Scala analysis: jioct12
12-tone JI version of the Messiaens octatonic scale
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: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 125/108 253.076139 semi-augmented whole tone 4: 6/5 315.641287 minor third 5: 5/4 386.313714 major third 6: 25/18 568.717426 classic augmented fourth 7: 36/25 631.282574 classic diminished fifth 8: 3/2 701.955001 perfect fifth 9: 5/3 884.358713 major sixth, BP sixth 10: 125/72 955.031140 classic augmented sixth 11: 9/5 1017.596288 just minor seventh, BP seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 648/625 62.5651 major diesis 3: 3125/2916 119.8386 quasi-equal 10-tone semitone 4: 648/625 62.5651 major diesis 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 10/9 182.4037 minor whole tone 7: 648/625 62.5651 major diesis 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 10/9 182.4037 minor whole tone 10: 25/24 70.6724 classic chromatic semitone, minor chroma 11: 648/625 62.5651 major diesis 12: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 648/625 62.565 cents major diesis 1: 4 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 3125/2916 119.839 cents quasi-equal 10-tone semitone 1: 3 10/9 182.404 cents minor whole tone 2: 4 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 2 10/9 182.404 cents minor whole tone 2: 2 144/125 244.969 cents classic diminished third 2: 4 125/108 253.076 cents semi-augmented whole tone 3: 1 144/125 244.969 cents classic diminished third 3: 2 125/108 253.076 cents semi-augmented whole tone 3: 8 6/5 315.641 cents minor third 3: 1 3125/2592 323.749 cents 4: 2 6/5 315.641 cents minor third 4: 2 3888/3125 378.206 cents 4: 4 5/4 386.314 cents major third 4: 2 625/486 435.480 cents 4: 2 4/3 498.045 cents perfect fourth 5: 1 5/4 386.314 cents major third 5: 3 162/125 448.879 cents 5: 4 4/3 498.045 cents perfect fourth 5: 4 25/18 568.717 cents classic augmented fourth 6: 2 864/625 560.610 cents 6: 4 25/18 568.717 cents classic augmented fourth 6: 4 36/25 631.283 cents classic diminished fifth 6: 2 625/432 639.390 cents 7: 4 36/25 631.283 cents classic diminished fifth 7: 4 3/2 701.955 cents perfect fifth 7: 3 125/81 751.121 cents 7: 1 8/5 813.686 cents minor sixth 8: 2 3/2 701.955 cents perfect fifth 8: 2 972/625 764.520 cents 8: 4 8/5 813.686 cents minor sixth 8: 2 3125/1944 821.794 cents 8: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 5184/3125 876.251 cents 9: 8 5/3 884.359 cents major sixth, BP sixth 9: 2 216/125 946.924 cents semi-augmented sixth 9: 1 125/72 955.031 cents classic augmented sixth 10: 4 216/125 946.924 cents semi-augmented sixth 10: 2 125/72 955.031 cents classic augmented sixth 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 4 50/27 1066.762 cents grave major seventh 11: 3 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 5832/3125 1080.161 cents 11: 4 48/25 1129.328 cents classic diminished octave 11: 4 625/324 1137.435 cents octave - major diesis Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.18182 = 46/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 133.2 253.1 315.6 386.3 568.7 631.3 702.0 884.4 955.0 1017.6 1200.0 70.7 : 62.6 182.4 245.0 315.6 498.0 560.6 631.3 813.7 884.4 946.9 1129.3 1200.0 133.2 : 119.8 182.4 253.1 435.5 498.0 568.7 751.1 821.8 884.4 1066.8 1137.4 1200.0 253.1 : 62.6 133.2 315.6 378.2 448.9 631.3 702.0 764.5 946.9 1017.6 1080.2 1200.0 315.6 : 70.7 253.1 315.6 386.3 568.7 639.4 702.0 884.4 955.0 1017.6 1137.4 1200.0 386.3 : 182.4 245.0 315.6 498.0 568.7 631.3 813.7 884.4 946.9 1066.8 1129.3 1200.0 568.7 : 62.6 133.2 315.6 386.3 448.9 631.3 702.0 764.5 884.4 946.9 1017.6 1200.0 631.3 : 70.7 253.1 323.7 386.3 568.7 639.4 702.0 821.8 884.4 955.0 1137.4 1200.0 702.0 : 182.4 253.1 315.6 498.0 568.7 631.3 751.1 813.7 884.4 1066.8 1129.3 1200.0 884.4 : 70.7 133.2 315.6 386.3 448.9 568.7 631.3 702.0 884.4 946.9 1017.6 1200.0 955.0 : 62.6 245.0 315.6 378.2 498.0 560.6 631.3 813.7 876.3 946.9 1129.3 1200.0 1017.6: 182.4 253.1 315.6 435.5 498.0 568.7 751.1 813.7 884.4 1066.8 1137.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.5651 .. 182.4037 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents 2: 133.2376 .. 253.0761 cents 3125/2916, 119.8386 cents 243/250,-49.1661 cents 3: 244.9689 .. 323.7486 cents 390625/373248, 78.7797 cents 15552/15625,-8.1073 cents 4: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 15552/15625,-8.1073 cents 5: 386.3137 .. 568.7174 cents 10/9, 182.4037 cents 15/16,-111.7313 cents 6: 560.6101 .. 639.3899 cents 390625/373248, 78.7797 cents 15552/15625,-8.1073 cents 7: 631.2826 .. 813.6863 cents 10/9, 182.4037 cents 15552/15625,-8.1073 cents 8: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 15/16,-111.7313 cents 9: 876.2514 .. 955.0311 cents 390625/373248, 78.7797 cents 15552/15625,-8.1073 cents 10: 946.9239 .. 1066.7624 cents 3125/2916, 119.8386 cents 15552/15625,-8.1073 cents 11: 1017.5963 .. 1137.4349 cents 3125/2916, 119.8386 cents 243/250,-49.1661 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 648/625, 62.5651 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.598334 Largest / Average step : 1.824037 Largest / Smallest step : 2.915420 Median interval of one step : 25/24, 70.6724 cents, amount: 4 Least squares average step : 93.60082 cents, oct.: 1123.20981 cents Scale is not proper Step pattern alph. order: ABCBADBADABD Step pattern size order : BACABDABDBAD Scale is not a Constant Structure Scale diversity : 1.266561 Lumma stability : 0.104275 Lumma impropriety factor : 0.308699 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.18182 = 46/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 10 Most common triad is 0.0 315.641 884.359 cents, amount: 8 Number of recognisable fifths : 6, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 41.6667% 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 7 and 8 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties -- Prime limit : 5 Odd number limit : 3125 (O: 3125 U: 3125) Highest odd numerator or denominator: 125 Scale harmonicity : 0.018868 Average absolute harmonicity : 0.163446 Specific harmonicity : 0.106253 Fundamental : 1/5400, -12.3987 octaves, 0.0484 Hz. Guide tone : 13500, 13.7207 octaves, 3531945.132 Hz. Exponens Consonantiae : 7.290000E+07, 26.11942 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 342.5, average 28.54167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.34728, average 1.11227 Sum of Tenney's harmonic distance : 25.98612, average 2.16551 Vogel's harmonic complexity : 23.83333 Wille's k value : 4687 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 11 Triangular lattice diameter : 6 Lattice compactness : 287.64154, average 3.68771 Lattice compactness (without 2's) : 233.78920, average 2.99730 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.66667 16 1 3: -3 .. 3 0.00000 18 1 5: -2 .. 3 0.50000 18 10 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 36 / 12 = 3.00000 Scale is weakly epimorphic with val: <12 17 27| Scale is weakly epimorphic with val: <12 17 31| Scale is weakly epimorphic with val: <12 18 25| Scale is weakly epimorphic with val: <12 18 29| Scale is weakly epimorphic with val: <12 18 31| Scale is weakly epimorphic with val: <12 19 29| Scale is weakly epimorphic with val: <12 21 31|
FIT/MODE
12: 1 0 2 0 1 2 0 1 2 1 0 2 N T3 SD: 27.5925 c. M:-46.9239 c. 13: 1 0 2 0 1 2 1 1 2 0 1 2 N SD: 27.0848 c. M: 40.9299 c. 14: 1 1 1 1 1 2 0 1 2 1 1 2 N D3 SD: 24.9300 c. M:-42.2577 c. 15: 1 1 1 1 1 2 1 1 2 1 1 2 N D3 SD: 13.5516 c. M:-26.7624 c. 19: 1 1 2 1 1 3 1 1 3 1 1 3 N SD: 5.1629 c. M: 7.6627 c. 34: 2 2 3 2 2 5 2 2 5 2 2 5 N G SD: 4.0636 c. M:-7.9389 c. 53: 3 3 5 3 3 8 3 3 8 3 3 8 N G SD: 2.3943 c. M: 4.0877 c. 72: 4 4 7 4 4 11 4 4 11 4 4 11 N G SD: 2.4986 c. M: 5.0311 c. 80: 5 4 8 4 5 12 4 5 12 5 4 12 N SD: 2.6296 c. M:-4.9689 c. 84: 5 4 9 4 5 13 4 5 13 5 4 13 N SD: 2.5308 c. M: 4.6661 c. 99: 6 5 10 5 6 15 5 6 15 6 5 15 N SD: 1.2653 c. M:-2.5446 c. 118: 7 6 12 6 7 18 6 7 18 7 6 18 N SD: 0.6767 c. M:-1.1611 c. 152: 9 8 15 8 9 23 8 9 23 9 8 23 N SD: 0.4983 c. M:-0.9730 c. 171: 10 9 17 9 10 26 9 10 26 10 9 26 N SD: 0.3233 c. M: 0.6452 c. 270: 16 14 27 14 16 41 14 16 41 16 14 41 N SD: 0.2654 c. M:-0.5244 c. 289: 17 15 29 15 17 44 15 17 44 17 15 44 N SD: 0.1818 c. M: 0.3656 c. 441: 26 23 44 23 26 67 23 26 67 26 23 67 N SD: 0.0596 c. M:-0.0958 c. 730: 43 38 73 38 43 111 38 43 111 43 38 111 N SD: 0.0467 c. M: 0.0869 c. 901: 53 47 90 47 53 137 47 53 137 53 47 137 N SD: 0.0529 c. M: 0.0922 c. 1053: 62 55 105 55 62 160 55 62 160 62 55 160 N SD: 0.0524 c. M:-0.0958 c. 1171: 69 61 117 61 69 178 61 69 178 69 61 178 N SD: 0.0263 c. M:-0.0500 c. 1342: 79 70 134 70 79 204 70 79 204 79 70 204 N SD: 0.0193 c. M: 0.0386 c. 1783: 105 93 178 93 105 271 93 105 271 105 93 271 N SD: 0.0118 c. M:-0.0210 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 x 3 x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x 5 x x 6 S SD: 23.5575 cents 4 x x x x 5 x x 6 x 7 x 8 S SD: 3.4487 cents 5 x x x 6 x 7 x x 8 x 9:10 S SD: 14.4012 cents 6 x x 7 x x 8 x 9:10 x 11:12 S SD: 13.1170 cents 7 x x 8 x 9 x 10:11 x 12:13:14 S SD: 16.2518 cents 8 x x 9 x 10:11 x 12:13:14 x 16 S SD: 9.9299 cents 9 x 10 x 11 x x 13:14:15 x 16:18 SD: 12.6825 cents 10 x 11 x 12:13:14 x 15:17 x 18:20 SD: 10.4472 cents 11 x 12 x 13:14:15:16:17:18:19:20:22 S SD: 8.5717 cents 12 x 13:14 x 15 x 17:18:20:21:22:24 SD: 5.2329 cents 13 x 14:15 x 16:18:19:20:22 x 23:26 SD: 7.8357 cents 14 x 15:16:17:18:19:20:21:23:24:25:28 SD: 7.3583 cents 15 x 16:17:18:19:21:22:23:25:26:27:30 SD: 6.4073 cents 16 x 17 x 19:20:22:23:24:27:28:29:32 SD: 4.7293 cents 17:18 x 20 x 21:24 x 26:28:30:31:34 SD: 8.3701 cents 18:19 x 21:22:23:25:26:27:30:31:32:36 SD: 5.6462 cents 20:21:22:23:24:25:28:29:30:33:35:36:40 SD: 3.8639 cents 24:25:26:28:29:30:33:35:36:40:42:43:48 SD: 3.1176 cents 25:26:27:29:30:31:35:36:38:42:43:45:50 SD: 3.0990 cents 36:38:39:42:43:45:50:52:54:60:63:65:72 SD: 2.7084 cents 39:41:42:45:47:49:54:56:59:65:68:70:78 SD: 2.3401 cents 44:46:48:51:53:55:61:63:66:73:76:79:88 SD: 2.1378 cents 46:48:50:53:55:58:64:66:69:77:80:83:92 SD: 2.0238 cents 48:50:52:56:58:60:67:69:72:80:83:86:96 SD: 1.9695 cents 49:51:53:57:59:61:68:71:74:82:85:88:98 SD: 1.8497 cents 50:52:54:58:60:63:69:72:75:83:87:90:100 SD: 1.6660 cents 52:54:56:60:62:65:72:75:78:87:90:94:104 SD: 1.5998 cents 64:67:69:74:77:80:89:92:96:107:111:115:128 SD: 1.0601 cents 75:78:81:87:90:94:104:108:113:125:130:135:150 SD: 0.9062 cents 95:99:103:110:114:119:132:137:143:158:165:171:190 SD: 0.9023 cents 96:100:104:111:115:120:133:138:144:160:167:173:192 SD: 0.7652 cents 100:104:108:116:120:125:139:144:150:167:174:180:200 SD: 0.5985 cents 140:146:151:162:168:175:194:202:210:233:243:252:280 SD: 0.5469 cents 160:167:173:185:192:200:222:230:240:267:278:288:320 SD: 0.5111 cents 164:171:177:190:197:205:228:236:246:273:285:295:328 SD: 0.4004 cents 196:204:212:227:235:245:272:282:294:327:340:353:392 SD: 0.3956 cents 216:225:233:250:259:270:300:311:324:360:375:389:432 SD: 0.2197 cents 336:350:363:389:403:420:467:484:504:560:583:605:672 SD: 0.1762 cents 450:469:486:521:540:563:625:648:675:750:781:810:900 SD: 0.1631 cents 476:496:514:551:571:595:661:685:714:793:826:857:952 SD: 0.1561 cents 484:504:523:560:581:605:672:697:726:807:840:871:968 SD: 0.1492 cents 500:521:540:579:600:625:694:720:750:833:868:900:1000 SD: 0.1398 cents 576:600:622:667:691:720:800:829:864:960:1000:1037:1152 SD: 0.1180 cents