Scala analysis: gamelan_om
Other Music gamelan (7 limit black keys)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major 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: 15/14 119.4428 major diatonic semitone 2: 21/20 84.4672 minor semitone 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: 3 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 5 15/14 119.443 cents major diatonic semitone 2: 1 49/45 147.428 cents BP minor semitone 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: 3 8/7 231.174 cents septimal whole tone 3: 4 7/6 266.871 cents septimal minor third 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 60/49 350.617 cents smaller approximation to neutral third 4: 4 56/45 378.602 cents septimal narrow major third 4: 4 5/4 386.314 cents major third 4: 4 9/7 435.084 cents septimal major third, BP third 5: 1 98/75 463.069 cents 5: 1 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: 1 135/98 554.527 cents 6: 1 112/81 561.006 cents 6: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 45/32 590.224 cents diatonic tritone 6: 1 64/45 609.776 cents 2nd tritone 6: 4 10/7 617.488 cents Euler's tritone 6: 1 81/56 638.994 cents 7: 1 196/135 645.473 cents 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: 1 32/21 729.219 cents wide fifth 7: 1 75/49 736.931 cents BP fifth 8: 4 14/9 764.916 cents septimal minor sixth 8: 4 8/5 813.686 cents minor sixth 8: 4 45/28 821.398 cents septimale wide minor sixth 9: 1 49/30 849.383 cents larger approximation to 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: 4 12/7 933.129 cents septimal major sixth 10: 3 7/4 968.826 cents harmonic seventh 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 90/49 1052.572 cents 11: 5 28/15 1080.557 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 3 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: 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 : 119.4 203.9 266.9 386.3 498.0 582.5 702.0 764.9 884.4 968.8 1088.3 1200.0 119.4 : 84.5 147.4 266.9 378.6 463.1 582.5 645.5 764.9 849.4 968.8 1080.6 1200.0 203.9 : 63.0 182.4 294.1 378.6 498.0 561.0 680.4 764.9 884.4 996.1 1115.5 1200.0 266.9 : 119.4 231.2 315.6 435.1 498.0 617.5 702.0 821.4 933.1 1052.6 1137.0 1200.0 386.3 : 111.7 196.2 315.6 378.6 498.0 582.5 702.0 813.7 933.1 1017.6 1080.6 1200.0 498.0 : 84.5 203.9 266.9 386.3 470.8 590.2 702.0 821.4 905.9 968.8 1088.3 1200.0 582.5 : 119.4 182.4 301.8 386.3 505.8 617.5 736.9 821.4 884.4 1003.8 1115.5 1200.0 702.0 : 63.0 182.4 266.9 386.3 498.0 617.5 702.0 764.9 884.4 996.1 1080.6 1200.0 764.9 : 119.4 203.9 323.4 435.1 554.5 639.0 702.0 821.4 933.1 1017.6 1137.0 1200.0 884.4 : 84.5 203.9 315.6 435.1 519.6 582.5 702.0 813.7 898.2 1017.6 1080.6 1200.0 968.8 : 119.4 231.2 350.6 435.1 498.0 617.5 729.2 813.7 933.1 996.1 1115.5 1200.0 1088.3: 111.7 231.2 315.6 378.6 498.0 609.8 694.2 813.7 876.6 996.1 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: 147.4281 .. 231.1741 cents 360/343, 83.7460 cents 686/675, 27.9853 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: 463.0694 .. 554.5269 cents 10125/9604, 91.4575 cents 686/675, 27.9853 cents 6: 561.0059 .. 638.9941 cents 6561/6272, 77.9882 cents 10976/10935, 6.4790 cents 7: 645.4731 .. 736.9306 cents 10125/9604, 91.4575 cents 10976/10935, 6.4790 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 686/675, 27.9853 cents 9: 849.3831 .. 933.1291 cents 360/343, 83.7460 cents 686/675, 27.9853 cents 10: 968.8259 .. 1052.5719 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1137.0391 cents 405/392, 56.4819 cents 686/675, 27.9853 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: 2 Most common interval of one step : 15/14, 119.4428 cents, amount: 5 Least squares average step : 98.32290 cents, oct.: 1179.87478 cents Scale is strictly proper Step pattern alph. order: ABCADBACABAD Step pattern size order : DBADCBDADBDC Scale is a Constant Structure, by a margin of 6.47900 cents Scale diversity : 1.477105 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.315154 Rothenberg efficiency : 0.295918 redundancy: 0.704082 Efficiency x scale size : 3.551010 Number of different interval sizes : 54 = 4.90909 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.90909 = 54/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 10976/10935, 6.4790 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 11 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval class 1 Scale is 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 : 135 (O: 135 U: 135) Highest odd numerator or denominator: 15 Scale harmonicity : 0.020392 Average absolute harmonicity : 0.186794 Specific harmonicity : 0.140960 Fundamental : 1/2520, -11.2992 octaves, 0.1038 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 3.175200E+06, 21.59842 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 80.0, average 6.66667 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 : 17.60906, average 1.46742 Vogel's harmonic complexity : 23.25000 Wille's k value : 2362 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 211.78589, average 2.71520 Lattice compactness (without 2's) : 139.63384, average 1.79018 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.75000 17 1 3: -2 .. 2 0.00000 10 3 5: -1 .. 1 0.25000 5 3 7: -1 .. 1 0.25000 5 5 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 20 / 12 = 1.66667 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: 19.5291 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: 11.3206 c. M: 21.4575 c. 22: 2 2 1 2 2 2 2 1 2 2 2 2 P D3 S SD: 9.5119 c. M:-17.4878 c. 31: 3 2 2 3 3 2 3 2 3 2 3 3 SP D3 SD: 5.2841 c. M: 10.3616 c. 41: 4 3 2 4 4 3 4 2 4 3 4 4 P SD: 3.5796 c. M: 6.3099 c. 53: 5 4 3 5 5 4 5 3 5 4 5 5 SP SD: 3.5685 c. M: 6.2353 c. 72: 7 5 4 7 7 5 7 4 7 5 7 7 SP SD: 2.4728 c. M: 4.9354 c. 94: 9 7 5 9 9 7 9 5 9 7 9 9 SP SD: 2.5993 c. M:-4.7218 c. 99: 10 7 5 10 9 7 10 5 10 7 10 9 P SD: 1.3738 c. M:-2.6404 c. 130: 13 9 7 13 12 9 13 7 13 9 13 12 SP SD: 0.9451 c. M:-1.7951 c. 171: 17 12 9 17 16 12 17 9 17 12 17 16 SP SD: 0.2764 c. M: 0.5494 c. 441: 44 31 23 44 41 31 44 23 44 31 44 41 SP SD: 0.1682 c. M: 0.2901 c. 612: 61 43 32 61 57 43 61 32 61 43 61 57 SP SD: 0.1234 c. M: 0.2100 c. 783: 78 55 41 78 73 55 78 41 78 55 78 73 SP SD: 0.1301 c. M: 0.2435 c. 935: 93 66 49 93 87 66 93 49 93 66 93 87 SP SD: 0.0968 c. M:-0.1616 c. 1106: 110 78 58 110 103 78 110 58 110 78 110 103 SP SD: 0.0650 c. M:-0.1280 c. 1236: 123 87 65 123 115 87 123 65 123 87 123 115 SP SD: 0.0774 c. M:-0.1326 c. 1277: 127 90 67 127 119 90 127 67 127 90 127 119 SP SD: 0.0636 c. M:-0.1033 c. 1407: 140 99 74 140 131 99 140 74 140 99 140 131 SP SD: 0.0568 c. M:-0.1161 c. 1547: 154 109 81 154 144 109 154 81 154 109 154 144 SP SD: 0.0494 c. M:-0.0978 c. 1677: 167 118 88 167 156 118 167 88 167 118 167 156 SP SD: 0.0539 c. M:-0.1034 c. 1718: 171 121 90 171 160 121 171 90 171 121 171 160 SP SD: 0.0422 c. M: 0.0747 c. 1848: 184 130 97 184 172 130 184 97 184 130 184 172 SP SD: 0.0314 c. M:-0.0569 c. 2019: 201 142 106 201 188 142 201 106 201 142 201 188 SP SD: 0.0273 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: 9.0133 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.1205 cents 13:14 x 15:16:17:18 x 20:22:23:24:26 S SD: 6.9310 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 7.9831 cents 15:16:17:18:19:20:21 x 23:25:26:28:30 SD: 5.8079 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 4.8500 cents 17:18:19:20:21:23:24 x 26:28:30:32:34 SD: 5.4269 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 5.0518 cents 20:21 x 23:25:27:28:30:31:33:35:38:40 SD: 5.1211 cents 23:25:26:27:29:31:32:35:36:38:40:43:46 SD: 4.2508 cents 24:26:27:28:30:32:34:36:37:40:42:45:48 SD: 2.6703 cents 32:34:36:37:40:43:45:48:50:53:56:60:64 SD: 2.4569 cents 40:43:45:47:50:53:56:60:62:67:70:75:80 SD: 1.6992 cents 48:51:54:56:60:64:67:72:75:80:84:90:96 SD: 1.4337 cents 56:60:63:65:70:75:78:84:87:93:98:105:112 SD: 1.3426 cents 72:77:81:84:90:96:101:108:112:120:126:135:144 SD: 0.3915 cents 168:180:189:196:210:224:235:252:261:280:294:315:336 SD: 0.2213 cents 240:257:270:280:300:320:336:360:373:400:420:450:480 SD: 0.1518 cents 360:386:405:420:450:480:504:540:560:600:630:675:720 SD: 0.1068 cents 408:437:459:476:510:544:571:612:635:680:714:765:816 SD: 0.1025 cents 432:463:486:504:540:576:605:648:672:720:756:810:864 SD: 0.0652 cents 600:643:675:700:750:800:840:900:933:1000:1050:1125:1200 SD: 0.0607 cents