Scala analysis: syndie2
Second Syndie scale = fogliano1.scl
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: 25/16 772.627428 classic augmented fifth 9: 5/3 884.358713 major sixth, BP sixth 10: 16/9 996.089998 Pythagorean minor 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: 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: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 16/15 111.7313 minor diatonic semitone 10: 16/15 111.7313 minor diatonic semitone 11: 135/128 92.1787 major chroma, major limma 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 : 70.7 182.4 315.6 386.3 498.0 568.7 702.0 772.6 884.4 996.1 1088.3 1200.0 70.7 : 111.7 245.0 315.6 427.4 498.0 631.3 702.0 813.7 925.4 1017.6 1129.3 1200.0 182.4 : 133.2 203.9 315.6 386.3 519.6 590.2 702.0 813.7 905.9 1017.6 1088.3 1200.0 315.6 : 70.7 182.4 253.1 386.3 457.0 568.7 680.4 772.6 884.4 955.0 1066.8 1200.0 386.3 : 111.7 182.4 315.6 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1129.3 1200.0 498.0 : 70.7 203.9 274.6 386.3 498.0 590.2 702.0 772.6 884.4 1017.6 1088.3 1200.0 568.7 : 133.2 203.9 315.6 427.4 519.6 631.3 702.0 813.7 946.9 1017.6 1129.3 1200.0 702.0 : 70.7 182.4 294.1 386.3 498.0 568.7 680.4 813.7 884.4 996.1 1066.8 1200.0 772.6 : 111.7 223.5 315.6 427.4 498.0 609.8 743.0 813.7 925.4 996.1 1129.3 1200.0 884.4 : 111.7 203.9 315.6 386.3 498.0 631.3 702.0 813.7 884.4 1017.6 1088.3 1200.0 996.1 : 92.2 203.9 274.6 386.3 519.6 590.2 702.0 772.6 905.9 976.5 1088.3 1200.0 1088.3: 111.7 182.4 294.1 427.4 498.0 609.8 680.4 813.7 884.4 996.1 1107.8 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 : 98.79381 cents, oct.: 1185.52573 cents Scale is strictly proper Step pattern alph. order: ABCABACABBDB Step pattern size order : ACDACADACCBC 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 41.6667% 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: 25 Scale harmonicity : 0.028409 Average absolute harmonicity : 0.187515 Specific harmonicity : 0.166404 Fundamental : 1/720, -9.4919 octaves, 0.3634 Hz. Guide tone : 1200, 10.2288 octaves, 313950.678 Hz. Exponens Consonantiae : 8.640000E+05, 19.72067 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 121.5, average 10.12500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.32955, average 0.86080 Sum of Tenney's harmonic distance : 20.33782, average 1.69482 Vogel's harmonic complexity : 16.83333 Wille's k value : 562 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 269.13595, average 3.45046 Lattice compactness (without 2's) : 149.00311, average 1.91030 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.41667 23 1 3: -2 .. 1 -0.50000 12 3 5: -1 .. 2 0.75000 11 8 Average exponent except 2's : 3 / 12 = 0.25000 Average absolute exponent except 2's: 23 / 12 = 1.91667 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: 17.6417 c. M:-31.2826 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 8.6757 c. M: 14.7327 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 6.8713 c. M:-11.9277 c. Meantone Chromatic (53/220-comma) 34: 2 3 4 2 3 2 4 2 3 3 3 3 P D3 SD: 4.1288 c. M: 7.8547 c. 53: 3 5 6 3 5 3 6 3 5 5 4 5 P SD: 1.6345 c. M: 2.8161 c. 118: 7 11 13 7 11 7 13 7 11 11 9 11 SP SD: 0.4169 c. M:-0.7741 c. 171: 10 16 19 10 16 10 19 10 16 16 13 16 SP SD: 0.3574 c. M: 0.6976 c. 289: 17 27 32 17 27 17 32 17 27 27 22 27 SP SD: 0.2399 c. M:-0.4498 c. 323: 19 30 36 19 30 19 36 19 30 30 25 30 SP SD: 0.2301 c. M: 0.4244 c. 441: 26 41 49 26 41 26 49 26 41 41 34 41 SP SD: 0.0995 c. M: 0.1716 c. 559: 33 52 62 33 52 33 62 33 52 52 43 52 SP SD: 0.1006 c. M:-0.1812 c. 612: 36 57 68 36 57 36 68 36 57 57 47 57 SP SD: 0.0507 c. M: 0.0900 c. 730: 43 68 81 43 68 43 81 43 68 68 56 68 SP SD: 0.0400 c. M:-0.0744 c. 1171: 69 109 130 69 109 69 130 69 109 109 90 109 SP SD: 0.0234 c. M:-0.0455 c. 1783: 105 166 198 105 166 105 198 105 166 166 137 166 SP SD: 0.0090 c. M: 0.0160 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: 6.8160 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.6719 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.3979 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 14.2040 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 7.3205 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 4.3872 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.9143 cents 11 x 12:13:14 x 15 x 17:18:20:21:22 SD: 9.6522 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 8.2282 cents 13 x 14 x 16:17:18 x 20:22:23:24:26 S SD: 9.3066 cents 14:15:16:17:18:19 x 21:22:23:25:26:28 SD: 8.8822 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 6.5325 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.4124 cents 18:19:20:22:23:24:25:27:28:30:32:34:36 SD: 4.7181 cents 20:21:22:24:25:27:28:30:31:33:36:38:40 SD: 4.2739 cents 24:25:27:29:30:32:33:36:38:40:43:45:48 SD: 3.3501 cents 28:29:31:34:35:37:39:42:44:47:50:53:56 SD: 3.1180 cents 36:38:40:43:45:48:50:54:56:60:64:68:72 SD: 2.3762 cents 44:46:49:53:55:59:61:66:69:73:78:83:88 SD: 1.7466 cents 48:50:53:58:60:64:67:72:75:80:85:90:96 SD: 1.6284 cents 54:56:60:65:68:72:75:81:84:90:96:101:108 SD: 1.5114 cents 64:67:71:77:80:85:89:96:100:107:114:120:128 SD: 1.1587 cents 72:75:80:86:90:96:100:108:113:120:128:135:144 SD: 0.9260 cents 80:83:89:96:100:107:111:120:125:133:142:150:160 SD: 0.8784 cents 90:94:100:108:113:120:125:135:141:150:160:169:180 SD: 0.8661 cents 96:100:107:115:120:128:133:144:150:160:171:180:192 SD: 0.6893 cents 116:121:129:139:145:155:161:174:181:193:206:218:232 SD: 0.6633 cents 120:125:133:144:150:160:167:180:188:200:213:225:240 SD: 0.6419 cents 126:131:140:151:158:168:175:189:197:210:224:236:252 SD: 0.5941 cents 144:150:160:173:180:192:200:216:225:240:256:270:288 SD: 0.1669 cents 360:375:400:432:450:480:500:540:563:600:640:675:720 SD: 0.1282 cents 432:450:480:518:540:576:600:648:675:720:768:810:864 SD: 0.1114 cents 504:525:560:605:630:672:700:756:788:840:896:945:1008 SD: 0.1032 cents 576:600:640:691:720:768:800:864:900:960:1024:1080:1152 SD: 0.0418 cents