Scala analysis: syndia4
81/80 and 2048/2025 Fokker block, Gene Ward Smith.
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: 6/5 315.641287 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: 8/5 813.686286 minor sixth 9: 27/16 905.865003 Pythagorean major 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: 16/15 111.7313 minor diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 16/15 111.7313 minor diatonic semitone 9: 135/128 92.1787 major chroma, major limma 10: 256/243 90.2250 limma, Pythagorean minor second 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: 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 : 92.2 203.9 315.6 386.3 498.0 590.2 702.0 813.7 905.9 996.1 1088.3 1200.0 92.2 : 111.7 223.5 294.1 405.9 498.0 609.8 721.5 813.7 903.9 996.1 1107.8 1200.0 203.9 : 111.7 182.4 294.1 386.3 498.0 609.8 702.0 792.2 884.4 996.1 1088.3 1200.0 315.6 : 70.7 182.4 274.6 386.3 498.0 590.2 680.4 772.6 884.4 976.5 1088.3 1200.0 386.3 : 111.7 203.9 315.6 427.4 519.6 609.8 702.0 813.7 905.9 1017.6 1129.3 1200.0 498.0 : 92.2 203.9 315.6 407.8 498.0 590.2 702.0 794.1 905.9 1017.6 1088.3 1200.0 590.2 : 111.7 223.5 315.6 405.9 498.0 609.8 702.0 813.7 925.4 996.1 1107.8 1200.0 702.0 : 111.7 203.9 294.1 386.3 498.0 590.2 702.0 813.7 884.4 996.1 1088.3 1200.0 813.7 : 92.2 182.4 274.6 386.3 478.5 590.2 702.0 772.6 884.4 976.5 1088.3 1200.0 905.9 : 90.2 182.4 294.1 386.3 498.0 609.8 680.4 792.2 884.4 996.1 1107.8 1200.0 996.1 : 92.2 203.9 296.1 407.8 519.6 590.2 702.0 794.1 905.9 1017.6 1109.8 1200.0 1088.3: 111.7 203.9 315.6 427.4 498.0 609.8 702.0 813.7 925.4 1017.6 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 : 99.89471 cents, oct.: 1198.73651 cents Scale is strictly proper Step pattern alph. order: ABBCBABBADAB Step pattern size order : CDDADCDDCBCD 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 Scale contains a complete diamond : 1 3 9 Formal octave complements present : 7 = 58.3333% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 135 Scale harmonicity : 0.026930 Average absolute harmonicity : 0.192635 Specific harmonicity : 0.163675 Fundamental : 1/5760, -12.4919 octaves, 0.0454 Hz. Guide tone : 2160, 11.0768 octaves, 565111.221 Hz. Exponens Consonantiae : 1.244160E+07, 23.56867 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 248.0, average 20.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.35064, average 0.94589 Sum of Tenney's harmonic distance : 22.66484, average 1.88874 Vogel's harmonic complexity : 20.16667 Wille's k value : 3037 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 351.17977, average 4.50230 Lattice compactness (without 2's) : 161.43331, average 2.06966 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 4 -1.16667 36 1 3: -2 .. 3 0.83333 16 5 5: -1 .. 1 0.16667 6 6 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 22 / 12 = 1.83333 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: 9.0658 c. M: 15.6413 c. Twelve-tone Chromatic (1/11-comma) 29: 2 3 3 1 3 2 3 3 2 2 2 3 P D3 SD: 9.2534 c. M:-15.3932 c. 31: 2 3 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 8.5425 c. M: 15.5424 c. 34: 3 3 3 2 3 3 3 3 3 2 3 3 SP B ME SD: 7.1998 c. M:-13.7036 c. Diaschismic-12, Pajara-12 41: 3 4 4 2 4 3 4 4 3 3 3 4 SP D3 SD: 3.9095 c. M:-6.3099 c. 53: 4 5 5 3 5 4 5 5 4 4 4 5 SP D3 SD: 1.0414 c. M: 1.6127 c. 65: 5 6 6 4 6 5 6 6 5 5 5 6 SP D3 SD: 0.9815 c. M: 1.7951 c. 118: 9 11 11 7 11 9 11 11 9 9 9 11 SP D3 SD: 0.4150 c. M: 0.7803 c. 323: 25 30 30 19 30 25 30 30 25 24 25 30 SP SD: 0.3754 c. M:-0.7005 c. 376: 29 35 35 22 35 29 35 35 29 28 29 35 SP SD: 0.2722 c. M:-0.5180 c. 429: 33 40 40 25 40 33 40 40 33 32 33 40 SP SD: 0.2590 c. M:-0.4426 c. 441: 34 41 41 26 41 34 41 41 34 33 34 41 SP SD: 0.1730 c. M:-0.3383 c. 494: 38 46 46 29 46 38 46 46 38 37 38 46 SP SD: 0.1103 c. M:-0.2079 c. 559: 43 52 52 33 52 43 52 52 43 42 43 52 SP SD: 0.0744 c. M:-0.1290 c. 612: 47 57 57 36 57 47 57 57 47 46 47 57 SP SD: 0.0260 c. M:-0.0450 c. 1171: 90 109 109 69 109 90 109 109 90 88 90 109 SP SD: 0.0259 c. M:-0.0501 c. 1783: 137 166 166 105 166 137 166 166 137 134 137 166 SP SD: 0.0138 c. M:-0.0254 c. 1901: 146 177 177 112 177 146 177 177 146 143 146 177 SP SD: 0.0137 c. M: 0.0260 c. 2395: 184 223 223 141 223 184 223 223 184 180 184 223 SP SD: 0.0119 c. M:-0.0223 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: 7.1688 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: 4.5694 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.9984 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.9322 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.8208 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.0461 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.8161 cents 11 x 12:13:14:15 x 17:18:19:20:21:22 SD: 11.9672 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.9651 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 8.5313 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.4618 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 4.9744 cents 20:21:23:24:25:27:28:30:32:34:36:38:40 SD: 4.6999 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.4692 cents 23:24:26:28:29:31:32:35:37:39:41:43:46 SD: 4.3898 cents 24:25:27:29:30:32:34:36:38:41:43:45:48 SD: 3.4668 cents 30:32:34:36:38:40:42:45:48:51:53:56:60 SD: 3.1965 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2526 cents 39:41:44:47:49:52:55:59:62:66:69:73:78 SD: 2.1351 cents 40:42:45:48:50:53:56:60:64:68:71:75:80 SD: 1.6818 cents 54:57:61:65:68:72:76:81:86:91:96:101:108 SD: 1.5248 cents 55:58:62:66:69:73:77:83:88:93:98:103:110 SD: 1.4788 cents 64:68:72:77:80:85:90:96:102:108:114:120:128 SD: 1.4111 cents 71:75:80:85:89:95:100:107:114:120:126:133:142 SD: 1.2398 cents 72:76:81:86:90:96:101:108:115:122:128:135:144 SD: 1.0017 cents 89:94:100:107:111:119:125:134:142:150:158:167:178 SD: 0.9947 cents 90:95:101:108:113:120:127:135:144:152:160:169:180 SD: 0.9264 cents 96:101:108:115:120:128:135:144:154:162:171:180:192 SD: 0.6404 cents 128:135:144:154:160:171:180:192:205:216:228:240:256 SD: 0.5649 cents 144:152:162:173:180:192:203:216:230:243:256:270:288 SD: 0.4810 cents 160:169:180:192:200:213:225:240:256:270:284:300:320 SD: 0.3839 cents 200:211:225:240:250:267:281:300:320:338:356:375:400 SD: 0.3590 cents 216:228:243:259:270:288:304:324:346:365:384:405:432 SD: 0.3279 cents 224:236:252:269:280:299:315:336:358:378:398:420:448 SD: 0.3053 cents 240:253:270:288:300:320:338:360:384:405:427:450:480 SD: 0.2518 cents 256:270:288:307:320:341:360:384:410:432:455:480:512 SD: 0.2231 cents 288:304:324:346:360:384:405:432:461:486:512:540:576 SD: 0.2141 cents 345:364:388:414:431:460:485:518:552:582:613:647:690 SD: 0.2064 cents 360:380:405:432:450:480:506:540:576:608:640:675:720 SD: 0.1824 cents 384:405:432:461:480:512:540:576:614:648:683:720:768 SD: 0.1331 cents 480:506:540:576:600:640:675:720:768:810:853:900:960 SD: 0.0909 cents