Scala analysis: xen09-chalmers-tritriadic-9-10-11
Tritriadic scale built from 9:10:11
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: 110/81 529.811653 4: 121/81 694.815881 two (undecimal neutral third) 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: 10/9 182.4037 minor whole tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 1458/1331 157.7762 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 : 182.4 347.4 529.8 694.8 852.6 1035.0 1200.0 182.4 : 165.0 347.4 512.4 670.2 852.6 1017.6 1200.0 347.4 : 182.4 347.4 505.2 687.6 852.6 1035.0 1200.0 529.8 : 165.0 322.8 505.2 670.2 852.6 1017.6 1200.0 694.8 : 157.8 340.2 505.2 687.6 852.6 1035.0 1200.0 852.6 : 182.4 347.4 529.8 694.8 877.2 1042.2 1200.0 1035.0: 165.0 347.4 512.4 694.8 859.8 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 : 172.27752 cents, oct.: 1205.94265 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : LMLMSLM 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 1 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 : 0.178331 Specific harmonicity : 0.069350 Fundamental : 1/891, -9.7993 octaves, 0.2936 Hz. Guide tone : 21780, 14.4107 octaves, 5698204.812 Hz. Exponens Consonantiae : 1.940598E+07, 24.21000 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 247.5, average 35.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.06969, average 1.15281 Sum of Tenney's harmonic distance : 16.83114, average 2.40445 Vogel's harmonic complexity : 24.85714 Wille's k value : 665 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 91.01747, average 3.25062 Lattice compactness (without 2's) : 85.08042, average 3.03859 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.85714 6 1 3: -4 .. 2 -1.42857 14 5: 0 .. 1 0.42857 3 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 23 / 7 = 3.28571 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: 8.6771 c. M: 15.5259 c. Lebeng 31: 5 4 5 4 4 5 4 SP M ME S SD: 7.3706 c. M:-12.1238 c. Neutral Hypodorian 34: 5 5 5 5 4 5 5 SP M ME S SD: 7.0765 c. M: 11.4664 c. 38: 6 5 6 5 5 6 5 SP M ME S SD: 4.6286 c. M:-7.1095 c. 45: 7 6 7 6 6 7 6 SP M ME S SD: 2.9011 c. M:-5.0042 c. 52: 8 7 8 7 7 8 7 SP M ME S SD: 1.9733 c. M:-3.4658 c. 59: 9 8 9 8 8 9 8 SP M ME S SD: 1.8091 c. M: 3.2905 c. 86: 13 12 13 12 11 13 12 SP T3 SD: 1.6645 c. M:-2.8585 c. 93: 14 13 14 13 12 14 13 SP T3 SD: 1.5560 c. M: 2.7377 c. 100: 15 14 15 14 13 15 14 SP T3 SD: 1.6961 c. M: 2.9958 c. 124: 19 17 19 17 16 19 17 SP T3 SD: 1.4207 c. M:-2.4464 c. 131: 20 18 20 18 17 20 18 SP T3 SD: 0.9001 c. M:-1.4861 c. 138: 21 19 21 19 18 21 19 SP T3 SD: 0.4667 c. M:-0.8363 c. 145: 22 20 22 20 19 22 20 SP T3 SD: 0.2904 c. M: 0.5130 c. 335: 51 46 51 46 44 51 46 SP T3 SD: 0.1942 c. M:-0.3376 c. 342: 52 47 52 47 45 52 47 SP T3 SD: 0.0544 c. M:-0.0919 c. 487: 74 67 74 67 64 74 67 SP T3 SD: 0.0493 c. M: 0.0882 c. 829: 126 114 126 114 109 126 114 SP T3 SD: 0.0101 c. M: 0.0167 c. 2000: 304 275 304 275 263 304 275 SP T3 SD: 0.0088 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: 3.5696 cents 3 x x 4 x 5 x 6 S SD: 14.9749 cents 4 x 5 x 6 x 7:8 S SD: 19.2728 cents 5 x 6:7 x 8:9:10 S SD: 14.9705 cents 6 x 7:8:9:10:11:12 S SD: 15.6008 cents 7:8:9 x 10:11:13:14 SD: 24.8923 cents 8:9:10:11:12:13:15:16 SD: 10.5687 cents 14:16:17:19:21:23:25:28 SD: 8.5453 cents 16:18:20:22:24:26:29:32 SD: 7.3742 cents 17:19:21:23:25:28:31:34 SD: 5.2959 cents 22:24:27:30:33:36:40:44 S SD: 4.8698 cents 26:29:32:35:39:43:47:52 SD: 4.3107 cents 27:30:33:37:40:44:49:54 SD: 3.2361 cents 28:31:34:38:42:46:51:56 SD: 2.3662 cents 36:40:44:49:54:59:65:72 SD: 2.1145 cents 44:49:54:60:66:72:80:88 SD: 1.8536 cents 45:50:55:61:67:74:82:90 SD: 1.6306 cents 55:61:67:75:82:90:100:110 SD: 1.4653 cents 71:79:87:96:106:116:129:142 SD: 1.3736 cents 72:80:88:98:108:118:131:144 SD: 1.2370 cents 81:90:99:110:121:133:147:162 SD: 0.9628 cents 89:99:109:121:133:146:162:178 SD: 0.9354 cents 99:110:121:134:148:162:180:198 SD: 0.8397 cents 109:121:133:148:163:178:198:218 SD: 0.7738 cents 117:130:143:159:175:191:213:234 SD: 0.7581 cents 126:140:154:171:188:206:229:252 SD: 0.4104 cents 154:171:188:209:230:252:280:308 SD: 0.3739 cents 198:220:242:269:296:324:360:396 SD: 0.2120 cents 324:360:396:440:484:530:589:648 SD: 0.0930 cents 567:630:693:770:847:928:1031:1134 SD: 0.0531 cents