Scala analysis: syndia5
Fifth 81/80 2048/2025 Fokker block = pipedum_12.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: 75/64 274.582429 classic augmented second 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: 405/256 794.133717 wide 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: 135/128 92.1787 major chroma, major limma 2: 16/15 111.7313 minor diatonic semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 16/15 111.7313 minor diatonic semitone 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: 135/128 92.1787 major chroma, major limma 9: 256/243 90.2250 limma, Pythagorean minor second 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: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 135/128 92.179 cents major chroma, major limma 1: 6 16/15 111.731 cents minor diatonic semitone 2: 3 10/9 182.404 cents minor whole tone 2: 1 4096/3645 201.956 cents narrow diminished third 2: 7 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 3: 1 75/64 274.582 cents classic augmented second 3: 5 32/27 294.135 cents Pythagorean minor third 3: 2 1215/1024 296.089 cents wide augmented second 3: 4 6/5 315.641 cents minor third 4: 5 5/4 386.314 cents major third 4: 3 512/405 405.866 cents narrow diminished fourth 4: 3 81/64 407.820 cents Pythagorean major third 4: 1 32/25 427.373 cents classic diminished fourth 5: 1 675/512 478.492 cents wide augmented third 5: 9 4/3 498.045 cents perfect fourth 5: 2 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: 2 40/27 680.449 cents grave fifth 7: 9 3/2 701.955 cents perfect fifth 7: 1 1024/675 721.508 cents narrow diminished sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 3 128/81 792.180 cents Pythagorean minor sixth 8: 3 405/256 794.134 cents wide augmented fifth 8: 5 8/5 813.686 cents minor sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 2 2048/1215 903.911 cents narrow diminished seventh 9: 5 27/16 905.865 cents Pythagorean major sixth 9: 1 128/75 925.418 cents diminished seventh 10: 1 225/128 976.537 cents augmented sixth 10: 7 16/9 996.090 cents Pythagorean minor seventh 10: 1 3645/2048 998.044 cents wide augmented sixth 10: 3 9/5 1017.596 cents just minor seventh, BP seventh 11: 6 15/8 1088.269 cents classic major seventh 11: 4 256/135 1107.821 cents octave - major chroma 11: 1 243/128 1109.775 cents Pythagorean major seventh 11: 1 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: 3.63636 = 40/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 203.9 274.6 386.3 498.0 590.2 702.0 794.1 884.4 996.1 1088.3 1200.0 92.2 : 111.7 182.4 294.1 405.9 498.0 609.8 702.0 792.2 903.9 996.1 1107.8 1200.0 203.9 : 70.7 182.4 294.1 386.3 498.0 590.2 680.4 792.2 884.4 996.1 1088.3 1200.0 274.6 : 111.7 223.5 315.6 427.4 519.6 609.8 721.5 813.7 925.4 1017.6 1129.3 1200.0 386.3 : 111.7 203.9 315.6 407.8 498.0 609.8 702.0 813.7 905.9 1017.6 1088.3 1200.0 498.0 : 92.2 203.9 296.1 386.3 498.0 590.2 702.0 794.1 905.9 976.5 1088.3 1200.0 590.2 : 111.7 203.9 294.1 405.9 498.0 609.8 702.0 813.7 884.4 996.1 1107.8 1200.0 702.0 : 92.2 182.4 294.1 386.3 498.0 590.2 702.0 772.6 884.4 996.1 1088.3 1200.0 794.1 : 90.2 202.0 294.1 405.9 498.0 609.8 680.4 792.2 903.9 996.1 1107.8 1200.0 884.4 : 111.7 203.9 315.6 407.8 519.6 590.2 702.0 813.7 905.9 1017.6 1109.8 1200.0 996.1 : 92.2 203.9 296.1 407.8 478.5 590.2 702.0 794.1 905.9 998.0 1088.3 1200.0 1088.3: 111.7 203.9 315.6 386.3 498.0 609.8 702.0 813.7 905.9 996.1 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 111.7313 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 2: 182.4037 .. 223.4626 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 3: 274.5824 .. 315.6413 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 478.4924 .. 519.5513 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 25/24, 70.6724 cents 7: 680.4487 .. 721.5076 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 9: 884.3587 .. 925.4176 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 10: 976.5374 .. 1017.5963 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 11: 1088.2687 .. 1129.3276 cents 128/125, 41.0589 cents 25/24, 70.6724 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 : 16/15, 111.7313 cents Average / Smallest step : 1.414979 Largest / Average step : 1.117313 Largest / Smallest step : 1.580974 Median interval of one step : 101.95500 cents, amount: 0 Most common interval of one step : 16/15, 111.7313 cents, amount: 6 Least squares average step : 99.16678 cents, oct.: 1190.00136 cents Scale is strictly proper Step pattern alph. order: ABCBBABADBAB Step pattern size order : CDADDCDCBDCD Scale is a Constant Structure, by a margin of 51.11986 cents Scale diversity : 1.288245 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.641549 Rothenberg efficiency : 0.393353 redundancy: 0.606647 Efficiency x scale size : 4.720238 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.63636 = 40/11 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: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 7 Number of recognisable fifths : 9, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 9 Formal octave complements present : 5 = 41.6667% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 405 Scale harmonicity : 0.024510 Average absolute harmonicity : 0.184944 Specific harmonicity : 0.154724 Fundamental : 1/2304, -11.1699 octaves, 0.1136 Hz. Guide tone : 32400, 14.9837 octaves, 8476668.316 Hz. Exponens Consonantiae : 7.464960E+07, 26.15363 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 618.5, average 51.54167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.70282, average 1.14190 Sum of Tenney's harmonic distance : 26.82320, average 2.23527 Vogel's harmonic complexity : 17.50000 Wille's k value : 1822 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 8 Triangular lattice diameter : 7 Lattice compactness : 385.66467, average 4.94442 Lattice compactness (without 2's) : 176.38259, average 2.26132 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 4 -2.33333 42 1 3: -2 .. 4 0.83333 18 4 5: 0 .. 2 0.66667 8 7 Average exponent except 2's : 18 / 12 = 1.50000 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: 10.9735 c. M:-25.4176 c. Twelve-tone Chromatic (1/11-comma) 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 11.6727 c. M:-24.0481 c. Jubilee-12 26: 2 2 2 2 3 2 2 2 2 3 2 2 SP D3 S SD: 12.4055 c. M:-19.4236 c. 27: 2 3 1 3 2 2 3 2 2 2 2 3 P D3 SD: 12.1642 c. M: 21.6020 c. 29: 2 3 1 3 3 2 3 2 2 3 2 3 P D3 SD: 11.4349 c. M: 26.3066 c. 30: 2 3 2 3 2 3 3 2 2 3 2 3 SP D3 SD: 10.2639 c. M:-18.0450 c. 31: 2 3 2 3 3 2 3 2 3 3 2 3 SP M ME SD: 9.3282 c. M: 19.9402 c. 32: 2 3 2 3 3 3 3 2 3 3 2 3 P D3 SD: 11.9544 c. M: 17.1787 c. 34: 3 3 2 3 3 3 3 3 2 3 3 3 SP B ME SD: 8.4200 c. M:-17.6310 c. Jubilee-12 35: 3 3 2 3 4 2 3 3 3 3 3 3 SP D3 SD: 8.8797 c. M:-16.2407 c. 36: 3 3 2 4 3 3 3 3 3 3 3 3 SP T3 SD: 8.4736 c. M:-15.6413 c. 38: 3 3 3 3 4 3 3 3 3 4 2 4 SP D3 SD: 9.1494 c. M: 14.5845 c. 39: 3 4 2 4 3 3 4 3 3 3 3 4 SP D3 SD: 8.0610 c. M:-13.6863 c. 41: 3 4 2 4 4 3 4 3 3 4 3 4 SP D3 SD: 4.8923 c. M: 11.1678 c. 49: 4 4 3 5 4 4 5 3 4 5 3 5 SP SD: 7.0270 c. M: 10.7177 c. 51: 4 5 3 4 5 4 5 4 4 4 4 5 SP D3 SD: 6.3500 c. M: 9.8431 c. 53: 4 5 3 5 5 4 5 4 4 5 4 5 SP D3 SD: 1.3581 c. M: 2.8843 c. 65: 5 6 4 6 6 5 6 5 5 6 5 6 SP D3 SD: 1.0669 c. M:-2.3406 c. 118: 9 11 7 11 11 9 11 9 9 11 9 11 SP D3 SD: 0.4355 c. M: 0.9134 c. 183: 14 17 11 17 17 14 17 14 14 17 14 17 SP D3 SD: 0.5387 c. M:-0.8872 c. 289: 22 27 17 27 27 22 27 22 22 27 22 27 SP D3 SD: 0.5105 c. M: 1.0541 c. 301: 23 28 18 28 28 23 28 23 23 28 23 28 SP D3 SD: 0.4688 c. M: 0.7782 c. 311: 24 29 18 29 29 24 29 24 23 29 24 29 SP SD: 0.4832 c. M: 0.7574 c. 323: 25 30 19 30 30 25 30 25 24 30 25 30 SP SD: 0.4311 c. M:-0.9127 c. 376: 29 35 22 35 35 29 35 29 28 35 29 35 SP SD: 0.2758 c. M:-0.5471 c. 429: 33 40 25 40 40 33 40 33 32 40 33 40 SP SD: 0.2604 c. M: 0.4566 c. 441: 34 41 26 41 41 34 41 34 33 41 34 41 SP SD: 0.2096 c. M:-0.4241 c. 494: 38 46 29 46 46 38 46 38 37 46 38 46 SP SD: 0.1094 c. M:-0.1983 c. 559: 43 52 33 52 52 43 52 43 42 52 43 52 SP SD: 0.0977 c. M:-0.1940 c. 612: 47 57 36 57 57 47 57 47 46 57 47 57 SP SD: 0.0313 c. M: 0.0726 c. 1171: 90 109 69 109 109 90 109 90 88 109 90 109 SP SD: 0.0332 c. M:-0.0593 c. 1289: 99 120 76 120 120 99 120 99 97 120 99 120 SP SD: 0.0282 c. M:-0.0491 c. 1783: 137 166 105 166 166 137 166 137 134 166 137 166 SP SD: 0.0157 c. M:-0.0334 c. 1901: 146 177 112 177 177 146 177 146 143 177 146 177 SP SD: 0.0137 c. M: 0.0254 c. 2395: 184 223 141 223 223 184 223 184 180 223 184 223 SP SD: 0.0117 c. M:-0.0208 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: 10.1786 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.6104 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.6529 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.0798 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.9702 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.7898 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 11.4797 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1445 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 8.7719 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 7.4064 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.9912 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.6203 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 4.6623 cents 20:21 x 23:25:27:28:30:32:33:36:38:40 SD: 5.2374 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2488 cents 23:24:26:27:29:31:32:35:36:38:41:43:46 SD: 4.2300 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 2.4562 cents 36:38:41:42:45:48:51:54:57:60:64:68:72 SD: 2.4170 cents 39:41:44:46:49:52:55:59:62:65:69:73:78 SD: 2.1251 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.6653 cents 54:57:61:63:68:72:76:81:85:90:96:101:108 SD: 1.6069 cents 56:59:63:66:70:75:79:84:89:93:100:105:112 SD: 1.5608 cents 57:60:64:67:71:76:80:86:90:95:101:107:114 SD: 1.3146 cents 71:75:80:83:89:95:100:107:112:118:126:133:142 SD: 1.2562 cents 72:76:81:84:90:96:101:108:114:120:128:135:144 SD: 0.7539 cents 111:117:125:130:139:148:156:167:176:185:197:208:222 SD: 0.6854 cents 128:135:144:150:160:171:180:192:203:213:228:240:256 SD: 0.5796 cents 144:152:162:169:180:192:203:216:228:240:256:270:288 SD: 0.4476 cents 168:177:189:197:210:224:236:252:266:280:299:315:336 SD: 0.3083 cents 216:228:243:253:270:288:304:324:342:360:384:405:432 SD: 0.2176 cents 256:270:288:300:320:341:360:384:405:427:455:480:512 SD: 0.1839 cents 384:405:432:450:480:512:540:576:608:640:683:720:768 SD: 0.1380 cents 495:522:557:580:619:660:696:743:783:825:880:928:990 SD: 0.1256 cents 512:540:576:600:640:683:720:768:810:853:910:960:1024 SD: 0.0968 cents 600:633:675:703:750:800:844:900:949:1000:1067:1125:1200 SD: 0.0863 cents