Scala analysis: syndie
81/80 and 128/125 Fokker block, Gene Ward Smith.
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: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 45/32 590.223716 diatonic tritone 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: 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 16/15 111.7313 minor diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 16/15 111.7313 minor diatonic semitone 10: 27/25 133.2376 large limma, BP small semitone, Zarlino 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: 6 10/9 182.404 cents minor whole tone 2: 4 9/8 203.910 cents major whole tone 2: 2 144/125 244.969 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: 4 25/18 568.717 cents classic augmented fourth 6: 2 45/32 590.224 cents diatonic tritone 6: 2 64/45 609.776 cents 2nd tritone 6: 4 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: 2 125/72 955.031 cents classic augmented sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 6 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: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 203.9 315.6 386.3 498.0 590.2 702.0 772.6 884.4 1017.6 1088.3 1200.0 70.7 : 133.2 245.0 315.6 427.4 519.6 631.3 702.0 813.7 946.9 1017.6 1129.3 1200.0 203.9 : 111.7 182.4 294.1 386.3 498.0 568.7 680.4 813.7 884.4 996.1 1066.8 1200.0 315.6 : 70.7 182.4 274.6 386.3 457.0 568.7 702.0 772.6 884.4 955.0 1088.3 1200.0 386.3 : 111.7 203.9 315.6 386.3 498.0 631.3 702.0 813.7 884.4 1017.6 1129.3 1200.0 498.0 : 92.2 203.9 274.6 386.3 519.6 590.2 702.0 772.6 905.9 1017.6 1088.3 1200.0 590.2 : 111.7 182.4 294.1 427.4 498.0 609.8 680.4 813.7 925.4 996.1 1107.8 1200.0 702.0 : 70.7 182.4 315.6 386.3 498.0 568.7 702.0 813.7 884.4 996.1 1088.3 1200.0 772.6 : 111.7 245.0 315.6 427.4 498.0 631.3 743.0 813.7 925.4 1017.6 1129.3 1200.0 884.4 : 133.2 203.9 315.6 386.3 519.6 631.3 702.0 813.7 905.9 1017.6 1088.3 1200.0 1017.6: 70.7 182.4 253.1 386.3 498.0 568.7 680.4 772.6 884.4 955.0 1066.8 1200.0 1088.3: 111.7 182.4 315.6 427.4 498.0 609.8 702.0 813.7 884.4 996.1 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 : 99.38937 cents, oct.: 1192.67243 cents Scale is strictly proper Step pattern alph. order: ABCACDCACBAC Step pattern size order : ADCACBCACDAC Scale is a Constant Structure, by a margin of 8.10728 cents Scale diversity : 1.352035 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.462330 Rothenberg efficiency : 0.395893 redundancy: 0.604107 Efficiency x scale size : 4.750722 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 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 : 3 5 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 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 5 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.029240 Average absolute harmonicity : 0.189769 Specific harmonicity : 0.165297 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 4.320000E+05, 18.72067 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 132.0, average 11.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.58482, average 0.88207 Sum of Tenney's harmonic distance : 20.24090, average 1.68674 Vogel's harmonic complexity : 15.58333 Wille's k value : 337 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 264.95327, average 3.39684 Lattice compactness (without 2's) : 150.01630, average 1.92329 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.41667 25 1 3: -1 .. 2 0.50000 12 3 5: -1 .. 2 0.50000 10 8 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 22 / 12 = 1.83333 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: 15.4157 c. M:-29.3276 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 10.7179 c. M: 21.8027 c. Meantone Chromatic (1/3-comma) 22: 1 3 2 1 2 2 2 1 2 3 1 2 N D3 SD: 10.7703 c. M:-18.7673 c. 28: 2 3 2 2 3 2 2 2 3 3 1 3 P D3 SD: 12.4236 c. M: 16.8401 c. 29: 2 3 3 1 3 2 3 2 2 4 1 3 P SD: 11.4351 c. M:-16.8865 c. 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 6.5578 c. M: 11.1447 c. Meantone Chromatic (53/220-comma) 34: 2 4 3 2 3 3 3 2 3 4 2 3 P D3 SD: 4.8653 c. M:-9.7763 c. 53: 3 6 5 3 5 4 5 3 5 6 3 5 P SD: 1.5073 c. M: 2.8161 c. 118: 7 13 11 7 11 9 11 7 11 13 7 11 SP SD: 0.3698 c. M: 0.6471 c. 171: 10 19 16 10 16 13 16 10 16 19 10 16 SP SD: 0.4090 c. M: 0.7500 c. 289: 17 32 27 17 27 22 27 17 27 32 17 27 SP SD: 0.2939 c. M: 0.6043 c. 323: 19 36 30 19 30 25 30 19 30 36 19 30 SP SD: 0.2560 c. M:-0.4884 c. 441: 26 49 41 26 41 34 41 26 41 49 26 41 SP SD: 0.1233 c. M:-0.2525 c. 494: 29 55 46 29 46 38 46 29 46 55 29 46 SP SD: 0.1311 c. M: 0.2271 c. 559: 33 62 52 33 52 43 52 33 52 62 33 52 SP SD: 0.0961 c. M:-0.1812 c. 612: 36 68 57 36 57 47 57 36 57 68 36 57 SP SD: 0.0442 c. M: 0.0842 c. 730: 43 81 68 43 68 56 68 43 68 81 43 68 SP SD: 0.0450 c. M: 0.0867 c. 1171: 69 130 109 69 109 90 109 69 109 130 69 109 SP SD: 0.0250 c. M:-0.0455 c. 1783: 105 198 166 105 166 137 166 105 166 198 105 166 SP SD: 0.0096 c. M:-0.0175 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: 8.3554 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.7006 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.6194 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.5307 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.2939 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.2953 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 10.3452 cents 12 x x 14:15:16:17:18:19:20:22:23:24 S SD: 7.4327 cents 13:14:15 x 16:17:18 x 20:22:23:24:26 S SD: 10.4132 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.8107 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 5.4226 cents 20:21:23:24:25:27:28:30:31:33:36:38:40 SD: 4.7008 cents 23:24:26:28:29:31:32:35:36:38:41:43:46 SD: 4.3956 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 2.4960 cents 39:41:44:47:49:52:55:59:61:65:70:73:78 SD: 2.1856 cents 40:42:45:48:50:53:56:60:63:67:72:75:80 SD: 2.0957 cents 45:47:51:54:56:60:63:68:70:75:81:84:90 SD: 2.0166 cents 48:50:54:58:60:64:68:72:75:80:86:90:96 SD: 1.6058 cents 56:58:63:67:70:75:79:84:88:93:101:105:112 SD: 1.5857 cents 64:67:72:77:80:85:90:96:100:107:115:120:128 SD: 1.1148 cents 72:75:81:86:90:96:101:108:113:120:130:135:144 SD: 1.0874 cents 80:83:90:96:100:107:113:120:125:133:144:150:160 SD: 1.0376 cents 89:93:100:107:111:119:125:134:139:148:160:167:178 SD: 1.0280 cents 94:98:106:113:118:125:132:141:147:157:169:176:188 SD: 0.9703 cents 96:100:108:115:120:128:135:144:150:160:173:180:192 SD: 0.3012 cents 216:225:243:259:270:288:304:324:338:360:389:405:432 SD: 0.2786 cents 240:250:270:288:300:320:338:360:375:400:432:450:480 SD: 0.2136 cents 288:300:324:346:360:384:405:432:450:480:518:540:576 SD: 0.2006 cents 336:350:378:403:420:448:473:504:525:560:605:630:672 SD: 0.1752 cents 360:375:405:432:450:480:506:540:563:600:648:675:720 SD: 0.1467 cents 384:400:432:461:480:512:540:576:600:640:691:720:768 SD: 0.0752 cents 480:500:540:576:600:640:675:720:750:800:864:900:960 SD: 0.0000 cents