Scala analysis: xen09-chalmers-tritriadic-6-10-11
Tritriadic scale built from 6:10:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 55/36 733.721654 undecimal semi-augmented fifth 3: 5/3 884.358713 major sixth, BP sixth 4: 121/72 898.725883 5: 20/11 1034.995772 large minor seventh 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: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 605/432 583.0846 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 121/120 14.3672 undecimal seconds comma, biyatisma 5: 1440/1331 136.2699 6: 121/120 14.3672 undecimal seconds comma, biyatisma 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 121/120 14.367 cents undecimal seconds comma, biyatisma 1: 1 1440/1331 136.270 cents 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 605/432 583.085 cents 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 55/36 733.722 cents undecimal semi-augmented fifth 3: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 3: 2 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 3: 1 6/5 315.641 cents minor third 3: 1 1331/864 748.089 cents 3: 2 5/3 884.359 cents major sixth, BP sixth 4: 2 6/5 315.641 cents minor third 4: 1 1728/1331 451.911 cents 4: 1 5/3 884.359 cents major sixth, BP sixth 4: 2 121/72 898.726 cents 4: 1 20/11 1034.996 cents large minor seventh 5: 2 72/55 466.278 cents undecimal semi-diminished fourth 5: 1 121/72 898.726 cents 5: 2 20/11 1034.996 cents large minor seventh 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 864/605 616.915 cents 6: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 1331/720 1063.730 cents 6: 2 240/121 1185.633 cents 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 : 150.6 733.7 884.4 898.7 1035.0 1049.4 1200.0 150.6 : 583.1 733.7 748.1 884.4 898.7 1049.4 1200.0 733.7 : 150.6 165.0 301.3 315.6 466.3 616.9 1200.0 884.4 : 14.4 150.6 165.0 315.6 466.3 1049.4 1200.0 898.7 : 136.3 150.6 301.3 451.9 1035.0 1185.6 1200.0 1035.0: 14.4 165.0 315.6 898.7 1049.4 1063.7 1200.0 1049.4: 150.6 301.3 884.4 1035.0 1049.4 1185.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.3672 .. 583.0846 cents 25/18, 568.7174 cents 121/120, 14.3672 cents 2: 150.6371 .. 733.7217 cents 605/432, 583.0846 cents 5184/6655,-432.4475 cents 3: 165.0042 .. 884.3587 cents 50/33, 719.3545 cents 18/25,-568.7174 cents 4: 315.6413 .. 1034.9958 cents 50/33, 719.3545 cents 18/25,-568.7174 cents 5: 466.2783 .. 1049.3629 cents 605/432, 583.0846 cents 18/25,-568.7174 cents 6: 616.9154 .. 1185.6328 cents 25/18, 568.7174 cents 5184/6655,-432.4475 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 121/120, 14.3672 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 605/432, 583.0846 cents Average / Smallest step : 11.931965 Largest / Average step : 3.401327 Largest / Smallest step : 40.584513 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 : 198.12298 cents, oct.: 1386.86083 cents Scale is not proper Step pattern alph. order: ABACDCA Step pattern size order : CDCABAC Scale is not a Constant Structure Scale diversity : 1.218389 Lumma stability : 0.023945 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 : 121/120, 14.3672 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 : 0 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 : 0.013523 Average absolute harmonicity : 0.184450 Specific harmonicity : 0.073689 Fundamental : 1/792, -9.6294 octaves, 0.3303 Hz. Guide tone : 7260, 12.8258 octaves, 1899401.604 Hz. Exponens Consonantiae : 5.749920E+06, 22.45511 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 183.0, average 26.14286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.64630, average 1.09233 Sum of Tenney's harmonic distance : 14.99644, average 2.14235 Vogel's harmonic complexity : 23.00000 Wille's k value : 665 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 84.91706, average 3.03275 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 11 1 3: -2 .. 1 -0.71429 7 5: 0 .. 1 0.42857 3 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 11 15 26| Scale is weakly epimorphic with val: <7 11 17 23| Scale is weakly epimorphic with val: <7 12 15 25| Scale is weakly epimorphic with val: <7 12 17 22| Scale is weakly epimorphic with val: <7 12 18 24|
FIT/MODE
7: 1 3 1 0 1 0 1 N SD: 28.4866 c. M: 48.0074 c. 8: 1 4 1 0 1 0 1 N SD: 10.2622 c. M:-16.2783 c. 23: 3 11 3 0 3 0 3 N SD: 6.5168 c. M: 11.7694 c. 31: 4 15 4 0 4 0 4 N SD: 5.9514 c. M:-10.1655 c. 39: 5 19 5 0 5 0 5 N SD: 6.2329 c. M:-11.1581 c. 41: 5 20 5 1 4 1 5 N SD: 6.1767 c. M: 10.6055 c. 48: 6 23 6 1 5 1 6 N SD: 6.1645 c. M: 9.9958 c. 49: 6 24 6 1 5 1 6 N SD: 4.3378 c. M:-7.3966 c. 56: 7 27 7 1 6 1 7 N SD: 3.8494 c. M: 6.4243 c. 57: 7 28 7 1 6 1 7 N SD: 3.4957 c. M:-6.5373 c. 64: 8 31 8 1 7 1 8 N SD: 2.1461 c. M: 3.7458 c. 72: 9 35 9 1 8 1 9 N SD: 0.9563 c. M: 1.6624 c. 80: 10 39 10 1 9 1 10 N SD: 0.8000 c. M:-1.2783 c. 152: 19 74 19 2 17 2 19 N SD: 0.6879 c. M:-1.2741 c. 167: 21 81 21 2 19 2 21 N SD: 0.4435 c. M: 0.7875 c. 175: 22 85 22 2 20 2 22 N SD: 0.2734 c. M: 0.4402 c. 247: 31 120 31 3 28 3 31 N SD: 0.1021 c. M: 0.1780 c. 422: 53 205 53 5 48 5 53 N SD: 0.0789 c. M: 0.1477 c. 502: 63 244 63 6 57 6 63 N SD: 0.0798 c. M:-0.1429 c. 669: 84 325 84 8 76 8 84 N SD: 0.0518 c. M: 0.0894 c. 749: 94 364 94 9 85 9 94 N SD: 0.0410 c. M:-0.0725 c. 924: 116 449 116 11 105 11 116 N SD: 0.0395 c. M:-0.0692 c. 1171: 147 569 147 14 133 14 147 N SD: 0.0096 c. M:-0.0170 c. 1418: 178 689 178 17 161 17 178 N SD: 0.0099 c. M: 0.0169 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x 3 x x x x 4 S SD: 15.8833 cents 3 x x 5 x x x 6 SD: 0.0000 cents 4:5:6 x x 7 x 8 S SD: 61.7105 cents 5:6 x 8 x 9 x 10 S SD: 45.0858 cents 6:7:9:10 x x 11:12 SD: 24.0993 cents 7:8:11 x 12 x 13:14 SD: 20.5401 cents 8:9:12:13 x x 15:16 SD: 17.0669 cents 9:10:14:15 x 16:17:18 SD: 13.0883 cents 10:11:15 x 17:18 x 20 SD: 8.7520 cents 11:12:17:18 x 20 x 22 SD: 7.4987 cents 12:13:18:20 x x 22:24 SD: 6.7961 cents 13:14:20 x 22 x 24:26 SD: 6.1178 cents 15:16:23:25 x 27:28:30 SD: 8.8647 cents 16:17:24 x 27:29 x 32 SD: 11.2717 cents 17:19:26:28:29:31 x 34 SD: 8.9396 cents 18:20:28:30 x x 33:36 SD: 8.9044 cents 19:21:29 x 32 x 35:38 SD: 4.8881 cents 21:23:32:35 x 38:39:42 SD: 4.1985 cents 22:24:34 x 37:40 x 44 SD: 3.9916 cents 23:25:35:38:39 x 42:46 SD: 4.0887 cents 24:26:37:40 x x 44:48 SD: 3.9548 cents 25:27:38 x 42:45:46:50 SD: 4.4826 cents 27:29:41:45 x 49:50:54 SD: 5.6489 cents 28:31:43 x 47:51 x 56 SD: 5.4704 cents 29:32:44:48:49 x 53:58 SD: 4.7008 cents 30:33:46:50 x x 55:60 SD: 3.1363 cents 31:34:47 x 52:56:57:62 SD: 3.4297 cents 32:35:49:53:54:58:59:64 SD: 2.5954 cents 33:36:50:55 x 60:61:66 SD: 3.3725 cents 34:37:52 x 57:62 x 68 SD: 1.6134 cents 35:38:53:58:59 x 64:70 SD: 3.5394 cents 36:39:55:60:61:65:66:72 SD: 3.1756 cents 37:40:57 x 62:67:68:74 SD: 3.8935 cents 38:41:58:63:64:69:70:76 SD: 3.3141 cents 40:44:61 x 67:73 x 80 SD: 3.4129 cents 41:45:63:68:69 x 75:82 SD: 2.8973 cents 42:46:64:70:71:76:77:84 SD: 2.2104 cents 43:47:66 x 72:78:79:86 SD: 2.0104 cents 44:48:67:73:74:80:81:88 SD: 1.7363 cents 46:50:70 x 77 x 84:92 SD: 2.6871 cents 47:51:72:78:79:85:86:94 SD: 2.2958 cents 49:53:75:82 x 89:90:98 SD: 2.8481 cents 50:55:76:83:84:91:92:100 SD: 2.7681 cents 51:56:78:85:86:93:94:102 SD: 2.3747 cents 52:57:79:87 x x 95:104 SD: 3.1255 cents 53:58:81:88:89:96:97:106 SD: 1.6051 cents 55:60:84:92 x 100:101:110 SD: 1.1546 cents 58:63:89:97 x 105:106:116 SD: 2.5516 cents 59:64:90:98:99:107:108:118 SD: 1.8712 cents 64:70:98:107:108:116:117:128 SD: 1.8598 cents 65:71:99:108:109:118:119:130 SD: 1.3466 cents 66:72:101:110:111:120:121:132 SD: 0.4487 cents 144:157:220:240:242:262:264:288 SD: 0.2235 cents 210:229:321:350:353:382:385:420 SD: 0.2083 cents 330:360:504:550:555:600:605:660 SD: 0.2029 cents 341:372:521:568:573:620:625:682 SD: 0.1627 cents 407:444:622:678:684:740:746:814 SD: 0.1544 cents 451:492:689:752:758:820:827:902 SD: 0.1230 cents 517:564:790:862:869:940:948:1034 SD: 0.1217 cents 582:635:889:970:978:1058:1067:1164 SD: 0.0752 cents