Scala analysis: syndie1
First Syndie scale ~ sauveur_ji.scl
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 27/20 519.551289 acute fourth 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 25/16 772.627428 classic augmented fifth 9: 27/16 905.865003 Pythagorean major sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 135/128 92.1787 major chroma, major limma 2: 16/15 111.7313 minor diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 135/128 92.179 cents major chroma, major limma 1: 5 16/15 111.731 cents minor diatonic semitone 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 5 10/9 182.404 cents minor whole tone 2: 5 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 144/125 244.969 cents classic diminished third 3: 1 125/108 253.076 cents semi-augmented whole tone 3: 2 75/64 274.582 cents classic augmented second 3: 2 32/27 294.135 cents Pythagorean minor third 3: 7 6/5 315.641 cents minor third 4: 8 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 5: 1 125/96 456.986 cents classic augmented third 5: 8 4/3 498.045 cents perfect fourth 5: 3 27/20 519.551 cents acute fourth 6: 3 25/18 568.717 cents classic augmented fourth 6: 3 45/32 590.224 cents diatonic tritone 6: 3 64/45 609.776 cents 2nd tritone 6: 3 36/25 631.283 cents classic diminished fifth 7: 3 40/27 680.449 cents grave fifth 7: 8 3/2 701.955 cents perfect fifth 7: 1 192/125 743.014 cents classic diminished sixth 8: 4 25/16 772.627 cents classic augmented fifth 8: 8 8/5 813.686 cents minor sixth 9: 7 5/3 884.359 cents major sixth, BP sixth 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 2 128/75 925.418 cents diminished seventh 9: 1 216/125 946.924 cents semi-augmented sixth 10: 1 125/72 955.031 cents classic augmented sixth 10: 1 225/128 976.537 cents augmented sixth 10: 5 16/9 996.090 cents Pythagorean minor seventh 10: 5 9/5 1017.596 cents just minor seventh, BP seventh 11: 2 50/27 1066.762 cents grave major seventh 11: 5 15/8 1088.269 cents classic major seventh 11: 1 256/135 1107.821 cents octave - major chroma 11: 4 48/25 1129.328 cents classic diminished octave 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 : 92.2 203.9 315.6 386.3 519.6 590.2 702.0 772.6 905.9 1017.6 1088.3 1200.0 92.2 : 111.7 223.5 294.1 427.4 498.0 609.8 680.4 813.7 925.4 996.1 1107.8 1200.0 203.9 : 111.7 182.4 315.6 386.3 498.0 568.7 702.0 813.7 884.4 996.1 1088.3 1200.0 315.6 : 70.7 203.9 274.6 386.3 457.0 590.2 702.0 772.6 884.4 976.5 1088.3 1200.0 386.3 : 133.2 203.9 315.6 386.3 519.6 631.3 702.0 813.7 905.9 1017.6 1129.3 1200.0 519.6 : 70.7 182.4 253.1 386.3 498.0 568.7 680.4 772.6 884.4 996.1 1066.8 1200.0 590.2 : 111.7 182.4 315.6 427.4 498.0 609.8 702.0 813.7 925.4 996.1 1129.3 1200.0 702.0 : 70.7 203.9 315.6 386.3 498.0 590.2 702.0 813.7 884.4 1017.6 1088.3 1200.0 772.6 : 133.2 245.0 315.6 427.4 519.6 631.3 743.0 813.7 946.9 1017.6 1129.3 1200.0 905.9 : 111.7 182.4 294.1 386.3 498.0 609.8 680.4 813.7 884.4 996.1 1066.8 1200.0 1017.6: 70.7 182.4 274.6 386.3 498.0 568.7 702.0 772.6 884.4 955.0 1088.3 1200.0 1088.3: 111.7 203.9 315.6 427.4 498.0 631.3 702.0 813.7 884.4 1017.6 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 133.2376 cents 648/625, 62.5651 cents 25/24, 70.6724 cents 2: 182.4037 .. 244.9689 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 3: 253.0761 .. 315.6413 cents 648/625, 62.5651 cents 15625/15552, 8.1073 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 456.9861 .. 519.5513 cents 648/625, 62.5651 cents 3125/3072, 29.6136 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 7: 680.4487 .. 743.0139 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 3125/3072, 29.6136 cents 9: 884.3587 .. 946.9239 cents 648/625, 62.5651 cents 25/24, 70.6724 cents 10: 955.0311 .. 1017.5963 cents 648/625, 62.5651 cents 15625/15552, 8.1073 cents 11: 1066.7624 .. 1129.3276 cents 648/625, 62.5651 cents 250/243, 49.1661 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 27/25, 133.2376 cents Average / Smallest step : 1.414979 Largest / Average step : 1.332376 Largest / Smallest step : 1.885284 Median interval of one step : 16/15, 111.7313 cents, amount: 5 Most common interval of one step : 16/15, 111.7313 cents, amount: 5 Least squares average step : 99.88567 cents, oct.: 1198.62802 cents Scale is strictly proper Step pattern alph. order: ABBCDCBCDBCB Step pattern size order : BCCADACADCAC Scale is a Constant Structure, by a margin of 8.10728 cents Scale diversity : 1.365796 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.462330 Rothenberg efficiency : 0.387296 redundancy: 0.612704 Efficiency x scale size : 4.647547 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 15625/15552, 8.1073 cents Number of recognisable fifths : 8, average 701.9550 cents Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 8 and 9 combined -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 135 Scale harmonicity : 0.028409 Average absolute harmonicity : 0.174128 Specific harmonicity : 0.163316 Fundamental : 1/640, -9.3219 octaves, 0.4088 Hz. Guide tone : 1350, 10.3987 octaves, 353194.513 Hz. Exponens Consonantiae : 8.640000E+05, 19.72067 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 276.5, average 23.04167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.00385, average 1.08365 Sum of Tenney's harmonic distance : 24.81290, average 2.06774 Vogel's harmonic complexity : 15.33333 Wille's k value : 337 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 284.21831, average 3.64382 Lattice compactness (without 2's) : 153.08502, average 1.96263 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -2.41667 33 1 3: 0 .. 3 1.50000 18 3 5: -1 .. 2 0.25000 9 8 Average exponent except 2's : 21 / 12 = 1.75000 Average absolute exponent except 2's: 27 / 12 = 2.25000 Scale is weakly epimorphic with val: <12 17 28| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 21 28|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.6045 c. M:-27.3726 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 15.2347 c. M: 29.0208 c. Meantone Chromatic (1/3-comma) 22: 2 2 2 1 3 1 2 1 3 2 1 2 N D3 SD: 14.0268 c. M:-25.9033 c. 24: 2 2 2 2 2 2 2 1 3 2 2 2 P T3 SD: 12.8573 c. M: 22.6274 c. 25: 2 2 3 1 3 1 3 1 3 2 2 2 P D3 SD: 11.4536 c. M:-20.3587 c. 26: 2 2 3 1 3 2 2 2 3 2 2 2 P D3 SD: 12.4861 c. M:-19.4236 c. 28: 2 3 2 2 3 2 2 2 3 3 1 3 P D3 SD: 10.0888 c. M: 16.8401 c. 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 9.7214 c. M: 16.3255 c. Meantone Chromatic (53/220-comma) 34: 3 3 3 2 4 2 3 2 4 3 2 3 P D3 SD: 7.5742 c. M:-13.7036 c. 39: 3 4 3 3 4 2 4 2 4 4 2 4 P SD: 8.1032 c. M:-13.6863 c. 40: 3 4 4 2 4 3 3 3 4 4 2 4 P SD: 7.9279 c. M:-14.3587 c. 41: 3 4 4 2 5 2 4 2 5 4 2 4 N SD: 5.6509 c. M: 11.6518 c. 49: 4 4 5 3 5 3 5 3 5 5 2 5 SP SD: 7.0385 c. M:-11.0460 c. 53: 4 5 5 3 6 3 5 3 6 5 3 5 P SD: 1.3541 c. M: 2.8161 c. 65: 5 6 6 4 7 4 6 4 7 6 4 6 SP SD: 1.5328 c. M:-2.7572 c. 118: 9 11 11 7 13 7 11 7 13 11 7 11 SP SD: 0.5015 c. M: 0.9072 c. 171: 13 16 16 10 19 10 16 10 19 16 10 16 SP SD: 0.5024 c. M: 0.9506 c. 289: 22 27 27 17 32 17 27 17 32 27 17 27 SP SD: 0.4460 c. M: 0.8292 c. 323: 25 30 30 19 36 19 30 19 36 30 19 30 SP SD: 0.4017 c. M:-0.7005 c. 376: 29 35 35 22 42 22 35 22 42 35 22 35 SP SD: 0.3510 c. M:-0.6615 c. 388: 30 36 36 23 43 23 36 23 43 36 23 36 SP SD: 0.3377 c. M:-0.6048 c. 441: 34 41 41 26 49 26 41 26 49 41 26 41 SP SD: 0.1782 c. M:-0.3383 c. 494: 38 46 46 29 55 29 46 29 55 46 29 46 SP SD: 0.1500 c. M:-0.2868 c. 559: 43 52 52 33 62 33 52 33 62 52 33 52 SP SD: 0.0900 c. M:-0.1812 c. 612: 47 57 57 36 68 36 57 36 68 57 36 57 SP SD: 0.0391 c. M: 0.0784 c. 1171: 90 109 109 69 130 69 109 69 130 109 69 109 SP SD: 0.0277 c. M:-0.0501 c. 1783: 137 166 166 105 198 105 166 105 198 166 105 166 SP SD: 0.0150 c. M:-0.0254 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: 10.1382 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: 8.3554 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.9452 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.0816 cents 8 x 9 x 10:11 x 12 x x 14:15:16 S SD: 8.3148 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.0387 cents 10 x 11:12 x x 14:15:16:17:18:19:20 S SD: 6.9815 cents 11 x 12:13:14:15 x x 17:19:20:21:22 SD: 9.9848 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 8.4316 cents 13:14:15 x 16 x 18 x 20:22:23:24:26 S SD: 9.3114 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.6756 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 5.1261 cents 16:17:18:19:20:22:23:24:25:27:29:30:32 SD: 4.6341 cents 20:21:23:24:25:27:28:30:31:34:36:38:40 SD: 4.1241 cents 24:25:27:29:30:32:34:36:38:41:43:45:48 SD: 3.9734 cents 25:26:28:30:31:34:35:38:39:42:45:47:50 SD: 3.4148 cents 31:33:35:37:39:42:44:47:48:52:56:58:62 SD: 3.2840 cents 32:34:36:38:40:43:45:48:50:54:58:60:64 SD: 2.2047 cents 39:41:44:47:49:53:55:59:61:66:70:73:78 SD: 2.0784 cents 40:42:45:48:50:54:56:60:63:68:72:75:80 SD: 1.8114 cents 54:57:61:65:68:73:76:81:84:91:97:101:108 SD: 1.5548 cents 55:58:62:66:69:74:77:83:86:93:99:103:110 SD: 1.3767 cents 64:68:72:77:80:86:90:96:100:108:115:120:128 SD: 1.3362 cents 71:75:80:85:89:96:100:107:111:120:128:133:142 SD: 1.0328 cents 80:84:90:96:100:108:113:120:125:135:144:150:160 SD: 0.9068 cents 89:94:100:107:111:120:125:134:139:150:160:167:178 SD: 0.8300 cents 96:101:108:115:120:130:135:144:150:162:173:180:192 SD: 0.6446 cents 128:135:144:154:160:173:180:192:200:216:230:240:256 SD: 0.4811 cents 160:169:180:192:200:216:225:240:250:270:288:300:320 SD: 0.2136 cents 256:270:288:307:320:346:360:384:400:432:461:480:512 SD: 0.2015 cents 352:371:396:422:440:475:495:528:550:594:634:660:704 SD: 0.2003 cents 384:405:432:461:480:518:540:576:600:648:691:720:768 SD: 0.1344 cents 480:506:540:576:600:648:675:720:750:810:864:900:960 SD: 0.0713 cents