Scala analysis: sevish
Sevish JI scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 11/8 551.317942 undecimal semi-augmented fourth 7: 3/2 701.955001 perfect fifth 8: 77/48 818.188848 9: 5/3 884.358713 major sixth, BP sixth 10: 27/16 905.865003 Pythagorean major sixth 11: 7/4 968.825906 harmonic seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 15/14 119.4428 major diatonic semitone 5: 21/20 84.4672 minor semitone 6: 22/21 80.5370 undecimal minor semitone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone 8: 77/72 116.2338 undecimal secor 9: 80/77 66.1699 10: 81/80 21.5063 syntonic comma, Didymus comma 11: 28/27 62.9609 Archytas' 1/3-tone 12: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 80/77 66.170 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 21/20 84.467 cents minor semitone 1: 1 77/72 116.234 cents undecimal secor 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 21/20 84.467 cents minor semitone 2: 1 81/77 87.676 cents 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 1 112/99 213.598 cents 2: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 3: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 1 9/8 203.910 cents major whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 1 33/28 284.447 cents undecimal minor third 3: 2 6/5 315.641 cents minor third 3: 2 40/33 333.041 cents 3: 2 11/9 347.408 cents undecimal neutral third 3: 1 9/7 435.084 cents septimal major third, BP third 4: 1 7/6 266.871 cents septimal minor third 4: 1 11/9 347.408 cents undecimal neutral third 4: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 1 99/80 368.914 cents 4: 1 96/77 381.811 cents 4: 1 5/4 386.314 cents major third 4: 1 80/63 413.578 cents wide major third 4: 1 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 77/60 431.875 cents 4: 1 9/7 435.084 cents septimal major third, BP third 4: 2 4/3 498.045 cents perfect fourth 5: 1 14/11 417.508 cents undecimal diminished fourth or major third 5: 2 9/7 435.084 cents septimal major third, BP third 5: 1 21/16 470.781 cents narrow fourth 5: 4 4/3 498.045 cents perfect fourth 5: 1 27/20 519.551 cents acute fourth 5: 1 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 112/81 561.006 cents 5: 1 10/7 617.488 cents Euler's tritone 6: 1 4/3 498.045 cents perfect fourth 6: 1 27/20 519.551 cents acute fourth 6: 2 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 108/77 585.721 cents 6: 1 77/54 614.279 cents 6: 1 10/7 617.488 cents Euler's tritone 6: 2 16/11 648.682 cents undecimal semi-diminished fifth 6: 1 40/27 680.449 cents grave fifth 6: 1 3/2 701.955 cents perfect fifth 7: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 1 81/56 638.994 cents 7: 1 16/11 648.682 cents undecimal semi-diminished fifth 7: 1 40/27 680.449 cents grave fifth 7: 4 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 7: 2 14/9 764.916 cents septimal minor sixth 7: 1 11/7 782.492 cents undecimal augmented fifth 8: 2 3/2 701.955 cents perfect fifth 8: 1 14/9 764.916 cents septimal minor sixth 8: 1 120/77 768.125 cents 8: 1 11/7 782.492 cents undecimal augmented fifth 8: 1 63/40 786.422 cents narrow minor sixth 8: 1 8/5 813.686 cents minor sixth 8: 1 77/48 818.189 cents 8: 1 160/99 831.086 cents 8: 1 44/27 845.453 cents neutral sixth 8: 1 18/11 852.592 cents undecimal neutral sixth 8: 1 12/7 933.129 cents septimal major sixth 9: 1 14/9 764.916 cents septimal minor sixth 9: 2 18/11 852.592 cents undecimal neutral sixth 9: 2 33/20 866.959 cents 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 56/33 915.553 cents 9: 2 12/7 933.129 cents septimal major sixth 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 10: 1 27/16 905.865 cents Pythagorean major sixth 10: 1 56/33 915.553 cents 10: 1 12/7 933.129 cents septimal major sixth 10: 1 7/4 968.826 cents harmonic seventh 10: 1 99/56 986.402 cents 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 20/11 1034.996 cents large minor seventh 10: 1 154/81 1112.324 cents 10: 1 40/21 1115.533 cents acute major seventh 11: 1 7/4 968.826 cents harmonic seventh 11: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 1 28/15 1080.557 cents grave major seventh 11: 1 144/77 1083.766 cents 11: 1 40/21 1115.533 cents acute major seventh 11: 1 21/11 1119.463 cents undecimal major seventh 11: 1 77/40 1133.830 cents 11: 2 27/14 1137.039 cents septimal major seventh 11: 1 64/33 1146.727 cents 33rd subharmonic 11: 1 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 9.45455 = 104/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 53.3 203.9 266.9 386.3 470.8 551.3 702.0 818.2 884.4 905.9 968.8 1200.0 53.3 : 150.6 213.6 333.0 417.5 498.0 648.7 764.9 831.1 852.6 915.6 1146.7 1200.0 203.9 : 63.0 182.4 266.9 347.4 498.0 614.3 680.4 702.0 764.9 996.1 1049.4 1200.0 266.9 : 119.4 203.9 284.4 435.1 551.3 617.5 639.0 702.0 933.1 986.4 1137.0 1200.0 386.3 : 84.5 165.0 315.6 431.9 498.0 519.6 582.5 813.7 867.0 1017.6 1080.6 1200.0 470.8 : 80.5 231.2 347.4 413.6 435.1 498.0 729.2 782.5 933.1 996.1 1115.5 1200.0 551.3 : 150.6 266.9 333.0 354.5 417.5 648.7 702.0 852.6 915.6 1035.0 1119.5 1200.0 702.0 : 116.2 182.4 203.9 266.9 498.0 551.3 702.0 764.9 884.4 968.8 1049.4 1200.0 818.2 : 66.2 87.7 150.6 381.8 435.1 585.7 648.7 768.1 852.6 933.1 1083.8 1200.0 884.4 : 21.5 84.5 315.6 368.9 519.6 582.5 702.0 786.4 867.0 1017.6 1133.8 1200.0 905.9 : 63.0 294.1 347.4 498.0 561.0 680.4 764.9 845.5 996.1 1112.3 1178.5 1200.0 968.8 : 231.2 284.4 435.1 498.0 617.5 702.0 782.5 933.1 1049.4 1115.5 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 231.1741 cents 640/567, 209.6678 cents 81/80, 21.5063 cents 2: 84.4672 .. 294.1350 cents 640/567, 209.6678 cents 147/160,-146.7069 cents 3: 150.6371 .. 435.0841 cents 33/28, 284.4470 cents 81/88,-143.4979 cents 4: 266.8709 .. 498.0450 cents 8/7, 231.1741 cents 49/54,-168.2132 cents 5: 417.5080 .. 617.4878 cents 55/49, 199.9798 cents 21/22,-80.5370 cents 6: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 14/15,-119.4428 cents 7: 582.5122 .. 782.4920 cents 55/49, 199.9798 cents 14/15,-119.4428 cents 8: 701.9550 .. 933.1291 cents 8/7, 231.1741 cents 21/22,-80.5370 cents 9: 764.9159 .. 1049.3629 cents 33/28, 284.4470 cents 49/54,-168.2132 cents 10: 905.8650 .. 1115.5328 cents 640/567, 209.6678 cents 81/88,-143.4979 cents 11: 968.8259 .. 1178.4937 cents 640/567, 209.6678 cents 147/160,-146.7069 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 4.649803 Largest / Average step : 2.311741 Largest / Smallest step : 10.749139 Median interval of one step : 82.50211 cents, amount: 0 Least squares average step : 95.38913 cents, oct.: 1144.66951 cents Scale is not proper Step pattern alph. order: ABCDEFBGHICJ Step pattern size order : BICHFEIGDACJ Scale is not a Constant Structure Scale diversity : 1.599893 Lumma stability : 0.035844 Lumma impropriety factor : 0.859221 Rothenberg efficiency : 0.271886 redundancy: 0.728114 Efficiency x scale size : 3.262626 Number of different interval sizes : 72 = 6.54545 / class Number of one step interval sizes : 10 Highest interval variety : 11 Mean interval variety : 9.45455 = 104/11 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 540/539, 3.2090 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 7, average 701.9550 cents Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 77 Scale harmonicity : 0.019405 Average absolute harmonicity : 0.169318 Specific harmonicity : 0.112227 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 20790, 14.3436 octaves, 5439195.503 Hz. Exponens Consonantiae : 1.995840E+06, 20.92856 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 177.5, average 14.79167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.71948, average 0.97662 Sum of Tenney's harmonic distance : 22.18174, average 1.84848 Vogel's harmonic complexity : 12.83333 Wille's k value : 49 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 238.45012, average 3.05705 Lattice compactness (without 2's) : 141.87627, average 1.81893 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.33333 30 1 3: -1 .. 3 0.41667 11 3 5: 0 .. 1 0.16667 2 2 7: 0 .. 1 0.33333 4 3 11: 0 .. 1 0.25000 3 3 Average exponent except 2's : 14 / 12 = 1.16667 Average absolute exponent except 2's: 20 / 12 = 1.66667
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 0 1 2 N T3 SD: 26.2881 c. M:-48.6821 c. 13: 1 1 1 1 1 1 2 1 1 0 1 2 N D3 SD: 25.5518 c. M:-46.5587 c. 15: 1 2 0 2 1 1 2 1 1 0 1 3 N SD: 19.3841 c. M:-36.0900 c. 16: 1 2 1 1 1 1 2 2 1 0 1 3 N SD: 19.0547 c. M:-33.1291 c. 18: 1 2 1 2 1 1 3 1 1 1 1 3 N SD: 18.4327 c. M:-31.3783 c. 19: 1 2 1 2 1 2 2 2 1 0 1 4 N SD: 14.9098 c. M: 28.6756 c. 20: 1 2 1 2 2 1 3 2 1 0 1 4 N SD: 16.8394 c. M: 26.8709 c. 21: 1 3 1 2 1 2 2 2 2 0 1 4 N SD: 16.6430 c. M:-29.9270 c. 22: 1 3 1 2 2 1 3 2 1 1 1 4 N SD: 11.2273 c. M:-21.4077 c. 24: 1 3 1 3 1 2 3 2 2 0 1 5 N SD: 12.5819 c. M: 20.7809 c. 26: 1 3 2 2 2 2 3 3 1 1 1 5 N SD: 11.2201 c. M: 19.2946 c. 28: 1 4 1 3 2 2 3 3 2 0 2 5 N SD: 9.9530 c. M:-16.8884 c. 31: 1 4 2 3 2 2 4 3 2 0 2 6 N SD: 8.1507 c. M: 15.5424 c. 38: 2 4 2 4 3 2 5 4 2 1 2 7 N SD: 9.3202 c. M: 14.4758 c. 40: 2 5 2 4 3 2 5 4 2 1 2 8 N SD: 8.4027 c. M: 14.3587 c. 41: 2 5 2 4 3 3 5 4 2 1 2 8 N SD: 3.6091 c. M: 6.3099 c. 69: 3 9 3 7 5 5 8 7 4 1 4 13 N SD: 3.8482 c. M: 6.3028 c. 72: 3 9 4 7 5 5 9 7 4 1 4 14 N SD: 2.8844 c. M: 5.8650 c. 87: 4 11 4 9 6 6 11 8 5 2 4 17 N SD: 2.8016 c. M: 4.8019 c. 94: 4 12 5 9 7 6 12 9 5 2 5 18 N SD: 1.8617 c. M: 3.5076 c. 130: 6 16 7 13 9 9 16 13 7 2 7 25 N SD: 1.5933 c. M:-3.3496 c. 151: 7 19 8 15 10 10 19 15 8 3 8 29 N SD: 2.2082 c. M:-3.3278 c. 152: 7 19 8 15 11 10 19 15 8 3 8 29 N SD: 1.7414 c. M:-2.9033 c. 171: 8 21 9 17 12 12 21 17 9 3 9 33 N SD: 1.5032 c. M:-3.0680 c. 175: 8 22 9 17 13 11 22 17 10 3 9 34 N SD: 1.8296 c. M: 2.7465 c. 176: 8 22 9 18 12 12 22 17 10 3 9 34 N SD: 1.1107 c. M:-2.3226 c. 183: 8 23 10 18 13 12 23 18 10 3 10 35 N SD: 1.0857 c. M:-1.9816 c. 217: 10 27 11 22 15 15 27 21 12 4 11 42 N SD: 1.0511 c. M:-2.0266 c. 224: 10 28 12 22 16 15 28 22 12 4 12 43 N SD: 0.6725 c. M:-1.4540 c. 248: 11 31 13 25 17 17 31 24 14 4 13 48 N SD: 0.7940 c. M: 1.4261 c. 270: 12 34 14 27 19 18 34 26 15 5 14 52 N SD: 0.3538 c. M:-0.8017 c. 342: 15 43 18 34 24 23 43 33 19 6 18 66 N SD: 0.4379 c. M: 0.6450 c. 453: 20 57 24 45 32 30 57 44 25 8 24 87 N SD: 0.4291 c. M:-0.7423 c. 472: 21 59 25 47 33 32 59 46 26 8 25 91 N SD: 0.3775 c. M: 0.7803 c. 494: 22 62 26 49 35 33 62 48 27 9 26 95 N SD: 0.2620 c. M:-0.4742 c. 612: 27 77 32 61 43 41 77 59 34 11 32 118 N SD: 0.2309 c. M: 0.5418 c. 653: 29 82 34 65 46 44 82 63 36 12 34 126 N SD: 0.2846 c. M: 0.4383 c. 670: 30 84 35 67 47 45 84 65 37 12 35 129 N SD: 0.3208 c. M:-0.5520 c. 701: 31 88 37 70 49 47 88 68 39 12 37 135 N SD: 0.2876 c. M:-0.6627 c. 742: 33 93 39 74 52 50 93 72 41 13 39 143 N SD: 0.1519 c. M:-0.2774 c. 836: 37 105 44 83 59 56 105 81 46 15 44 161 N SD: 0.1090 c. M: 0.1893 c. 1012: 45 127 53 101 71 68 127 98 56 18 53 195 N SD: 0.1078 c. M:-0.2476 c. 1106: 49 139 58 110 78 74 139 107 61 20 58 213 N SD: 0.0859 c. M: 0.1425 c. 1506: 67 189 79 150 106 101 189 146 83 27 79 290 N SD: 0.0996 c. M:-0.1405 c. 1578: 70 198 83 157 111 106 198 153 87 28 83 304 N SD: 0.0676 c. M: 0.1616 c. 1848: 82 232 97 184 130 124 232 179 102 33 97 356 N SD: 0.0253 c. M:-0.0569 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: 9.0880 cents 4 x x x 5 x x 6 x x x 7:8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x x 9:10 S SD: 15.1664 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 14.1711 cents 7 x 8 x x 9:10 x 11 x 12 x 14 S SD: 15.2876 cents 8 x 9 x 10 x 11:12:13 x x 14:16 S SD: 3.1913 cents 9 x 10 x 11:12 x x 14:15 x 16:18 S SD: 11.3397 cents 10 x 11:12 x 13:14:15:16 x 17:18:20 S SD: 9.7511 cents 11 x 12:13:14 x 15:17 x 18 x 19:22 SD: 11.6652 cents 12 x x 14:15:16:17:18:19:20 x 21:24 S SD: 6.9625 cents 13:14 x 15:16:17:18:20:21 x 22:23:26 SD: 9.6696 cents 14:15:16 x x 18:19:21:22:23:24:25:28 SD: 10.3777 cents 15:16:17:18:19:20:21:23:24:25 x 26:30 SD: 9.0654 cents 16:17:18:19:20:21:22:24:26 x 27:28:32 S SD: 5.8274 cents 18:19:20:21:23:24:25:27:29:30 x 32:36 SD: 6.6694 cents 19:20:21:22:24:25:26:29:30 x 32:33:38 SD: 6.1855 cents 20:21 x 23:25:26:28:30:32:33:34:35:40 SD: 5.2440 cents 21:22:24:25:26:28:29:32:34:35 x 37:42 SD: 6.3768 cents 22:23:25:26:28:29:30:33:35 x 37:39:44 SD: 5.2520 cents 23:24:26:27:29:30:32:35:37:38:39:40:46 SD: 4.0973 cents 24:25:27:28:30:32:33:36:39:40:41:42:48 SD: 3.7234 cents 25:26:28:29:31:33:34:38:40 x 42:44:50 SD: 3.7768 cents 28:29:32:33:35:37:39:42:45 x 47:49:56 SD: 3.8992 cents 29:30:33:34:36:38:40:44:47:48:49:51:58 SD: 3.3346 cents 30:31:34:35:38:39:41:45:48:50:51:53:60 SD: 3.2695 cents 31:32:35:36:39:41:43:47:50 x 52:54:62 SD: 3.1978 cents 32:33:36:37:40:42:44:48:51:53:54:56:64 SD: 1.8373 cents 34:35:38:40:43:45:47:51:55:57 x 60:68 SD: 3.6093 cents 35:36:39:41:44:46:48:53:56:58:59:61:70 SD: 2.5126 cents 37:38:42:43:46:49:51:56:59:62 x 65:74 SD: 3.1011 cents 38:39:43:44:48:50:52:57:61:63:64:67:76 SD: 2.6645 cents 40:41:45:47:50:53:55:60:64:67:68:70:80 SD: 2.3422 cents 48:50:54:56:60:63:66:72:77:80:81:84:96 SD: 1.4500 cents 61:63:69:71:76:80:84:92:98:102:103:107:122 SD: 1.4391 cents 64:66:72:75:80:84:88:96:103:107:108:112:128 SD: 0.9134 cents 96:99:108:112:120:126:132:144:154:160:162:168:192 SD: 0.0000 cents