Scala analysis: majsyn2
Second 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: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 10/9 182.403712 minor whole tone 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 25/18 568.717426 classic augmented fourth 7: 3/2 701.955001 perfect fifth 8: 125/81 751.121138 9: 5/3 884.358713 major sixth, BP sixth 10: 9/5 1017.596288 just minor seventh, BP 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 16/15 111.7313 minor diatonic semitone 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 250/243 49.1661 maximal diesis, Porcupine comma 9: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 10: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 11: 250/243 49.1661 maximal diesis, Porcupine comma 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 : 70.7 182.4 315.6 386.3 498.0 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 70.7 : 111.7 245.0 315.6 427.4 498.0 631.3 680.4 813.7 946.9 996.1 1129.3 1200.0 182.4 : 133.2 203.9 315.6 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1088.3 1200.0 315.6 : 70.7 182.4 253.1 386.3 435.5 568.7 702.0 751.1 884.4 955.0 1066.8 1200.0 386.3 : 111.7 182.4 315.6 364.8 498.0 631.3 680.4 813.7 884.4 996.1 1129.3 1200.0 498.0 : 70.7 203.9 253.1 386.3 519.6 568.7 702.0 772.6 884.4 1017.6 1088.3 1200.0 568.7 : 133.2 182.4 315.6 448.9 498.0 631.3 702.0 813.7 946.9 1017.6 1129.3 1200.0 702.0 : 49.2 182.4 315.6 364.8 498.0 568.7 680.4 813.7 884.4 996.1 1066.8 1200.0 751.1 : 133.2 266.5 315.6 448.9 519.6 631.3 764.5 835.2 946.9 1017.6 1150.8 1200.0 884.4 : 133.2 182.4 315.6 386.3 498.0 631.3 702.0 813.7 884.4 1017.6 1066.8 1200.0 1017.6: 49.2 182.4 253.1 364.8 498.0 568.7 680.4 751.1 884.4 933.5 1066.8 1200.0 1066.8: 133.2 203.9 315.6 448.9 519.6 631.3 702.0 835.2 884.4 1017.6 1150.8 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 : 98.49603 cents, oct.: 1181.95237 cents Scale is not proper Step pattern alph. order: ABCABACDCCDC Step pattern size order : BCDBCBDADDAD 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 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 58.3333% Scale is n-1 differentially coherent in interval classes 1 and 2 combined 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: 125 Scale harmonicity : 0.021459 Average absolute harmonicity : 0.180435 Specific harmonicity : 0.135257 Fundamental : 1/3240, -11.6618 octaves, 0.0807 Hz. Guide tone : 4500, 12.1357 octaves, 1177315.044 Hz. Exponens Consonantiae : 1.458000E+07, 23.79749 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 225.5, average 18.79167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.28379, average 0.94032 Sum of Tenney's harmonic distance : 22.28715, average 1.85726 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 : 254.61242, average 3.26426 Lattice compactness (without 2's) : 199.56108, average 2.55848 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.08333 13 1 3: -4 .. 2 -0.83333 18 2 5: -1 .. 3 0.83333 14 9 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 32 / 12 = 2.66667 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: 23.5161 c. M:-48.8789 c. Twelve-tone Chromatic (1/11-comma) 14: 1 1 2 1 1 1 1 1 1 2 1 1 P D3 I SD: 25.6763 c. M:-47.5233 c. 15: 1 1 2 1 1 1 2 0 2 2 0 2 N D3 SD: 17.6261 c. M: 31.1211 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 5.8369 c. M: 7.5145 c. Meantone Chromatic (1/3-comma) 34: 2 3 4 2 3 2 4 1 4 4 1 4 N SD: 4.9245 c. M: 9.9447 c. 46: 3 4 5 3 4 3 5 2 5 5 2 5 P SD: 3.7809 c. M:-7.5884 c. 53: 3 5 6 3 5 3 6 2 6 6 2 6 N SD: 1.9575 c. M: 3.9513 c. 72: 4 7 8 4 7 4 8 3 8 8 3 8 N SD: 1.8681 c. M: 4.0058 c. 99: 6 9 11 6 9 6 11 4 11 11 4 11 N SD: 0.9693 c. M:-2.0548 c. 118: 7 11 13 7 11 7 13 5 13 13 5 13 N SD: 0.6609 c. M:-1.4212 c. 152: 9 14 17 9 14 9 17 6 17 17 6 17 N SD: 0.6478 c. M: 1.1211 c. 171: 10 16 19 10 16 10 19 7 19 19 7 19 N SD: 0.2336 c. M: 0.4970 c. 270: 16 25 30 16 25 16 30 11 30 30 11 30 N SD: 0.2197 c. M:-0.4387 c. 289: 17 27 32 17 27 17 32 12 32 32 12 32 N SD: 0.2345 c. M:-0.4360 c. 422: 25 39 47 25 39 25 47 17 47 47 17 47 N SD: 0.3380 c. M:-0.4176 c. 441: 26 41 49 26 41 26 49 18 49 49 18 49 N SD: 0.0724 c. M: 0.1007 c. 612: 36 57 68 36 57 36 68 25 68 68 25 68 N SD: 0.0677 c. M: 0.1407 c. 730: 43 68 81 43 68 43 81 30 81 81 30 81 N SD: 0.0536 c. M:-0.1117 c. 901: 53 84 100 53 84 53 100 37 100 100 37 100 N SD: 0.0536 c. M: 0.0842 c. 1171: 69 109 130 69 109 69 130 48 130 130 48 130 N SD: 0.0194 c. M:-0.0364 c. 1342: 79 125 149 79 125 79 149 55 149 149 55 149 N SD: 0.0152 c. M: 0.0316 c. 1783: 105 166 198 105 166 105 198 73 198 198 73 198 N SD: 0.0130 c. M: 0.0275 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: 12.1926 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 12.8136 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.6302 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 14.6543 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.2934 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 6.6582 cents 10 x 11:12 x 13:14:15 x 17:18:19:20 SD: 8.2881 cents 11 x 12:13:14 x 15 x 17:18:20 x 22 SD: 8.8460 cents 12 x 13:14:15:16:17:18:19:20 x 22:24 S SD: 8.8048 cents 13 x 14 x 16:17:18 x 20:22:23:24:26 S SD: 8.9256 cents 14:15:16:17:18:19 x 21:22:23:25:26:28 SD: 9.2324 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 5.6708 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.6172 cents 17:18:19:20:21:23:24 x 26:28:31 x 34 SD: 7.1441 cents 18:19:20:22:23:24:25:27:28:30:32:33:36 SD: 5.2297 cents 19:20:21:23:24:25:26 x 29:32:34:35:38 SD: 5.0076 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.2375 cents 21:22:23:25:26:28:29 x 32:35:38:39:42 SD: 3.9297 cents 23:24:26:28:29:31:32 x 35:38:41:43:46 SD: 5.3595 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 2.9804 cents 28:29:31:34:35:37:39:42:43:47:50:52:56 SD: 2.9576 cents 36:38:40:43:45:48:50:54:56:60:65:67:72 SD: 2.4772 cents 44:46:49:53:55:59:61:66:68:73:79:81:88 SD: 1.6602 cents 54:56:60:65:68:72:75:81:83:90:97:100:108 SD: 1.4720 cents 64:67:71:77:80:85:89:96:99:107:115:119:128 SD: 1.3362 cents 70:73:78:84:88:93:97:105:108:117:126:130:140 SD: 1.2600 cents 72:75:80:86:90:96:100:108:111:120:130:133:144 SD: 0.8928 cents 90:94:100:108:113:120:125:135:139:150:162:167:180 SD: 0.8083 cents 96:100:107:115:120:128:133:144:148:160:173:178:192 SD: 0.6907 cents 100:104:111:120:125:133:139:150:154:167:180:185:200 SD: 0.6419 cents 116:121:129:139:145:155:161:174:179:193:209:215:232 SD: 0.5486 cents 120:125:133:144:150:160:167:180:185:200:216:222:240 SD: 0.5051 cents 144:150:160:173:180:192:200:216:222:240:259:267:288 SD: 0.3059 cents 216:225:240:259:270:288:300:324:333:360:389:400:432 SD: 0.1968 cents 360:375:400:432:450:480:500:540:556:600:648:667:720 SD: 0.1361 cents 460:479:511:552:575:613:639:690:710:767:828:852:920 SD: 0.1244 cents 504:525:560:605:630:672:700:756:778:840:907:933:1008 SD: 0.0874 cents 576:600:640:691:720:768:800:864:889:960:1037:1067:1152 SD: 0.0698 cents