Scala analysis: boogie
Paul Hjelmstad's boogie woogie scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 21/16 470.780907 narrow fourth 4: 45/32 590.223716 diatonic tritone 5: 3/2 701.955001 perfect fifth 6: 27/16 905.865003 Pythagorean major sixth 7: 7/4 968.825906 harmonic seventh 8: 15/8 1088.268715 classic major seventh 9: 63/32 1172.735908 octave - septimal comma 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 21/20 84.4672 minor semitone 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 7: 28/27 62.9609 Archytas' 1/3-tone 8: 15/14 119.4428 major diatonic semitone 9: 21/20 84.4672 minor semitone 10: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 3: 1 8/7 231.174 cents septimal whole tone 3: 1 7/6 266.871 cents septimal minor third 3: 2 6/5 315.641 cents minor third 3: 1 56/45 378.602 cents septimal narrow major third 3: 2 5/4 386.314 cents major third 3: 1 80/63 413.578 cents wide major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 4: 1 32/27 294.135 cents Pythagorean minor third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 21/16 470.781 cents narrow fourth 4: 5 4/3 498.045 cents perfect fourth 4: 1 27/20 519.551 cents acute fourth 4: 1 45/32 590.224 cents diatonic tritone 5: 2 4/3 498.045 cents perfect fourth 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 3 10/7 617.488 cents Euler's tritone 5: 2 3/2 701.955 cents perfect fifth 6: 1 64/45 609.776 cents 2nd tritone 6: 1 40/27 680.449 cents grave fifth 6: 5 3/2 701.955 cents perfect fifth 6: 1 32/21 729.219 cents wide fifth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 7: 1 32/21 729.219 cents wide fifth 7: 1 14/9 764.916 cents septimal minor sixth 7: 1 63/40 786.422 cents narrow minor sixth 7: 2 8/5 813.686 cents minor sixth 7: 1 45/28 821.398 cents septimale wide minor sixth 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 1 12/7 933.129 cents septimal major sixth 7: 1 7/4 968.826 cents harmonic seventh 8: 1 8/5 813.686 cents minor sixth 8: 1 5/3 884.359 cents major sixth, BP sixth 8: 2 12/7 933.129 cents septimal major sixth 8: 2 7/4 968.826 cents harmonic seventh 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 1 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 15/8 1088.269 cents classic major seventh 9: 2 16/9 996.090 cents Pythagorean minor seventh 9: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 2 28/15 1080.557 cents grave major seventh 9: 1 15/8 1088.269 cents classic major seventh 9: 2 40/21 1115.533 cents acute major seventh 9: 1 27/14 1137.039 cents septimal major seventh 9: 1 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.66667 = 20/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 203.9 386.3 470.8 590.2 702.0 905.9 968.8 1088.3 1172.7 1200.0 203.9 : 182.4 266.9 386.3 498.0 702.0 764.9 884.4 968.8 996.1 1200.0 386.3 : 84.5 203.9 315.6 519.6 582.5 702.0 786.4 813.7 1017.6 1200.0 470.8 : 119.4 231.2 435.1 498.0 617.5 702.0 729.2 933.1 1115.5 1200.0 590.2 : 111.7 315.6 378.6 498.0 582.5 609.8 813.7 996.1 1080.6 1200.0 702.0 : 203.9 266.9 386.3 470.8 498.0 702.0 884.4 968.8 1088.3 1200.0 905.9 : 63.0 182.4 266.9 294.1 498.0 680.4 764.9 884.4 996.1 1200.0 968.8 : 119.4 203.9 231.2 435.1 617.5 702.0 821.4 933.1 1137.0 1200.0 1088.3: 84.5 111.7 315.6 498.0 582.5 702.0 813.7 1017.6 1080.6 1200.0 1172.7: 27.3 231.2 413.6 498.0 617.5 729.2 933.1 996.1 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 203.9100 cents 567/512, 176.6459 cents 64/63, 27.2641 cents 2: 111.7313 .. 386.3137 cents 75/64, 274.5824 cents 128/135,-92.1787 cents 3: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 32/35,-155.1396 cents 4: 294.1350 .. 590.2237 cents 1215/1024, 296.0887 cents 512/567,-176.6459 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 128/135,-92.1787 cents 6: 609.7763 .. 905.8650 cents 1215/1024, 296.0887 cents 128/135,-92.1787 cents 7: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 512/567,-176.6459 cents 8: 813.6863 .. 1088.2687 cents 75/64, 274.5824 cents 32/35,-155.1396 cents 9: 996.0900 .. 1172.7359 cents 567/512, 176.6459 cents 128/135,-92.1787 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 4.401394 Largest / Average step : 1.699250 Largest / Smallest step : 7.479068 Median interval of one step : 115.58705 cents, amount: 0 Least squares average step : 134.38258 cents, oct.: 1343.82583 cents Scale is not proper Step pattern alph. order: ABCDEAFDCG Step pattern size order : GFCEDGBECA Scale is not a Constant Structure Scale diversity : 1.498310 Lumma stability : 0.045440 Lumma impropriety factor : 0.706607 Rothenberg efficiency : 0.398968 redundancy: 0.601032 Efficiency x scale size : 3.989683 Number of different interval sizes : 40 = 4.44444 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.66667 = 20/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 7, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 10.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval class 4 Scale is differentially coherent in interval class 5 Scale is differentially coherent in interval classes 6 and 7 combined Scale is differentially coherent in interval classes 7 and 8 combined -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 63 Scale harmonicity : 0.032588 Average absolute harmonicity : 0.192662 Specific harmonicity : 0.171763 Fundamental : 1/32, -5.0000 octaves, 8.1758 Hz. Guide tone : 1890, 10.8842 octaves, 494472.318 Hz. Exponens Consonantiae : 6.048000E+04, 15.88417 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 160.0, average 16.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.35766, average 1.03577 Sum of Tenney's harmonic distance : 19.38856, average 1.93886 Vogel's harmonic complexity : 9.40000 Wille's k value : 31 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 163.97790, average 2.98142 Lattice compactness (without 2's) : 89.25349, average 1.62279 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.80000 30 1 3: 0 .. 3 1.20000 12 3 5: 0 .. 1 0.30000 3 3 7: 0 .. 1 0.30000 3 3 Average exponent except 2's : 18 / 10 = 1.80000 Average absolute exponent except 2's: 18 / 10 = 1.80000
FIT/MODE
10: 2 1 1 1 1 2 0 1 1 0 N T3 S SD: 25.1422 c. M:-54.1350 c. 12: 2 2 1 1 1 2 1 1 1 0 N SD: 17.4440 c. M:-31.1741 c. 19: 3 3 1 2 2 3 1 2 1 1 N SD: 20.1068 c. M: 35.8938 c. 20: 3 3 2 2 2 3 1 2 2 0 N SD: 16.4143 c. M:-27.2641 c. 21: 4 3 1 2 2 4 1 2 2 0 N SD: 15.5758 c. M:-27.2641 c. 22: 4 3 2 2 2 4 1 2 2 0 N SD: 14.6729 c. M:-27.2641 c. 24: 4 4 1 3 2 4 1 3 1 1 N SD: 13.3312 c. M: 22.7359 c. 25: 4 4 2 2 3 4 1 3 1 1 N SD: 12.4624 c. M: 20.7359 c. 28: 5 4 2 3 2 5 2 2 2 1 N SD: 11.4635 c. M:-16.8884 c. 29: 5 4 2 3 3 5 1 3 2 1 N SD: 11.1031 c. M: 17.1018 c. 31: 5 5 2 3 3 5 2 3 2 1 N SD: 8.1172 c. M: 15.5424 c. 33: 6 5 2 3 3 6 2 3 2 1 N SD: 9.2544 c. M:-14.2718 c. 34: 6 5 2 4 3 6 1 4 2 1 N SD: 8.9956 c. M: 15.8847 c. 36: 6 6 2 4 3 6 2 4 2 1 N SD: 7.2969 c. M:-13.6863 c. 40: 7 6 3 4 3 7 2 4 3 1 N SD: 7.4988 c. M: 11.9550 c. 41: 7 6 3 4 4 7 2 4 3 1 N SD: 3.2924 c. M: 5.8259 c. 53: 9 8 4 5 5 9 3 5 4 1 N SD: 2.6950 c. M:-4.7590 c. 77: 13 12 5 8 7 13 4 8 5 2 N SD: 2.4561 c. M: 3.9047 c. 87: 15 13 6 9 8 15 4 9 6 2 N SD: 2.3620 c. M:-4.4798 c. 94: 16 14 7 9 9 16 5 9 7 2 N SD: 1.9451 c. M: 3.3350 c. 99: 17 15 7 10 9 17 5 10 7 2 N SD: 2.3042 c. M:-3.7157 c. 118: 20 18 8 12 11 20 6 12 8 3 N SD: 1.6730 c. M: 3.2444 c. 130: 22 20 9 13 12 22 7 13 9 3 N SD: 0.7681 c. M:-1.3786 c. 171: 29 26 12 17 16 29 9 17 12 4 N SD: 0.5225 c. M: 0.8061 c. 301: 51 46 21 30 28 51 16 30 21 7 N SD: 0.4418 c. M: 0.8816 c. 311: 53 47 22 31 29 53 16 31 22 7 N SD: 0.4078 c. M:-0.8874 c. 354: 60 54 25 35 33 60 19 35 25 8 N SD: 0.4200 c. M: 0.7803 c. 400: 68 61 28 40 37 68 21 40 28 9 N SD: 0.4225 c. M:-0.7763 c. 441: 75 67 31 44 41 75 23 44 31 10 N SD: 0.1480 c. M:-0.2574 c. 612: 104 93 43 61 57 104 32 61 43 14 N SD: 0.1074 c. M: 0.1985 c. 665: 113 101 47 66 62 113 35 66 47 15 N SD: 0.1349 c. M:-0.1966 c. 795: 135 121 56 79 74 135 42 79 56 18 N SD: 0.1289 c. M:-0.2307 c. 1053: 179 160 74 105 98 179 55 105 74 24 N SD: 0.0910 c. M: 0.1649 c. 1106: 188 168 78 110 103 188 58 110 78 25 N SD: 0.0747 c. M:-0.1393 c. 1236: 210 188 87 123 115 210 65 123 87 28 N SD: 0.0697 c. M:-0.1061 c. 1277: 217 194 90 127 119 217 67 127 90 29 N SD: 0.0515 c. M: 0.0960 c. 1407: 239 214 99 140 131 239 74 140 99 32 N SD: 0.0486 c. M: 0.1081 c. 1718: 292 261 121 171 160 292 90 171 121 39 N SD: 0.0354 c. M:-0.0721 c. 1848: 314 281 130 184 172 314 97 184 130 42 N SD: 0.0253 c. M:-0.0499 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x 4 x x 5 x x x 6 S SD: 11.5751 cents 4 x 5 x x 6 x 7 x x 8 S SD: 0.0000 cents 5 x 6 x 7 x 8:9 x x 10 S SD: 25.2424 cents 6:7 x 8 x 9:10 x 11 x 12 S SD: 13.6255 cents 7:8 x 9:10:11:12 x 13 x 14 S SD: 14.4737 cents 8:9:10 x 11:12 x 14:15 x 16 S SD: 5.5580 cents 9:10:11:12:13:14:15:16:17 x 18 S SD: 11.2245 cents 10:11 x 13:14:15:17:18:19 x 20 SD: 8.7636 cents 11:12:14 x 15:17 x 19:21 x 22 SD: 14.8499 cents 12:14:15:16:17:18:20:21:23 x 24 SD: 9.1497 cents 13:15:16:17:18:20:22:23:24 x 26 SD: 8.9071 cents 14:16 x 18:20:21:24:25:26 x 28 S SD: 8.8406 cents 15:17:19:20:21:23:25:26:28 x 30 SD: 6.7916 cents 16:18:20:21:23:24:27:28:30 x 32 SD: 4.2278 cents 23:26:29:30:32:35:39:40:43:45:46 SD: 4.1242 cents 24:27:30:32:34:36:41:42:45:47:48 SD: 3.7976 cents 25:28:31:33:35:38:42:44:47:49:50 SD: 3.4248 cents 31:35:39:41:44:47:52:54:58:61:62 SD: 3.3537 cents 32:36:40:42:45:48:54:56:60:63:64 S SD: 0.0000 cents