Scala analysis: pelog_mal
Malaysian Pelog, Pierre Genest: Diff?rentes gammes encore en usage
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 13/8 840.527662 tridecimal neutral sixth 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/13 359.4723 tridecimal neutral third 1: 13/12 138.5727 tridecimal 2/3-tone 2: 16/13 359.4723 tridecimal neutral third 3: 9/8 203.9100 major whole tone 4: 13/12 138.5727 tridecimal 2/3-tone 5: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 16/13 359.472 cents tridecimal neutral third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 3 4/3 498.045 cents perfect fourth 2: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 13/9 636.618 cents tridecimal diminished fifth 3: 3 3/2 701.955 cents perfect fifth 3: 1 64/39 857.517 cents 39th subharmonic 4: 2 13/8 840.528 cents tridecimal neutral sixth 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 2 24/13 1061.427 cents tridecimal neutral 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 : 138.6 498.0 702.0 840.5 1200.0 138.6 : 359.5 563.4 702.0 1061.4 1200.0 498.0 : 203.9 342.5 702.0 840.5 1200.0 702.0 : 138.6 498.0 636.6 996.1 1200.0 840.5 : 359.5 498.0 857.5 1061.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 359.4723 cents 192/169, 220.8997 cents 13/12, 138.5727 cents 2: 342.4827 .. 563.3823 cents 192/169, 220.8997 cents 507/512,-16.9897 cents 3: 636.6177 .. 857.5173 cents 192/169, 220.8997 cents 169/162, 73.2353 cents 4: 840.5277 .. 1061.4273 cents 192/169, 220.8997 cents 507/512,-16.9897 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 1.731943 Largest / Average step : 1.497801 Largest / Smallest step : 2.594107 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 229.13888 cents, oct.: 1145.69439 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCAB Step pattern size order : SLMSL Scale is a Constant Structure, by a margin of 16.98968 cents Scale diversity : 1.456082 Lumma stability : 0.291984 Lumma impropriety factor : 0.028316 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 : 512/507, 16.9897 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 138.573 498.045 cents Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 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 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 39 U: 39) Highest odd numerator or denominator: 13 Scale harmonicity : 0.030781 Average absolute harmonicity : 0.312810 Specific harmonicity : 0.145809 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 3.744000E+03, 11.87036 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 30.5, average 6.10000 Mersenne's string divisions : 525 Sum of van Prooijen's expressibility: 3.18213, average 0.63643 Sum of Tenney's harmonic distance : 6.36852, average 1.27370 Vogel's harmonic complexity : 10.00000 Wille's k value : 19 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 40.59006, average 2.70600 Lattice compactness (without 2's) : 17.89292, average 1.19286 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.60000 9 1 3: -1 .. 1 -0.20000 3 2 13: 0 .. 1 0.40000 2 2 Average exponent except 2's : 1 / 5 = 0.20000 Average absolute exponent except 2's: 5 / 5 = 1.00000 Scale is weakly epimorphic with val: <5 7 21| Scale is JI-epimorphic with val: <5 8 19| = patent Scale is weakly epimorphic with val: <5 9 17|
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 71.0104 c. M:-119.4723 c. 7: 1 2 1 1 2 P M ME S SD: 19.4067 c. M:-32.8559 c. Thai mode 5 10: 1 3 2 1 3 P T3 SD: 14.1171 c. M: 18.5727 c. 17: 2 5 3 2 5 P T3 SD: 4.0071 c. M:-6.5312 c. Malaysian Pelog 36: 4 11 6 4 11 N T3 SD: 4.1678 c. M: 7.1943 c. 43: 5 13 7 5 13 N T3 SD: 3.1172 c. M:-4.2806 c. 53: 6 16 9 6 16 N T3 SD: 1.7448 c. M: 2.7918 c. 60: 7 18 10 7 18 N T3 SD: 1.4114 c. M:-1.9550 c. 70: 8 21 12 8 21 N T3 SD: 0.8889 c. M: 1.4298 c. 130: 15 39 22 15 39 N T3 SD: 0.3572 c. M: 0.5277 c. 147: 17 44 25 17 44 N T3 SD: 0.1669 c. M:-0.2887 c. 277: 32 83 47 32 83 N T3 SD: 0.1067 c. M:-0.1499 c. 424: 49 127 72 49 127 N T3 SD: 0.0665 c. M:-0.1066 c. 641: 74 192 109 74 192 N T3 SD: 0.0517 c. M:-0.0731 c. 771: 89 231 131 89 231 N T3 SD: 0.0360 c. M: 0.0607 c. 918: 106 275 156 106 275 N T3 SD: 0.0063 c. M: 0.0106 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: 14.6104 cents 4 x 5:6:7:8 S SD: 42.5326 cents 5:6:7 x 8:10 S SD: 49.5028 cents 6:7:8:9:10:12 S SD: 27.1158 cents 7:8:9 x 11:14 SD: 31.5310 cents 8:9:11:12:13:16 SD: 16.8606 cents 10:11:13:15:16:20 SD: 11.5590 cents 12:13:16:18:20:24 SD: 8.7662 cents 14:15:19:21:23:28 SD: 8.1557 cents 21:23:28:32:34:42 SD: 6.7578 cents 22:24:29:33:36:44 SD: 5.2252 cents 24:26:32:36:39:48 SD: 0.0000 cents