Scala analysis: xen12-chalmers-tritriadic-mt-3-11-27
Tritriadic M->T scale built from 3:11:27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 9/8 203.910002 major whole tone 4: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 5: 121/72 898.725883 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 128/121 97.3641 undecimal semitone 3: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 1331/972 544.1788 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 128/121 97.364 cents undecimal semitone 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 1331/972 544.179 cents 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 9/8 203.910 cents major whole tone 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 121/81 694.816 cents two (undecimal neutral third) 3: 1 9/8 203.910 cents major whole tone 3: 2 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 1331/864 748.089 cents 3: 2 44/27 845.453 cents neutral sixth 4: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 1 1728/1331 451.911 cents 4: 1 44/27 845.453 cents neutral sixth 4: 2 121/72 898.726 cents 4: 1 16/9 996.090 cents Pythagorean minor seventh 5: 2 162/121 505.184 cents 5: 1 121/72 898.726 cents 5: 2 16/9 996.090 cents Pythagorean minor seventh 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 1944/1331 655.821 cents 6: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 121/64 1102.636 cents two (undecimal semi-augmented fourth) 6: 2 64/33 1146.727 cents 33rd subharmonic Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 53.3 150.6 203.9 354.5 898.7 1049.4 1200.0 53.3 : 97.4 150.6 301.3 845.5 996.1 1146.7 1200.0 150.6 : 53.3 203.9 748.1 898.7 1049.4 1102.6 1200.0 203.9 : 150.6 694.8 845.5 996.1 1049.4 1146.7 1200.0 354.5 : 544.2 694.8 845.5 898.7 996.1 1049.4 1200.0 898.7 : 150.6 301.3 354.5 451.9 505.2 655.8 1200.0 1049.4: 150.6 203.9 301.3 354.5 505.2 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 544.1788 cents 968/729, 490.9059 cents 33/32, 53.2729 cents 2: 150.6371 .. 694.8159 cents 1331/972, 544.1788 cents 11664/14641,-393.5418 cents 3: 203.9100 .. 845.4529 cents 352/243, 641.5429 cents 729/968,-490.9059 cents 4: 354.5471 .. 996.0900 cents 352/243, 641.5429 cents 729/968,-490.9059 cents 5: 505.1841 .. 1049.3629 cents 1331/972, 544.1788 cents 729/968,-490.9059 cents 6: 655.8212 .. 1146.7271 cents 968/729, 490.9059 cents 11664/14641,-393.5418 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1331/972, 544.1788 cents Average / Smallest step : 3.217929 Largest / Average step : 3.174376 Largest / Smallest step : 10.214919 Median interval of one step : 12/11, 150.6371 cents, amount: 3 Most common interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 154.10195 cents, oct.: 1078.71362 cents Scale is not proper Step pattern alph. order: ABACDCC Step pattern size order : ABACDCC Scale is not a Constant Structure Scale diversity : 1.450033 Lumma stability : 0.088788 Lumma impropriety factor : 0.748938 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 161051/157464, 38.9947 cents Most common intervals : 12/11, 150.6371 cents & inv., amount: 5 Most common triad is 0.0 150.637 1049.363 cents, amount: 3 Number of recognisable fifths : 2, average 694.8159 cents Scale contains a complete diamond : 3 11 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.013355 Average absolute harmonicity : 0.186769 Specific harmonicity : 0.076174 Fundamental : 1/3168, -11.6294 octaves, 0.0826 Hz. Guide tone : 13068, 13.6738 octaves, 3418922.887 Hz. Exponens Consonantiae : 4.139942E+07, 25.30311 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 183.5, average 26.21429 Mersenne's string divisions : 721048965 Sum of van Prooijen's expressibility: 8.06969, average 1.15281 Sum of Tenney's harmonic distance : 15.83605, average 2.26229 Vogel's harmonic complexity : 25.42857 Wille's k value : 1633 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 110.95565, average 3.96270 Lattice compactness (without 2's) : 67.12282, average 2.39724 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.42857 16 1 3: -2 .. 3 0.57143 10 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 22| Scale is weakly epimorphic with val: <7 12 25|
FIT/MODE
7: 0 1 0 1 3 1 1 N SD: 30.7604 c. M: 53.2729 c. 15: 1 1 1 1 7 2 2 N SD: 23.1032 c. M:-36.0900 c. 16: 1 1 1 2 7 2 2 N SD: 13.8234 c. M:-21.7271 c. 17: 1 1 1 2 8 2 2 N SD: 11.3459 c. M:-18.9212 c. 23: 1 2 1 3 10 3 3 N SD: 7.0279 c. M: 11.7694 c. 24: 1 2 1 3 11 3 3 N SD: 2.6487 c. M: 4.5471 c. 64: 3 5 3 8 29 8 8 N SD: 1.6765 c. M:-2.9771 c. 71: 3 6 3 9 32 9 9 N SD: 1.7322 c. M: 2.9512 c. 88: 4 7 4 11 40 11 11 N SD: 0.7980 c. M:-1.2741 c. 112: 5 9 5 14 51 14 14 N SD: 0.7162 c. M:-1.2741 c. 135: 6 11 6 17 61 17 17 N SD: 0.6158 c. M:-1.0085 c. 159: 7 13 7 20 72 20 20 N SD: 0.3394 c. M: 0.6127 c. 223: 10 18 10 28 101 28 28 N SD: 0.3779 c. M:-0.6099 c. 247: 11 20 11 31 112 31 31 N SD: 0.0961 c. M:-0.1684 c. 518: 23 42 23 65 235 65 65 N SD: 0.0697 c. M:-0.1158 c. 677: 30 55 30 85 307 85 85 N SD: 0.0543 c. M: 0.0972 c. 765: 34 62 34 96 347 96 96 N SD: 0.0527 c. M:-0.0976 c. 924: 41 75 41 116 419 116 116 N SD: 0.0160 c. M: 0.0262 c. 1171: 52 95 52 147 531 147 147 N SD: 0.0125 c. M:-0.0217 c. 2095: 93 170 93 263 950 263 263 N SD: 0.0083 c. M: 0.0147 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 98.3854 cents 3 x x x 4:5 x 6 S SD: 48.0718 cents 4 x x x 5:7 x 8 SD: 25.6540 cents 5 x x x 6:8:9:10 S SD: 24.6912 cents 6 x x 7 x 10:11:12 SD: 16.1448 cents 7 x x 8:9:12:13:14 S SD: 18.8808 cents 8 x x 9:10:13:15:16 SD: 15.3751 cents 9 x x 10:11:15:17:18 SD: 11.6464 cents 10 x 11 x 12:17:18:20 SD: 11.1818 cents 11 x 12 x 14:18:20:22 SD: 15.8730 cents 12 x 13:14:15:20:22:24 S SD: 12.1623 cents 13 x 14:15:16:22:24:26 SD: 8.7171 cents 14 x 15:16:17:24:26:28 SD: 10.1902 cents 15 x 16:17:18:25:28:30 SD: 11.0177 cents 16 x 17:18:20:27:29:32 SD: 9.9140 cents 17:18 x 19:21:29:31:34 SD: 9.2791 cents 18:19 x 20:22:30:33:36 SD: 8.0733 cents 19:20:21 x 23:32:35:38 SD: 8.2033 cents 21:22:23:24:26:35:39:42 SD: 7.1001 cents 22:23:24:25:27:37:40:44 SD: 4.6768 cents 23:24:25:26:28:39:42:46 SD: 4.5359 cents 25:26:27:28:31:42:46:50 SD: 4.3683 cents 30:31:33:34:37:50:55:60 SD: 3.6729 cents 31:32:34:35:38:52:57:62 SD: 1.8507 cents 56:58:61:63:69:94:103:112 SD: 1.7218 cents 65:67:71:73:80:109:119:130 SD: 1.0927 cents 66:68:72:74:81:111:121:132 SD: 0.8842 cents 88:91:96:99:108:148:161:176 SD: 0.8712 cents 97:100:106:109:119:163:178:194 SD: 0.5741 cents 167:172:182:188:205:281:306:334 SD: 0.5491 cents 185:191:202:208:227:311:339:370 SD: 0.4186 cents 198:204:216:223:243:333:363:396 SD: 0.4038 cents 254:262:277:286:312:427:466:508 SD: 0.3761 cents 256:264:279:288:314:430:469:512 SD: 0.3551 cents 263:271:287:296:323:442:482:526 SD: 0.3075 cents 264:272:288:297:324:444:484:528 SD: 0.2935 cents 287:296:313:323:352:482:526:574 SD: 0.2711 cents 320:330:349:360:393:538:587:640 SD: 0.2526 cents 352:363:384:396:432:592:645:704 SD: 0.2255 cents 353:364:385:397:433:593:647:706 SD: 0.2013 cents 383:395:418:431:470:644:702:766 SD: 0.1973 cents 448:462:489:504:550:753:821:896 SD: 0.1927 cents 449:463:490:505:551:755:823:898 SD: 0.1878 cents 505:521:551:568:620:849:926:1010 SD: 0.1852 cents 550:567:600:619:675:924:1008:1100 SD: 0.1733 cents 551:568:601:620:676:926:1010:1102 SD: 0.1468 cents 576:594:628:648:707:968:1056:1152 SD: 0.1467 cents