Scala analysis: pentatonic-proper_5-prime
Strictly proper 2-3-7-11-13 pentatonic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63/52 332.208246 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 3/2 701.955001 perfect fifth 4: 7/4 968.825906 harmonic seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 63/52 332.2082 2: 143/126 219.1097 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 7/6 266.8709 septimal minor third 5: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 143/126 219.110 cents 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 63/52 332.208 cents 2: 1 26/21 369.747 cents 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 4/3 498.045 cents perfect fourth 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 13/9 636.618 cents tridecimal diminished fifth 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 3/2 701.955 cents perfect fifth 3: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 21/13 830.253 cents 4: 1 104/63 867.792 cents 4: 1 12/7 933.129 cents septimal major sixth 4: 1 7/4 968.826 cents harmonic seventh 4: 1 252/143 980.890 cents 4: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 332.2 551.3 702.0 968.8 1200.0 332.2 : 219.1 369.7 636.6 867.8 1200.0 551.3 : 150.6 417.5 648.7 980.9 1200.0 702.0 : 266.9 498.0 830.3 1049.4 1200.0 968.8 : 231.2 563.4 782.5 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 332.2082 cents 231/208, 181.5712 cents 12/11, 150.6371 cents 2: 369.7468 .. 563.3823 cents 189/169, 193.6356 cents 1352/1323, 37.5385 cents 3: 636.6177 .. 830.2532 cents 189/169, 193.6356 cents 169/162, 73.2353 cents 4: 867.7918 .. 1049.3629 cents 231/208, 181.5712 cents 1352/1323, 37.5385 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 63/52, 332.2082 cents Average / Smallest step : 1.593233 Largest / Average step : 1.384201 Largest / Smallest step : 2.205355 Median interval of one step : 8/7, 231.1741 cents, amount: 1 Least squares average step : 243.92750 cents, oct.: 1219.63752 cents Scale is strictly proper Step pattern alph. order: ABCDE Step pattern size order : EBADC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 37.53851 cents Scale diversity : 1.670930 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.374655 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 : 144/143, 12.0644 cents Number of recognisable fifths : 1, average 701.9550 cents Best fifths form a closed circle Length of longest harmonic part : 2 at degree 3 Formal octave complements present : 1 = 20.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 13 Odd number limit : 143 (O: 143 U: 143) Highest odd numerator or denominator: 63 Scale harmonicity : 0.016679 Average absolute harmonicity : 0.285295 Specific harmonicity : 0.104157 Fundamental : 1/104, -6.7004 octaves, 2.5156 Hz. Guide tone : 1386, 10.4367 octaves, 362613.034 Hz. Exponens Consonantiae : 1.441440E+05, 17.13715 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 76.5, average 15.30000 Mersenne's string divisions : 72105 Sum of van Prooijen's expressibility: 4.16295, average 0.83259 Sum of Tenney's harmonic distance : 7.98617, average 1.59723 Vogel's harmonic complexity : 18.80000 Wille's k value : 71 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 37.34736, average 2.48982 Lattice compactness (without 2's) : 21.75549, average 1.45037 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.40000 9 1 3: 0 .. 2 0.60000 3 1 7: 0 .. 1 0.40000 2 1 11: 0 .. 1 0.20000 1 1 13: -1 .. 0 -0.20000 1 1 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 13 16 18| Scale is weakly epimorphic with val: <5 7 13 19 21| Scale is weakly epimorphic with val: <5 7 14 16 20| Scale is weakly epimorphic with val: <5 8 14 16 18| Scale is JI-epimorphic with val: <5 8 14 17 19| = patent Scale is weakly epimorphic with val: <5 9 13 16 19| Scale is weakly epimorphic with val: <5 9 13 17 20|
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 52.9001 c. M: 92.2082 c. 6: 2 1 1 1 1 P M ME S SD: 59.2458 c. M:-98.0450 c. 7: 2 1 1 2 1 P M ME S SD: 32.6131 c. M:-59.7455 c. Thai mode 6 9: 2 2 1 2 2 SP M ME I SD: 37.7469 c. M: 65.5416 c. 10: 3 2 1 2 2 P T3 SD: 26.6302 c. M:-48.6821 c. 11: 3 2 1 3 2 P T3 SD: 22.2495 c. M: 47.4095 c. 14: 4 2 2 3 3 P SD: 22.0133 c. M: 37.0322 c. 15: 4 3 2 3 3 SP T3 SD: 11.2066 c. M:-18.0450 c. 22: 6 4 3 5 4 SP SD: 7.4627 c. M:-12.9923 c. 26: 7 5 3 6 5 SP SD: 6.0499 c. M: 9.6473 c. 41: 11 8 5 9 8 SP SD: 5.2368 c. M: 10.2570 c. 43: 12 8 5 10 8 SP SD: 5.1907 c. M:-7.9183 c. 46: 13 8 6 10 9 SP SD: 3.9713 c. M:-6.9222 c. 58: 16 11 7 13 11 SP SD: 3.7366 c. M:-7.3027 c. 61: 17 11 8 13 12 SP SD: 3.6893 c. M:-6.2417 c. 68: 19 12 9 15 13 SP SD: 3.0395 c. M: 4.2591 c. 72: 20 13 9 16 14 SP SD: 1.5157 c. M: 2.1592 c. 94: 26 17 12 21 18 SP SD: 1.2419 c. M: 2.3818 c. 130: 36 24 16 29 25 SP SD: 1.1610 c. M:-2.5282 c. 152: 42 28 19 34 29 SP SD: 1.2278 c. M:-2.2267 c. 166: 46 30 21 37 32 SP SD: 0.9356 c. M: 1.9204 c. 176: 49 32 22 39 34 SP SD: 0.9972 c. M:-1.8827 c. 181: 50 33 23 40 35 SP SD: 0.7756 c. M: 1.0417 c. 198: 55 36 25 44 38 SP SD: 0.8025 c. M:-1.1251 c. 202: 56 37 25 45 39 SP SD: 0.7411 c. M:-1.1573 c. 224: 62 41 28 50 43 SP SD: 0.4288 c. M:-0.8170 c. 296: 82 54 37 66 57 SP SD: 0.2913 c. M: 0.6036 c. 311: 86 57 39 69 60 SP SD: 0.3302 c. M:-0.4505 c. 383: 106 70 48 85 74 SP SD: 0.3165 c. M: 0.6797 c. 405: 112 74 51 90 78 SP SD: 0.2214 c. M: 0.3564 c. 477: 132 87 60 106 92 SP SD: 0.2176 c. M: 0.3745 c. 581: 161 106 73 129 112 SP SD: 0.2132 c. M:-0.3219 c. 607: 168 111 76 135 117 SP SD: 0.1446 c. M:-0.2471 c. 701: 194 128 88 156 135 SP SD: 0.0887 c. M: 0.1112 c. 1282: 355 234 161 285 247 SP SD: 0.0517 c. M:-0.0850 c. 1889: 523 345 237 420 364 SP SD: 0.0484 c. M:-0.0849 c. 1983: 549 362 249 441 382 SP SD: 0.0173 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: 33.2878 cents 4:5 x 6:7:8 S SD: 13.5264 cents 8:10:11:12:14:16 S SD: 10.8211 cents 14:17:19:21:25:28 SD: 8.3686 cents 16:19:22:24:28:32 SD: 6.9390 cents 19:23:26:29:33:38 SD: 6.7774 cents 24:29:33:36:42:48 SD: 0.9172 cents 56:68:77:84:98:112 SD: 0.7843 cents 80:97:110:120:140:160 SD: 0.2747 cents 104:126:143:156:182:208 SD: 0.0000 cents