Scala analysis: trance1
Michael's scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 151/125 327.144546 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 302/275 162.1403 3: 500/453 170.9005 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 302/275 162.140 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 500/453 170.900 cents 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: 1 151/125 327.145 cents 2: 1 40/33 333.041 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 375/302 374.810 cents 2: 1 5/4 386.314 cents major third 3: 1 33/25 480.646 cents 2 pentatones 3: 2 4/3 498.045 cents perfect fourth 3: 1 302/225 509.548 cents 3: 1 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 625/453 557.214 cents 4: 1 906/625 642.786 cents 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 1 225/151 690.452 cents 4: 2 3/2 701.955 cents perfect fifth 4: 1 50/33 719.354 cents 3 pentatones 5: 1 8/5 813.686 cents minor sixth 5: 1 604/375 825.190 cents 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 5: 1 250/151 872.855 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: 1 453/250 1029.100 cents 6: 1 20/11 1034.996 cents large minor seventh 6: 1 275/151 1037.860 cents 6: 1 50/27 1066.762 cents grave major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 165.0 327.1 498.0 702.0 884.4 1017.6 1200.0 165.0 : 162.1 333.0 537.0 719.4 852.6 1035.0 1200.0 327.1 : 170.9 374.8 557.2 690.5 872.9 1037.9 1200.0 498.0 : 203.9 386.3 519.6 702.0 867.0 1029.1 1200.0 702.0 : 182.4 315.6 498.0 663.0 825.2 996.1 1200.0 884.4 : 133.2 315.6 480.6 642.8 813.7 1017.6 1200.0 1017.6: 182.4 347.4 509.5 680.4 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 203.9100 cents 25/24, 70.6724 cents 27/25, 133.2376 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 480.6455 .. 557.2142 cents 15625/14949, 76.5687 cents 132/125, 94.3318 cents 4: 642.7858 .. 719.3545 cents 15625/14949, 76.5687 cents 410418/390625, 85.5717 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 132/125, 94.3318 cents 6: 996.0900 .. 1066.7624 cents 25/24, 70.6724 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.286638 Largest / Average step : 1.189475 Largest / Smallest step : 1.530424 Median interval of one step : 500/453, 170.9005 cents, amount: 1 Most common interval of one step : 10/9, 182.4037 cents, amount: 2 Least squares average step : 171.77585 cents, oct.: 1202.43098 cents Scale is strictly proper Step pattern alph. order: ABCDEFE Step pattern size order : CBDFEAE Scale is a Constant Structure, by a margin of 85.57167 cents Scale diversity : 1.404956 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.636811 Rothenberg efficiency : 0.326531 redundancy: 0.673469 Efficiency x scale size : 2.285714 Number of different interval sizes : 36 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 605/604, 2.8639 cents Number of recognisable fifths : 4, average 703.4291 cents Number of appreciable fifths : 3, average 698.1206 cents 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 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 151 Odd number limit : 625 (O: 625 U: 625) Highest odd numerator or denominator: 151 Scale harmonicity : 0.018254 Fundamental : 1/750, -9.5507 octaves, 0.3488 Hz. Guide tone : 298980, 18.1897 octaves, 78220811.514 Hz. Exponens Consonantiae : 2.242350E+08, 27.74044 octaves Euler's gradus suavitatis : 186 Sum of Mann's harmonic distance : 167.0, average 23.85714 Mersenne's string divisions : 19320 Sum of van Prooijen's expressibility: 5.82782, average 0.83255 Sum of Tenney's harmonic distance : 11.30495, average 1.61499 Vogel's harmonic complexity : 39.85714 Wille's k value : 562 Wilson's harmonic complexity : 191 Rectangular lattice diameter : 9 Triangular lattice diameter : 4 Lattice compactness : 70.59727, average 2.52133 Lattice compactness (without 2's) : 57.20892, average 2.04318 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.14286 5 1 3: -1 .. 2 0.14286 5 2 5: -3 .. 1 -0.57143 6 2 11: 0 .. 1 0.14286 1 1 151: 0 .. 1 0.14286 1 1 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 18 24 52| Scale is JI-epimorphic with val: <7 11 16 24 50| Scale is weakly epimorphic with val: <7 11 17 26 52| Scale is weakly epimorphic with val: <7 12 16 22 51|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 15.4773 c. M: 27.2159 c. Lebeng 15: 2 2 2 3 2 2 2 SP M ME I SD: 13.3537 c. M:-22.4037 c. Miller's Porcupine-7 19: 3 2 3 3 3 2 3 SP M ME I SD: 11.2243 c. M:-24.4695 c. Nineteen-tone Dorian 22: 3 3 3 4 3 3 3 SP M ME I SD: 9.1903 c. M:-18.7673 c. Minor quasi-equal Heptatonic, Miller's Porcupine-7 27: 4 3 4 5 4 3 4 SP T3 I SD: 9.4855 c. M: 16.0334 c. 29: 4 4 4 5 4 4 4 SP M ME I SD: 8.7990 c. M:-16.8865 c. Miller's Porcupine-7 34: 5 4 5 6 5 4 5 SP T3 I SD: 6.4559 c. M:-11.4664 c. 38: 5 5 6 6 6 4 6 SP SD: 6.9044 c. M: 11.3551 c. 39: 5 6 5 7 6 4 6 SP SD: 7.4305 c. M:-11.3170 c. 41: 6 5 6 7 6 5 6 SP T3 I SD: 5.6807 c. M:-10.6055 c. 48: 7 6 7 8 7 6 7 SP T3 I SD: 6.0304 c. M:-9.9958 c. 50: 7 7 7 8 8 5 8 SP SD: 6.1373 c. M: 9.5963 c. 51: 7 7 7 9 8 5 8 SP SD: 4.8598 c. M:-9.7589 c. 53: 7 7 8 9 8 6 8 SP SD: 4.6159 c. M: 10.1634 c. 58: 8 8 8 10 9 6 9 SP SD: 2.9850 c. M:-5.2965 c. 65: 9 9 9 11 10 7 10 SP SD: 2.2816 c. M:-5.1631 c. 73: 10 10 10 13 11 8 11 SP SD: 3.0332 c. M: 4.8943 c. 80: 11 11 11 14 12 9 12 SP SD: 2.1675 c. M:-3.0450 c. 87: 12 12 12 15 13 10 13 SP SD: 2.1375 c. M:-3.8899 c. 99: 14 13 14 17 15 11 15 SP SD: 1.8873 c. M:-4.6927 c. 111: 15 15 16 19 17 12 17 SP SD: 1.8354 c. M: 2.8421 c. 118: 16 16 17 20 18 13 18 SP SD: 1.1288 c. M: 2.2924 c. 125: 17 17 18 21 19 14 19 SP SD: 1.0570 c. M: 1.8042 c. 183: 25 25 26 31 28 20 28 SP SD: 0.7655 c. M: 1.2028 c. 205: 28 28 29 35 31 23 31 SP SD: 0.6773 c. M: 1.1018 c. 217: 30 29 31 37 33 24 33 SP SD: 0.5357 c. M:-0.8944 c. 224: 31 30 32 38 34 25 34 SP SD: 0.4748 c. M:-1.0672 c. 304: 42 41 43 52 46 34 46 SP SD: 0.5942 c. M:-0.8248 c. 335: 46 45 48 57 51 37 51 SP SD: 0.4959 c. M: 1.1744 c. 342: 47 46 49 58 52 38 52 SP SD: 0.3382 c. M: 0.8288 c. 349: 48 47 50 59 53 39 53 SP SD: 0.4310 c. M: 0.6911 c. 400: 55 54 57 68 61 44 61 SP SD: 0.3363 c. M:-0.6413 c. 407: 56 55 58 69 62 45 62 SP SD: 0.2146 c. M: 0.3973 c. 605: 83 82 86 103 92 67 92 SP SD: 0.2109 c. M: 0.3761 c. 612: 84 83 87 104 93 68 93 SP SD: 0.1637 c. M:-0.3064 c. 829: 114 112 118 141 126 92 126 SP SD: 0.0600 c. M: 0.0957 c. 1665: 229 225 237 283 253 185 253 SP SD: 0.0414 c. M:-0.0627 c. 2072: 285 280 295 352 315 230 315 SP SD: 0.0390 c. M:-0.0755 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: 19.1695 cents 5 x 6:7 x 8:9:10 S SD: 22.1464 cents 6 x 7:8:9:10:11:12 S SD: 11.3554 cents 7:8 x 9:11:12:13:14 SD: 23.6495 cents 8:9:10:11:12:13:14:16 S SD: 15.7483 cents 9:10:11:12:14:15:16:18 S SD: 10.2419 cents 10:11:12:13:15:17:18:20 SD: 8.1175 cents 18:20:22:24:27:30:32:36 S SD: 4.8987 cents 20:22:24:27:30:33:36:40 S SD: 4.2800 cents 24:26:29:32:36:40:43:48 SD: 3.9471 cents 30:33:36:40:45:50:54:60 SD: 1.6433 cents 48:53:58:64:72:80:86:96 SD: 1.4819 cents 72:79:87:96:108:120:130:144 SD: 0.9882 cents 90:99:109:120:135:150:162:180 SD: 0.6361 cents 120:132:145:160:180:200:216:240 SD: 0.0682 cents 390:429:471:520:585:650:702:780 SD: 0.0630 cents 510:561:616:680:765:850:918:1020 SD: 0.0321 cents