Scala analysis: ji_12
Basic JI with 7-limit tritone
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: 6/5 315.641287 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: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 9/5 1017.596288 just minor seventh, BP 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: 16/15 111.7313 minor diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 21/20 84.467 cents minor semitone 1: 1 135/128 92.179 cents major chroma, major limma 1: 5 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 4 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 5 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 8/7 231.174 cents septimal whole tone 3: 1 7/6 266.871 cents septimal minor third 3: 2 75/64 274.582 cents classic augmented second 3: 2 32/27 294.135 cents Pythagorean minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 6 6/5 315.641 cents minor third 4: 1 56/45 378.602 cents septimal narrow major third 4: 7 5/4 386.314 cents major third 4: 3 32/25 427.373 cents classic diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 5: 1 21/16 470.781 cents narrow fourth 5: 8 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 2 27/20 519.551 cents acute fourth 6: 2 25/18 568.717 cents classic augmented fourth 6: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 3 45/32 590.224 cents diatonic tritone 6: 3 64/45 609.776 cents 2nd tritone 6: 1 10/7 617.488 cents Euler's tritone 6: 2 36/25 631.283 cents classic diminished fifth 7: 2 40/27 680.449 cents grave fifth 7: 1 112/75 694.243 cents marvelous fifth 7: 8 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 8: 1 14/9 764.916 cents septimal minor sixth 8: 3 25/16 772.627 cents classic augmented fifth 8: 7 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 9: 6 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 2 128/75 925.418 cents diminished seventh 9: 1 12/7 933.129 cents septimal major sixth 10: 1 7/4 968.826 cents harmonic seventh 10: 1 225/128 976.537 cents augmented sixth 10: 5 16/9 996.090 cents Pythagorean minor seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 4 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 50/27 1066.762 cents grave major seventh 11: 1 28/15 1080.557 cents grave major seventh 11: 5 15/8 1088.269 cents classic major seventh 11: 1 256/135 1107.821 cents octave - major chroma 11: 1 40/21 1115.533 cents acute major seventh 11: 3 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.90909 = 54/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 203.9 315.6 386.3 498.0 582.5 702.0 813.7 884.4 1017.6 1088.3 1200.0 111.7 : 92.2 203.9 274.6 386.3 470.8 590.2 702.0 772.6 905.9 976.5 1088.3 1200.0 203.9 : 111.7 182.4 294.1 378.6 498.0 609.8 680.4 813.7 884.4 996.1 1107.8 1200.0 315.6 : 70.7 182.4 266.9 386.3 498.0 568.7 702.0 772.6 884.4 996.1 1088.3 1200.0 386.3 : 111.7 196.2 315.6 427.4 498.0 631.3 702.0 813.7 925.4 1017.6 1129.3 1200.0 498.0 : 84.5 203.9 315.6 386.3 519.6 590.2 702.0 813.7 905.9 1017.6 1088.3 1200.0 582.5 : 119.4 231.2 301.8 435.1 505.8 617.5 729.2 821.4 933.1 1003.8 1115.5 1200.0 702.0 : 111.7 182.4 315.6 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1080.6 1200.0 813.7 : 70.7 203.9 274.6 386.3 498.0 590.2 702.0 772.6 884.4 968.8 1088.3 1200.0 884.4 : 133.2 203.9 315.6 427.4 519.6 631.3 702.0 813.7 898.2 1017.6 1129.3 1200.0 1017.6: 70.7 182.4 294.1 386.3 498.0 568.7 680.4 764.9 884.4 996.1 1066.8 1200.0 1088.3: 111.7 223.5 315.6 427.4 498.0 609.8 694.2 813.7 925.4 996.1 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 133.2376 cents 648/625, 62.5651 cents 25/24, 70.6724 cents 2: 182.4037 .. 231.1741 cents 36/35, 48.7704 cents 250/243, 49.1661 cents 3: 266.8709 .. 315.6413 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 28/27, 62.9609 cents 5: 470.7809 .. 519.5513 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 7: 680.4487 .. 729.2191 cents 36/35, 48.7704 cents 250/243, 49.1661 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 9: 884.3587 .. 933.1291 cents 36/35, 48.7704 cents 28/27, 62.9609 cents 10: 968.8259 .. 1017.5963 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 11: 1066.7624 .. 1129.3276 cents 648/625, 62.5651 cents 250/243, 49.1661 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 27/25, 133.2376 cents Average / Smallest step : 1.414979 Largest / Average step : 1.332376 Largest / Smallest step : 1.885284 Median interval of one step : 16/15, 111.7313 cents, amount: 5 Most common interval of one step : 16/15, 111.7313 cents, amount: 5 Least squares average step : 99.88669 cents, oct.: 1198.64032 cents Scale is strictly proper Step pattern alph. order: ABACADEACFCA Step pattern size order : DCDADBEDAFAD Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.406595 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.505599 Rothenberg efficiency : 0.333664 redundancy: 0.666336 Efficiency x scale size : 4.003968 Number of different interval sizes : 54 = 4.90909 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.90909 = 54/11 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: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 5 Number of recognisable fifths : 9, average 701.0982 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 5 15 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 75.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 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 classes 4 and 5 combined Scale is differentially coherent in interval classes 8 and 9 combined Limited inverse transpositions with margin 48.7704 cents: 7 -- Rational properties -- Prime limit : 7 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.026257 Average absolute harmonicity : 0.195553 Specific harmonicity : 0.167532 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 5040, 12.2992 octaves, 1318592.849 Hz. Exponens Consonantiae : 6.048000E+05, 19.20610 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 76.5, average 6.37500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.85589, average 0.73799 Sum of Tenney's harmonic distance : 17.22867, average 1.43572 Vogel's harmonic complexity : 11.91667 Wille's k value : 112 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 249.74880, average 3.20191 Lattice compactness (without 2's) : 136.80131, average 1.75386 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.16667 20 1 3: -1 .. 2 0.33333 10 3 5: -1 .. 1 -0.16667 8 7 7: 0 .. 1 0.08333 1 1 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 Scale is weakly epimorphic with val: <12 21 25 32| Scale is weakly epimorphic with val: <12 21 26 34| Scale is weakly epimorphic with val: <12 21 31 32|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.1709 c. M: 17.5963 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 9.5531 c. M: 14.5845 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 5.7719 c. M: 11.1447 c. Genus diatonico-chromaticum 41: 4 3 4 2 4 3 4 4 2 5 2 4 SP SD: 4.6574 c. M:-6.7940 c. 53: 5 4 5 3 5 4 5 5 3 6 3 5 SP SD: 2.0735 c. M:-6.1671 c. Genus diatonico-chromaticum 72: 7 5 7 4 7 5 7 7 4 8 4 7 SP SD: 2.7847 c. M: 4.9354 c. Genus diatonico-chromaticum 84: 8 6 8 5 8 6 8 8 5 9 5 8 SP SD: 2.2655 c. M: 3.9100 c. 87: 8 7 8 5 8 6 9 8 5 10 5 8 SP SD: 1.8750 c. M: 3.2018 c. 99: 9 8 9 6 9 7 10 9 6 11 6 9 SP SD: 1.5023 c. M:-2.6404 c. 118: 11 9 11 7 11 8 12 11 7 13 7 11 SP SD: 0.8813 c. M: 2.8512 c. 130: 12 10 12 8 12 9 13 12 8 14 8 12 SP SD: 1.2576 c. M: 2.2117 c. 140: 13 11 13 8 13 10 14 13 8 16 8 13 SP SD: 1.1616 c. M:-2.4037 c. 152: 14 12 14 9 14 11 15 14 9 17 9 14 SP SD: 0.9045 c. M:-1.6983 c. 159: 15 12 15 9 15 11 16 15 9 18 9 15 SP SD: 1.1352 c. M:-1.4763 c. 171: 16 13 16 10 16 12 17 16 10 19 10 16 SP SD: 0.3080 c. M:-0.5494 c. 323: 30 25 30 19 30 23 32 30 19 36 19 30 SP SD: 0.3158 c. M:-0.7695 c. 441: 41 34 41 26 41 31 44 41 26 49 26 41 SP SD: 0.1158 c. M: 0.1993 c. 612: 57 47 57 36 57 43 61 57 36 68 36 57 SP SD: 0.0559 c. M: 0.1593 c. 783: 73 60 73 46 73 55 78 73 46 87 46 73 SP SD: 0.0928 c. M:-0.1461 c. 1053: 98 81 98 62 98 74 105 98 62 117 62 98 SP SD: 0.0657 c. M: 0.1760 c. 1106: 103 85 103 65 103 78 110 103 65 123 65 103 SP SD: 0.0726 c. M:-0.1280 c. 1236: 115 95 115 73 115 87 123 115 73 137 73 115 SP SD: 0.0761 c. M: 0.1206 c. 1277: 119 98 119 75 119 90 127 119 75 142 75 119 SP SD: 0.0798 c. M:-0.1033 c. 1395: 130 107 130 82 130 98 139 130 82 155 82 130 SP SD: 0.0722 c. M: 0.1466 c. 1407: 131 108 131 83 131 99 140 131 83 156 83 131 SP SD: 0.0542 c. M: 0.1123 c. 1718: 160 132 160 101 160 121 171 160 101 191 101 160 SP SD: 0.0513 c. M:-0.0987 c. 1848: 172 142 172 109 172 130 184 172 109 205 109 172 SP SD: 0.0423 c. M: 0.0638 c. 1901: 177 146 177 112 177 134 189 177 112 211 112 177 SP SD: 0.0393 c. M:-0.1285 c. 2019: 188 155 188 119 188 142 201 188 119 224 119 188 SP SD: 0.0330 c. M: 0.0629 c. 2342: 218 180 218 138 218 165 233 218 138 260 138 218 SP SD: 0.0265 c. M:-0.0668 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: 12.1926 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 0.0000 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.7006 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.7546 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.9766 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.5603 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1666 cents 11:12 x 13:14:15 x 17 x 18:20:21:22 SD: 10.9178 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 7.2182 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 8.5850 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.3700 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 3.9055 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.4125 cents 30:32:34:36:38:40:42:45:48:50:54:56:60 SD: 2.2799 cents 40:43:45:48:50:53:56:60:64:67:72:75:80 SD: 1.6113 cents 48:51:54:58:60:64:67:72:77:80:86:90:96 SD: 1.4455 cents 60:64:68:72:75:80:84:90:96:100:108:113:120 SD: 1.2422 cents 72:77:81:86:90:96:101:108:115:120:130:135:144 SD: 0.9650 cents 80:85:90:96:100:107:112:120:128:133:144:150:160 SD: 0.8074 cents 90:96:101:108:113:120:126:135:144:150:162:169:180 SD: 0.7630 cents 104:111:117:125:130:139:146:156:166:173:187:195:208 SD: 0.7477 cents 105:112:118:126:131:140:147:158:168:175:189:197:210 SD: 0.5626 cents 120:128:135:144:150:160:168:180:192:200:216:225:240 SD: 0.0000 cents