Scala analysis: xen09-chalmers-tritriadic-9-11-13
Tritriadic scale built from 9:11:13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 169/162 73.235320 2: 11/9 347.407941 undecimal neutral third 3: 18/13 563.382340 tridecimal augmented fourth 4: 13/9 636.617660 tridecimal diminished fifth 5: 22/13 910.790281 tridecimal major sixth 6: 143/81 984.025601 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 162/143 215.9744 1: 169/162 73.2353 2: 198/169 274.1726 3: 162/143 215.9744 4: 169/162 73.2353 5: 198/169 274.1726 6: 169/162 73.2353 7: 162/143 215.9744
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 169/162 73.235 cents 1: 2 162/143 215.974 cents 1: 2 198/169 274.173 cents 2: 3 13/11 289.210 cents tridecimal minor third 2: 3 11/9 347.408 cents undecimal neutral third 2: 1 2916/2197 490.147 cents 3: 1 2197/1782 362.445 cents 3: 1 1859/1458 420.643 cents 3: 5 18/13 563.382 cents tridecimal augmented fourth 4: 5 13/9 636.618 cents tridecimal diminished fifth 4: 1 2916/1859 779.357 cents 4: 1 3564/2197 837.555 cents 5: 1 2197/1458 709.853 cents 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 3 22/13 910.790 cents tridecimal major sixth 6: 2 169/99 925.827 cents 6: 2 143/81 984.026 cents 6: 3 324/169 1126.765 cents two (tridecimal augmented fourth) 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 : 73.2 347.4 563.4 636.6 910.8 984.0 1200.0 73.2 : 274.2 490.1 563.4 837.6 910.8 1126.8 1200.0 347.4 : 216.0 289.2 563.4 636.6 852.6 925.8 1200.0 563.4 : 73.2 347.4 420.6 636.6 709.9 984.0 1200.0 636.6 : 274.2 347.4 563.4 636.6 910.8 1126.8 1200.0 910.8 : 73.2 289.2 362.4 636.6 852.6 925.8 1200.0 984.0 : 216.0 289.2 563.4 779.4 852.6 1126.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.2353 .. 274.1726 cents 32076/28561, 200.9373 cents 169/162, 73.2353 cents 2: 289.2097 .. 490.1470 cents 32076/28561, 200.9373 cents 2197/2178, 15.0371 cents 3: 362.4450 .. 563.3823 cents 32076/28561, 200.9373 cents 4826809/5196312,-127.7020 cents 4: 636.6177 .. 837.5550 cents 32076/28561, 200.9373 cents 169/162, 73.2353 cents 5: 709.8530 .. 910.7903 cents 32076/28561, 200.9373 cents 4826809/5196312,-127.7020 cents 6: 925.8274 .. 1126.7647 cents 32076/28561, 200.9373 cents 2197/2178, 15.0371 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 169/162, 73.2353 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 198/169, 274.1726 cents Average / Smallest step : 2.340791 Largest / Average step : 1.599340 Largest / Smallest step : 3.743721 Median interval of one step : 162/143, 215.9744 cents, amount: 2 Most common interval of one step : 169/162, 73.2353 cents, amount: 3 Least squares average step : 170.44838 cents, oct.: 1193.13869 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : SLMSLSM Scale is a Constant Structure, by a margin of 15.03710 cents Scale diversity : 1.378690 Lumma stability : 0.208150 Lumma impropriety factor : 0.212837 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 : 2197/2178, 15.0371 cents Most common intervals : 18/13, 563.3823 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 347.408 636.618 cents Most common triad is 0.0 563.382 636.618 cents, amount: 3 Number of recognisable fifths : 1, average 709.8530 cents Scale contains a complete diamond : 9 13 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 169 Scale harmonicity : 0.009742 Average absolute harmonicity : 0.167953 Specific harmonicity : 0.051837 Fundamental : 1/2106, -11.0403 octaves, 0.1242 Hz. Guide tone : 33462, 15.0302 octaves, 8754514.666 Hz. Exponens Consonantiae : 7.047097E+07, 26.07053 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 333.0, average 47.57143 Mersenne's string divisions : 379246560 Sum of van Prooijen's expressibility: 8.76645, average 1.25235 Sum of Tenney's harmonic distance : 17.69166, average 2.52738 Vogel's harmonic complexity : 30.42857 Wille's k value : 1098 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 89.84605, average 3.20879 Lattice compactness (without 2's) : 85.08042, average 3.03859 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.28571 4 1 3: -4 .. 2 -1.42857 14 11: 0 .. 1 0.42857 3 1 13: -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 JI-epimorphic with val: <7 10 22 24| Scale is weakly epimorphic with val: <7 10 23 26| Scale is weakly epimorphic with val: <7 10 24 28| Scale is weakly epimorphic with val: <7 11 23 24| Scale is JI-epimorphic with val: <7 11 24 26| = patent Scale is weakly epimorphic with val: <7 11 25 28| Scale is weakly epimorphic with val: <7 12 22 27| Scale is weakly epimorphic with val: <7 12 23 29| Scale is weakly epimorphic with val: <7 12 25 26| Scale is JI-epimorphic with val: <7 12 26 28|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 46.3950 c. M: 73.2353 c. 10: 1 2 2 0 3 0 2 N SD: 33.8611 c. M:-49.2097 c. 11: 1 2 2 1 2 1 2 P M ME S SD: 23.2610 c. M: 38.0630 c. Orgone-7 13: 1 3 2 1 3 1 2 N T3 SD: 17.5508 c. M:-31.3590 c. 15: 1 3 3 1 3 1 3 N M DE S SD: 18.3034 c. M: 30.7903 c. 17: 1 4 3 1 4 1 3 N T3 SD: 3.8889 c. M:-6.8568 c. 45: 3 10 8 3 10 3 8 N T3 SD: 3.6483 c. M:-6.7647 c. 49: 3 11 9 3 11 3 9 N T3 SD: 2.9818 c. M: 4.6678 c. 62: 4 14 11 4 14 4 11 N T3 SD: 2.3265 c. M:-4.1840 c. 66: 4 15 12 4 15 4 12 N T3 SD: 1.3073 c. M: 2.2074 c. 83: 5 19 15 5 19 5 15 N T3 SD: 0.5757 c. M: 0.9462 c. 211: 13 48 38 13 48 13 38 N T3 SD: 0.4915 c. M: 0.8377 c. 228: 14 52 41 14 52 14 41 N T3 SD: 0.2413 c. M:-0.4489 c. 245: 15 56 44 15 56 15 44 N T3 SD: 0.2594 c. M:-0.4642 c. 311: 19 71 56 19 71 19 56 N T3 SD: 0.1010 c. M: 0.1793 c. 556: 34 127 100 34 127 34 100 N T3 SD: 0.0919 c. M:-0.1471 c. 639: 39 146 115 39 146 39 115 N T3 SD: 0.0068 c. M:-0.0120 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: 32.6687 cents 3 x x 4 x 5 x 6 S SD: 23.4937 cents 4 x 5 x 6 x 7:8 S SD: 19.3869 cents 5 x 6:7 x 8:9:10 S SD: 21.8461 cents 6 x 7:8:9:10:11:12 S SD: 23.5654 cents 7 x 9 x 10:12 x 14 SD: 23.1194 cents 8:9:10:11:12 x 14:16 S SD: 25.4051 cents 9:10:11:12:13:15:16:18 SD: 18.6432 cents 10:11:12:14 x 17:18:20 SD: 17.4684 cents 11:12:13:15:16:19 x 22 SD: 17.8541 cents 12:13:15 x 17:20:21:24 SD: 14.7596 cents 13:14:16:18:19:22:23:26 SD: 8.5788 cents 16:17:20:22:23:27:28:32 SD: 7.8119 cents 18:19:22:25:26:30:32:36 SD: 5.1259 cents 22:23:27:30:32:37:39:44 SD: 4.6857 cents 23:24:28:32:33:39:41:46 SD: 3.3335 cents 39:41:48:54:56:66:69:78 SD: 3.0069 cents 41:43:50:57:59:69:72:82 SD: 2.7416 cents 42:44:51:58:61:71:74:84 SD: 2.5032 cents 45:47:55:62:65:76:79:90 SD: 1.9390 cents 49:51:60:68:71:83:87:98 SD: 1.8661 cents 63:66:77:87:91:107:111:126 SD: 1.5985 cents 67:70:82:93:97:113:118:134 SD: 1.4174 cents 68:71:83:94:98:115:120:136 SD: 0.8190 cents 94:98:115:130:136:159:166:188 SD: 0.5918 cents 117:122:143:162:169:198:207:234 SD: 0.5434 cents 140:146:171:194:202:237:247:280 SD: 0.4213 cents 162:169:198:224:234:274:286:324 SD: 0.3668 cents 234:244:286:324:338:396:413:468 SD: 0.1308 cents 585:610:715:810:845:990:1033:1170 SD: 0.1245 cents 598:624:731:828:864:1012:1056:1196 SD: 0.1164 cents