Scala analysis: syndia3
Third 81/80 2048/2025 Fokker block
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: 1215/1024 296.088718 wide augmented second 4: 5/4 386.313714 major third 5: 675/512 478.492430 wide augmented third 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 405/256 794.133717 wide augmented fifth 9: 27/16 905.865003 Pythagorean major sixth 10: 225/128 976.537429 augmented sixth 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: 135/128 92.1787 major chroma, major limma 4: 256/243 90.2250 limma, Pythagorean minor second 5: 135/128 92.1787 major chroma, major limma 6: 16/15 111.7313 minor diatonic semitone 7: 16/15 111.7313 minor diatonic semitone 8: 135/128 92.1787 major chroma, major limma 9: 16/15 111.7313 minor diatonic semitone 10: 25/24 70.6724 classic chromatic semitone, minor chroma 11: 16/15 111.7313 minor diatonic semitone 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: 4 10/9 182.404 cents minor whole tone 2: 6 9/8 203.910 cents major whole tone 2: 2 256/225 223.463 cents Neapolitan diminished third 3: 2 75/64 274.582 cents classic augmented second 3: 4 32/27 294.135 cents Pythagorean minor third 3: 1 1215/1024 296.089 cents wide augmented second 3: 5 6/5 315.641 cents minor third 4: 6 5/4 386.314 cents major third 4: 2 512/405 405.866 cents narrow diminished fourth 4: 2 81/64 407.820 cents Pythagorean major third 4: 2 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: 2 25/16 772.627 cents classic augmented fifth 8: 2 128/81 792.180 cents Pythagorean minor sixth 8: 2 405/256 794.134 cents wide augmented fifth 8: 6 8/5 813.686 cents minor sixth 9: 5 5/3 884.359 cents major sixth, BP sixth 9: 1 2048/1215 903.911 cents narrow diminished seventh 9: 4 27/16 905.865 cents Pythagorean major sixth 9: 2 128/75 925.418 cents diminished seventh 10: 2 225/128 976.537 cents augmented sixth 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 4 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: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 203.9 296.1 386.3 478.5 590.2 702.0 794.1 905.9 976.5 1088.3 1200.0 92.2 : 111.7 203.9 294.1 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1107.8 1200.0 203.9 : 92.2 182.4 274.6 386.3 498.0 590.2 702.0 772.6 884.4 996.1 1088.3 1200.0 296.1 : 90.2 182.4 294.1 405.9 498.0 609.8 680.4 792.2 903.9 996.1 1107.8 1200.0 386.3 : 92.2 203.9 315.6 407.8 519.6 590.2 702.0 813.7 905.9 1017.6 1109.8 1200.0 478.5 : 111.7 223.5 315.6 427.4 498.0 609.8 721.5 813.7 925.4 1017.6 1107.8 1200.0 590.2 : 111.7 203.9 315.6 386.3 498.0 609.8 702.0 813.7 905.9 996.1 1088.3 1200.0 702.0 : 92.2 203.9 274.6 386.3 498.0 590.2 702.0 794.1 884.4 976.5 1088.3 1200.0 794.1 : 111.7 182.4 294.1 405.9 498.0 609.8 702.0 792.2 884.4 996.1 1107.8 1200.0 905.9 : 70.7 182.4 294.1 386.3 498.0 590.2 680.4 772.6 884.4 996.1 1088.3 1200.0 976.5 : 111.7 223.5 315.6 427.4 519.6 609.8 702.0 813.7 925.4 1017.6 1129.3 1200.0 1088.3: 111.7 203.9 315.6 407.8 498.0 590.2 702.0 813.7 905.9 1017.6 1088.3 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 : 99.11261 cents, oct.: 1189.35128 cents Scale is strictly proper Step pattern alph. order: ABACABBABDBB Step pattern size order : CDCBCDDCDADD Scale is a Constant Structure, by a margin of 51.11986 cents Scale diversity : 1.287197 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.641549 Rothenberg efficiency : 0.409689 redundancy: 0.590311 Efficiency x scale size : 4.916270 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 : 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: 6 Number of recognisable fifths : 9, average 701.9550 cents Best fifths form a closed circle 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 n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.026930 Average absolute harmonicity : 0.160945 Specific harmonicity : 0.152417 Fundamental : 1/1024, -10.0000 octaves, 0.2555 Hz. Guide tone : 12150, 13.5687 octaves, 3178750.618 Hz. Exponens Consonantiae : 1.244160E+07, 23.56867 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 2440.0, average 203.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 19.39485, average 1.61624 Sum of Tenney's harmonic distance : 37.45665, average 3.12139 Vogel's harmonic complexity : 15.83333 Wille's k value : 607 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 377.04741, average 4.83394 Lattice compactness (without 2's) : 171.67520, average 2.20096 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 1 -4.83333 60 1 3: 0 .. 5 2.16667 26 3 5: 0 .. 2 0.83333 10 8 Average exponent except 2's : 36 / 12 = 3.00000 Average absolute exponent except 2's: 36 / 12 = 3.00000 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: 11.5397 c. M:-23.4626 c. Twelve-tone Chromatic (1/11-comma) 25: 2 2 2 2 2 2 3 2 2 1 3 2 P D3 SD: 12.2276 c. M:-21.8663 c. 28: 2 3 2 2 2 3 2 3 2 2 2 3 SP B D3 SD: 10.7341 c. M:-20.1520 c. 30: 2 3 2 3 2 3 3 2 3 1 3 3 P D3 SD: 11.5806 c. M:-18.0450 c. 31: 2 3 2 3 2 3 3 2 3 2 3 3 SP M ME SD: 12.9315 c. M: 25.1210 c. 32: 2 3 3 2 3 3 3 2 3 2 3 3 SP D3 SD: 9.4735 c. M: 17.1787 c. 33: 3 3 2 3 2 3 3 3 3 2 3 3 SP D3 SD: 9.1716 c. M:-16.9122 c. 36: 3 3 3 3 2 4 3 3 3 2 4 3 SP T3 SD: 8.2774 c. M:-13.6863 c. 40: 3 4 3 3 3 4 3 3 4 3 3 4 SP D3 SD: 8.1408 c. M: 14.1337 c. 41: 3 4 3 3 3 4 4 3 4 2 4 4 SP D3 SD: 5.4267 c. M: 10.6838 c. 52: 4 5 4 4 4 5 4 4 5 3 5 5 SP SD: 6.3470 c. M:-9.7763 c. 53: 4 5 4 4 4 5 5 4 5 3 5 5 SP D3 SD: 1.6568 c. M: 3.0207 c. 65: 5 6 5 5 5 6 6 5 6 4 6 6 SP D3 SD: 1.0051 c. M:-1.9241 c. 118: 9 11 9 9 9 11 11 9 11 7 11 11 SP D3 SD: 0.5860 c. M: 1.1735 c. 183: 14 17 14 14 14 17 17 14 17 11 17 17 SP D3 SD: 0.5570 c. M: 1.0068 c. 301: 23 28 23 23 23 28 28 23 28 18 28 28 SP D3 SD: 0.5365 c. M: 1.0721 c. 311: 24 29 24 23 24 29 29 24 29 18 29 29 SP SD: 0.5268 c. M:-1.0174 c. 323: 25 30 25 24 25 30 30 25 30 19 30 30 SP SD: 0.6075 c. M:-1.1249 c. 364: 28 34 28 27 28 34 34 28 34 21 34 34 SP SD: 0.4643 c. M:-0.7284 c. 376: 29 35 29 28 29 35 35 29 35 22 35 35 SP SD: 0.3528 c. M:-0.7198 c. 429: 33 40 33 32 33 40 40 33 40 25 40 40 SP SD: 0.2567 c. M:-0.4287 c. 441: 34 41 34 33 34 41 41 34 41 26 41 41 SP SD: 0.2947 c. M:-0.5099 c. 494: 38 46 38 37 38 46 46 38 46 29 46 46 SP SD: 0.1315 c. M:-0.2676 c. 559: 43 52 43 42 43 52 52 43 52 33 52 52 SP SD: 0.1246 c. M:-0.2196 c. 612: 47 57 47 46 47 57 57 47 57 36 57 57 SP SD: 0.0328 c. M: 0.0668 c. 1289: 99 120 99 97 99 120 120 99 120 76 120 120 SP SD: 0.0278 c. M: 0.0465 c. 1783: 137 166 137 134 137 166 166 137 166 105 166 166 SP SD: 0.0221 c. M:-0.0414 c. 1901: 146 177 146 143 146 177 177 146 177 112 177 177 SP SD: 0.0167 c. M: 0.0340 c. 2395: 184 223 184 180 184 223 223 184 223 141 223 223 SP SD: 0.0139 c. M:-0.0282 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: 9.6886 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.9279 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 10.0198 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.4460 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 9.6090 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.6296 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.8699 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2815 cents 11 x 12:13:14 x 15 x 17 x 19:21:22 SD: 12.6430 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.7564 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 8.6055 cents 14:15:16:17 x 18:20:21:22:24:25:26:28 S SD: 7.9327 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 5.7957 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 3.9039 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 3.7452 cents 31:33:35:37:39:41:44:47:49:52:54:58:62 SD: 3.2559 cents 32:34:36:38:40:42:45:48:51:54:56:60:64 S SD: 1.7628 cents 54:57:61:64:68:71:76:81:85:91:95:101:108 SD: 1.5492 cents 57:60:64:68:71:75:80:86:90:96:100:107:114 SD: 1.4702 cents 64:68:72:76:80:84:90:96:101:108:113:120:128 SD: 1.4482 cents 69:73:78:82:86:91:97:104:109:116:121:129:138 SD: 1.4263 cents 70:74:79:83:88:92:98:105:111:118:123:131:140 SD: 1.3542 cents 71:75:80:84:89:94:100:107:112:120:125:133:142 SD: 1.2704 cents 72:76:81:85:90:95:101:108:114:122:127:135:144 SD: 1.1391 cents 79:83:89:94:99:104:111:119:125:133:139:148:158 SD: 1.1067 cents 86:91:97:102:108:113:121:129:136:145:151:161:172 SD: 1.0710 cents 88:93:99:104:110:116:124:132:139:149:155:165:176 SD: 0.9327 cents 96:101:108:114:120:127:135:144:152:162:169:180:192 SD: 0.6700 cents 112:118:126:133:140:148:158:168:177:189:197:210:224 SD: 0.6251 cents 128:135:144:152:160:169:180:192:203:216:225:240:256 SD: 0.4316 cents 160:169:180:190:200:211:225:240:253:270:281:300:320 SD: 0.2882 cents 256:270:288:304:320:338:360:384:405:432:450:480:512 SD: 0.2443 cents 311:328:350:369:389:410:437:467:492:525:547:583:622 SD: 0.2425 cents 327:345:368:388:409:431:460:491:517:552:575:613:654 SD: 0.2273 cents 352:371:396:418:440:464:495:528:557:594:619:660:704 SD: 0.1684 cents 424:447:477:503:530:559:596:636:671:716:745:795:848 SD: 0.1548 cents 440:464:495:522:550:580:619:660:696:743:773:825:880 SD: 0.1449 cents 512:540:576:608:640:675:720:768:810:864:900:960:1024 SD: 0.1187 cents 584:616:657:693:730:770:821:876:924:986:1027:1095:1168 SD: 0.1092 cents