Scala analysis: xen09-chalmers-tritriadic-11-20-18
Tritriadic scale built from 11:20:18
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 11/9 347.407941 undecimal neutral third 3: 162/121 505.184119 4: 180/121 687.587831 5: 18/11 852.592059 undecimal neutral sixth 6: 20/11 1034.995772 large minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 10/9 182.4037 minor whole tone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 1458/1331 157.7762 4: 10/9 182.4037 minor whole tone 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 10/9 182.4037 minor whole tone 7: 11/10 165.0042 Ptolemy's second, 4/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1458/1331 157.776 cents 1: 3 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 3 10/9 182.404 cents minor whole tone 2: 1 729/605 322.780 cents 2: 1 1620/1331 340.180 cents 2: 5 11/9 347.408 cents undecimal neutral third 3: 3 162/121 505.184 cents 3: 2 121/90 512.412 cents 3: 2 110/81 529.812 cents 4: 2 81/55 670.188 cents 4: 2 180/121 687.588 cents 4: 3 121/81 694.816 cents two (undecimal neutral third) 5: 5 18/11 852.592 cents undecimal neutral sixth 5: 1 1331/810 859.820 cents 5: 1 1210/729 877.220 cents 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 20/11 1034.996 cents large minor seventh 6: 1 1331/729 1042.224 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 347.4 505.2 687.6 852.6 1035.0 1200.0 182.4 : 165.0 322.8 505.2 670.2 852.6 1017.6 1200.0 347.4 : 157.8 340.2 505.2 687.6 852.6 1035.0 1200.0 505.2 : 182.4 347.4 529.8 694.8 877.2 1042.2 1200.0 687.6 : 165.0 347.4 512.4 694.8 859.8 1017.6 1200.0 852.6 : 182.4 347.4 529.8 694.8 852.6 1035.0 1200.0 1035.0: 165.0 347.4 512.4 670.2 852.6 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 157.7762 .. 182.4037 cents 6655/6561, 24.6275 cents 1458/1331, 157.7762 cents 2: 322.7804 .. 347.4079 cents 6655/6561, 24.6275 cents 6561/6050, 140.3767 cents 3: 505.1841 .. 529.8117 cents 6655/6561, 24.6275 cents 1458/1331, 157.7762 cents 4: 670.1883 .. 694.8159 cents 6655/6561, 24.6275 cents 6561/6050, 140.3767 cents 5: 852.5921 .. 877.2196 cents 6655/6561, 24.6275 cents 1458/1331, 157.7762 cents 6: 1017.5963 .. 1042.2238 cents 6655/6561, 24.6275 cents 6561/6050, 140.3767 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1458/1331, 157.7762 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.086530 Largest / Average step : 1.064022 Largest / Smallest step : 1.156092 Median interval of one step : 11/10, 165.0042 cents, amount: 3 Least squares average step : 171.54327 cents, oct.: 1200.80291 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : LMSLMLM Scale is a Constant Structure, by a margin of 140.37669 cents Scale diversity : 1.126523 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.876862 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 : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 14641/14580, 7.2281 cents Most common intervals : 11/9, 347.4079 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 182.404 347.408 cents Most common triad is 0.0 347.408 852.592 cents, amount: 3 Number of recognisable fifths : 5, average 691.9247 cents Number of appreciable fifths : 3, average 694.8159 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 9 11 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Limited transpositions with margin 24.6275 cents: 1 2 3 4 5 6 Limited inverse transpositions with margin 24.6275 cents: 1 2 3 4 5 6 -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.012667 Average absolute harmonicity : 0.177178 Specific harmonicity : 0.068252 Fundamental : 1/1089, -10.0888 octaves, 0.2402 Hz. Guide tone : 17820, 14.1212 octaves, 4662167.574 Hz. Exponens Consonantiae : 1.940598E+07, 24.21000 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 343.0, average 49.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.24399, average 1.17771 Sum of Tenney's harmonic distance : 17.52035, average 2.50291 Vogel's harmonic complexity : 25.14286 Wille's k value : 665 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 90.38038, average 3.22787 Lattice compactness (without 2's) : 83.83777, average 2.99421 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.14286 8 1 3: -2 .. 4 0.57143 12 5: 0 .. 1 0.42857 3 1 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 15 24| Scale is weakly epimorphic with val: <7 10 16 26| Scale is weakly epimorphic with val: <7 10 18 23| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 12 16 22| Scale is JI-epimorphic with val: <7 12 18 26|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 6.4309 c. M: 10.9751 c. Lebeng 31: 5 4 4 5 4 5 4 SP M ME S SD: 6.7367 c. M:-11.1447 c. Neutral Lydian, Dicot-7 38: 6 5 5 6 5 6 5 SP M ME S SD: 4.6544 c. M:-7.1490 c. 45: 7 6 6 7 6 7 6 SP M ME S SD: 3.3705 c. M:-5.7455 c. 52: 8 7 7 8 7 8 7 SP M ME S SD: 2.6354 c. M:-4.7199 c. 59: 9 8 8 9 8 9 8 SP M ME S SD: 2.3120 c. M:-3.9376 c. 66: 10 9 9 10 9 10 9 SP M ME S SD: 2.2722 c. M:-3.9068 c. 86: 13 12 11 13 12 13 12 SP T3 SD: 2.2094 c. M: 3.8669 c. 93: 14 13 12 14 13 14 13 SP T3 SD: 2.0755 c. M: 3.7169 c. 100: 15 14 13 15 14 15 14 SP T3 SD: 2.0608 c. M: 3.5878 c. 107: 16 15 14 16 15 16 15 SP T3 SD: 2.1257 c. M: 3.4757 c. 110: 17 15 14 17 15 17 15 SP T3 SD: 2.0097 c. M: 3.3659 c. 117: 18 16 15 18 16 18 16 SP T3 SD: 1.5198 c. M: 2.6200 c. 124: 19 17 16 19 17 19 17 SP T3 SD: 1.0944 c. M: 1.9583 c. 131: 20 18 17 20 18 20 18 SP T3 SD: 0.7350 c. M: 1.3673 c. 138: 21 19 18 21 19 21 19 SP T3 SD: 0.4683 c. M: 0.8363 c. 145: 22 20 19 22 20 22 20 SP T3 SD: 0.3861 c. M: 0.6913 c. 283: 43 39 37 43 39 43 39 SP T3 SD: 0.3966 c. M: 0.6620 c. 328: 50 45 43 50 45 50 45 SP T3 SD: 0.2923 c. M:-0.5231 c. 335: 51 46 44 51 46 51 46 SP T3 SD: 0.1604 c. M:-0.2829 c. 342: 52 47 45 52 47 52 47 SP T3 SD: 0.0735 c. M:-0.1315 c. 487: 74 67 64 74 67 74 67 SP T3 SD: 0.0638 c. M: 0.1135 c. 822: 125 113 108 125 113 125 113 SP T3 SD: 0.0480 c. M:-0.0780 c. 829: 126 114 109 126 114 126 114 SP T3 SD: 0.0092 c. M: 0.0153 c. 2000: 304 275 263 304 275 304 275 SP T3 SD: 0.0089 c. M:-0.0159 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 7.1836 cents 3 x x 4 x 5 x 6 S SD: 10.8530 cents 4 x 5 x 6 x 7:8 S SD: 19.5233 cents 5 x 6:7 x 8:9:10 S SD: 18.7672 cents 6 x 7:8:9:10:11:12 S SD: 14.8690 cents 7:8 x 9:10:11:13:14 SD: 22.6495 cents 8:9:10:11:12:13:15:16 SD: 12.2011 cents 9:10:11:12:13:15:16:18 SD: 10.2735 cents 12:13:15:16:18:20:22:24 SD: 10.0079 cents 14:16:17:19:21:23:25:28 SD: 9.3510 cents 15:17:18:20:22:25:27:30 SD: 9.2023 cents 16:18:20:21:24:26:29:32 SD: 8.5010 cents 17:19:21:23:25:28:31:34 SD: 5.1920 cents 18:20:22:24:27:29:33:36 SD: 4.9255 cents 26:29:32:35:39:43:47:52 SD: 4.3421 cents 27:30:33:36:40:44:49:54 SD: 1.8250 cents 45:50:55:60:67:74:82:90 SD: 1.6945 cents 53:59:65:71:79:87:96:106 SD: 1.6355 cents 55:61:67:74:82:90:100:110 SD: 1.6306 cents 63:70:77:84:94:103:115:126 SD: 1.6110 cents 71:79:87:95:106:116:129:142 SD: 1.2304 cents 72:80:88:96:107:118:131:144 SD: 1.1299 cents 80:89:98:107:119:131:145:160 SD: 1.0494 cents 82:91:100:110:122:134:149:164 SD: 0.8733 cents 109:121:133:146:162:178:198:218 SD: 0.7697 cents 127:141:155:170:189:208:231:254 SD: 0.4812 cents 154:171:188:206:229:252:280:308 SD: 0.4104 cents 162:180:198:217:241:265:295:324 SD: 0.4095 cents 189:210:231:253:281:309:344:378 SD: 0.3698 cents 207:230:253:277:308:339:376:414 SD: 0.3396 cents 215:239:263:288:320:352:391:430 SD: 0.3305 cents 225:250:275:301:335:368:409:450 SD: 0.3199 cents 242:269:296:324:360:396:440:484 SD: 0.2120 cents 324:360:396:434:482:530:589:648 SD: 0.1540 cents 369:410:451:494:549:604:671:738 SD: 0.0898 cents