Scala analysis: syndie3
Third Syndie scale ~ duodene.scl = efg33355.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: 32/27 294.134997 Pythagorean 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: 40/27 680.448711 grave 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: 50/27 1066.762425 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 16/15 111.7313 minor diatonic semitone 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: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 16/15 111.7313 minor diatonic semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 135/128 92.179 cents major chroma, major limma 1: 6 16/15 111.731 cents minor diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino 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: 3 75/64 274.582 cents classic augmented second 3: 3 32/27 294.135 cents Pythagorean minor third 3: 6 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: 1 675/512 478.492 cents wide augmented third 5: 9 4/3 498.045 cents perfect fourth 5: 2 27/20 519.551 cents acute fourth 6: 2 25/18 568.717 cents classic augmented fourth 6: 4 45/32 590.224 cents diatonic tritone 6: 4 64/45 609.776 cents 2nd tritone 6: 2 36/25 631.283 cents classic diminished fifth 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: 4 25/16 772.627 cents classic augmented fifth 8: 8 8/5 813.686 cents minor sixth 9: 6 5/3 884.359 cents major sixth, BP sixth 9: 3 27/16 905.865 cents Pythagorean major sixth 9: 3 128/75 925.418 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: 1 50/27 1066.762 cents grave major seventh 11: 6 15/8 1088.269 cents classic major seventh 11: 2 256/135 1107.821 cents octave - major chroma 11: 3 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: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 182.4 294.1 386.3 498.0 568.7 680.4 772.6 884.4 996.1 1066.8 1200.0 70.7 : 111.7 223.5 315.6 427.4 498.0 609.8 702.0 813.7 925.4 996.1 1129.3 1200.0 182.4 : 111.7 203.9 315.6 386.3 498.0 590.2 702.0 813.7 884.4 1017.6 1088.3 1200.0 294.1 : 92.2 203.9 274.6 386.3 478.5 590.2 702.0 772.6 905.9 976.5 1088.3 1200.0 386.3 : 111.7 182.4 294.1 386.3 498.0 609.8 680.4 813.7 884.4 996.1 1107.8 1200.0 498.0 : 70.7 182.4 274.6 386.3 498.0 568.7 702.0 772.6 884.4 996.1 1088.3 1200.0 568.7 : 111.7 203.9 315.6 427.4 498.0 631.3 702.0 813.7 925.4 1017.6 1129.3 1200.0 680.4 : 92.2 203.9 315.6 386.3 519.6 590.2 702.0 813.7 905.9 1017.6 1088.3 1200.0 772.6 : 111.7 223.5 294.1 427.4 498.0 609.8 721.5 813.7 925.4 996.1 1107.8 1200.0 884.4 : 111.7 182.4 315.6 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1088.3 1200.0 996.1 : 70.7 203.9 274.6 386.3 498.0 590.2 702.0 772.6 884.4 976.5 1088.3 1200.0 1066.8: 133.2 203.9 315.6 427.4 519.6 631.3 702.0 813.7 905.9 1017.6 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 .. 223.4626 cents 128/125, 41.0589 cents 250/243, 49.1661 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: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 7: 680.4487 .. 721.5076 cents 128/125, 41.0589 cents 250/243, 49.1661 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: 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: 6 Most common interval of one step : 16/15, 111.7313 cents, amount: 6 Least squares average step : 98.09899 cents, oct.: 1177.18790 cents Scale is strictly proper Step pattern alph. order: ABBCBABCBBAD Step pattern size order : ACCBCACBCCAD Scale is a Constant Structure, by a margin of 49.16614 cents Scale diversity : 1.332962 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.569861 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2048/2025, 19.5526 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 Scale is fully connected 5-limit major-minor triadic Scale is a complete genus musicum : 2^m 3^3 5^2 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 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 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 5 Odd number limit : 675 (O: 675 U: 675) Highest odd numerator or denominator: 27 Scale harmonicity : 0.033557 Average absolute harmonicity : 0.164625 Specific harmonicity : 0.166273 Fundamental : 1/432, -8.7549 octaves, 0.6056 Hz. Guide tone : 800, 9.6439 octaves, 209300.452 Hz. Exponens Consonantiae : 3.456000E+05, 18.39874 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 203.5, average 16.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.27146, average 1.02262 Sum of Tenney's harmonic distance : 25.10363, average 2.09197 Vogel's harmonic complexity : 14.08333 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 297.54165, average 3.81464 Lattice compactness (without 2's) : 149.93204, average 1.92221 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.58333 27 1 3: -3 .. 0 -1.50000 18 3 5: 0 .. 2 1.00000 12 8 Average exponent except 2's :-6 / 12 =-0.50000 Average absolute exponent except 2's: 30 / 12 = 2.50000 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 25| Scale is weakly epimorphic with val: <12 21 26| Scale is weakly epimorphic with val: <12 21 28| Scale is weakly epimorphic with val: <12 21 29| Scale is weakly epimorphic with val: <12 21 31|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 20.1454 c. M:-33.2376 c. Twelve-tone Chromatic (1/11-comma) 16: 1 1 2 1 2 1 1 1 2 1 1 2 P D3 SD: 19.2536 c. M: 32.4037 c. 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 18.3499 c. M: 33.3725 c. 18: 1 2 1 2 1 2 1 2 1 2 1 2 SP B ME SD: 19.3611 c. M: 31.3783 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 10.6433 c. M:-21.6545 c. Meantone Chromatic (1/3-comma) 27: 2 2 3 2 2 2 2 2 3 2 2 3 P D3 SD: 12.3556 c. M: 18.3122 c. 28: 2 2 3 2 3 1 3 2 3 2 2 3 SP D3 SD: 9.9266 c. M:-16.2407 c. 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 10.3506 c. M:-17.1085 c. Meantone Chromatic (53/220-comma) 33: 2 3 3 3 3 2 3 2 3 3 2 4 P SD: 9.8928 c. M: 14.2718 c. 34: 2 3 3 3 3 2 3 3 3 3 2 4 SP D3 SD: 6.1236 c. M: 11.7821 c. 46: 3 4 4 4 4 3 4 4 4 4 3 5 SP D3 SD: 5.0720 c. M:-9.9813 c. 53: 3 5 5 4 5 3 5 4 5 5 3 6 SP SD: 1.7414 c. M: 2.8161 c. 118: 7 11 11 9 11 7 11 9 11 11 7 13 SP SD: 0.6022 c. M:-1.0342 c. 171: 10 16 16 13 16 10 16 13 16 16 10 19 SP SD: 0.3657 c. M: 0.6976 c. 289: 17 27 27 22 27 17 27 22 27 27 17 32 SP SD: 0.3355 c. M:-0.6747 c. 323: 19 30 30 25 30 19 30 25 30 30 19 36 SP SD: 0.3517 c. M: 0.6365 c. 388: 23 36 36 30 36 23 36 30 36 36 23 43 SP SD: 0.2889 c. M:-0.5684 c. 441: 26 41 41 34 41 26 41 34 41 41 26 49 SP SD: 0.1259 c. M: 0.2574 c. 559: 33 52 52 43 52 33 52 43 52 52 33 62 SP SD: 0.1038 c. M:-0.1812 c. 612: 36 57 57 47 57 36 57 47 57 57 36 68 SP SD: 0.0580 c. M: 0.0958 c. 1171: 69 109 109 90 109 69 109 90 109 109 69 130 SP SD: 0.0230 c. M:-0.0455 c. 1783: 105 166 166 137 166 105 166 137 166 166 105 198 SP SD: 0.0138 c. M: 0.0239 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: 10.7531 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: 8.6813 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 10.5852 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.4734 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 14.0232 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.2489 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 7.5927 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.2938 cents 11 x 12:13:14 x 15:16:17:18 x 20:22 S SD: 8.8914 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 6.9676 cents 13 x 14:15:16:17:18:19:20:22:23:24:26 S SD: 8.6371 cents 14:15:16:17:18:19 x 21:22:23:25:26:28 SD: 9.5789 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 6.4869 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.7892 cents 18:19:20:21:23:24:25:27:28:30:32:33:36 SD: 4.9594 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 4.5890 cents 21:22:23:25:26:28:29:31:33:35:37:39:42 SD: 3.2823 cents 27:28:30:32:34:36:38:40:42:45:48:50:54 SD: 2.3688 cents 39:41:43:46:49:52:54:58:61:65:69:72:78 SD: 2.2877 cents 43:45:48:51:54:57:60:64:67:72:76:80:86 SD: 2.1740 cents 44:46:49:52:55:59:61:65:69:73:78:81:88 SD: 1.7496 cents 48:50:53:57:60:64:67:71:75:80:85:89:96 SD: 1.3481 cents 64:67:71:76:80:85:89:95:100:107:114:119:128 SD: 1.3048 cents 69:72:77:82:86:92:96:102:108:115:123:128:138 SD: 1.1062 cents 72:75:80:85:90:96:100:107:113:120:128:133:144 SD: 1.0301 cents 75:78:83:89:94:100:104:111:117:125:133:139:150 SD: 0.9160 cents 93:97:103:110:116:124:129:138:145:155:165:172:186 SD: 0.8590 cents 96:100:107:114:120:128:133:142:150:160:171:178:192 SD: 0.7582 cents 108:113:120:128:135:144:150:160:169:180:192:200:216 SD: 0.6745 cents 123:128:137:146:154:164:171:182:192:205:219:228:246 SD: 0.6207 cents 135:141:150:160:169:180:188:200:211:225:240:250:270 SD: 0.5854 cents 141:147:157:167:176:188:196:209:220:235:251:261:282 SD: 0.5135 cents 144:150:160:171:180:192:200:213:225:240:256:267:288 SD: 0.4033 cents 189:197:210:224:236:252:263:280:295:315:336:350:378 SD: 0.3611 cents 216:225:240:256:270:288:300:320:338:360:384:400:432 SD: 0.2136 cents 288:300:320:341:360:384:400:427:450:480:512:533:576 SD: 0.2017 cents 357:372:397:423:446:476:496:529:558:595:635:661:714 SD: 0.1922 cents 384:400:427:455:480:512:533:569:600:640:683:711:768 SD: 0.1683 cents 405:422:450:480:506:540:563:600:633:675:720:750:810 SD: 0.1586 cents 432:450:480:512:540:576:600:640:675:720:768:800:864 SD: 0.0000 cents