Scala analysis: syndia2
Second 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: 16/15 111.731285 minor diatonic semitone 2: 256/225 223.462571 Neapolitan diminished third 3: 6/5 315.641287 minor third 4: 32/25 427.372572 classic diminished fourth 5: 4/3 498.044999 perfect fourth 6: 64/45 609.776284 2nd tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 128/75 925.417571 diminished seventh 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 256/135 1107.821284 octave - major chroma 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 16/15 111.7313 minor diatonic semitone 2: 16/15 111.7313 minor diatonic semitone 3: 135/128 92.1787 major chroma, major limma 4: 16/15 111.7313 minor diatonic semitone 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 8: 16/15 111.7313 minor diatonic semitone 9: 16/15 111.7313 minor diatonic semitone 10: 135/128 92.1787 major chroma, major limma 11: 256/243 90.2250 limma, Pythagorean minor second 12: 135/128 92.1787 major chroma, major limma
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: 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: 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: 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: 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: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 223.5 315.6 427.4 498.0 609.8 702.0 813.7 925.4 1017.6 1107.8 1200.0 111.7 : 111.7 203.9 315.6 386.3 498.0 590.2 702.0 813.7 905.9 996.1 1088.3 1200.0 223.5 : 92.2 203.9 274.6 386.3 478.5 590.2 702.0 794.1 884.4 976.5 1088.3 1200.0 315.6 : 111.7 182.4 294.1 386.3 498.0 609.8 702.0 792.2 884.4 996.1 1107.8 1200.0 427.4 : 70.7 182.4 274.6 386.3 498.0 590.2 680.4 772.6 884.4 996.1 1088.3 1200.0 498.0 : 111.7 203.9 315.6 427.4 519.6 609.8 702.0 813.7 925.4 1017.6 1129.3 1200.0 609.8 : 92.2 203.9 315.6 407.8 498.0 590.2 702.0 813.7 905.9 1017.6 1088.3 1200.0 702.0 : 111.7 223.5 315.6 405.9 498.0 609.8 721.5 813.7 925.4 996.1 1107.8 1200.0 813.7 : 111.7 203.9 294.1 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1088.3 1200.0 925.4 : 92.2 182.4 274.6 386.3 498.0 590.2 702.0 772.6 884.4 976.5 1088.3 1200.0 1017.6: 90.2 182.4 294.1 405.9 498.0 609.8 680.4 792.2 884.4 996.1 1107.8 1200.0 1107.8: 92.2 203.9 315.6 407.8 519.6 590.2 702.0 794.1 905.9 1017.6 1109.8 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 : 101.35059 cents, oct.: 1216.20708 cents Scale is strictly proper Step pattern alph. order: AABACABAABDB Step pattern size order : DDCDADCDDCBC Scale is a Constant Structure, by a margin of 51.11986 cents Scale diversity : 1.286153 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.641549 Rothenberg efficiency : 0.415278 redundancy: 0.584722 Efficiency x scale size : 4.983333 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 : 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 Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% 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 Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties -- Prime limit : 5 Odd number limit : 675 (O: 675 U: 675) Highest odd numerator or denominator: 225 Scale harmonicity : 0.028463 Average absolute harmonicity : 0.174540 Specific harmonicity : 0.160585 Fundamental : 1/1350, -10.3987 octaves, 0.1938 Hz. Guide tone : 2304, 11.1699 octaves, 602785.302 Hz. Exponens Consonantiae : 3.110400E+06, 21.56867 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 662.5, average 55.20833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.89125, average 1.15760 Sum of Tenney's harmonic distance : 28.91472, average 2.40956 Vogel's harmonic complexity : 17.16667 Wille's k value : 1012 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 342.35964, average 4.38923 Lattice compactness (without 2's) : 158.28513, average 2.02930 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 8 3.66667 46 1 3: -3 .. 2 -0.50000 14 2 5: -2 .. 0 -1.00000 12 9 Average exponent except 2's :-18 / 12 =-1.50000 Average absolute exponent except 2's: 26 / 12 = 2.16667 Scale is weakly epimorphic with val: <12 19 25| 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: 15.7835 c. M: 27.3726 c. Twelve-tone Chromatic (1/11-comma) 22: 2 2 2 2 1 2 2 2 2 2 1 2 SP B ME SD: 9.6190 c. M:-18.7673 c. 28: 3 2 2 3 2 2 2 3 3 2 2 2 P D3 S SD: 11.9154 c. M:-17.4396 c. 31: 3 3 2 3 2 3 2 3 3 2 3 2 SP M ME SD: 7.2794 c. M:-14.7594 c. 34: 3 3 3 3 2 3 3 3 3 3 2 3 SP B ME SD: 7.0907 c. M: 13.7036 c. 39: 4 3 3 4 2 4 3 3 4 3 3 3 SP D3 SD: 6.8538 c. M: 13.6863 c. 41: 4 4 3 4 2 4 3 4 4 3 3 3 SP D3 SD: 6.8695 c. M:-11.6518 c. 43: 4 4 3 4 3 4 3 4 4 3 4 3 SP M ME SD: 6.3546 c. M: 12.9451 c. 44: 4 4 4 4 2 4 4 4 4 3 4 3 SP D3 SD: 7.3696 c. M:-11.6314 c. 48: 4 5 4 4 3 4 4 5 4 4 3 4 SP B D3 SD: 6.9557 c. M: 11.7313 c. 50: 5 4 4 5 3 4 4 5 5 3 4 4 SP SD: 6.7655 c. M:-10.5824 c. 53: 5 5 4 5 3 5 4 5 5 4 4 4 SP D3 SD: 1.7686 c. M:-2.9525 c. 65: 6 6 5 6 4 6 5 6 6 5 5 5 SP D3 SD: 1.5380 c. M: 2.7572 c. 118: 11 11 9 11 7 11 9 11 11 9 9 9 SP D3 SD: 0.3482 c. M:-0.6533 c. 323: 30 30 25 30 19 30 25 30 30 25 24 25 SP SD: 0.3522 c. M: 0.7005 c. 376: 35 35 29 35 22 35 29 35 35 29 28 29 SP SD: 0.2415 c. M:-0.4888 c. 441: 41 41 34 41 26 41 34 41 41 34 33 34 SP SD: 0.1902 c. M: 0.3383 c. 494: 46 46 38 46 29 46 38 46 46 38 37 38 SP SD: 0.1074 c. M:-0.2175 c. 559: 52 52 43 52 33 52 43 52 52 43 42 43 SP SD: 0.1200 c. M: 0.2068 c. 612: 57 57 47 57 36 57 47 57 57 47 46 47 SP SD: 0.0451 c. M:-0.0784 c. 1171: 109 109 90 109 69 109 90 109 109 90 88 90 SP SD: 0.0356 c. M: 0.0638 c. 1783: 166 166 137 166 105 166 137 166 166 137 134 137 SP SD: 0.0126 c. M: 0.0254 c. 2395: 223 223 184 223 141 223 184 223 223 184 180 184 SP SD: 0.0118 c. M:-0.0238 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: 13.6863 cents 4 x x x 5 x x 6 x 7 x x 8 S SD: 14.9376 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.4528 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 11.2783 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 7.1651 cents 8 x 9 x 10:11 x 12:13:14 x 15:16 S SD: 11.1054 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.9308 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 6.6024 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 9.2672 cents 12:13:14 x 15:16:17:18:19:20:22:23:24 S SD: 7.9784 cents 13:14:15:16 x 17:18:20:21:22:23:25:26 SD: 9.0716 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 5.0505 cents 20:21:23:24:26:27:28:30:32:34:36:38:40 SD: 4.6167 cents 21:22:24:25:27:28:30:32:34:36:38:40:42 SD: 4.3360 cents 24:26:27:29:31:32:34:36:38:41:43:46:48 SD: 3.9766 cents 26:28:30:31:33:35:37:39:42:44:47:49:52 SD: 3.8503 cents 28:30:32:34:36:37:40:42:45:48:50:53:56 SD: 2.9081 cents 30:32:34:36:38:40:43:45:48:51:54:57:60 SD: 2.0639 cents 44:47:50:53:56:59:63:66:70:75:79:83:88 SD: 2.0179 cents 45:48:51:54:58:60:64:68:72:77:81:85:90 SD: 1.7056 cents 50:53:57:60:64:67:71:75:80:85:90:95:100 SD: 1.3653 cents 60:64:68:72:77:80:85:90:96:102:108:114:120 SD: 1.0847 cents 75:80:85:90:96:100:107:113:120:128:135:142:150 SD: 0.9908 cents 78:83:89:94:100:104:111:117:125:133:140:148:156 SD: 0.9881 cents 86:92:98:103:110:115:122:129:138:147:155:163:172 SD: 0.9431 cents 90:96:102:108:115:120:128:135:144:154:162:171:180 SD: 0.7757 cents 116:124:132:139:148:155:165:174:186:198:209:220:232 SD: 0.7558 cents 120:128:137:144:154:160:171:180:192:205:216:228:240 SD: 0.7493 cents 124:132:141:149:159:165:176:186:198:212:223:235:248 SD: 0.7332 cents 125:133:142:150:160:167:178:188:200:213:225:237:250 SD: 0.7042 cents 130:139:148:156:166:173:185:195:208:222:234:247:260 SD: 0.6476 cents 132:141:150:158:169:176:188:198:211:225:238:250:264 SD: 0.6263 cents 135:144:154:162:173:180:192:203:216:230:243:256:270 SD: 0.5984 cents 140:149:159:168:179:187:199:210:224:239:252:265:280 SD: 0.5843 cents 146:156:166:175:187:195:208:219:234:249:263:277:292 SD: 0.5630 cents 150:160:171:180:192:200:213:225:240:256:270:284:300 SD: 0.4255 cents 180:192:205:216:230:240:256:270:288:307:324:341:360 SD: 0.3337 cents 210:224:239:252:269:280:299:315:336:358:378:398:420 SD: 0.2673 cents 225:240:256:270:288:300:320:338:360:384:405:427:450 SD: 0.2415 cents 240:256:273:288:307:320:341:360:384:410:432:455:480 SD: 0.2259 cents 270:288:307:324:346:360:384:405:432:461:486:512:540 SD: 0.2015 cents 300:320:341:360:384:400:427:450:480:512:540:569:600 SD: 0.1826 cents 405:432:461:486:518:540:576:608:648:691:729:768:810 SD: 0.1793 cents 420:448:478:504:538:560:597:630:672:717:756:796:840 SD: 0.1665 cents 436:465:496:523:558:581:620:654:698:744:785:827:872 SD: 0.1471 cents 450:480:512:540:576:600:640:675:720:768:810:853:900 SD: 0.0564 cents