Scala analysis: pentatonic-2_3_7_11_13
Pentatonic, primes 2-3-7-11-13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 11/8 551.317942 undecimal semi-augmented 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: 7/6 266.8709 septimal minor third 2: 33/28 284.4470 undecimal minor third 3: 12/11 150.6371 undecimal neutral second, 3/4-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: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 33/28 284.447 cents undecimal minor third 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 4/3 498.045 cents perfect fourth 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 56/39 626.343 cents 3: 1 39/28 573.657 cents 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 22/13 910.790 cents tridecimal major sixth 4: 1 13/8 840.528 cents tridecimal neutral sixth 4: 1 56/33 915.553 cents 4: 1 12/7 933.129 cents septimal major sixth 4: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 4: 1 24/13 1061.427 cents tridecimal neutral seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 266.9 551.3 702.0 840.5 1200.0 266.9 : 284.4 435.1 573.7 933.1 1200.0 551.3 : 150.6 289.2 648.7 915.6 1200.0 702.0 : 138.6 498.0 764.9 1049.4 1200.0 840.5 : 359.5 626.3 910.8 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: 289.2097 .. 626.3432 cents 616/507, 337.1335 cents 169/176,-70.2626 cents 3: 573.6568 .. 910.7903 cents 616/507, 337.1335 cents 1521/1568,-52.6865 cents 4: 840.5277 .. 1061.4273 cents 192/169, 220.8997 cents 169/176,-70.2626 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 : 7/6, 266.8709 cents, amount: 1 Least squares average step : 233.40877 cents, oct.: 1167.04386 cents Scale is not proper Step pattern alph. order: ABCDE Step pattern size order : CDBAE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 4.76268 cents Scale diversity : 1.626538 Lumma stability : 0.230954 Lumma impropriety factor : 0.161010 Rothenberg efficiency : 0.400000 redundancy: 0.600000 Efficiency x scale size : 2.000000 Number of different interval sizes : 20 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 364/363, 4.7627 cents Number of recognisable fifths : 1, average 701.9550 cents Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 20.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 39 U: 39) Highest odd numerator or denominator: 13 Scale harmonicity : 0.016679 Average absolute harmonicity : 0.286273 Specific harmonicity : 0.116590 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 6006, 12.5522 octaves, 1571323.145 Hz. Exponens Consonantiae : 1.441440E+05, 17.13715 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 30.5, average 6.10000 Mersenne's string divisions : 25935 Sum of van Prooijen's expressibility: 3.47756, average 0.69551 Sum of Tenney's harmonic distance : 6.66395, average 1.33279 Vogel's harmonic complexity : 10.80000 Wille's k value : 19 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 37.24335, average 2.48289 Lattice compactness (without 2's) : 18.77124, average 1.25142 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.40000 9 1 3: -1 .. 1 0.00000 2 1 7: 0 .. 1 0.20000 1 1 11: 0 .. 1 0.20000 1 1 13: 0 .. 1 0.20000 1 1 Average exponent except 2's : 3 / 5 = 0.60000 Average absolute exponent except 2's: 5 / 5 = 1.00000 Scale is weakly epimorphic with val: <5 7 13 18 19| Scale is weakly epimorphic with val: <5 7 15 16 19| Scale is weakly epimorphic with val: <5 7 15 19 21| Scale is JI-epimorphic with val: <5 8 14 17 19| = patent Scale is weakly epimorphic with val: <5 8 15 16 19| Scale is weakly epimorphic with val: <5 8 15 19 21| Scale is weakly epimorphic with val: <5 9 15 17 18|
FIT/MODE
5: 1 1 1 0 2 N T3 SD: 64.2819 c. M: 120.5277 c. 7: 2 1 1 1 2 N D3 I SD: 39.2049 c. M:-75.9862 c. 9: 2 2 1 1 3 N SD: 25.3426 c. M: 40.5277 c. 13: 3 3 2 1 4 N SD: 17.5237 c. M:-36.5065 c. 17: 4 4 2 2 5 N SD: 9.7674 c. M:-15.4820 c. 24: 5 6 3 3 7 N SD: 8.7168 c. M: 16.8709 c. 26: 6 6 3 3 8 N SD: 7.6907 c. M:-10.0522 c. 31: 7 7 4 4 9 N SD: 7.1350 c. M:-11.0852 c. 33: 7 8 4 4 10 N SD: 8.0703 c. M: 12.3255 c. 37: 8 9 5 4 11 N SD: 6.2595 c. M:-11.5585 c. 39: 9 9 5 4 12 N SD: 6.8641 c. M:-10.0522 c. 41: 9 10 5 5 12 N SD: 4.5417 c. M:-8.2528 c. 44: 10 10 6 5 13 N SD: 5.3642 c. M:-7.1359 c. 46: 10 11 6 5 14 N SD: 4.1699 c. M: 6.0013 c. 50: 11 12 6 6 15 N SD: 2.9815 c. M: 5.9550 c. 63: 14 15 8 7 19 N SD: 1.7302 c. M:-2.8069 c. 94: 21 22 12 11 28 N SD: 1.5020 c. M: 2.3818 c. 104: 23 25 13 12 31 N SD: 1.7519 c. M:-2.5282 c. 111: 25 26 14 13 33 N SD: 1.9743 c. M:-3.3994 c. 113: 25 27 14 13 34 N SD: 1.1303 c. M: 1.5896 c. 157: 35 37 20 18 47 N SD: 0.7724 c. M:-1.2297 c. 207: 46 49 26 24 62 N SD: 0.3612 c. M: 0.5933 c. 270: 60 64 34 31 81 N SD: 0.2947 c. M: 0.5277 c. 431: 96 102 54 50 129 N SD: 0.2748 c. M:-0.4145 c. 477: 106 113 60 55 143 N SD: 0.2293 c. M: 0.3745 c. 494: 110 117 62 57 148 N SD: 0.1606 c. M:-0.3356 c. 607: 135 144 76 70 182 N SD: 0.1952 c. M: 0.3300 c. 701: 156 166 88 81 210 N SD: 0.1024 c. M:-0.1762 c. 971: 216 230 122 112 291 N SD: 0.0974 c. M: 0.1569 c. 1012: 225 240 127 117 303 N SD: 0.0936 c. M:-0.1838 c. 1219: 271 289 153 141 365 N SD: 0.0915 c. M:-0.1614 c. 1282: 285 304 161 148 384 N SD: 0.0576 c. M: 0.1002 c. 1489: 331 353 187 172 446 N SD: 0.0636 c. M: 0.1147 c. 1506: 335 357 189 174 451 N SD: 0.0679 c. M:-0.1098 c. 1619: 360 384 203 187 485 N SD: 0.0650 c. M:-0.1336 c. 1713: 381 406 215 198 513 N SD: 0.0495 c. M:-0.1028 c. 1776: 395 421 223 205 532 N SD: 0.0372 c. M:-0.0720 c. 1983: 441 470 249 229 594 N SD: 0.0171 c. M: 0.0320 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: 22.9956 cents 4:5 x 6:7:8 S SD: 43.8228 cents 5:6:7 x 8:10 S SD: 15.9532 cents 6:7:8:9:10:12 S SD: 13.7973 cents 7:8:10 x 11:14 SD: 23.7445 cents 8:9:11:12:13:16 SD: 12.5922 cents 11:13:15:17:18:22 SD: 11.8694 cents 13:15:18:20:21:26 SD: 10.0762 cents 14:16:19:21:23:28 SD: 9.2616 cents 16:19:22:24:26:32 SD: 6.1284 cents 18:21:25:27:29:36 SD: 4.5764 cents 24:28:33:36:39:48 SD: 0.0000 cents