Scala analysis: just7_12
7-limit 12 tone scale
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: 8/5 813.686286 minor sixth 9: 12/7 933.129094 septimal major 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: 16/15 111.7313 minor diatonic semitone 9: 15/14 119.4428 major diatonic semitone 10: 49/48 35.6968 slendro diesis, septimal 1/6-tone 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: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 21/20 84.467 cents minor semitone 1: 1 135/128 92.179 cents major chroma, major limma 1: 4 16/15 111.731 cents minor diatonic semitone 1: 4 15/14 119.443 cents major diatonic semitone 2: 3 35/32 155.140 cents septimal neutral second 2: 1 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 2 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 4 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 2 75/64 274.582 cents classic augmented second 3: 1 32/27 294.135 cents Pythagorean minor third 3: 4 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 3: 1 60/49 350.617 cents smaller approximation to 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: 3 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 1 49/36 533.742 cents Arabic lute acute fourth 6: 2 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: 2 10/7 617.488 cents Euler's tritone 6: 1 72/49 666.258 cents Arabic lute grave fifth 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 1 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 3 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 49/30 849.383 cents larger approximation to neutral sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 2 128/75 925.418 cents diminished seventh 9: 3 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 1 225/128 976.537 cents augmented sixth 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 3 64/35 1044.860 cents septimal neutral seventh 11: 4 28/15 1080.557 cents grave major seventh 11: 4 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: 1 27/14 1137.039 cents septimal major seventh 11: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.27273 = 58/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 203.9 266.9 386.3 498.0 582.5 702.0 813.7 933.1 968.8 1088.3 1200.0 111.7 : 92.2 155.1 274.6 386.3 470.8 590.2 702.0 821.4 857.1 976.5 1088.3 1200.0 203.9 : 63.0 182.4 294.1 378.6 498.0 609.8 729.2 764.9 884.4 996.1 1107.8 1200.0 266.9 : 119.4 231.2 315.6 435.1 546.8 666.3 702.0 821.4 933.1 1044.9 1137.0 1200.0 386.3 : 111.7 196.2 315.6 427.4 546.8 582.5 702.0 813.7 925.4 1017.6 1080.6 1200.0 498.0 : 84.5 203.9 315.6 435.1 470.8 590.2 702.0 813.7 905.9 968.8 1088.3 1200.0 582.5 : 119.4 231.2 350.6 386.3 505.8 617.5 729.2 821.4 884.4 1003.8 1115.5 1200.0 702.0 : 111.7 231.2 266.9 386.3 498.0 609.8 702.0 764.9 884.4 996.1 1080.6 1200.0 813.7 : 119.4 155.1 274.6 386.3 498.0 590.2 653.2 772.6 884.4 968.8 1088.3 1200.0 933.1 : 35.7 155.1 266.9 378.6 470.8 533.7 653.2 764.9 849.4 968.8 1080.6 1200.0 968.8 : 119.4 231.2 342.9 435.1 498.0 617.5 729.2 813.7 933.1 1044.9 1164.3 1200.0 1088.3: 111.7 223.5 315.6 378.6 498.0 609.8 694.2 813.7 925.4 1044.9 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 119.4428 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 3: 266.8709 .. 350.6169 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 686/675, 27.9853 cents 5: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 6: 533.7418 .. 666.2582 cents 2592/2401, 132.5164 cents 1715/1728,-13.0736 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 1715/1728,-13.0736 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 9: 849.3831 .. 933.1291 cents 360/343, 83.7460 cents 686/675, 27.9853 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1164.3032 cents 360/343, 83.7460 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 2.801371 Largest / Average step : 1.194428 Largest / Smallest step : 3.346036 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 99.58657 cents, oct.: 1195.03881 cents Scale is not proper Step pattern alph. order: ABCDAEDADFDA Step pattern size order : EDBFECFEFAFE Scale is a Constant Structure, by a margin of 13.07357 cents Scale diversity : 1.536573 Lumma stability : 0.284621 Lumma impropriety factor : 0.021789 Rothenberg efficiency : 0.275896 redundancy: 0.724104 Efficiency x scale size : 3.310750 Number of different interval sizes : 58 = 5.27273 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.27273 = 58/11 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: 6 Number of recognisable fifths : 7, average 700.8534 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 15 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 7 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 classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.020673 Average absolute harmonicity : 0.189310 Specific harmonicity : 0.142881 Fundamental : 1/840, -9.7142 octaves, 0.3115 Hz. Guide tone : 5040, 12.2992 octaves, 1318592.849 Hz. Exponens Consonantiae : 4.233600E+06, 22.01345 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 81.5, average 6.79167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.03900, average 0.75325 Sum of Tenney's harmonic distance : 17.91693, average 1.49308 Vogel's harmonic complexity : 19.25000 Wille's k value : 787 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 257.26299, average 3.29824 Lattice compactness (without 2's) : 127.62314, average 1.63619 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.00000 24 1 3: -1 .. 2 0.16667 8 3 5: -1 .. 1 -0.08333 5 4 7: -1 .. 1 0.16667 4 4 Average exponent except 2's : 3 / 12 = 0.25000 Average absolute exponent except 2's: 17 / 12 = 1.41667 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: 18.5866 c. M: 33.1291 c. Twelve-tone Chromatic (1/11-comma) 18: 2 1 1 2 2 1 2 1 2 1 1 2 P D3 SD: 20.0641 c. M:-35.2883 c. 19: 2 1 1 2 2 1 2 2 2 0 2 2 N SD: 12.6196 c. M: 21.4575 c. 22: 2 2 1 2 2 2 2 2 2 1 2 2 P D3 I SD: 8.6752 c. M:-17.4878 c. 31: 3 2 2 3 3 2 3 3 3 1 3 3 P SD: 4.4645 c. M: 10.3616 c. 41: 4 3 2 4 4 3 4 4 4 1 4 4 N SD: 3.7331 c. M: 5.8259 c. 53: 5 4 3 5 5 4 5 5 5 2 5 5 P SD: 3.1042 c. M:-6.1671 c. 72: 7 5 4 7 7 5 7 7 7 2 7 7 N SD: 2.8112 c. M: 4.9354 c. 77: 7 6 4 8 7 5 8 7 8 2 8 7 N SD: 2.6950 c. M: 5.8888 c. 84: 8 6 5 8 8 6 8 8 8 3 8 8 P SD: 2.8177 c. M: 4.5577 c. 87: 8 7 4 9 8 6 9 8 9 2 9 8 N SD: 2.6546 c. M: 4.8019 c. 94: 9 7 5 9 9 7 9 9 9 3 9 9 N SD: 2.4082 c. M:-4.7218 c. 99: 9 8 5 10 9 7 10 9 10 3 10 9 N SD: 1.5029 c. M:-2.6404 c. 118: 11 9 6 12 11 8 12 11 12 3 12 11 N SD: 1.5321 c. M: 2.8512 c. 130: 12 10 7 13 12 9 13 12 13 4 13 12 N SD: 0.8734 c. M:-1.3786 c. 140: 13 11 7 14 13 10 14 13 14 4 14 13 N SD: 0.8487 c. M:-1.8043 c. 171: 16 13 9 17 16 12 17 16 17 5 17 16 N SD: 0.3340 c. M:-0.5494 c. 301: 28 23 16 30 28 21 30 28 30 9 30 28 N SD: 0.3132 c. M: 0.5877 c. 441: 41 34 23 44 41 31 44 41 44 13 44 41 N SD: 0.1443 c. M: 0.2042 c. 612: 57 47 32 61 57 43 61 57 61 18 61 57 N SD: 0.1132 c. M: 0.2042 c. 913: 85 70 48 91 85 64 91 85 91 27 91 85 N SD: 0.1187 c. M: 0.2559 c. 935: 87 72 49 93 87 66 93 87 93 28 93 87 N SD: 0.0960 c. M:-0.1616 c. 1106: 103 85 58 110 103 78 110 103 110 33 110 103 N SD: 0.0568 c. M:-0.1280 c. 1236: 115 95 65 123 115 87 123 115 123 37 123 115 N SD: 0.0773 c. M:-0.1194 c. 1277: 119 98 67 127 119 90 127 119 127 38 127 119 N SD: 0.0624 c. M:-0.1033 c. 1407: 131 108 74 140 131 99 140 131 140 42 140 131 N SD: 0.0464 c. M: 0.0801 c. 1547: 144 119 81 154 144 109 154 144 154 46 154 144 N SD: 0.0413 c. M:-0.0978 c. 1718: 160 132 90 171 160 121 171 160 171 51 171 160 N SD: 0.0366 c. M: 0.0506 c. 1848: 172 142 97 184 172 130 184 172 184 55 184 172 N SD: 0.0307 c. M: 0.0499 c. 2019: 188 155 106 201 188 142 201 188 201 60 201 188 N SD: 0.0240 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: 16.2568 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: 13.7943 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.3979 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.6835 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.1441 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 11.4219 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.4486 cents 11:12 x 13:14:15 x 17:18:19 x 21:22 SD: 11.0151 cents 12:13 x 14:15:16:17:18:19 x 21:23:24 SD: 5.4007 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 7.4023 cents 14:15:16 x 18:19:20:21:22:24:25:26:28 S SD: 8.0363 cents 15:16:17:18:19:20:21:23:24 x 26:28:30 SD: 6.3307 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.3781 cents 17:18:19:20:21:23:24:26:27:29:30:32:34 SD: 4.8534 cents 19:20:21:22:24:25:27:29:30 x 33:36:38 SD: 6.4854 cents 20:21 x 23:25:27:28:30:32:34:35:38:40 SD: 4.6015 cents 24:26:27:28:30:32:34:36:38:41:42:45:48 SD: 3.2330 cents 30:32:34:35:38:40:42:45:48:51:53:56:60 SD: 2.9199 cents 32:34:36:37:40:43:45:48:51:55:56:60:64 SD: 2.0313 cents 40:43:45:47:50:53:56:60:64:69:70:75:80 SD: 1.9852 cents 47:50:53:55:59:63:66:71:75:81:82:88:94 SD: 1.9015 cents 48:51:54:56:60:64:67:72:77:82:84:90:96 SD: 0.9468 cents 72:77:81:84:90:96:101:108:115:123:126:135:144 SD: 0.7329 cents 120:128:135:140:150:160:168:180:192:206:210:225:240 SD: 0.2002 cents 240:256:270:280:300:320:336:360:384:411:420:450:480 SD: 0.1504 cents 312:333:351:364:390:416:437:468:499:535:546:585:624 SD: 0.1292 cents 360:384:405:420:450:480:504:540:576:617:630:675:720 SD: 0.0334 cents 480:512:540:560:600:640:672:720:768:823:840:900:960 SD: 0.0250 cents