Scala analysis: schisdia1
Schisdia 32805/32768 2048/2025 scale
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: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 81/64 407.820003 Pythagorean major third 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: 27/16 905.865003 Pythagorean major sixth 10: 3645/2048 998.043719 wide augmented sixth 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: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 135/128 92.1787 major chroma, major limma 5: 256/243 90.2250 limma, Pythagorean minor second 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: 135/128 92.1787 major chroma, major limma 10: 135/128 92.1787 major chroma, major limma 11: 524288/492075 109.7776 12: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 6 135/128 92.179 cents major chroma, major limma 1: 1 524288/492075 109.778 cents 1: 4 16/15 111.731 cents minor diatonic semitone 2: 1 10/9 182.404 cents minor whole tone 2: 1 18225/16384 184.357 cents two (major chroma, major limma) 2: 3 4096/3645 201.956 cents narrow diminished third 2: 7 9/8 203.910 cents major whole tone 3: 5 32/27 294.135 cents Pythagorean minor third 3: 4 1215/1024 296.089 cents wide augmented second 3: 1 65536/54675 313.688 cents 3: 2 6/5 315.641 cents minor third 4: 3 5/4 386.314 cents major third 4: 1 164025/131072 388.267 cents 4: 5 512/405 405.866 cents narrow diminished fourth 4: 3 81/64 407.820 cents Pythagorean major third 5: 9 4/3 498.045 cents perfect fourth 5: 2 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 5: 1 8192/6075 517.598 cents 6: 6 45/32 590.224 cents diatonic tritone 6: 6 64/45 609.776 cents 2nd tritone 7: 1 6075/4096 682.402 cents 7: 2 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 7: 9 3/2 701.955 cents perfect fifth 8: 3 128/81 792.180 cents Pythagorean minor sixth 8: 5 405/256 794.134 cents wide augmented fifth 8: 1 262144/164025 811.733 cents two (narrow diminished fourth) 8: 3 8/5 813.686 cents minor sixth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 54675/32768 886.312 cents 9: 4 2048/1215 903.911 cents narrow diminished seventh 9: 5 27/16 905.865 cents Pythagorean major sixth 10: 7 16/9 996.090 cents Pythagorean minor seventh 10: 3 3645/2048 998.044 cents wide augmented sixth 10: 1 32768/18225 1015.643 cents 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 1 492075/262144 1090.222 cents 11: 6 256/135 1107.821 cents octave - major chroma 11: 1 243/128 1109.775 cents Pythagorean major seventh 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 : 111.7 203.9 315.6 407.8 498.0 609.8 702.0 813.7 905.9 998.0 1107.8 1200.0 111.7 : 92.2 203.9 296.1 386.3 498.0 590.2 702.0 794.1 886.3 996.1 1088.3 1200.0 203.9 : 111.7 203.9 294.1 405.9 498.0 609.8 702.0 794.1 903.9 996.1 1107.8 1200.0 315.6 : 92.2 182.4 294.1 386.3 498.0 590.2 682.4 792.2 884.4 996.1 1088.3 1200.0 407.8 : 90.2 202.0 294.1 405.9 498.0 590.2 700.0 792.2 903.9 996.1 1107.8 1200.0 498.0 : 111.7 203.9 315.6 407.8 500.0 609.8 702.0 813.7 905.9 1017.6 1109.8 1200.0 609.8 : 92.2 203.9 296.1 388.3 498.0 590.2 702.0 794.1 905.9 998.0 1088.3 1200.0 702.0 : 111.7 203.9 296.1 405.9 498.0 609.8 702.0 813.7 905.9 996.1 1107.8 1200.0 813.7 : 92.2 184.4 294.1 386.3 498.0 590.2 702.0 794.1 884.4 996.1 1088.3 1200.0 905.9 : 92.2 202.0 294.1 405.9 498.0 609.8 702.0 792.2 903.9 996.1 1107.8 1200.0 998.0 : 109.8 202.0 313.7 405.9 517.6 609.8 700.0 811.7 903.9 1015.6 1107.8 1200.0 1107.8: 92.2 203.9 296.1 407.8 500.0 590.2 702.0 794.1 905.9 998.0 1090.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 111.7313 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 2: 182.4037 .. 203.9100 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 3: 294.1350 .. 315.6413 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 4: 386.3137 .. 407.8200 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 5: 498.0450 .. 517.5976 cents 2048/2025, 19.5526 cents 256/243, 90.2250 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 7: 682.4024 .. 701.9550 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 8: 792.1800 .. 813.6863 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 9: 884.3587 .. 905.8650 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 10: 996.0900 .. 1017.5963 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 11: 1088.2687 .. 1109.7750 cents 81/80, 21.5063 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.108340 Largest / Average step : 1.117313 Largest / Smallest step : 1.238363 Median interval of one step : 135/128, 92.1787 cents, amount: 6 Most common interval of one step : 135/128, 92.1787 cents, amount: 6 Least squares average step : 100.59857 cents, oct.: 1207.18282 cents Scale is strictly proper Step pattern alph. order: ABABCABABBDB Step pattern size order : DBDBADBDBBCB Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 1.148749 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.807743 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 : 11, average 701.5998 cents Best fifths form a closed circle 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% Limited inverse transpositions with margin 21.5063 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 492075 (O: 492075 U: 492075) Highest odd numerator or denominator: 3645 Scale harmonicity : 0.017921 Average absolute harmonicity : 0.180297 Specific harmonicity : 0.121396 Fundamental : 1/276480, -18.0768 octaves, 0.0009 Hz. Guide tone : 933120, 19.8317 octaves, 244128047.494 Hz. Exponens Consonantiae : 2.579890E+11, 37.90852 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 3234.0, average 269.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.16761, average 1.26397 Sum of Tenney's harmonic distance : 30.69623, average 2.55802 Vogel's harmonic complexity : 25.83333 Wille's k value : 246037 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 11 Triangular lattice diameter : 11 Lattice compactness : 522.42852, average 6.69780 Lattice compactness (without 2's) : 237.27857, average 3.04203 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 8 0.00000 50 1 3: -3 .. 6 0.83333 24 5 5: -1 .. 1 -0.33333 6 6 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 30 / 12 = 2.50000 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: 8.4095 c. M: 15.6413 c. Twelve-tone Chromatic (1/11-comma) 29: 3 2 3 2 2 3 2 3 2 2 3 2 SP M ME SD: 8.5900 c. M:-15.3932 c. 37: 3 3 4 3 2 4 3 3 3 3 3 3 SP D3 SD: 8.9599 c. M: 14.4340 c. 41: 4 3 4 3 3 4 3 4 3 3 4 3 SP M ME SD: 3.6608 c. M:-6.3099 c. 53: 5 4 5 4 4 5 4 5 4 4 5 4 SP M ME SD: 1.0951 c. M: 1.8173 c. 65: 6 5 6 5 5 6 5 6 5 5 6 5 SP M ME SD: 1.0407 c. M: 1.7951 c. 118: 11 9 11 9 9 11 9 11 9 9 11 9 SP M DE SD: 0.6401 c. M: 1.4335 c. 183: 17 14 17 14 14 17 14 17 14 14 17 14 SP M DE SD: 0.7165 c. M: 1.3224 c. 289: 27 22 27 22 22 27 22 27 22 22 27 22 SP M DE SD: 0.6491 c. M: 1.5039 c. 311: 29 24 29 24 23 29 24 29 24 24 28 24 SP SD: 0.6739 c. M:-1.3132 c. 323: 30 25 30 25 24 30 25 30 25 25 29 25 SP SD: 0.5784 c. M:-1.3371 c. 351: 33 27 32 27 27 32 27 33 27 27 32 27 SP SD: 0.8609 c. M: 1.2293 c. 352: 33 27 33 27 26 33 27 33 27 27 32 27 SP SD: 0.8045 c. M:-1.4042 c. 364: 34 28 34 28 27 34 28 34 28 28 33 28 SP SD: 0.5618 c. M:-0.9712 c. 376: 35 29 35 29 28 35 29 35 29 29 34 29 SP SD: 0.4106 c. M:-0.8925 c. 429: 40 33 40 33 32 40 33 40 33 33 39 33 SP SD: 0.3255 c. M:-0.5716 c. 441: 41 34 41 34 33 41 34 41 34 34 40 34 SP SD: 0.2575 c. M:-0.5957 c. 482: 45 37 45 37 36 45 37 45 37 37 44 37 SP SD: 0.3070 c. M:-0.5413 c. 494: 46 38 46 38 37 46 38 46 38 38 45 38 SP SD: 0.1609 c. M:-0.3368 c. 547: 51 42 51 42 41 51 42 51 42 42 50 42 SP SD: 0.1472 c. M:-0.2636 c. 559: 52 43 52 43 42 52 43 52 43 43 51 43 SP SD: 0.0857 c. M:-0.1674 c. 612: 57 47 57 47 46 57 47 57 47 47 56 47 SP SD: 0.0241 c. M:-0.0450 c. 1783: 166 137 166 137 134 166 137 166 137 137 163 137 SP SD: 0.0214 c. M:-0.0494 c. 1901: 177 146 177 146 143 177 146 177 146 146 174 146 SP SD: 0.0202 c. M: 0.0427 c. 2395: 223 184 223 184 180 223 184 223 184 184 219 184 SP SD: 0.0172 c. M:-0.0356 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: 9.0699 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.7101 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 12.3319 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.6544 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.0631 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.9216 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.8812 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 10.2230 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.7996 cents 13:14:15:16 x 17:18:20:21:22:23:25:26 SD: 9.2328 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.2180 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.2338 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 5.1901 cents 18:19:20:22:23:24:26:27:29:30:32:34:36 SD: 4.8949 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.7640 cents 24:26:27:29:30:32:34:36:38:41:43:46:48 SD: 4.2713 cents 26:28:29:31:33:35:37:39:42:44:46:49:52 SD: 3.1603 cents 30:32:34:36:38:40:43:45:48:51:53:57:60 SD: 2.1818 cents 40:43:45:48:51:53:57:60:64:68:71:76:80 SD: 2.1576 cents 42:45:47:50:53:56:60:63:67:71:75:80:84 SD: 1.9510 cents 45:48:51:54:57:60:64:68:72:76:80:85:90 S SD: 1.6251 cents 57:61:64:68:72:76:81:86:91:96:101:108:114 SD: 1.5561 cents 60:64:68:72:76:80:85:90:96:101:107:114:120 SD: 1.3250 cents 64:68:72:77:81:85:91:96:102:108:114:121:128 SD: 1.1399 cents 78:83:88:94:99:104:111:117:125:132:139:148:156 SD: 1.0519 cents 80:85:90:96:101:107:114:120:128:135:142:152:160 SD: 0.9788 cents 86:92:97:103:109:115:122:129:138:145:153:163:172 SD: 0.9721 cents 90:96:101:108:114:120:128:135:144:152:160:171:180 SD: 0.5110 cents 135:144:152:162:171:180:192:203:216:228:240:256:270 SD: 0.4420 cents 150:160:169:180:190:200:213:225:240:253:267:284:300 SD: 0.4085 cents 192:205:216:230:243:256:273:288:307:324:342:364:384 SD: 0.3287 cents 210:224:236:252:266:280:299:315:336:354:374:398:420 SD: 0.3195 cents 240:256:270:288:304:320:341:360:384:405:427:455:480 SD: 0.1942 cents 360:384:405:432:456:480:512:540:576:608:641:683:720 SD: 0.1924 cents 400:427:450:480:506:533:569:600:640:675:712:759:800 SD: 0.1881 cents 422:450:475:506:534:563:600:633:675:712:751:800:844 SD: 0.1866 cents 432:461:486:518:547:576:614:648:691:729:769:819:864 SD: 0.1819 cents 448:478:504:538:567:597:637:672:717:756:797:850:896 SD: 0.1801 cents 450:480:506:540:570:600:640:675:720:759:801:853:900 SD: 0.1665 cents 464:495:522:557:587:619:660:696:742:783:826:880:928 SD: 0.1437 cents 512:546:576:614:648:683:728:768:819:864:911:971:1024 SD: 0.1389 cents 528:563:594:634:668:704:751:792:845:891:940:1001:1056 SD: 0.1348 cents 550:587:619:660:696:733:782:825:880:928:979:1043:1100 SD: 0.1311 cents 585:624:658:702:740:780:832:878:936:987:1041:1109:1170 SD: 0.1285 cents 600:640:675:720:759:800:853:900:960:1013:1068:1138:1200 SD: 0.1201 cents