Scala analysis: syndia1
First 81/80 2048/2025 Fokker block = ramis.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: 10/9 182.403712 minor whole tone 3: 32/27 294.134997 Pythagorean 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: 128/81 792.179997 Pythagorean minor sixth 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: 135/128 92.1787 major chroma, major limma 2: 256/243 90.2250 limma, Pythagorean minor second 3: 16/15 111.7313 minor diatonic semitone 4: 135/128 92.1787 major chroma, major limma 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: 256/243 90.2250 limma, Pythagorean minor second 9: 135/128 92.1787 major chroma, major limma 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: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 135/128 92.179 cents major chroma, major limma 1: 5 16/15 111.731 cents minor diatonic semitone 2: 2 10/9 182.404 cents minor whole tone 2: 2 4096/3645 201.956 cents narrow diminished third 2: 8 9/8 203.910 cents major whole tone 3: 6 32/27 294.135 cents Pythagorean minor third 3: 3 1215/1024 296.089 cents wide augmented second 3: 3 6/5 315.641 cents minor third 4: 4 5/4 386.314 cents major third 4: 4 512/405 405.866 cents narrow diminished fourth 4: 4 81/64 407.820 cents Pythagorean major third 5: 10 4/3 498.045 cents perfect fourth 5: 1 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 5: 1 27/20 519.551 cents acute fourth 6: 6 45/32 590.224 cents diatonic tritone 6: 6 64/45 609.776 cents 2nd tritone 7: 1 40/27 680.449 cents grave fifth 7: 1 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 7: 10 3/2 701.955 cents perfect fifth 8: 4 128/81 792.180 cents Pythagorean minor sixth 8: 4 405/256 794.134 cents wide augmented fifth 8: 4 8/5 813.686 cents minor sixth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 3 2048/1215 903.911 cents narrow diminished seventh 9: 6 27/16 905.865 cents Pythagorean major sixth 10: 8 16/9 996.090 cents Pythagorean minor seventh 10: 2 3645/2048 998.044 cents wide augmented sixth 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 5 15/8 1088.269 cents classic major seventh 11: 5 256/135 1107.821 cents octave - major chroma 11: 2 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.90909 = 32/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 182.4 294.1 386.3 498.0 590.2 702.0 792.2 884.4 996.1 1088.3 1200.0 92.2 : 90.2 202.0 294.1 405.9 498.0 609.8 700.0 792.2 903.9 996.1 1107.8 1200.0 182.4 : 111.7 203.9 315.6 407.8 519.6 609.8 702.0 813.7 905.9 1017.6 1109.8 1200.0 294.1 : 92.2 203.9 296.1 407.8 498.0 590.2 702.0 794.1 905.9 998.0 1088.3 1200.0 386.3 : 111.7 203.9 315.6 405.9 498.0 609.8 702.0 813.7 905.9 996.1 1107.8 1200.0 498.0 : 92.2 203.9 294.1 386.3 498.0 590.2 702.0 794.1 884.4 996.1 1088.3 1200.0 590.2 : 111.7 202.0 294.1 405.9 498.0 609.8 702.0 792.2 903.9 996.1 1107.8 1200.0 702.0 : 90.2 182.4 294.1 386.3 498.0 590.2 680.4 792.2 884.4 996.1 1088.3 1200.0 792.2 : 92.2 203.9 296.1 407.8 500.0 590.2 702.0 794.1 905.9 998.0 1109.8 1200.0 884.4 : 111.7 203.9 315.6 407.8 498.0 609.8 702.0 813.7 905.9 1017.6 1107.8 1200.0 996.1 : 92.2 203.9 296.1 386.3 498.0 590.2 702.0 794.1 905.9 996.1 1088.3 1200.0 1088.3: 111.7 203.9 294.1 405.9 498.0 609.8 702.0 813.7 903.9 996.1 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 111.7313 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 2: 182.4037 .. 203.9100 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 3: 294.1350 .. 315.6413 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 4: 386.3137 .. 407.8200 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 5: 498.0450 .. 519.5513 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 25/24, 70.6724 cents 7: 680.4487 .. 701.9550 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 8: 792.1800 .. 813.6863 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 9: 884.3587 .. 905.8650 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 10: 996.0900 .. 1017.5963 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 11: 1088.2687 .. 1109.7750 cents 81/80, 21.5063 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.108340 Largest / Average step : 1.117313 Largest / Smallest step : 1.238363 Median interval of one step : 135/128, 92.1787 cents, amount: 5 Least squares average step : 99.16680 cents, oct.: 1190.00165 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: ABCACACBACAC Step pattern size order : MSLMLMLSMLML Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 1.148093 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.804487 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.90909 = 32/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Most common triad is 0.0 498.045 701.955 cents, amount: 8 Number of recognisable fifths : 11, average 701.7774 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 25.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties -- Prime limit : 5 Odd number limit : 10935 (O: 10935 U: 10935) Highest odd numerator or denominator: 135 Scale harmonicity : 0.025597 Average absolute harmonicity : 0.185410 Specific harmonicity : 0.151960 Fundamental : 1/10368, -13.3399 octaves, 0.0252 Hz. Guide tone : 17280, 14.0768 octaves, 4520889.768 Hz. Exponens Consonantiae : 1.791590E+08, 27.41667 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 353.5, average 29.45833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.56015, average 1.04668 Sum of Tenney's harmonic distance : 25.17538, average 2.09795 Vogel's harmonic complexity : 20.16667 Wille's k value : 5467 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 8 Triangular lattice diameter : 8 Lattice compactness : 413.65353, average 5.30325 Lattice compactness (without 2's) : 195.66483, average 2.50852 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 7 0.16667 38 1 3: -4 .. 3 -0.50000 20 5 5: 0 .. 1 0.50000 6 6 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 26 / 12 = 2.16667 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.8084 c. M:-17.5963 c. Twelve-tone Chromatic (1/11-comma) 29: 2 2 3 2 3 2 3 2 2 3 2 3 SP M ME SD: 9.7733 c. M: 16.8865 c. 34: 3 2 3 3 3 3 3 2 3 3 3 3 SP B ME SD: 8.3598 c. M: 15.7094 c. 38: 3 3 3 3 4 3 3 3 3 4 2 4 SP D3 SD: 8.3543 c. M: 14.5845 c. 39: 3 3 4 3 3 3 4 3 3 3 3 4 SP D3 SD: 8.4560 c. M:-13.6863 c. 41: 3 3 4 3 4 3 4 3 3 4 3 4 SP M ME SD: 4.0666 c. M: 6.7940 c. 53: 4 4 5 4 5 4 5 4 4 5 4 5 SP M ME SD: 1.0289 c. M: 1.6127 c. 65: 5 5 6 5 6 5 6 5 5 6 5 6 SP M ME SD: 1.1773 c. M:-2.2117 c. 118: 9 9 11 9 11 9 11 9 9 11 9 11 SP M DE SD: 0.5229 c. M:-1.0403 c. 171: 13 13 16 13 16 13 16 13 13 16 13 16 SP M DE SD: 0.5133 c. M: 0.9506 c. 289: 22 22 27 22 27 22 27 22 22 27 22 27 SP M DE SD: 0.4900 c. M:-0.8996 c. 323: 25 24 30 25 30 25 30 24 25 30 25 30 SP D3 SD: 0.4432 c. M: 0.8487 c. 376: 29 28 35 29 35 29 35 28 29 35 29 35 SP D3 SD: 0.3495 c. M: 0.6906 c. 388: 30 29 36 30 36 30 36 29 30 36 30 36 SP D3 SD: 0.3212 c. M:-0.6048 c. 429: 33 32 40 33 40 33 40 32 33 40 33 40 SP D3 SD: 0.3295 c. M: 0.5855 c. 441: 34 33 41 34 41 34 41 33 34 41 34 41 SP D3 SD: 0.1934 c. M: 0.3433 c. 494: 38 37 46 38 46 38 46 37 38 46 38 46 SP D3 SD: 0.1428 c. M: 0.2772 c. 547: 42 41 51 42 51 42 51 41 42 51 42 51 SP D3 SD: 0.1697 c. M: 0.3196 c. 559: 43 42 52 43 52 43 52 42 43 52 43 52 SP D3 SD: 0.0732 c. M:-0.1290 c. 612: 47 46 57 47 57 47 57 46 47 57 47 57 SP D3 SD: 0.0282 c. M: 0.0508 c. 1171: 90 88 109 90 109 90 109 88 90 109 90 109 SP D3 SD: 0.0266 c. M:-0.0501 c. 1783: 137 134 166 137 166 137 166 134 137 166 137 166 SP D3 SD: 0.0165 c. M: 0.0319 c. 1901: 146 143 177 146 177 146 177 143 146 177 146 177 SP D3 SD: 0.0178 c. M:-0.0346 c. 2395: 184 180 223 184 223 184 223 180 184 223 184 223 SP D3 SD: 0.0154 c. M: 0.0297 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: 7.6080 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.9180 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.9735 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.5153 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.5135 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3294 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 10.2448 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 6.4477 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 9.4857 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.3311 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.9148 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.5381 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 4.7522 cents 20:21:22:24:25:27:28:30:32:33:36:38:40 SD: 4.6400 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.7496 cents 27:28:30:32:34:36:38:41:43:45:48:51:54 SD: 3.5502 cents 32:34:36:38:40:43:45:48:51:53:57:60:64 SD: 2.8442 cents 33:35:37:39:41:44:46:50:52:55:59:62:66 SD: 2.8155 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 1.9029 cents 48:51:53:57:60:64:68:72:76:80:85:90:96 SD: 1.8875 cents 52:55:58:62:65:69:73:78:82:87:92:98:104 SD: 1.7871 cents 54:57:60:64:68:72:76:81:85:90:96:101:108 SD: 1.2680 cents 71:75:79:84:89:95:100:107:112:118:126:133:142 SD: 1.1829 cents 72:76:80:85:90:96:101:108:114:120:128:135:144 SD: 0.7344 cents 108:114:120:128:135:144:152:162:171:180:192:203:216 SD: 0.4837 cents 162:171:180:192:203:216:228:243:256:270:288:304:324 SD: 0.4109 cents 180:190:200:213:225:240:253:270:284:300:320:338:360 SD: 0.4081 cents 200:211:222:237:250:267:281:300:316:333:356:375:400 SD: 0.3549 cents 216:228:240:256:270:288:304:324:341:360:384:405:432 SD: 0.2192 cents 288:304:320:341:360:384:405:432:455:480:512:540:576 SD: 0.1876 cents 360:380:400:427:450:480:506:540:569:600:640:675:720 SD: 0.1807 cents 384:405:427:455:480:512:540:576:607:640:683:720:768 SD: 0.1443 cents 512:540:569:607:640:683:720:768:809:853:910:960:1024 SD: 0.1111 cents 584:616:649:692:730:779:821:876:923:973:1038:1095:1168 SD: 0.1066 cents