Scala analysis: bubble-08-almighty-fractal
Sevish: Almighty Fractal, Bubble
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 10/9 182.4037 minor whole tone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 2 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 2 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 20/11 1034.996 cents large minor seventh 6: 2 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 347.4 498.0 702.0 884.4 1049.4 1200.0 182.4 : 165.0 315.6 519.6 702.0 867.0 1017.6 1200.0 347.4 : 150.6 354.5 537.0 702.0 852.6 1035.0 1200.0 498.0 : 203.9 386.3 551.3 702.0 884.4 1049.4 1200.0 702.0 : 182.4 347.4 498.0 680.4 845.5 996.1 1200.0 884.4 : 165.0 315.6 498.0 663.0 813.7 1017.6 1200.0 1049.4: 150.6 333.0 498.0 648.7 852.6 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 203.9100 cents 33/32, 53.2729 cents 12/11, 150.6371 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 16/15, 111.7313 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1049.3629 cents 33/32, 53.2729 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.138024 Largest / Average step : 1.189475 Largest / Smallest step : 1.353651 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 173.55104 cents, oct.: 1214.85729 cents Scale is strictly proper Step pattern alph. order: ABCDABC Step pattern size order : CBADCBA Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.313255 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.704636 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 4 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 70.6724 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 33 (O: 33 U: 33) Highest odd numerator or denominator: 11 Scale harmonicity : 0.028104 Average absolute harmonicity : 0.252019 Specific harmonicity : 0.152508 Fundamental : 1/18, -4.1699 octaves, 14.5348 Hz. Guide tone : 660, 9.3663 octaves, 172672.873 Hz. Exponens Consonantiae : 1.188000E+04, 13.53625 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 39.5, average 5.64286 Mersenne's string divisions : 271320 Sum of van Prooijen's expressibility: 4.69024, average 0.67003 Sum of Tenney's harmonic distance : 9.10388, average 1.30055 Vogel's harmonic complexity : 9.28571 Wille's k value : 16 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 60.59909, average 2.16425 Lattice compactness (without 2's) : 44.51877, average 1.58996 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.28571 6 1 3: -2 .. 1 -0.85714 8 2 5: 0 .. 1 0.28571 2 2 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 17 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 16.2202 c. M: 27.2159 c. Lebeng 17: 3 2 2 3 3 2 2 SP D3 S SD: 17.4075 c. M:-33.2883 c. Pseudo Rast 19: 3 3 2 3 3 3 2 SP M ME S SD: 15.7683 c. M:-31.5394 c. Nineteen-tone Major, Ionian 22: 3 3 3 4 3 3 3 SP M ME I SD: 12.8938 c. M: 20.1352 c. Minor quasi-equal Heptatonic, Miller's Porcupine-7 24: 4 3 3 4 4 3 3 SP D3 S SD: 9.0162 c. M:-17.5963 c. Arabic Diatonic, Maqam Rast, Quasi-equal Heptatonic, Neutral Diatonic Phrygian 27: 4 4 3 5 4 4 3 SP T3 SD: 9.0664 c. M:-17.3037 c. 29: 4 4 4 5 4 4 4 SP M ME I SD: 12.0480 c. M: 16.8865 c. Miller's Porcupine-7 31: 5 4 4 5 5 4 4 SP D3 S SD: 5.7578 c. M:-11.1447 c. Neutral Diatonic Phrygian, Rast 34: 5 5 4 6 5 5 4 SP T3 SD: 5.2125 c. M:-9.4606 c. 38: 6 5 5 6 6 5 5 SP D3 S SD: 5.4365 c. M: 7.2577 c. 41: 6 6 5 7 6 6 5 SP T3 SD: 4.1304 c. M: 6.7940 c. 46: 7 6 6 8 7 6 6 SP SD: 4.1643 c. M: 8.2775 c. 53: 8 7 7 9 8 7 7 SP SD: 4.2378 c. M: 7.8535 c. 58: 9 8 7 10 9 8 7 SP SD: 3.7675 c. M:-5.8095 c. 65: 10 9 8 11 10 9 8 SP SD: 2.0153 c. M:-3.3613 c. 72: 11 10 9 12 11 10 9 SP SD: 1.5438 c. M:-2.5921 c. 111: 17 15 14 19 17 15 14 SP SD: 1.2070 c. M:-2.1278 c. 118: 18 16 15 20 18 16 15 SP SD: 1.0029 c. M: 1.9053 c. 145: 22 20 18 25 22 20 18 SP SD: 1.1174 c. M:-1.6715 c. 152: 23 21 19 26 23 21 19 SP SD: 0.5379 c. M: 0.8248 c. 183: 28 25 23 31 28 25 23 SP SD: 0.5957 c. M:-1.2028 c. 224: 34 31 28 38 34 31 28 SP SD: 0.4418 c. M:-0.8063 c. 270: 41 37 34 46 41 37 34 SP SD: 0.3698 c. M: 0.7413 c. 335: 51 46 42 57 51 46 42 SP SD: 0.2169 c. M:-0.4174 c. 342: 52 47 43 58 52 47 43 SP SD: 0.1533 c. M: 0.2401 c. 494: 75 68 62 84 75 68 62 SP SD: 0.1078 c. M: 0.2175 c. 677: 103 93 85 115 103 93 85 SP SD: 0.0830 c. M:-0.1665 c. 829: 126 114 104 141 126 114 104 SP SD: 0.0696 c. M: 0.0957 c. 836: 127 115 105 142 127 115 105 SP SD: 0.0801 c. M: 0.1482 c. 1019: 155 140 128 173 155 140 128 SP SD: 0.0794 c. M:-0.1282 c. 1171: 178 161 147 199 178 161 147 SP SD: 0.0088 c. M:-0.0136 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 23.7887 cents 6 x 7:8:9:10:11:12 S SD: 13.4228 cents 7:8 x 9:11:12:13:14 SD: 20.8875 cents 8:9:10:11:12:13:15:16 SD: 12.9749 cents 9:10:11:12:14:15:17:18 SD: 11.6366 cents 10:11:12:13:15:17:18:20 SD: 10.5148 cents 12:13:15:16:18:20:22:24 SD: 8.3725 cents 17:19:21:23:26:28:31:34 SD: 7.4466 cents 18:20:22:24:27:30:33:36 S SD: 0.0000 cents