Scala analysis: xen09-chalmers-tritriadic-17-16-14
Tritriadic scale built from 17:16:14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 17/14 336.129503 supraminor third 3: 392/289 527.740994 4: 448/289 758.915087 5: 28/17 863.870497 submajor sixth 6: 32/17 1095.044590 17th subharmonic 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 17/16 104.9554 17th harmonic 1: 8/7 231.1741 septimal whole tone 2: 17/16 104.9554 17th harmonic 3: 5488/4913 191.6115 4: 8/7 231.1741 septimal whole tone 5: 17/16 104.9554 17th harmonic 6: 8/7 231.1741 septimal whole tone 7: 17/16 104.9554 17th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 17/16 104.955 cents 17th harmonic 1: 1 5488/4913 191.611 cents 1: 3 8/7 231.174 cents septimal whole tone 2: 1 343/289 296.567 cents 2: 5 17/14 336.130 cents supraminor third 2: 1 6272/4913 422.786 cents 3: 2 289/224 441.085 cents 3: 3 392/289 527.741 cents 3: 2 68/49 567.304 cents 4: 2 49/34 632.696 cents 4: 3 289/196 672.259 cents two (supraminor third) 4: 2 448/289 758.915 cents 5: 1 4913/3136 777.214 cents 5: 5 28/17 863.870 cents submajor sixth 5: 1 578/343 903.433 cents 6: 3 7/4 968.826 cents harmonic seventh 6: 1 4913/2744 1008.389 cents 6: 3 32/17 1095.045 cents 17th subharmonic 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 : 231.2 336.1 527.7 758.9 863.9 1095.0 1200.0 231.2 : 105.0 296.6 527.7 632.7 863.9 968.8 1200.0 336.1 : 191.6 422.8 527.7 758.9 863.9 1095.0 1200.0 527.7 : 231.2 336.1 567.3 672.3 903.4 1008.4 1200.0 758.9 : 105.0 336.1 441.1 672.3 777.2 968.8 1200.0 863.9 : 231.2 336.1 567.3 672.3 863.9 1095.0 1200.0 1095.0: 105.0 336.1 441.1 632.7 863.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 231.1741 cents 128/119, 126.2187 cents 17/16, 104.9554 cents 2: 296.5669 .. 422.7856 cents 128/119, 126.2187 cents 2401/2312, 65.3928 cents 3: 441.0849 .. 567.3036 cents 128/119, 126.2187 cents 1419857/1404928, 18.2993 cents 4: 632.6964 .. 758.9151 cents 128/119, 126.2187 cents 2401/2312, 65.3928 cents 5: 777.2144 .. 903.4331 cents 128/119, 126.2187 cents 1419857/1404928, 18.2993 cents 6: 968.8259 .. 1095.0446 cents 128/119, 126.2187 cents 2401/2312, 65.3928 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.633347 Largest / Average step : 1.348516 Largest / Smallest step : 2.202593 Median interval of one step : 5488/4913, 191.6115 cents, amount: 1 Least squares average step : 177.22812 cents, oct.: 1240.59682 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : LSMLSLS Scale is a Constant Structure, by a margin of 18.29933 cents Scale diversity : 1.424963 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.368907 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 : 1419857/1404928, 18.2993 cents Most common intervals : 17/14, 336.1295 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 231.174 336.130 cents Most common triad is 0.0 336.130 863.870 cents, amount: 3 Number of recognisable fifths : 0 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 : 7 17 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 class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 4913 (O: 4913 U: 4913) Highest odd numerator or denominator: 289 Scale harmonicity : 0.007800 Average absolute harmonicity : 0.168068 Specific harmonicity : 0.043102 Fundamental : 1/4046, -11.9823 octaves, 0.0647 Hz. Guide tone : 53312, 15.7022 octaves, 13947782.137 Hz. Exponens Consonantiae : 2.157004E+08, 27.68445 octaves Euler's gradus suavitatis : 74 Sum of Mann's harmonic distance : 780.5, average 111.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.45824, average 1.35118 Sum of Tenney's harmonic distance : 20.00536, average 2.85791 Vogel's harmonic complexity : 34.57143 Wille's k value : 2456 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 101.34480, average 3.61946 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 6 2.71429 21 1 7: -1 .. 2 0.28571 6 1 17: -2 .. 1 -0.71429 7 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 18 31| Scale is weakly epimorphic with val: <7 19 30| Scale is JI-epimorphic with val: <7 20 29| = patent Scale is weakly epimorphic with val: <7 22 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 44.1072 c. M: 73.2008 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 27.3533 c. M: 47.7410 c. Sethares Neutral, Beatles-7, Dichotic-7 11: 2 1 2 2 1 2 1 P M ME S SD: 9.8477 c. M:-17.7136 c. 21: 4 2 3 4 2 4 2 SP T3 SD: 9.4359 c. M: 16.0579 c. 25: 5 2 4 5 2 5 2 P T3 SD: 5.8643 c. M:-9.0849 c. 32: 6 3 5 6 3 6 3 SP T3 SD: 5.1518 c. M: 8.9151 c. 36: 7 3 6 7 3 7 3 P T3 SD: 4.4113 c. M:-7.7516 c. 46: 9 4 7 9 4 9 4 SP T3 SD: 3.2327 c. M: 6.0019 c. 57: 11 5 9 11 5 11 5 SP T3 SD: 0.7880 c. M: 1.4252 c. 125: 24 11 20 24 11 24 11 SP T3 SD: 0.4441 c. M: 0.7741 c. 182: 35 16 29 35 16 35 16 SP T3 SD: 0.3810 c. M: 0.6733 c. 264: 51 23 42 51 23 51 23 SP T3 SD: 0.3670 c. M:-0.6441 c. 275: 53 24 44 53 24 53 24 SP T3 SD: 0.2036 c. M:-0.3576 c. 332: 64 29 53 64 29 64 29 SP T3 SD: 0.0906 c. M:-0.1512 c. 457: 88 40 73 88 40 88 40 SP T3 SD: 0.0570 c. M: 0.1019 c. 789: 152 69 126 152 69 152 69 SP T3 SD: 0.0117 c. M:-0.0203 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: 28.4800 cents 3 x x 4 x 5 x 6 S SD: 12.0260 cents 4 x 5 x 6:7 x 8 S SD: 32.3830 cents 5 x 6:7 x 8:9:10 S SD: 21.8507 cents 6:7 x 8:9:10:11:12 S SD: 14.8204 cents 7:8 x 10:11:12:13:14 S SD: 19.6864 cents 8:9:10:11:12:13:15:16 SD: 12.4973 cents 9:10:11:12:14:15:17:18 SD: 8.8978 cents 10:11:12:14 x 16:19:20 SD: 17.1412 cents 11 x 13:15:17:18:21:22 SD: 9.1857 cents 14:16:17:19:22:23:26:28 SD: 4.7835 cents 20:23:24:27:31:33:38:40 SD: 4.2227 cents 28:32:34:38:43:46:53:56 SD: 2.7718 cents 34:39:41:46:53:56:64:68 SD: 2.4631 cents 42:48:51:57:65:69:79:84 SD: 0.7858 cents 118:135:143:160:183:194:222:236 SD: 0.7419 cents 126:144:153:171:195:208:237:252 SD: 0.7296 cents 127:145:154:172:197:209:239:254 SD: 0.6273 cents 154:176:187:209:239:254:290:308 SD: 0.4761 cents 182:208:221:247:282:300:343:364 SD: 0.3968 cents 196:224:238:266:304:323:369:392 SD: 0.2374 cents 238:272:289:323:369:392:448:476 SD: 0.1408 cents 527:602:640:715:817:868:992:1054 SD: 0.1363 cents 547:625:664:742:848:901:1030:1094 SD: 0.1324 cents 587:671:713:796:910:967:1105:1174 SD: 0.1218 cents 589:673:715:799:913:970:1109:1178 SD: 0.1194 cents