Scala analysis: handblue
"Handy Blues" of Pitch Palette, 7-limit
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 135/128 92.1787 major chroma, major limma 3: 28/27 62.9609 Archytas' 1/3-tone 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 15/14 119.4428 major diatonic semitone 10: 21/20 84.4672 minor semitone 11: 15/14 119.4428 major diatonic semitone 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 21/20 84.467 cents minor semitone 1: 1 135/128 92.179 cents major chroma, major limma 1: 3 16/15 111.731 cents minor diatonic semitone 1: 4 15/14 119.443 cents major diatonic semitone 2: 1 35/32 155.140 cents septimal neutral second 2: 3 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 4 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 2 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 1 75/64 274.582 cents classic augmented second 3: 1 32/27 294.135 cents Pythagorean minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 1 135/112 323.353 cents septimal wide minor third 3: 1 128/105 342.905 cents septimal neutral third 4: 3 56/45 378.602 cents septimal narrow major third 4: 5 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 3 9/7 435.084 cents septimal major third, BP third 5: 2 21/16 470.781 cents narrow fourth 5: 7 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 1 27/20 519.551 cents acute fourth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 1 112/81 561.006 cents 6: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 45/32 590.224 cents diatonic tritone 6: 2 64/45 609.776 cents 2nd tritone 6: 3 10/7 617.488 cents Euler's tritone 6: 1 81/56 638.994 cents 7: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 1 40/27 680.449 cents grave fifth 7: 1 112/75 694.243 cents marvelous fifth 7: 7 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 8: 3 14/9 764.916 cents septimal minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 5 8/5 813.686 cents minor sixth 8: 3 45/28 821.398 cents septimale wide minor sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 1 224/135 876.647 cents narrow septimal major sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 1 128/75 925.418 cents diminished seventh 9: 3 12/7 933.129 cents septimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 1 225/128 976.537 cents augmented sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 3 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 64/35 1044.860 cents septimal neutral seventh 11: 4 28/15 1080.557 cents grave major seventh 11: 3 15/8 1088.269 cents classic major seventh 11: 1 256/135 1107.821 cents octave - major chroma 11: 2 40/21 1115.533 cents acute major seventh 11: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.45455 = 60/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 203.9 266.9 386.3 498.0 582.5 702.0 764.9 884.4 968.8 1088.3 1200.0 111.7 : 92.2 155.1 274.6 386.3 470.8 590.2 653.2 772.6 857.1 976.5 1088.3 1200.0 203.9 : 63.0 182.4 294.1 378.6 498.0 561.0 680.4 764.9 884.4 996.1 1107.8 1200.0 266.9 : 119.4 231.2 315.6 435.1 498.0 617.5 702.0 821.4 933.1 1044.9 1137.0 1200.0 386.3 : 111.7 196.2 315.6 378.6 498.0 582.5 702.0 813.7 925.4 1017.6 1080.6 1200.0 498.0 : 84.5 203.9 266.9 386.3 470.8 590.2 702.0 813.7 905.9 968.8 1088.3 1200.0 582.5 : 119.4 182.4 301.8 386.3 505.8 617.5 729.2 821.4 884.4 1003.8 1115.5 1200.0 702.0 : 63.0 182.4 266.9 386.3 498.0 609.8 702.0 764.9 884.4 996.1 1080.6 1200.0 764.9 : 119.4 203.9 323.4 435.1 546.8 639.0 702.0 821.4 933.1 1017.6 1137.0 1200.0 884.4 : 84.5 203.9 315.6 427.4 519.6 582.5 702.0 813.7 898.2 1017.6 1080.6 1200.0 968.8 : 119.4 231.2 342.9 435.1 498.0 617.5 729.2 813.7 933.1 996.1 1115.5 1200.0 1088.3: 111.7 223.5 315.6 378.6 498.0 609.8 694.2 813.7 876.6 996.1 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 119.4428 cents 405/392, 56.4819 cents 28/27, 62.9609 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 3: 266.8709 .. 342.9054 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 5: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 6: 561.0059 .. 638.9941 cents 6561/6272, 77.9882 cents 245/243, 14.1905 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 245/243, 14.1905 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 9: 857.0946 .. 933.1291 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1137.0391 cents 405/392, 56.4819 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 1.588287 Largest / Average step : 1.194428 Largest / Smallest step : 1.897095 Median interval of one step : 16/15, 111.7313 cents, amount: 3 Most common interval of one step : 15/14, 119.4428 cents, amount: 4 Least squares average step : 98.31103 cents, oct.: 1179.73242 cents Scale is strictly proper Step pattern alph. order: ABCDAEDCDEDA Step pattern size order : DCAEDBEAEBED Scale is a Constant Structure, by a margin of 14.19052 cents Scale diversity : 1.506364 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.366564 Rothenberg efficiency : 0.286869 redundancy: 0.713131 Efficiency x scale size : 3.442424 Number of different interval sizes : 60 = 5.45455 / class Number of one step interval sizes : 5 Highest interval variety : 7 Mean interval variety : 5.45455 = 60/11 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 : 8, average 700.9911 cents Best fifths 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 : 5 = 41.6667% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 7 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.024538 Average absolute harmonicity : 0.189077 Specific harmonicity : 0.148800 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 5040, 12.2992 octaves, 1318592.849 Hz. Exponens Consonantiae : 1.814400E+06, 20.79106 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 81.0, average 6.75000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.14814, average 0.76235 Sum of Tenney's harmonic distance : 17.66705, average 1.47225 Vogel's harmonic complexity : 15.91667 Wille's k value : 337 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 240.26561, average 3.08033 Lattice compactness (without 2's) : 136.31636, average 1.74765 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 -0.33333 20 1 3: -2 .. 2 -0.16667 10 3 5: -1 .. 1 0.08333 5 4 7: 0 .. 1 0.33333 4 4 Average exponent except 2's : 3 / 12 = 0.25000 Average absolute exponent except 2's: 19 / 12 = 1.58333 Scale is JI-epimorphic with val: <12 19 28 34| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.0093 c. M:-35.0841 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 1 2 2 1 2 1 2 1 2 2 P D3 SD: 11.9141 c. M: 21.4575 c. 22: 2 2 1 2 2 2 2 1 2 2 2 2 P D3 S SD: 9.0624 c. M:-17.4878 c. 31: 3 2 2 3 3 2 3 2 3 2 3 3 SP D3 SD: 5.3497 c. M: 10.3616 c. 41: 4 3 2 4 4 3 4 2 4 3 4 4 P SD: 3.8371 c. M: 6.3099 c. 53: 5 4 3 5 5 4 5 3 5 4 5 5 SP SD: 3.1106 c. M:-6.1671 c. 72: 7 5 4 7 7 5 7 4 7 5 7 7 SP SD: 2.7390 c. M: 4.9354 c. 77: 7 6 4 8 7 5 8 4 8 5 8 7 SP SD: 2.7356 c. M: 5.8888 c. 87: 8 7 4 9 8 6 9 4 9 6 9 8 P SD: 2.9394 c. M: 6.2952 c. 94: 9 7 5 9 9 7 9 5 9 7 9 9 SP SD: 2.4218 c. M:-4.7218 c. 99: 9 8 5 10 9 7 10 5 10 7 10 9 SP SD: 1.4858 c. M:-2.6404 c. 118: 11 9 6 12 11 8 12 6 12 8 12 11 SP SD: 1.5024 c. M: 2.8512 c. 130: 12 10 7 13 12 9 13 7 13 9 13 12 SP SD: 0.9719 c. M:-1.7951 c. 171: 16 13 9 17 16 12 17 9 17 12 17 16 SP SD: 0.3159 c. M:-0.5494 c. 441: 41 34 23 44 41 31 44 23 44 31 44 41 SP SD: 0.1543 c. M: 0.2901 c. 612: 57 47 32 61 57 43 61 32 61 43 61 57 SP SD: 0.1142 c. M: 0.2100 c. 935: 87 72 49 93 87 66 93 49 93 66 93 87 SP SD: 0.0960 c. M:-0.1616 c. 1106: 103 85 58 110 103 78 110 58 110 78 110 103 SP SD: 0.0594 c. M:-0.1280 c. 1277: 119 98 67 127 119 90 127 67 127 90 127 119 SP SD: 0.0627 c. M:-0.1033 c. 1407: 131 108 74 140 131 99 140 74 140 99 140 131 SP SD: 0.0556 c. M:-0.1161 c. 1547: 144 119 81 154 144 109 154 81 154 109 154 144 SP SD: 0.0500 c. M:-0.0978 c. 1718: 160 132 90 171 160 121 171 90 171 121 171 160 SP SD: 0.0429 c. M: 0.0747 c. 1848: 172 142 97 184 172 130 184 97 184 130 184 172 SP SD: 0.0319 c. M:-0.0569 c. 2019: 188 155 106 201 188 142 201 106 201 142 201 188 SP SD: 0.0266 c. M: 0.0467 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 16.8946 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.4843 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 11.2511 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 6.7248 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.4694 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 11.0777 cents 11:12 x 13:14:15 x x 17:18:19:21:22 SD: 9.3762 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.3990 cents 13:14 x 15:16:17:18 x 20:22:23:24:26 S SD: 7.0711 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 8.0138 cents 15:16:17:18:19:20:21 x 23:25:26:28:30 SD: 5.7654 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 4.7311 cents 17:18:19:20:21:23:24 x 26:28:30:32:34 SD: 5.2279 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.8131 cents 20:21 x 23:25:27:28:30:31:33:35:38:40 SD: 4.7179 cents 23:25:26:27:29:31:32:35:36:38:40:43:46 SD: 4.5990 cents 24:26:27:28:30:32:34:36:37:40:42:45:48 SD: 3.0972 cents 30:32:34:35:38:40:42:45:47:50:53:56:60 SD: 2.8500 cents 32:34:36:37:40:43:45:48:50:53:56:60:64 SD: 2.2131 cents 40:43:45:47:50:53:56:60:62:67:70:75:80 SD: 1.9792 cents 47:50:53:55:59:63:66:71:73:78:82:88:94 SD: 1.8191 cents 48:51:54:56:60:64:67:72:75:80:84:90:96 SD: 0.9575 cents 72:77:81:84:90:96:101:108:112:120:126:135:144 SD: 0.4718 cents 120:128:135:140:150:160:168:180:187:200:210:225:240 SD: 0.2574 cents 192:205:216:224:240:256:269:288:299:320:336:360:384 SD: 0.2393 cents 240:256:270:280:300:320:336:360:373:400:420:450:480 SD: 0.1289 cents 288:307:324:336:360:384:403:432:448:480:504:540:576 SD: 0.1181 cents 360:384:405:420:450:480:504:540:560:600:630:675:720 SD: 0.0000 cents