Scala analysis: majsyn1
First Majsyn 648/625 81/80 scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 250/243 49.166137 maximal diesis, Porcupine comma 2: 10/9 182.403712 minor whole tone 3: 6/5 315.641287 minor third 4: 100/81 364.807424 grave major third 5: 4/3 498.044999 perfect fourth 6: 25/18 568.717426 classic augmented fourth 7: 40/27 680.448711 grave fifth 8: 125/81 751.121138 9: 5/3 884.358713 major sixth, BP sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 50/27 1066.762425 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 250/243 49.1661 maximal diesis, Porcupine comma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 250/243 49.1661 maximal diesis, Porcupine comma 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 16/15 111.7313 minor diatonic semitone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 10: 16/15 111.7313 minor diatonic semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 250/243 49.166 cents maximal diesis, Porcupine comma 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 5 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 7 10/9 182.404 cents minor whole tone 2: 3 9/8 203.910 cents major whole tone 2: 1 144/125 244.969 cents classic diminished third 2: 1 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 3 125/108 253.076 cents semi-augmented whole tone 3: 9 6/5 315.641 cents minor third 4: 3 100/81 364.807 cents grave major third 4: 5 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 3 162/125 448.879 cents 5: 1 625/486 435.480 cents 5: 7 4/3 498.045 cents perfect fourth 5: 4 27/20 519.551 cents acute fourth 6: 6 25/18 568.717 cents classic augmented fourth 6: 6 36/25 631.283 cents classic diminished fifth 7: 4 40/27 680.449 cents grave fifth 7: 7 3/2 701.955 cents perfect fifth 7: 1 972/625 764.520 cents 8: 3 125/81 751.121 cents 8: 1 25/16 772.627 cents classic augmented fifth 8: 5 8/5 813.686 cents minor sixth 8: 3 81/50 835.193 cents acute minor sixth 9: 9 5/3 884.359 cents major sixth, BP sixth 9: 3 216/125 946.924 cents semi-augmented sixth 10: 1 1250/729 933.525 cents 10: 1 125/72 955.031 cents classic augmented sixth 10: 3 16/9 996.090 cents Pythagorean minor seventh 10: 7 9/5 1017.596 cents just minor seventh, BP seventh 11: 5 50/27 1066.762 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 3 48/25 1129.328 cents classic diminished octave 11: 2 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 49.2 182.4 315.6 364.8 498.0 568.7 680.4 751.1 884.4 996.1 1066.8 1200.0 49.2 : 133.2 266.5 315.6 448.9 519.6 631.3 702.0 835.2 946.9 1017.6 1150.8 1200.0 182.4 : 133.2 182.4 315.6 386.3 498.0 568.7 702.0 813.7 884.4 1017.6 1066.8 1200.0 315.6 : 49.2 182.4 253.1 364.8 435.5 568.7 680.4 751.1 884.4 933.5 1066.8 1200.0 364.8 : 133.2 203.9 315.6 386.3 519.6 631.3 702.0 835.2 884.4 1017.6 1150.8 1200.0 498.0 : 70.7 182.4 253.1 386.3 498.0 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 568.7 : 111.7 182.4 315.6 427.4 498.0 631.3 680.4 813.7 946.9 996.1 1129.3 1200.0 680.4 : 70.7 203.9 315.6 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1088.3 1200.0 751.1 : 133.2 245.0 315.6 448.9 498.0 631.3 764.5 813.7 946.9 1017.6 1129.3 1200.0 884.4 : 111.7 182.4 315.6 364.8 498.0 631.3 680.4 813.7 884.4 996.1 1066.8 1200.0 996.1 : 70.7 203.9 253.1 386.3 519.6 568.7 702.0 772.6 884.4 955.0 1088.3 1200.0 1066.8: 133.2 182.4 315.6 448.9 498.0 631.3 702.0 813.7 884.4 1017.6 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 133.2376 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents 2: 182.4037 .. 266.4751 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents 3: 253.0761 .. 315.6413 cents 648/625, 62.5651 cents 78125/78732,-13.3990 cents 4: 364.8074 .. 448.8789 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents 5: 435.4799 .. 519.5513 cents 6561/6250, 84.0714 cents 78125/78732,-13.3990 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 7: 680.4487 .. 764.5201 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents 8: 751.1211 .. 835.1926 cents 6561/6250, 84.0714 cents 78125/78732,-13.3990 cents 9: 884.3587 .. 946.9239 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 10: 933.5249 .. 1017.5963 cents 6561/6250, 84.0714 cents 78125/78732,-13.3990 cents 11: 1066.7624 .. 1150.8339 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 250/243, 49.1661 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 27/25, 133.2376 cents Average / Smallest step : 2.033920 Largest / Average step : 1.332376 Largest / Smallest step : 2.709946 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Most common interval of one step : 27/25, 133.2376 cents, amount: 5 Least squares average step : 97.76813 cents, oct.: 1173.21751 cents Scale is not proper Step pattern alph. order: ABBABCDCBDCB Step pattern size order : ADDADBCBDCBD Scale is a Constant Structure, by a margin of 8.10728 cents Scale diversity : 1.363385 Lumma stability : 0.327774 Lumma impropriety factor : 0.044663 Rothenberg efficiency : 0.419108 redundancy: 0.580892 Efficiency x scale size : 5.029293 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 9 Most common triad is 0.0 315.641 884.359 cents, amount: 6 Number of recognisable fifths : 7, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 3 5 Formal octave complements present : 3 = 25.0000% 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 : 5 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 243 Scale harmonicity : 0.021459 Average absolute harmonicity : 0.155647 Specific harmonicity : 0.131524 Fundamental : 1/2430, -11.2467 octaves, 0.1077 Hz. Guide tone : 6000, 12.5507 octaves, 1569753.392 Hz. Exponens Consonantiae : 1.458000E+07, 23.79749 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 570.0, average 47.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.43522, average 1.20293 Sum of Tenney's harmonic distance : 29.66043, average 2.47170 Vogel's harmonic complexity : 21.58333 Wille's k value : 1687 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 259.94275, average 3.33260 Lattice compactness (without 2's) : 208.55431, average 2.67377 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.25000 17 1 3: -5 .. 1 -2.16667 28 2 5: -1 .. 3 1.16667 16 9 Average exponent except 2's :-12 / 12 =-1.00000 Average absolute exponent except 2's: 44 / 12 = 3.66667 Scale is weakly epimorphic with val: <12 17 26| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 20 29|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 28.1297 c. M:-50.8339 c. Twelve-tone Chromatic (1/11-comma) 15: 0 2 2 0 2 1 1 1 2 1 1 2 N D3 SD: 28.8529 c. M: 49.1661 c. 16: 1 1 2 1 2 1 1 1 2 1 1 2 P D3 SD: 19.9425 c. M: 32.4037 c. 18: 1 2 2 0 2 2 1 1 2 2 1 2 N D3 SD: 19.8271 c. M: 31.4741 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 9.1482 c. M:-14.4363 c. Meantone Chromatic (1/3-comma) 27: 1 3 3 1 3 2 2 2 3 2 2 3 P D3 SD: 8.5694 c. M: 18.3122 c. 34: 1 4 4 1 4 2 3 2 4 3 2 4 N SD: 7.7934 c. M: 13.8720 c. 42: 2 4 5 2 4 3 4 2 5 4 2 5 N SD: 7.0406 c. M: 12.3307 c. 45: 2 5 5 2 5 2 5 2 5 4 3 5 N SD: 6.8994 c. M:-12.8846 c. 46: 2 5 5 2 5 3 4 3 5 4 3 5 P SD: 3.1647 c. M:-5.4006 c. 53: 2 6 6 2 6 3 5 3 6 5 3 6 N SD: 2.1954 c. M: 3.9513 c. 72: 3 8 8 3 8 4 7 4 8 7 4 8 N SD: 1.8262 c. M:-3.9100 c. 99: 4 11 11 4 11 6 9 6 11 9 6 11 N SD: 1.0133 c. M: 2.1506 c. 118: 5 13 13 5 13 7 11 7 13 11 7 13 N SD: 0.9161 c. M:-1.6813 c. 171: 7 19 19 7 19 10 16 10 19 16 10 19 N SD: 0.2003 c. M:-0.4012 c. 441: 18 49 49 18 49 26 41 26 49 41 26 49 N SD: 0.1167 c. M: 0.1865 c. 612: 25 68 68 25 68 36 57 36 68 57 36 68 N SD: 0.0811 c. M: 0.1465 c. 730: 30 81 81 30 81 43 68 43 81 68 43 81 N SD: 0.0826 c. M:-0.1489 c. 901: 37 100 100 37 100 53 84 53 100 84 53 100 N SD: 0.0794 c. M:-0.1364 c. 1000: 41 111 111 41 111 59 93 59 111 93 59 111 N SD: 0.0513 c. M: 0.0900 c. 1171: 48 130 130 48 130 69 109 69 130 109 69 130 N SD: 0.0171 c. M:-0.0317 c. 1342: 55 149 149 55 149 79 125 79 149 125 79 149 N SD: 0.0169 c. M:-0.0352 c. 1783: 73 198 198 73 198 105 166 105 198 166 105 198 N SD: 0.0195 c. M: 0.0355 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: 10.7531 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: 10.2114 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.5162 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.3450 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 15.7196 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.6759 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 6.6570 cents 10 x 11:12 x 13:14:15 x 17:18:19:20 SD: 8.9506 cents 11 x 12:13:14 x 15:16:17:18 x 20:22 S SD: 10.2607 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.8237 cents 13 x 14 x 16:17:18:19:20:22:23:24:26 S SD: 7.4095 cents 14 x 16:17 x 19 x 21:22:23:25:26:28 SD: 8.5261 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 7.6075 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 7.4562 cents 17:18:19:20:21:23:24:25:26:28:30:31:34 SD: 6.9207 cents 18:19:20 x 22:24:25:27:28:30:32:33:36 SD: 5.1690 cents 19:20:21:23 x 25:26:28:29:32:34:35:38 SD: 5.7904 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 5.2393 cents 21:22:23:25:26:28:29:31:32:35:37:39:42 SD: 4.3312 cents 23:24:26 x 28:31:32:34:35:38:41:43:46 SD: 5.4276 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 4.3967 cents 25:26:28:30:31:33:35:37:39:42:44:46:50 SD: 3.7847 cents 26:27:29:31:32:35:36:39:40:43:46:48:52 SD: 3.2583 cents 29:30:32:35:36:39:40:43:45:48:52:54:58 SD: 3.0458 cents 30:31:33:36:37:40:42:44:46:50:53:56:60 SD: 2.9910 cents 33:34:37:40:41:44:46:49:51:55:59:61:66 SD: 2.4189 cents 35:36:39:42:43:47:49:52:54:58:62:65:70 SD: 2.0808 cents 39:40:43:47:48:52:54:58:60:65:69:72:78 SD: 1.8434 cents 46:47:51:55:57:61:64:68:71:77:82:85:92 SD: 1.7518 cents 54:56:60:65:67:72:75:80:83:90:96:100:108 SD: 1.5399 cents 60:62:67:72:74:80:83:89:93:100:107:111:120 SD: 1.3897 cents 64:66:71:77:79:85:89:95:99:107:114:119:128 SD: 1.2170 cents 69:71:77:83:85:92:96:102:106:115:123:128:138 SD: 1.1904 cents 72:74:80:86:89:96:100:107:111:120:128:133:144 SD: 0.9249 cents 81:83:90:97:100:108:113:120:125:135:144:150:162 SD: 0.9121 cents 90:93:100:108:111:120:125:133:139:150:160:167:180 SD: 0.8055 cents 108:111:120:130:133:144:150:160:167:180:192:200:216 SD: 0.6573 cents 129:133:143:155:159:172:179:191:199:215:229:239:258 SD: 0.6118 cents 135:139:150:162:167:180:188:200:208:225:240:250:270 SD: 0.5453 cents 141:145:157:169:174:188:196:209:218:235:251:261:282 SD: 0.5148 cents 144:148:160:173:178:192:200:213:222:240:256:267:288 SD: 0.4306 cents 162:167:180:194:200:216:225:240:250:270:288:300:324 SD: 0.4140 cents 170:175:189:204:210:227:236:252:262:283:302:315:340 SD: 0.4023 cents 180:185:200:216:222:240:250:267:278:300:320:333:360 SD: 0.3291 cents 216:222:240:259:267:288:300:320:333:360:384:400:432 SD: 0.2942 cents 234:241:260:281:289:312:325:347:361:390:416:433:468 SD: 0.2670 cents 270:278:300:324:333:360:375:400:417:450:480:500:540 SD: 0.2178 cents 306:315:340:367:378:408:425:453:472:510:544:567:612 SD: 0.2089 cents 324:333:360:389:400:432:450:480:500:540:576:600:648 SD: 0.1623 cents 414:426:460:497:511:552:575:613:639:690:736:767:828 SD: 0.1253 cents 486:500:540:583:600:648:675:720:750:810:864:900:972 SD: 0.0495 cents