Scala analysis: xen12-wilson-40-5C3-dekany-03
1-3-7-9-11 5C3 Dekany, Figure 40
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: 33/28 284.447037 undecimal minor third 4: 9/7 435.084095 septimal major third, BP third 5: 11/8 551.317942 undecimal semi-augmented fourth 6: 3/2 701.955001 perfect fifth 7: 11/7 782.492036 undecimal augmented fifth 8: 99/56 986.402038 9: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-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: 22/21 80.5370 undecimal minor semitone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 77/72 116.2338 undecimal secor 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 22/21 80.5370 undecimal minor semitone 8: 9/8 203.9100 major whole tone 9: 28/27 62.9609 Archytas' 1/3-tone 10: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 77/72 116.234 cents undecimal secor 1: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 2: 2 9/8 203.910 cents major whole tone 2: 1 112/99 213.598 cents 2: 3 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 33/28 284.447 cents undecimal minor third 3: 1 7/6 266.871 cents septimal minor third 3: 1 33/28 284.447 cents undecimal minor third 3: 3 11/9 347.408 cents undecimal neutral third 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 96/77 381.811 cents 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 4: 1 14/11 417.508 cents undecimal diminished fourth or major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 21/16 470.781 cents narrow fourth 4: 5 4/3 498.045 cents perfect fourth 4: 1 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 4/3 498.045 cents perfect fourth 5: 2 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 88/63 578.582 cents 5: 1 108/77 585.721 cents 5: 1 77/54 614.279 cents 5: 1 63/44 621.418 cents 5: 2 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 3/2 701.955 cents perfect fifth 6: 1 16/11 648.682 cents undecimal semi-diminished fifth 6: 5 3/2 701.955 cents perfect fifth 6: 1 32/21 729.219 cents wide fifth 6: 2 14/9 764.916 cents septimal minor sixth 6: 1 11/7 782.492 cents undecimal augmented fifth 7: 1 14/9 764.916 cents septimal minor sixth 7: 2 11/7 782.492 cents undecimal augmented fifth 7: 1 77/48 818.189 cents 7: 1 44/27 845.453 cents neutral sixth 7: 3 18/11 852.592 cents undecimal neutral sixth 7: 1 56/33 915.553 cents 7: 1 12/7 933.129 cents septimal major sixth 8: 1 56/33 915.553 cents 8: 3 12/7 933.129 cents septimal major sixth 8: 3 7/4 968.826 cents harmonic seventh 8: 1 99/56 986.402 cents 8: 2 16/9 996.090 cents Pythagorean minor seventh 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 1 144/77 1083.766 cents 9: 2 21/11 1119.463 cents undecimal major seventh 9: 1 27/14 1137.039 cents septimal major seventh 9: 1 64/33 1146.727 cents 33rd subharmonic Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 53.3 203.9 284.4 435.1 551.3 702.0 782.5 986.4 1049.4 1200.0 53.3 : 150.6 231.2 381.8 498.0 648.7 729.2 933.1 996.1 1146.7 1200.0 203.9 : 80.5 231.2 347.4 498.0 578.6 782.5 845.5 996.1 1049.4 1200.0 284.4 : 150.6 266.9 417.5 498.0 702.0 764.9 915.6 968.8 1119.5 1200.0 435.1 : 116.2 266.9 347.4 551.3 614.3 764.9 818.2 968.8 1049.4 1200.0 551.3 : 150.6 231.2 435.1 498.0 648.7 702.0 852.6 933.1 1083.8 1200.0 702.0 : 80.5 284.4 347.4 498.0 551.3 702.0 782.5 933.1 1049.4 1200.0 782.5 : 203.9 266.9 417.5 470.8 621.4 702.0 852.6 968.8 1119.5 1200.0 986.4 : 63.0 213.6 266.9 417.5 498.0 648.7 764.9 915.6 996.1 1200.0 1049.4: 150.6 203.9 354.5 435.1 585.7 702.0 852.6 933.1 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 203.9100 cents 12/11, 150.6371 cents 33/32, 53.2729 cents 2: 203.9100 .. 284.4470 cents 22/21, 80.5370 cents 1/1, 0.0000 cents 3: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 4: 417.5080 .. 551.3179 cents 121/112, 133.8100 cents 98/99,-17.5761 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 32/33,-53.2729 cents 6: 648.6821 .. 782.4920 cents 121/112, 133.8100 cents 32/33,-53.2729 cents 7: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 8: 915.5530 .. 996.0900 cents 22/21, 80.5370 cents 98/99,-17.5761 cents 9: 996.0900 .. 1146.7271 cents 12/11, 150.6371 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 2.252551 Largest / Average step : 1.699250 Largest / Smallest step : 3.827647 Median interval of one step : 133.43545 cents, amount: 0 Most common interval of one step : 12/11, 150.6371 cents, amount: 4 Least squares average step : 116.45719 cents, oct.: 1164.57187 cents Scale is not proper Step pattern alph. order: ABCBDBCEFB Step pattern size order : AECEDECFBE Scale is not a Constant Structure Scale diversity : 1.497083 Lumma stability : 0.088788 Lumma impropriety factor : 0.147375 Rothenberg efficiency : 0.343571 redundancy: 0.656429 Efficiency x scale size : 3.435714 Number of different interval sizes : 40 = 4.44444 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 6.00000 = 6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 6, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 10.0000% 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 : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.023547 Average absolute harmonicity : 0.168090 Specific harmonicity : 0.108024 Fundamental : 1/672, -9.3923 octaves, 0.3893 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.330560E+05, 17.02167 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 188.0, average 18.80000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.54245, average 1.05424 Sum of Tenney's harmonic distance : 20.11953, average 2.01195 Vogel's harmonic complexity : 19.50000 Wille's k value : 346 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 158.62985, average 2.88418 Lattice compactness (without 2's) : 90.11134, average 1.63839 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.70000 19 1 3: -1 .. 2 0.80000 10 2 7: -1 .. 0 -0.40000 4 1 11: 0 .. 1 0.60000 6 6 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 20 / 10 = 2.00000
FIT/MODE
10: 0 1 1 1 1 1 1 2 0 2 N T3 SD: 67.4990 c. M: 101.9550 c. 11: 0 2 0 2 1 1 1 2 0 2 N SD: 38.2822 c. M: 67.5448 c. 12: 1 1 1 2 1 1 1 2 1 1 P D3 SD: 34.7620 c. M:-64.9159 c. 14: 0 2 1 2 1 2 1 2 1 2 P D3 SD: 29.6091 c. M: 53.2729 c. 16: 1 2 1 2 1 2 1 3 1 2 P D3 SD: 19.9664 c. M: 32.4920 c. 17: 1 2 1 2 2 2 1 3 1 2 N SD: 9.0730 c. M:-17.3153 c. 31: 1 4 2 4 3 4 2 5 2 4 N SD: 10.6621 c. M: 18.6601 c. 33: 1 5 2 4 3 4 3 5 2 4 N SD: 10.2166 c. M:-17.5080 c. 38: 2 4 3 5 3 5 3 6 2 5 N SD: 8.7984 c. M: 14.4758 c. 39: 2 5 2 5 4 5 2 7 2 5 N SD: 7.0984 c. M: 13.2613 c. 41: 2 5 3 5 4 5 3 7 2 5 N SD: 5.3820 c. M:-8.7199 c. 46: 2 6 3 6 4 6 3 8 2 6 N SD: 4.2127 c. M:-8.3942 c. 63: 3 8 4 8 6 8 4 11 3 8 N SD: 2.9696 c. M:-5.6138 c. 72: 3 9 5 9 7 9 5 12 4 9 N SD: 2.1540 c. M: 3.9100 c. 89: 4 11 6 11 9 11 6 15 5 11 N SD: 1.7634 c. M: 3.6234 c. 113: 5 14 8 14 11 14 8 19 6 14 N SD: 1.6846 c. M:-3.3487 c. 118: 5 15 8 15 11 15 8 20 6 15 N SD: 1.4072 c. M: 2.4255 c. 135: 6 17 9 17 13 17 9 23 7 17 N SD: 0.3152 c. M:-0.5344 c. 342: 15 43 23 43 33 43 23 58 18 43 N SD: 0.3336 c. M: 0.6414 c. 359: 16 45 24 45 35 45 24 61 19 45 N SD: 0.2737 c. M: 0.5437 c. 477: 21 60 32 60 46 60 32 81 25 60 N SD: 0.2384 c. M: 0.4428 c. 494: 22 62 33 62 48 62 33 84 26 62 N SD: 0.1765 c. M: 0.3058 c. 629: 28 79 42 79 61 79 42 107 33 79 N SD: 0.1522 c. M: 0.2981 c. 742: 33 93 50 93 72 93 50 126 39 93 N SD: 0.1524 c. M:-0.2573 c. 836: 37 105 56 105 81 105 56 142 44 105 N SD: 0.1587 c. M: 0.2776 c. 877: 39 110 59 110 85 110 59 149 46 110 N SD: 0.1071 c. M:-0.1762 c. 1012: 45 127 68 127 98 127 68 172 53 127 N SD: 0.0910 c. M:-0.1592 c. 1219: 54 153 82 153 118 153 82 207 64 153 N SD: 0.0749 c. M: 0.1364 c. 1354: 60 170 91 170 131 170 91 230 71 170 N SD: 0.0577 c. M: 0.0972 c. 1506: 67 189 101 189 146 189 101 256 79 189 N SD: 0.0558 c. M:-0.1135 c. 1713: 76 215 115 215 166 215 115 291 90 215 N SD: 0.0376 c. M: 0.0623 c. 1848: 82 232 124 232 179 232 124 314 97 232 N SD: 0.0221 c. M: 0.0384 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x x 4 x 5 x x 6 S SD: 38.3186 cents 4 x x x 5 x 6 x 7 x 8 S SD: 12.9602 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 12.4777 cents 6 x x 7 x 8:9 x x 11:12 SD: 11.2195 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 13.1388 cents 8 x 9 x 10:11:12:13:14:15:16 S SD: 10.8752 cents 9 x 10:11 x 12 x 14:16:17:18 S SD: 14.5255 cents 10 x 11:12:13:14:15:16:18 x 20 S SD: 9.4967 cents 11 x 12:13:14:15 x 17:19:20:22 SD: 9.7079 cents 12 x x 14:15:17:18:19:21:22:24 SD: 9.5510 cents 13:14 x 15:17:18 x 20:23:24:26 SD: 12.1690 cents 14:15:16:17:18:19:21:22:25:26:28 SD: 9.5429 cents 16:17:18:19:21:22:24:25:28:29:32 SD: 7.0098 cents 17:18:19:20:22:23:26:27:30:31:34 SD: 6.8567 cents 18:19:20:21:23:25:27:28:32:33:36 SD: 5.6731 cents 21:22:24:25:27:29:32:33:37:39:42 SD: 5.5873 cents 22:23:25:26:28:30:33:35:39:40:44 SD: 4.5670 cents 24:25:27:28:31:33:36:38:42:44:48 SD: 3.3989 cents 30:31:34:35:39:41:45:47:53:55:60 SD: 3.1465 cents 32:33:36:38:41:44:48:50:57:59:64 SD: 2.3900 cents 38:39:43:45:49:52:57:60:67:70:76 SD: 2.2168 cents 40:41:45:47:51:55:60:63:71:73:80 SD: 2.1786 cents 54:56:61:64:69:74:81:85:95:99:108 SD: 2.1610 cents 55:57:62:65:71:76:83:86:97:101:110 SD: 2.0954 cents 56:58:63:66:72:77:84:88:99:103:112 SD: 0.9350 cents 94:97:106:111:121:129:141:148:166:172:188 SD: 0.8394 cents 96:99:108:113:123:132:144:151:170:176:192 SD: 0.7226 cents 128:132:144:151:165:176:192:201:226:235:256 SD: 0.5941 cents 150:155:169:177:193:206:225:236:265:275:300 SD: 0.5915 cents 152:157:171:179:195:209:228:239:269:279:304 SD: 0.5719 cents 158:163:178:186:203:217:237:248:279:290:316 SD: 0.5263 cents 168:173:189:198:216:231:252:264:297:308:336 SD: 0.2500 cents 224:231:252:264:288:308:336:352:396:411:448 SD: 0.1405 cents 392:404:441:462:504:539:588:616:693:719:784 SD: 0.1338 cents 448:462:504:528:576:616:672:704:792:821:896 SD: 0.0703 cents