Scala analysis: xen09-chalmers-tritriadic-14-16-17
Tritriadic scale built from 14:16:17
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: 68/49 567.303597 4: 289/196 672.259006 two (supraminor third) 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: 8/7 231.1741 septimal whole tone 4: 17/16 104.9554 17th harmonic 5: 5488/4913 191.6115 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 : 231.2 336.1 567.3 672.3 863.9 1095.0 1200.0 231.2 : 105.0 336.1 441.1 632.7 863.9 968.8 1200.0 336.1 : 231.2 336.1 527.7 758.9 863.9 1095.0 1200.0 567.3 : 105.0 296.6 527.7 632.7 863.9 968.8 1200.0 672.3 : 191.6 422.8 527.7 758.9 863.9 1095.0 1200.0 863.9 : 231.2 336.1 567.3 672.3 903.4 1008.4 1200.0 1095.0: 105.0 336.1 441.1 672.3 777.2 968.8 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 : 175.60000 cents, oct.: 1229.20000 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : LSLSMLS 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 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 : 0.168933 Specific harmonicity : 0.043835 Fundamental : 1/3332, -11.7022 octaves, 0.0785 Hz. Guide tone : 64736, 15.9823 octaves, 16936592.595 Hz. Exponens Consonantiae : 2.157004E+08, 27.68445 octaves Euler's gradus suavitatis : 74 Sum of Mann's harmonic distance : 372.5, average 53.21429 Mersenne's string divisions : 86195655 Sum of van Prooijen's expressibility: 8.68754, average 1.24108 Sum of Tenney's harmonic distance : 18.11486, average 2.58784 Vogel's harmonic complexity : 34.28571 Wille's k value : 2456 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 97.39117, average 3.47826 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 5 1.42857 16 1 7: -2 .. 1 -0.71429 7 1 17: -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 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: 39.7684 c. M: 66.4732 c. Lebeng 10: 2 1 2 1 1 2 1 P M ME S SD: 26.1646 c. M:-47.7410 c. 11: 2 1 2 1 2 2 1 P M ME S SD: 12.7276 c. M: 21.8491 c. 21: 4 2 4 2 3 4 2 SP T3 SD: 7.3912 c. M:-13.4553 c. 25: 5 2 5 2 4 5 2 P T3 SD: 5.7796 c. M:-8.9554 c. 32: 6 3 6 3 5 6 3 SP T3 SD: 4.2992 c. M: 7.5446 c. 36: 7 3 7 3 6 7 3 P T3 SD: 3.3066 c. M: 5.5923 c. 57: 11 5 11 5 9 11 5 SP T3 SD: 0.8066 c. M:-1.4252 c. 125: 24 11 24 11 20 24 11 SP T3 SD: 0.5253 c. M: 0.9036 c. 182: 35 16 35 16 29 35 16 SP T3 SD: 0.3014 c. M: 0.5391 c. 275: 53 24 53 24 44 53 24 SP T3 SD: 0.1528 c. M: 0.2590 c. 332: 64 29 64 29 53 64 29 SP T3 SD: 0.1003 c. M:-0.1663 c. 457: 88 40 88 40 73 88 40 SP T3 SD: 0.0716 c. M: 0.1264 c. 514: 99 45 99 45 82 99 45 SP T3 SD: 0.0681 c. M:-0.1145 c. 789: 152 69 152 69 126 152 69 SP T3 SD: 0.0089 c. M: 0.0157 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: 14.8480 cents 3 x x 4 x 5 x 6 S SD: 24.0752 cents 4 x 5 x 6:7 x 8 S SD: 30.0166 cents 5 x 6:7 x 8:9:10 S SD: 19.1497 cents 6:7 x 8:9:10:11:12 S SD: 16.2099 cents 7:8:9:10 x 12:13:14 S SD: 22.1435 cents 8:9:10:11:12:13:15:16 SD: 10.0914 cents 11 x 13:15:16:18:21:22 SD: 11.0580 cents 13:15:16:18:19:21:24:26 SD: 8.2416 cents 14:16:17:19:21:23:26:28 SD: 7.7427 cents 15:17:18:21:22:25:28:30 SD: 5.6702 cents 19:22:23:26:28:31:36:38 SD: 5.5841 cents 23:26:28:32:34:38:43:46 SD: 3.4545 cents 28:32:34:39:41:46:53:56 SD: 2.4631 cents 34:39:41:47:50:56:64:68 SD: 2.2657 cents 42:48:51:58:62:69:79:84 SD: 1.4111 cents 57:65:69:79:84:94:107:114 SD: 1.2490 cents 70:80:85:97:103:115:132:140 SD: 0.9952 cents 85:97:103:118:125:140:160:170 SD: 0.9129 cents 93:106:113:129:137:153:175:186 SD: 0.7890 cents 111:127:135:154:164:183:209:222 SD: 0.7406 cents 126:144:153:175:186:208:237:252 SD: 0.6854 cents 127:145:154:176:187:209:239:254 SD: 0.6793 cents 139:159:169:193:205:229:262:278 SD: 0.5322 cents 154:176:187:214:227:254:290:308 SD: 0.4935 cents 168:192:204:233:248:277:316:336 SD: 0.4552 cents 181:207:220:251:267:298:341:362 SD: 0.4323 cents 196:224:238:272:289:323:369:392 SD: 0.1408 cents 434:496:527:602:640:715:817:868 SD: 0.1363 cents 518:592:629:719:764:853:975:1036 SD: 0.1003 cents