Scala analysis: mohajira-to-slendro
From Mohajira to Aeolian and Slendros
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 49/40 351.338099 larger approximation to neutral 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: 49/30 849.383098 larger approximation to neutral sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 21/20 84.4672 minor semitone 2: 15/14 119.4428 major diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 49/48 35.6968 slendro diesis, septimal 1/6-tone 5: 160/147 146.7069 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 54/49 168.2132 Zalzal's mujannab 11: 55/54 31.7667 telepathma 12: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 160/147 146.707 cents 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 54/49 168.213 cents Zalzal's mujannab 2: 2 49/45 147.428 cents BP minor semitone 2: 2 10/9 182.404 cents minor whole tone 2: 1 55/49 199.980 cents quasi-equal major second 2: 3 9/8 203.910 cents major whole tone 2: 3 8/7 231.174 cents septimal whole tone 2: 1 63/55 235.104 cents 3: 1 55/48 235.677 cents undecimal semi-augmented whole tone 3: 4 7/6 266.871 cents septimal minor third 3: 1 32/27 294.135 cents Pythagorean minor third 3: 3 6/5 315.641 cents minor third 3: 2 60/49 350.617 cents smaller approximation to neutral third 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 1 11/9 347.408 cents undecimal neutral third 4: 2 49/40 351.338 cents larger approximation to neutral third 4: 1 56/45 378.602 cents septimal narrow major third 4: 3 5/4 386.314 cents major third 4: 1 80/63 413.578 cents wide major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 4: 1 72/55 466.278 cents undecimal semi-diminished fourth 5: 1 55/42 466.851 cents 5: 1 21/16 470.781 cents narrow fourth 5: 7 4/3 498.045 cents perfect fourth 5: 1 147/110 501.975 cents 5: 1 27/20 519.551 cents acute fourth 5: 1 135/98 554.527 cents 6: 2 49/36 533.742 cents Arabic lute acute fourth 6: 1 11/8 551.318 cents undecimal semi-augmented fourth 6: 2 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: 2 10/7 617.488 cents Euler's tritone 6: 1 16/11 648.682 cents undecimal semi-diminished fifth 6: 2 72/49 666.258 cents Arabic lute grave fifth 7: 1 196/135 645.473 cents 7: 1 40/27 680.449 cents grave fifth 7: 1 220/147 698.025 cents 7: 7 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 7: 1 84/55 733.149 cents 8: 1 55/36 733.722 cents undecimal semi-augmented fifth 8: 1 49/32 737.652 cents 8: 2 14/9 764.916 cents septimal minor sixth 8: 1 63/40 786.422 cents narrow minor sixth 8: 3 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 8: 2 80/49 848.662 cents smaller approximation to neutral sixth 8: 1 18/11 852.592 cents undecimal neutral sixth 9: 1 44/27 845.453 cents neutral sixth 9: 2 49/30 849.383 cents larger approximation to neutral sixth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 4 12/7 933.129 cents septimal major sixth 9: 1 96/55 964.323 cents 10: 1 110/63 964.896 cents 10: 3 7/4 968.826 cents harmonic seventh 10: 3 16/9 996.090 cents Pythagorean minor seventh 10: 1 98/55 1000.020 cents quasi-equal minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 90/49 1052.572 cents 11: 1 49/27 1031.787 cents 11: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 1 147/80 1053.293 cents 11: 2 28/15 1080.557 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 2 96/49 1164.303 cents 11: 1 108/55 1168.233 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.90909 = 76/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 203.9 315.6 351.3 498.0 582.5 702.0 813.7 849.4 1017.6 1049.4 1200.0 84.5 : 119.4 231.2 266.9 413.6 498.0 617.5 729.2 764.9 933.1 964.9 1115.5 1200.0 203.9 : 111.7 147.4 294.1 378.6 498.0 609.8 645.5 813.7 845.5 996.1 1080.6 1200.0 315.6 : 35.7 182.4 266.9 386.3 498.0 533.7 702.0 733.7 884.4 968.8 1088.3 1200.0 351.3 : 146.7 231.2 350.6 462.3 498.0 666.3 698.0 848.7 933.1 1052.6 1164.3 1200.0 498.0 : 84.5 203.9 315.6 351.3 519.6 551.3 702.0 786.4 905.9 1017.6 1053.3 1200.0 582.5 : 119.4 231.2 266.9 435.1 466.9 617.5 702.0 821.4 933.1 968.8 1115.5 1200.0 702.0 : 111.7 147.4 315.6 347.4 498.0 582.5 702.0 813.7 849.4 996.1 1080.6 1200.0 813.7 : 35.7 203.9 235.7 386.3 470.8 590.2 702.0 737.7 884.4 968.8 1088.3 1200.0 849.4 : 168.2 200.0 350.6 435.1 554.5 666.3 702.0 848.7 933.1 1052.6 1164.3 1200.0 1017.6: 31.8 182.4 266.9 386.3 498.0 533.7 680.4 764.9 884.4 996.1 1031.8 1200.0 1049.4: 150.6 235.1 354.5 466.3 502.0 648.7 733.1 852.6 964.3 1000.0 1168.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 168.2132 cents 2916/2695, 136.4465 cents 55/54, 31.7667 cents 2: 147.4281 .. 235.1043 cents 81/77, 87.6762 cents 2401/2430,-20.7851 cents 3: 235.6767 .. 354.5471 cents 648/605, 118.8704 cents 3025/3024, 0.5724 cents 4: 347.4079 .. 466.2783 cents 648/605, 118.8704 cents 242/243,-7.1391 cents 5: 466.8507 .. 554.5269 cents 81/77, 87.6762 cents 3025/3024, 0.5724 cents 6: 533.7418 .. 666.2582 cents 2592/2401, 132.5164 cents 2401/2430,-20.7851 cents 7: 645.4731 .. 733.1493 cents 81/77, 87.6762 cents 2401/2430,-20.7851 cents 8: 733.7217 .. 852.5921 cents 648/605, 118.8704 cents 3025/3024, 0.5724 cents 9: 845.4529 .. 964.3233 cents 648/605, 118.8704 cents 242/243,-7.1391 cents 10: 964.8957 .. 1052.5719 cents 81/77, 87.6762 cents 3025/3024, 0.5724 cents 11: 1031.7868 .. 1168.2333 cents 2916/2695, 136.4465 cents 2401/2430,-20.7851 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 54/49, 168.2132 cents Average / Smallest step : 3.147955 Largest / Average step : 1.682132 Largest / Smallest step : 5.295276 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 98.48683 cents, oct.: 1181.84197 cents Scale is not proper Step pattern alph. order: ABCDEABCDFGH Step pattern size order : CEDBFCEDBHAG Scale is a Constant Structure, by a margin of 0.57240 cents Scale diversity : 1.557789 Lumma stability : 0.054852 Lumma impropriety factor : 0.081182 Rothenberg efficiency : 0.270665 redundancy: 0.729335 Efficiency x scale size : 3.247980 Number of different interval sizes : 76 = 6.90909 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 6.90909 = 76/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 3025/3024, 0.5724 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 : 8, average 701.4637 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 11 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 49 Scale harmonicity : 0.016905 Average absolute harmonicity : 0.176375 Specific harmonicity : 0.113203 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 38808, 15.2441 octaves, 10153164.938 Hz. Exponens Consonantiae : 4.656960E+06, 22.15096 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 154.0, average 12.83333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.84977, average 0.90415 Sum of Tenney's harmonic distance : 21.19452, average 1.76621 Vogel's harmonic complexity : 13.16667 Wille's k value : 73 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 234.96507, average 3.01237 Lattice compactness (without 2's) : 145.38520, average 1.86391 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.33333 18 1 3: -1 .. 2 0.33333 10 3 5: -1 .. 0 -0.58333 7 3 7: 0 .. 2 0.50000 6 4 11: 0 .. 1 0.08333 1 1 Average exponent except 2's : 4 / 12 = 0.33333 Average absolute exponent except 2's: 24 / 12 = 2.00000 Scale is weakly epimorphic with val: <12 19 27 33 41| Scale is JI-epimorphic with val: <12 19 28 34 42| = patent
FIT/MODE
12: 1 1 1 0 2 1 1 1 0 2 0 2 N T3 SD: 27.1149 c. M: 51.3381 c. 13: 1 1 1 1 1 1 1 2 0 2 0 2 N D3 SD: 27.8672 c. M: 55.8012 c. 14: 1 1 2 0 2 1 1 1 1 2 0 2 N D3 S SD: 20.6180 c. M: 42.2577 c. 15: 1 2 1 0 2 1 2 1 1 2 0 2 N SD: 20.8084 c. M:-36.0900 c. 16: 1 2 1 1 2 1 1 2 0 3 0 2 N SD: 20.1471 c. M:-32.4037 c. 17: 1 2 1 1 2 1 2 1 1 2 1 2 P M ME SD: 18.3823 c. M: 37.2157 c. Schism-12 18: 1 2 2 0 2 2 2 1 1 2 1 2 N D3 SD: 19.0163 c. M: 31.3783 c. 19: 1 2 2 0 3 1 2 2 0 3 0 3 N SD: 19.6726 c. M: 38.8366 c. 20: 1 2 2 1 2 2 2 1 1 3 0 3 N SD: 19.4462 c. M: 33.6863 c. 24: 2 2 2 1 3 2 2 2 1 3 1 3 P T3 SD: 10.4650 c. M: 17.5963 c. 27: 2 3 2 1 3 2 3 2 1 4 1 3 N SD: 9.6428 c. M:-18.3122 c. 31: 2 3 3 1 4 2 3 3 1 4 1 4 P SD: 5.8161 c. M: 11.1447 c. 41: 3 4 4 1 5 3 4 4 1 6 1 5 N SD: 3.6450 c. M:-6.7940 c. 58: 4 6 5 2 7 4 6 5 2 8 2 7 N SD: 3.5390 c. M: 6.7897 c. 65: 5 6 6 2 8 5 6 6 2 9 2 8 N SD: 3.5323 c. M:-8.2570 c. 72: 5 7 7 2 9 5 7 7 2 10 2 9 N SD: 1.7858 c. M: 3.9100 c. 99: 7 10 9 3 12 7 10 9 3 14 3 12 N SD: 1.7864 c. M:-5.1825 c. 113: 8 11 11 3 14 8 11 11 3 16 3 14 N SD: 1.8819 c. M:-4.0128 c. 130: 9 13 12 4 16 9 13 12 4 18 4 16 N SD: 1.3831 c. M:-2.9448 c. 167: 12 16 16 5 20 12 17 15 5 24 4 21 N SD: 1.6920 c. M:-2.7630 c. 171: 12 17 16 5 21 12 17 16 5 24 5 21 N SD: 0.9756 c. M:-3.2686 c. 175: 12 18 16 5 22 12 17 17 5 24 5 22 N SD: 1.7631 c. M: 2.7391 c. 178: 13 17 17 5 22 12 18 17 5 25 5 22 N SD: 1.6709 c. M:-3.1733 c. 181: 13 18 17 5 22 13 18 17 5 26 4 23 N SD: 1.6621 c. M:-3.3982 c. 183: 13 18 17 6 22 13 18 17 6 25 5 23 N SD: 1.3563 c. M:-3.0759 c. 184: 13 18 17 6 22 13 19 17 5 26 5 23 N SD: 1.6213 c. M: 2.5978 c. 185: 13 18 18 5 23 13 18 17 6 26 5 23 N SD: 1.5996 c. M: 2.8755 c. 195: 14 19 18 6 24 14 19 18 6 27 5 25 N SD: 1.5537 c. M: 3.2091 c. 198: 14 20 18 6 24 14 20 18 6 28 5 25 N SD: 1.0086 c. M:-2.1506 c. 202: 14 20 19 6 25 14 20 19 6 28 6 25 N SD: 1.1672 c. M:-2.1222 c. 212: 15 21 20 6 26 15 21 20 6 30 5 27 N SD: 0.9550 c. M: 2.1931 c. 224: 16 22 21 7 27 16 22 21 7 31 6 28 N SD: 1.1370 c. M:-2.4026 c. 229: 16 23 21 7 28 16 23 21 7 32 6 29 N SD: 0.8230 c. M: 1.4592 c. 270: 19 27 25 8 33 19 27 25 8 38 7 34 N SD: 0.3160 c. M:-0.5344 c. 342: 24 34 32 10 42 24 34 32 10 48 9 43 N SD: 0.2573 c. M: 0.4609 c. 612: 43 61 57 18 75 43 61 57 18 86 16 77 N SD: 0.1900 c. M: 0.3635 c. 836: 59 83 78 25 102 59 83 78 25 117 22 105 N SD: 0.1958 c. M:-0.3777 c. 894: 63 89 83 27 109 63 89 83 27 125 24 112 N SD: 0.1936 c. M:-0.3398 c. 935: 66 93 87 28 114 66 93 87 28 131 25 117 N SD: 0.2118 c. M:-0.4766 c. 954: 67 95 89 28 117 67 95 89 28 134 25 120 N SD: 0.1968 c. M: 0.3947 c. 966: 68 96 90 29 118 68 96 90 29 135 26 121 N SD: 0.1736 c. M:-0.3265 c. 1065: 75 106 99 32 130 75 106 99 32 149 28 134 N SD: 0.1512 c. M: 0.3489 c. 1106: 78 110 103 33 135 78 110 103 33 155 29 139 N SD: 0.1207 c. M:-0.1990 c. 1236: 87 123 115 37 151 87 123 115 37 173 33 155 N SD: 0.0868 c. M:-0.1516 c. 1448: 102 144 135 43 177 102 144 135 43 203 38 182 N SD: 0.0868 c. M: 0.1917 c. 1506: 106 150 140 45 184 106 150 140 45 211 40 189 N SD: 0.0645 c. M: 0.1405 c. 1547: 109 154 144 46 189 109 154 144 46 217 41 194 N SD: 0.0744 c. M:-0.1522 c. 1578: 111 157 147 47 193 111 157 147 47 221 42 198 N SD: 0.0586 c. M: 0.1077 c. 1848: 130 184 172 55 226 130 184 172 55 259 49 232 N SD: 0.0382 c. M: 0.0638 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: 11.6585 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 15.0038 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 x 11:12 S SD: 10.0026 cents 7 x 8 x x 9:10 x 11 x x 13:14 SD: 14.3399 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.8163 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 11.1891 cents 10 x 11:12 x 13:14:15:16 x 18 x 20 S SD: 7.3259 cents 11 x 12:13 x 15 x 17 x 18 x 20:22 SD: 12.7280 cents 12:13 x 14:15:16:17:18:19:20 x 22:24 S SD: 9.2201 cents 13:14:15 x 16:17:18:20:21 x 23:24:26 SD: 9.2934 cents 14:15:16 x 17:19:20:21:22:23:25:26:28 SD: 7.1141 cents 15:16:17:18 x 20:21:23:24:25:27:28:30 SD: 6.1327 cents 16:17:18:19:20:21:22:24 x 26:29 x 32 SD: 6.2531 cents 17:18:19:20:21:23:24:26:27:28 x 31:34 SD: 5.8649 cents 18:19:20 x 22:24:25:27:29 x 32:33:36 SD: 3.6848 cents 19:20:21:23 x 25:27:29:30:31:34:35:38 SD: 5.7403 cents 20:21:23:24:25:27:28:30:32:33:36:37:40 SD: 5.0608 cents 21:22:24:25:26:28:29:32 x 34:38:39:42 SD: 5.3067 cents 22:23:25:26:27:29:31:33:35:36 x 40:44 SD: 3.9617 cents 23:24:26 x 28:31:32:35:37:38:41:42:46 SD: 4.2653 cents 24:25:27:29 x 32:34:36:38:39:43:44:48 SD: 3.1821 cents 26:27:29:31:32:35:36:39:42 x 47:48:52 SD: 3.9541 cents 28:29:32 x 34:37:39:42:45:46:50:51:56 SD: 4.3928 cents 30:32:34:36:37:40:42:45:48:49:54:55:60 SD: 2.6930 cents 33:35:37:40 x 44:46:50:53:54:59:61:66 SD: 3.3915 cents 34:36:38:41:42:45:48:51:54:56:61:62:68 SD: 3.2112 cents 35:37:39:42:43:47:49:53:56:57:63:64:70 SD: 2.5063 cents 39:41:44:47:48:52:55:59:62:64:70:72:78 SD: 2.4808 cents 40:42:45:48:49:53:56:60:64:65:72:73:80 SD: 1.3397 cents 65:68:73:78:80:87:91:98:104:106:117:119:130 SD: 1.3207 cents 66:69:74:79:81:88:92:99:106:108:119:121:132 SD: 1.2856 cents 78:82:88:94:96:104:109:117:125:127:140:143:156 SD: 1.2394 cents 79:83:89:95:97:105:111:119:126:129:142:145:158 SD: 1.1756 cents 80:84:90:96:98:107:112:120:128:131:144:147:160 SD: 0.6671 cents 120:126:135:144:147:160:168:180:192:196:216:220:240 SD: 0.0000 cents