonic complexity : 7.40000 Wille's k value : 13 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 40.24154, average 2.68277 Lattice compactness (without 2's) : 23.22677, average 1.54845 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.20000 7 1 3: -1 .. 2 0.20000 5 3 5: 0 .. 1 0.20000 1 1 Average exponent except 2's : 2 / 5 = 0.40000 Average absolute exponent except 2's: 6 / 5 = 1.20000 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: 39.1799 c. M:-75.6413 c. 7: 1 2 1 1 2 P M ME S SD: 21.5558 c. M: 32.4814 c. Thai mode 5 12: 2 3 2 2 3 SP M ME S SD: 7.3155 c. M:-15.6413 c. Scottish Pentatonic, Blues Major, Ritusen, Ritsu (Gagaku): Japan, Zhi, Zheng: China, Ujo, P'yongjo: Korea, Bac: Vietnam, Lai Soutsanaen, Lai Po Sai, Lai Soi: Laos, Raga Arabhi, Devakriya, Durga, Jaldhar Kedar, Suddha Saveri, Major complement 19: 3 5 3 3 5 SP M DE S SD: 7.9074 c. M: 14.4363 c. 22: 4 5 4 3 6 SP SD: 9.3895 c. M:-14.2718 c. 29: 5 7 5 4 8 SP SD: 7.0757 c. M: 15.3932 c. 31: 5 8 5 5 8 SP M DE S SD: 6.2708 c. M: 10.3616 c. 34: 6 8 6 5 9 SP SD: 4.3947 c. M:-7.8547 c. 41: 7 10 7 6 11 SP SD: 2.8713 c. M: 6.3099 c. 46: 8 11 8 7 12 SP SD: 2.8671 c. M:-4.7857 c. 53: 9 13 9 8 14 SP SD: 0.6038 c. M: 1.3398 c. 118: 20 29 20 18 31 SP SD: 0.3334 c. M: 0.5202 c. 171: 29 42 29 26 45 SP SD: 0.2295 c. M: 0.4012 c. 335: 57 82 57 51 88 SP SD: 0.2378 c. M:-0.4174 c. 376: 64 92 64 57 99 SP SD: 0.2361 c. M:-0.3453 c. 388: 66 95 66 59 102 SP SD: 0.1414 c. M:-0.2137 c. 441: 75 108 75 67 116 SP SD: 0.0940 c. M:-0.1716 c. 494: 84 121 84 75 130 SP SD: 0.1008 c. M: 0.1482 c. 559: 95 137 95 85 147 SP SD: 0.0375 c. M:-0.0778 c. 612: 104 150 104 93 161 SP SD: 0.0211 c. M: 0.0450 c. 1171: 199 287 199 178 308 SP SD: 0.0117 c. M:-0.0183 c. 1783: 303 437 303 271 469 SP SD: 0.0092 c. M:-0.0160 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: 0.0000 cents 4 x 5:6:7:8 S SD: 35.0166 cents 5:6:7 x 8:10 S SD: 39.2215 cents 6:7:8:9:10:12 S SD: 12.5922 cents 14:16:19:21:23:28 SD: 9.5975 cents 15:17:20:23:25:30 SD: 8.0277 cents 16:18:21:24:27:32 SD: 6.9451 cents 18:20:24:27:30:36 S SD: 4.3013 cents 24:27:32:36:40:48 SD: 0.0000 cents