Scala analysis: ragisyn5
Ragisyn 6561/6250 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: 1000/729 547.211136 7: 40/27 680.448711 grave 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: 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: 250/243 49.1661 maximal diesis, Porcupine comma 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 4 250/243 49.166 cents maximal diesis, Porcupine comma 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 7 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 8 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 2 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 2 2500/2187 231.570 cents 3: 1 125/108 253.076 cents semi-augmented whole tone 3: 7 6/5 315.641 cents minor third 3: 2 243/200 337.148 cents acute minor third 4: 5 100/81 364.807 cents grave major third 4: 3 5/4 386.314 cents major third 4: 3 162/125 448.879 cents 4: 1 6561/5000 470.385 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: 2 1000/729 547.211 cents 6: 4 25/18 568.717 cents classic augmented fourth 6: 4 36/25 631.283 cents classic diminished fifth 6: 2 729/500 652.789 cents 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: 1 10000/6561 729.615 cents two (grave major third) 8: 3 125/81 751.121 cents 8: 3 8/5 813.686 cents minor sixth 8: 5 81/50 835.193 cents acute minor sixth 9: 2 400/243 862.852 cents grave major sixth 9: 7 5/3 884.359 cents major sixth, BP sixth 9: 1 216/125 946.924 cents semi-augmented sixth 9: 2 2187/1250 968.430 cents 10: 2 1250/729 933.525 cents 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 8 9/5 1017.596 cents just minor seventh, BP seventh 11: 7 50/27 1066.762 cents grave major seventh 11: 1 48/25 1129.328 cents classic diminished octave 11: 4 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 49.2 182.4 315.6 364.8 498.0 547.2 680.4 751.1 884.4 1017.6 1066.8 1200.0 49.2 : 133.2 266.5 315.6 448.9 498.0 631.3 702.0 835.2 968.4 1017.6 1150.8 1200.0 182.4 : 133.2 182.4 315.6 364.8 498.0 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 315.6 : 49.2 182.4 231.6 364.8 435.5 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 364.8 : 133.2 182.4 315.6 386.3 519.6 652.8 702.0 835.2 884.4 1017.6 1150.8 1200.0 498.0 : 49.2 182.4 253.1 386.3 519.6 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 547.2 : 133.2 203.9 337.1 470.4 519.6 652.8 702.0 835.2 968.4 1017.6 1150.8 1200.0 680.4 : 70.7 203.9 337.1 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 751.1 : 133.2 266.5 315.6 448.9 498.0 631.3 764.5 813.7 946.9 996.1 1129.3 1200.0 884.4 : 133.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 862.9 996.1 1066.8 1200.0 1017.6: 49.2 182.4 231.6 364.8 498.0 547.2 680.4 729.6 862.9 933.5 1066.8 1200.0 1066.8: 133.2 182.4 315.6 448.9 498.0 631.3 680.4 813.7 884.4 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: 231.5698 .. 337.1476 cents 531441/500000, 105.5777 cents 1562500/1594323,-34.9053 cents 4: 364.8074 .. 470.3852 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 5: 435.4799 .. 519.5513 cents 6561/6250, 84.0714 cents 1562500/1594323,-34.9053 cents 6: 547.2111 .. 652.7889 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 7: 680.4487 .. 764.5201 cents 6561/6250, 84.0714 cents 20000/19683, 27.6598 cents 8: 729.6148 .. 835.1926 cents 531441/500000, 105.5777 cents 1562500/1594323,-34.9053 cents 9: 862.8524 .. 968.4302 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 10: 933.5249 .. 1017.5963 cents 6561/6250, 84.0714 cents 1562500/1594323,-34.9053 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 : 27/25, 133.2376 cents, amount: 7 Most common interval of one step : 27/25, 133.2376 cents, amount: 7 Least squares average step : 97.90047 cents, oct.: 1174.80567 cents Scale is not proper Step pattern alph. order: ABBABABCBBAB Step pattern size order : SLLSLSLMLLSL Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.391857 Lumma stability : 0.256087 Lumma impropriety factor : 0.116351 Rothenberg efficiency : 0.377447 redundancy: 0.622553 Efficiency x scale size : 4.529365 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 78732/78125, 13.3990 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 8 Most common triad is 0.0 182.404 1017.596 cents, amount: 5 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 : 5 = 41.6667% Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 5 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 729 Scale harmonicity : 0.020027 Average absolute harmonicity : 0.151647 Specific harmonicity : 0.110016 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 9000, 13.1357 octaves, 2354630.088 Hz. Exponens Consonantiae : 3.280500E+07, 24.96741 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 1407.5, average 117.29167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.90000, average 1.32500 Sum of Tenney's harmonic distance : 32.36479, average 2.69707 Vogel's harmonic complexity : 23.58333 Wille's k value : 3280 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 12 Triangular lattice diameter : 8 Lattice compactness : 294.97324, average 3.78171 Lattice compactness (without 2's) : 265.31345, average 3.40145 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.25000 15 1 3: -6 .. 2 -2.16667 32 1 5: -1 .. 3 1.16667 18 10 Average exponent except 2's :-12 / 12 =-1.00000 Average absolute exponent except 2's: 50 / 12 = 4.16667 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 0 1 2 0 1 1 1 1 1 2 0 2 N T3 SD: 62.2245 c. M: 98.0450 c. 13: 1 1 1 1 1 1 1 1 2 1 1 1 P M ME SD: 27.8046 c. M:-43.1416 c. 14: 1 1 2 0 2 0 2 1 1 2 0 2 N D3 SD: 23.7810 c. M: 38.1910 c. 16: 1 1 2 1 2 0 2 1 2 2 0 2 N SD: 20.1916 c. M: 32.4037 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 10.3908 c. M:-21.2099 c. Meantone Chromatic (1/3-comma) 24: 1 3 2 1 3 1 3 1 3 2 1 3 P T3 SD: 12.9248 c. M:-19.5513 c. 26: 1 3 3 1 3 1 3 1 3 3 1 3 N M DE SD: 7.1547 c. M: 12.6596 c. Meantone Chromatic (4/9-comma) 27: 1 3 3 1 3 1 3 2 3 3 1 3 N SD: 7.5154 c. M: 13.8778 c. 39: 2 4 4 2 4 2 4 2 5 4 2 4 N SD: 7.4256 c. M: 12.6596 c. 42: 2 4 5 2 4 2 5 2 5 5 1 5 N SD: 7.7007 c. M: 12.3307 c. 45: 2 5 5 2 5 2 5 2 5 5 2 5 N M DE SD: 7.0009 c. M:-12.8846 c. Meantone Chromatic (2/5-comma) 46: 2 5 5 2 5 2 5 3 5 5 2 5 N SD: 2.4274 c. M:-5.4006 c. 53: 2 6 6 2 6 2 6 3 6 6 2 6 N SD: 2.3596 c. M: 3.9513 c. 72: 3 8 8 3 8 3 8 4 8 8 3 8 N SD: 1.5591 c. M:-2.8846 c. 99: 4 11 11 4 11 4 11 6 11 11 4 11 N SD: 0.9204 c. M: 1.7566 c. 171: 7 19 19 7 19 7 19 10 19 19 7 19 N SD: 0.1472 c. M:-0.2530 c. 441: 18 49 49 18 49 18 49 26 49 49 18 49 N SD: 0.1343 c. M: 0.2724 c. 559: 23 62 62 23 62 23 62 33 62 62 23 62 N SD: 0.1260 c. M:-0.2205 c. 612: 25 68 68 25 68 25 68 36 68 68 25 68 N SD: 0.0896 c. M: 0.1523 c. 783: 32 87 87 32 87 32 87 46 87 87 32 87 N SD: 0.0785 c. M: 0.1633 c. 829: 34 92 92 34 92 34 92 49 92 92 34 92 N SD: 0.0740 c. M:-0.1454 c. 901: 37 100 100 37 100 37 100 53 100 100 37 100 N SD: 0.0880 c. M:-0.1807 c. 954: 39 106 106 39 106 39 106 56 106 106 39 106 N SD: 0.0799 c. M: 0.1777 c. 1000: 41 111 111 41 111 41 111 59 111 111 41 111 N SD: 0.0374 c. M:-0.0789 c. 1171: 48 130 130 48 130 48 130 69 130 130 48 130 N SD: 0.0148 c. M:-0.0317 c. 1342: 55 149 149 55 149 55 149 79 149 149 55 149 N SD: 0.0161 c. M:-0.0318 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: 14.3692 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 14.3674 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 x 10:11:12 x 13:14 S SD: 16.7172 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.8160 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 7.0729 cents 10 x 11:12 x 13:14:15 x 17:18:19:20 SD: 9.3509 cents 11 x 12:13:14 x 15:16:17:18:20 x 22 S SD: 9.2414 cents 12 x 13:14:15:16 x 18:19:20 x 22:24 S SD: 9.6239 cents 13 x 14 x 16:17:18:19:20:22:23:24:26 S SD: 8.0899 cents 14 x 16:17 x x 19:21:22:23:25:26:28 SD: 8.1826 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 7.8736 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 7.0316 cents 17:18:19:20:21 x 23:25:26:28:31 x 34 SD: 7.5230 cents 18:19:20 x 22:24:25:27:28:30:32:33:36 SD: 5.8620 cents 19:20:21:23 x 25:26:28:29:32:34:35:38 SD: 5.2917 cents 20:21:22:24:25:27 x 30:31:33:36:37:40 SD: 5.2223 cents 21:22:23:25:26:28:29:31:32:35:38:39:42 SD: 4.2324 cents 23:24:26 x 28:31:32:34:35:38:41:43:46 SD: 6.0418 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 4.0661 cents 25:26:28:30:31:33:34:37:39:42:45:46:50 SD: 3.5268 cents 26:27:29:31:32:35:36:39:40:43:47:48:52 SD: 3.4828 cents 27:28:30:32:33:36:37:40:42:45:49:50:54 SD: 3.0621 cents 29:30:32:35:36:39:40:43:45:48:52:54:58 SD: 2.7719 cents 30:31:33:36:37:40:41:44:46:50:54:56:60 SD: 2.6631 cents 33:34:37:40:41:44:45:49:51:55:59:61:66 SD: 2.5671 cents 35:36:39:42:43:47:48:52:54:58:63:65:70 SD: 1.6562 cents 54:56:60:65:67:72:74:80:83:90:97:100:108 SD: 1.5749 cents 60:62:67:72:74:80:82:89:93:100:108:111:120 SD: 1.2963 cents 64:66:71:77:79:85:88:95:99:107:115:119:128 SD: 1.2447 cents 69:71:77:83:85:92:95:102:106:115:124:128:138 SD: 1.2403 cents 70:72:78:84:86:93:96:104:108:117:126:130:140 SD: 1.2003 cents 72:74:80:86:89:96:99:107:111:120:130:133:144 SD: 1.0817 cents 75:77:83:90:93:100:103:111:116:125:135:139:150 SD: 0.9960 cents 81:83:90:97:100:108:111:120:125:135:146:150:162 SD: 0.6947 cents 99:102:110:119:122:132:136:147:153:165:178:183:198 SD: 0.6798 cents 110:113:122:132:136:147:151:163:170:183:198:204:220 SD: 0.6597 cents 129:133:143:155:159:172:177:191:199:215:232:239:258 SD: 0.5737 cents 135:139:150:162:167:180:185:200:208:225:243:250:270 SD: 0.4130 cents 170:175:189:204:210:227:233:252:262:283:306:315:340 SD: 0.4009 cents 180:185:200:216:222:240:247:267:278:300:324:333:360 SD: 0.3329 cents 210:216:233:252:259:280:288:311:324:350:378:389:420 SD: 0.2664 cents 270:278:300:324:333:360:370:400:417:450:486:500:540 SD: 0.2613 cents 285:293:317:342:352:380:391:422:440:475:513:528:570 SD: 0.2257 cents 315:324:350:378:389:420:432:467:486:525:567:583:630 SD: 0.1496 cents 414:426:460:497:511:552:568:613:639:690:745:767:828 SD: 0.1335 cents 486:500:540:583:600:648:667:720:750:810:875:900:972 SD: 0.0935 cents