Scala analysis: mistyschism1
Mistyschism scale 2048/2025 67108864/66430125
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 524288/492075 109.777564 2: 9/8 203.910002 major whole tone 3: 1215/1024 296.088718 wide augmented second 4: 512/405 405.866283 narrow diminished fourth 5: 4/3 498.044999 perfect fourth 6: 64/45 609.776284 2nd tritone 7: 3/2 701.955001 perfect fifth 8: 262144/164025 811.732565 two (narrow diminished fourth) 9: 2048/1215 903.911282 narrow diminished seventh 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: 524288/492075 109.7776 2: 4428675/4194304 94.1324 3: 135/128 92.1787 major chroma, major limma 4: 524288/492075 109.7776 5: 135/128 92.1787 major chroma, major limma 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 8: 524288/492075 109.7776 9: 135/128 92.1787 major chroma, major limma 10: 4428675/4194304 94.1324 11: 524288/492075 109.7776 12: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 135/128 92.179 cents major chroma, major limma 1: 2 4428675/4194304 94.132 cents 1: 4 524288/492075 109.778 cents 1: 1 16/15 111.731 cents minor diatonic semitone 2: 2 597871125/536870912 186.311 cents 2: 6 4096/3645 201.956 cents narrow diminished third 2: 4 9/8 203.910 cents major whole tone 3: 2 32/27 294.135 cents Pythagorean minor third 3: 7 1215/1024 296.089 cents wide augmented second 3: 1 311.73385 cents 3: 2 65536/54675 313.688 cents 4: 4 164025/131072 388.267 cents 4: 8 512/405 405.866 cents narrow diminished fourth 5: 8 4/3 498.045 cents perfect fourth 5: 3 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 5: 1 268435456/199290375 515.644 cents 6: 2 45/32 590.224 cents diatonic tritone 6: 4 1476225/1048576 592.177 cents two (wide augmented second) 6: 4 2097152/1476225 607.823 cents 6: 2 64/45 609.776 cents 2nd tritone 7: 1 199290375/134217728 684.356 cents 7: 3 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 7: 8 3/2 701.955 cents perfect fifth 8: 8 405/256 794.134 cents wide augmented fifth 8: 4 262144/164025 811.733 cents two (narrow diminished fourth) 9: 2 54675/32768 886.312 cents 9: 1 1793613375/10737418 888.266 cents 9: 7 2048/1215 903.911 cents narrow diminished seventh 9: 2 27/16 905.865 cents Pythagorean major sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 6 3645/2048 998.044 cents wide augmented sixth 10: 2 1073741824/59787112 1013.689 cents 11: 1 15/8 1088.269 cents classic major seventh 11: 4 492075/262144 1090.222 cents 11: 2 8388608/4428675 1105.868 cents 11: 5 256/135 1107.821 cents octave - major chroma 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 : 109.8 203.9 296.1 405.9 498.0 609.8 702.0 811.7 903.9 998.0 1107.8 1200.0 109.8 : 94.1 186.3 296.1 388.3 500.0 592.2 702.0 794.1 888.3 998.0 1090.2 1200.0 203.9 : 92.2 202.0 294.1 405.9 498.0 607.8 700.0 794.1 903.9 996.1 1105.9 1200.0 296.1 : 109.8 202.0 313.7 405.9 515.6 607.8 702.0 811.7 903.9 1013.7 1107.8 1200.0 405.9 : 92.2 203.9 296.1 405.9 498.0 592.2 702.0 794.1 903.9 998.0 1090.2 1200.0 498.0 : 111.7 203.9 313.7 405.9 500.0 609.8 702.0 811.7 905.9 998.0 1107.8 1200.0 609.8 : 92.2 202.0 294.1 388.3 498.0 590.2 700.0 794.1 886.3 996.1 1088.3 1200.0 702.0 : 109.8 202.0 296.1 405.9 498.0 607.8 702.0 794.1 903.9 996.1 1107.8 1200.0 811.7 : 92.2 186.3 296.1 388.3 498.0 592.2 684.4 794.1 886.3 998.0 1090.2 1200.0 903.9 : 94.1 203.9 296.1 405.9 500.0 592.2 702.0 794.1 905.9 998.0 1107.8 1200.0 998.0 : 109.8 202.0 311.7 405.9 498.0 607.8 700.0 811.7 903.9 1013.7 1105.9 1200.0 1107.8: 92.2 202.0 296.1 388.3 498.0 590.2 702.0 794.1 903.9 996.1 1090.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 111.7313 cents 2048/2025, 19.5526 cents 135/128, 92.1787 cents 2: 186.3112 .. 203.9100 cents 67108864/66430125, 17.5988 cents 74.57987 cents 3: 294.1350 .. 313.6876 cents 2048/2025, 19.5526 cents 256/243, 90.2250 cents 4: 388.2674 .. 405.8663 cents 67108864/66430125, 17.5988 cents 74.57987 cents 5: 498.0450 .. 515.6438 cents 67108864/66430125, 17.5988 cents 135/128, 92.1787 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 74.57987 cents 7: 684.3562 .. 701.9550 cents 67108864/66430125, 17.5988 cents 74.57987 cents 8: 794.1337 .. 811.7326 cents 67108864/66430125, 17.5988 cents 135/128, 92.1787 cents 9: 886.3124 .. 905.8650 cents 2048/2025, 19.5526 cents 74.57987 cents 10: 996.0900 .. 1013.6888 cents 67108864/66430125, 17.5988 cents 256/243, 90.2250 cents 11: 1088.2687 .. 1107.8213 cents 2048/2025, 19.5526 cents 74.57987 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.084849 Largest / Average step : 1.117313 Largest / Smallest step : 1.212116 Median interval of one step : 4428675/4194304, 94.1324 cents, amount: 2 Most common interval of one step : 135/128, 92.1787 cents, amount: 5 Least squares average step : 100.44220 cents, oct.: 1205.30640 cents Scale is strictly proper Step pattern alph. order: ABCACDCACBAC Step pattern size order : CBACADACABCA Scale is a Constant Structure, by a margin of 74.57987 cents Scale diversity : 1.131653 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.830537 Rothenberg efficiency : 0.395893 redundancy: 0.604107 Efficiency x scale size : 4.750722 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 Number of recognisable fifths : 11, average 701.4222 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 5 = 41.6667% Limited transpositions with margin 19.5526 cents: 10 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 5 Odd number limit : too high to compute Highest odd numerator or denominator: 492075 Scale harmonicity : 0.011211 Average absolute harmonicity : 0.156635 Specific harmonicity : 0.067517 Fundamental : 1/1007769600, -29.9085 octaves, 0.0000 Hz. Guide tone : 1911029760, 30.8317 octaves, 499974241267.034 Hz. Exponens Consonantiae : 1.925878E+18, 60.74022 octaves Euler's gradus suavitatis : 73 Sum of Mann's harmonic distance : 727588.0, average 60632.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 28.93728, average 2.41144 Sum of Tenney's harmonic distance : 58.73925, average 4.89494 Vogel's harmonic complexity : 45.08333 Wille's k value : 896806687 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 18 Triangular lattice diameter : 18 Lattice compactness : 953.60890, average 12.22576 Lattice compactness (without 2's) : 422.20395, average 5.41287 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 19 4.08333 99 1 3: -9 .. 6 -1.50000 46 3 5: -2 .. 1 -0.50000 10 8 Average exponent except 2's :-24 / 12 =-2.00000 Average absolute exponent except 2's: 56 / 12 = 4.66667 Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 21 28|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.3362 c. M: 11.7326 c. Twelve-tone Chromatic (1/11-comma) 41: 4 3 3 4 3 4 3 4 3 3 4 3 SP M ME SD: 4.1307 c. M:-7.7796 c. Twelve-tone Chromatic (1/44-comma positive) 53: 5 4 4 5 4 5 4 5 4 4 5 4 SP M ME SD: 1.8332 c. M:-3.4300 c. Meantone Chromatic (1/315-comma) 65: 6 5 5 6 5 6 5 6 5 5 6 5 SP M ME SD: 0.6455 c. M: 1.1206 c. Meantone Chromatic (1/52-comma) 142: 13 11 11 13 11 13 11 13 11 11 13 11 SP M DE SD: 0.6690 c. M: 1.3256 c. Meantone Chromatic (1/39-comma), Photia-12 207: 19 16 16 19 16 19 16 19 16 16 19 16 SP M DE SD: 0.6097 c. M: 1.0806 c. 272: 25 21 21 25 21 25 21 25 21 21 25 21 SP M DE SD: 0.5968 c. M: 0.9849 c. 328: 30 26 25 30 25 31 25 30 25 26 30 25 SP SD: 0.5982 c. M:-1.1993 c. 337: 31 26 26 31 26 31 26 31 26 26 31 26 SP M DE SD: 0.5957 c. M: 1.0111 c. 340: 31 27 26 31 26 32 26 31 26 27 31 26 SP SD: 0.4844 c. M:-0.8120 c. 352: 32 28 27 32 27 33 27 32 27 28 32 27 SP SD: 0.4695 c. M:-0.8199 c. 393: 36 31 30 36 30 37 30 36 30 31 36 30 SP SD: 0.4423 c. M:-0.9107 c. 405: 37 32 31 37 31 38 31 37 31 32 37 31 SP SD: 0.3214 c. M:-0.5941 c. 417: 38 33 32 38 32 39 32 38 32 33 38 32 SP SD: 0.2960 c. M:-0.5174 c. 458: 42 36 35 42 35 43 35 42 35 36 42 35 SP SD: 0.3483 c. M:-0.7041 c. 470: 43 37 36 43 36 44 36 43 36 37 43 36 SP SD: 0.2157 c. M:-0.4365 c. 482: 44 38 37 44 37 45 37 44 37 38 44 37 SP SD: 0.1695 c. M:-0.2965 c. 535: 49 42 41 49 41 50 41 49 41 42 49 41 SP SD: 0.1579 c. M:-0.3172 c. 547: 50 43 42 50 42 51 42 50 42 43 50 42 SP SD: 0.0739 c. M:-0.1281 c. 612: 56 48 47 56 47 57 47 56 47 48 56 47 SP SD: 0.0175 c. M:-0.0321 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: 6.5175 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.7891 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.7763 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.3677 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.7623 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.0876 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.9170 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1937 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 10.1677 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.7141 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.4064 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.9160 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.4414 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 4.9736 cents 18:19:20:21:23:24:26:27:29:30:32:34:36 SD: 4.7629 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.1439 cents 26:28:29:31:33:35:37:39:42:44:46:49:52 SD: 3.3002 cents 30:32:34:36:38:40:43:45:48:51:53:57:60 SD: 2.8119 cents 32:34:36:38:40:43:46:48:51:54:57:61:64 SD: 2.6907 cents 33:35:37:39:42:44:47:50:53:56:59:63:66 SD: 2.6264 cents 38:40:43:45:48:51:54:57:61:64:68:72:76 SD: 2.4110 cents 42:45:47:50:53:56:60:63:67:71:75:80:84 SD: 1.6837 cents 48:51:54:57:61:64:68:72:77:81:85:91:96 SD: 1.3825 cents 64:68:72:76:81:85:91:96:102:108:114:121:128 SD: 0.9544 cents 80:85:90:95:101:107:114:120:128:135:142:152:160 SD: 0.8821 cents 90:96:101:107:114:120:128:135:144:152:160:171:180 SD: 0.7260 cents 118:126:133:140:149:157:168:177:189:199:210:224:236 SD: 0.6688 cents 128:136:144:152:162:171:182:192:205:216:228:243:256 SD: 0.6647 cents 135:144:152:160:171:180:192:203:216:228:240:256:270 SD: 0.6365 cents 136:145:153:161:172:181:193:204:217:229:242:258:272 SD: 0.6110 cents 144:153:162:171:182:192:205:216:230:243:256:273:288 SD: 0.5085 cents 166:177:187:197:210:221:236:249:265:280:295:315:332 SD: 0.4505 cents 182:194:205:216:230:243:259:273:291:307:324:345:364 SD: 0.3236 cents 216:230:243:256:273:288:307:324:345:364:384:410:432 SD: 0.3156 cents 232:247:261:275:293:309:330:348:371:391:413:440:464 SD: 0.2951 cents 242:258:272:287:306:323:344:363:387:408:431:459:484 SD: 0.2794 cents 246:262:277:292:311:328:350:369:393:415:438:466:492 SD: 0.2649 cents 258:275:290:306:326:344:367:387:412:435:459:489:516 SD: 0.2276 cents 306:326:344:363:387:408:435:459:489:516:545:580:612 SD: 0.1956 cents 336:358:378:399:425:448:478:504:537:566:598:637:672 SD: 0.1774 cents 398:424:448:472:503:531:566:597:636:671:708:755:796 SD: 0.1771 cents 408:435:459:484:516:544:580:612:652:688:726:774:816 SD: 0.1607 cents 462:492:520:548:584:616:657:693:738:779:822:876:924 SD: 0.1487 cents 488:520:549:579:617:651:694:732:780:823:869:925:976 SD: 0.1472 cents 504:537:567:598:637:672:717:756:805:850:897:956:1008 SD: 0.1352 cents 552:588:621:655:698:736:785:828:882:930:982:1047:1104 SD: 0.1174 cents 568:605:639:674:718:757:808:852:908:957:1011:1077:1136 SD: 0.1132 cents