Scala analysis: xen09-chalmers-tritriadic-6-8-11
Tritriadic scale built from 6:8:11
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: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 16/11 648.682058 undecimal semi-diminished fifth 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: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 121/108 196.7709 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 1331/1152 250.0438 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: 5 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 121/108 196.771 cents 1: 1 1331/1152 250.044 cents 2: 3 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 121/96 400.681 cents 3: 1 1728/1331 451.911 cents 3: 3 4/3 498.045 cents perfect fourth 3: 3 11/8 551.318 cents undecimal semi-augmented fourth 4: 3 16/11 648.682 cents undecimal semi-diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 1331/864 748.089 cents 5: 2 192/121 799.319 cents 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 3 121/72 898.726 cents 6: 1 2304/1331 949.956 cents 6: 1 216/121 1003.229 cents 6: 5 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 150.6 347.4 498.0 648.7 898.7 1049.4 1200.0 150.6 : 196.8 347.4 498.0 748.1 898.7 1049.4 1200.0 347.4 : 150.6 301.3 551.3 702.0 852.6 1003.2 1200.0 498.0 : 150.6 400.7 551.3 702.0 852.6 1049.4 1200.0 648.7 : 250.0 400.7 551.3 702.0 898.7 1049.4 1200.0 898.7 : 150.6 301.3 451.9 648.7 799.3 950.0 1200.0 1049.4: 150.6 301.3 498.0 648.7 799.3 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 250.0438 cents 14641/13824, 99.4068 cents 12/11, 150.6371 cents 2: 301.2741 .. 400.6809 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 3: 451.9112 .. 551.3179 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 4: 648.6821 .. 748.0888 cents 14641/13824, 99.4068 cents 128/121, 97.3641 cents 5: 799.3191 .. 898.7259 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 6: 949.9562 .. 1049.3629 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1331/1152, 250.0438 cents Average / Smallest step : 1.138024 Largest / Average step : 1.458589 Largest / Smallest step : 1.659909 Median interval of one step : 12/11, 150.6371 cents, amount: 5 Most common interval of one step : 12/11, 150.6371 cents, amount: 5 Least squares average step : 172.31517 cents, oct.: 1206.20616 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : SMSSLSS Scale is a Constant Structure, by a margin of 51.23029 cents Scale diversity : 1.396184 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.502966 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 : 1331/1296, 46.1338 cents Most common intervals : 12/11, 150.6371 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 1049.363 cents Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle 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 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.014379 Average absolute harmonicity : 0.201971 Specific harmonicity : 0.081787 Fundamental : 1/792, -9.6294 octaves, 0.3303 Hz. Guide tone : 5808, 12.5038 octaves, 1519521.283 Hz. Exponens Consonantiae : 4.599936E+06, 22.13318 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 145.0, average 20.71429 Mersenne's string divisions : 285250140 Sum of van Prooijen's expressibility: 6.72548, average 0.96078 Sum of Tenney's harmonic distance : 13.50159, average 1.92880 Vogel's harmonic complexity : 21.71429 Wille's k value : 665 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 92.09685, average 3.28917 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.71429 13 1 3: -2 .. 1 -0.71429 7 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 25| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 12 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 24.6390 c. M: 41.5830 c. Lebeng 13: 2 2 1 2 3 1 2 P D3 SD: 25.9598 c. M: 36.5065 c. 15: 2 2 2 2 3 2 2 SP M ME S SD: 15.4836 c. M: 27.4079 c. 17: 2 3 2 2 4 2 2 P T3 SD: 10.4355 c. M:-18.9212 c. 24: 3 4 3 3 5 3 3 SP T3 SD: 1.4498 c. M:-2.5921 c. 87: 11 14 11 11 18 11 11 SP T3 SD: 1.5186 c. M: 2.5804 c. 104: 13 17 13 13 22 13 13 SP T3 SD: 1.4130 c. M: 2.5282 c. 111: 14 18 14 14 23 14 14 SP T3 SD: 0.9070 c. M: 1.4620 c. 135: 17 22 17 17 28 17 17 SP T3 SD: 0.5361 c. M: 0.9481 c. 159: 20 26 20 20 33 20 20 SP T3 SD: 0.3305 c. M: 0.6127 c. 183: 23 30 23 23 38 23 23 SP T3 SD: 0.2843 c. M:-0.4983 c. 311: 39 51 39 39 65 39 39 SP T3 SD: 0.2547 c. M: 0.4505 c. 335: 42 55 42 42 70 42 42 SP T3 SD: 0.2207 c. M:-0.3786 c. 446: 56 73 56 56 93 56 56 SP T3 SD: 0.1918 c. M: 0.3227 c. 470: 59 77 59 59 98 59 59 SP T3 SD: 0.1130 c. M: 0.1739 c. 494: 62 81 62 62 103 62 62 SP T3 SD: 0.0554 c. M: 0.0991 c. 677: 85 111 85 85 141 85 85 SP T3 SD: 0.0373 c. M:-0.0624 c. 1147: 144 188 144 144 239 144 144 SP T3 SD: 0.0375 c. M: 0.0671 c. 1171: 147 192 147 147 244 147 147 SP T3 SD: 0.0070 c. M: 0.0126 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: 26.6365 cents 3 x x 4 x 5 x 6 S SD: 4.7891 cents 4 x 5 x 6:7 x 8 S SD: 24.0646 cents 5 x 6 x 7:8:9:10 S SD: 23.3482 cents 6 x 7:8:9:10:11:12 S SD: 16.2708 cents 7:8 x 9:10:12:13:14 S SD: 19.0802 cents 8:9:10:11:12:13:15:16 SD: 17.4545 cents 9:10:11:12:13:15:17:18 SD: 9.0713 cents 12:13:15:16:17:20:22:24 SD: 8.9812 cents 13:14:16:17:19:22:24:26 SD: 6.6005 cents 18:20:22:24:26:30:33:36 SD: 5.2704 cents 22:24:27:29:32:37:40:44 SD: 3.6437 cents 31:34:38:41:45:52:57:62 SD: 2.6982 cents 42:46:51:56:61:71:77:84 SD: 2.4104 cents 44:48:54:59:64:74:81:88 SD: 2.0195 cents 53:58:65:71:77:89:97:106 SD: 1.7256 cents 54:59:66:72:79:91:99:108 SD: 1.6264 cents 66:72:81:88:96:111:121:132 SD: 1.0367 cents 90:98:110:120:131:151:165:180 SD: 0.6380 cents 132:144:161:176:192:222:242:264 SD: 0.5442 cents 156:170:191:208:227:262:286:312 SD: 0.5395 cents 176:192:215:235:256:296:323:352 SD: 0.4892 cents 185:202:226:247:269:311:339:370 SD: 0.4513 cents 198:216:242:264:288:333:363:396 SD: 0.1857 cents 288:314:352:384:419:484:528:576 SD: 0.1529 cents 473:516:578:631:688:795:867:946 SD: 0.1500 cents 486:530:594:648:707:817:891:972 SD: 0.1181 cents 504:550:616:672:733:847:924:1008 SD: 0.0873 cents 594:648:726:792:864:998:1089:1188 SD: 0.0619 cents