Scala analysis: xen09-chalmers-tritriadic-17-15-14
Tritriadic scale built from 17:15:14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 17/14 336.129503 supraminor third 3: 392/289 527.740994 4: 420/289 647.183802 5: 28/17 863.870497 submajor sixth 6: 30/17 983.313305 septendecimal minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 17/15 216.6867 septendecimal whole tone 1: 15/14 119.4428 major diatonic semitone 2: 17/15 216.6867 septendecimal whole tone 3: 5488/4913 191.6115 4: 15/14 119.4428 major diatonic semitone 5: 17/15 216.6867 septendecimal whole tone 6: 15/14 119.4428 major diatonic semitone 7: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 15/14 119.443 cents major diatonic semitone 1: 1 5488/4913 191.611 cents 1: 3 17/15 216.687 cents septendecimal whole tone 2: 1 5880/4913 311.054 cents 2: 5 17/14 336.130 cents supraminor third 2: 1 5488/4335 408.298 cents 3: 2 255/196 455.572 cents 3: 3 392/289 527.741 cents 3: 2 289/210 552.816 cents 4: 2 420/289 647.184 cents 4: 3 289/196 672.259 cents two (supraminor third) 4: 2 392/255 744.428 cents 5: 1 4335/2744 791.702 cents 5: 5 28/17 863.870 cents submajor sixth 5: 1 4913/2940 888.946 cents 6: 3 30/17 983.313 cents septendecimal minor seventh 6: 1 4913/2744 1008.389 cents 6: 3 28/15 1080.557 cents grave major seventh 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 : 119.4 336.1 527.7 647.2 863.9 983.3 1200.0 119.4 : 216.7 408.3 527.7 744.4 863.9 1080.6 1200.0 336.1 : 191.6 311.1 527.7 647.2 863.9 983.3 1200.0 527.7 : 119.4 336.1 455.6 672.3 791.7 1008.4 1200.0 647.2 : 216.7 336.1 552.8 672.3 888.9 1080.6 1200.0 863.9 : 119.4 336.1 455.6 672.3 863.9 983.3 1200.0 983.3 : 216.7 336.1 552.8 744.4 863.9 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 216.6867 cents 238/225, 97.2439 cents 15/14, 119.4428 cents 2: 311.0543 .. 408.2982 cents 238/225, 97.2439 cents 88200/83521, 94.3676 cents 3: 455.5723 .. 552.8162 cents 238/225, 97.2439 cents 1105425/1075648, 47.2741 cents 4: 647.1838 .. 744.4277 cents 238/225, 97.2439 cents 88200/83521, 94.3676 cents 5: 791.7018 .. 888.9457 cents 238/225, 97.2439 cents 1105425/1075648, 47.2741 cents 6: 983.3133 .. 1080.5572 cents 238/225, 97.2439 cents 88200/83521, 94.3676 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 1.435236 Largest / Average step : 1.264006 Largest / Smallest step : 1.814146 Median interval of one step : 5488/4913, 191.6115 cents, amount: 1 Least squares average step : 168.44923 cents, oct.: 1179.14462 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : SLMSLSL Scale is a Constant Structure, by a margin of 47.27413 cents Scale diversity : 1.398446 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.513781 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 : 83521/82320, 25.0752 cents Most common intervals : 17/14, 336.1295 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 119.443 336.130 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% Limited inverse transpositions with margin 97.2439 cents: 4 -- Rational properties -- Prime limit : 17 Odd number limit : 4913 (O: 4913 U: 4913) Highest odd numerator or denominator: 289 Scale harmonicity : 0.007447 Average absolute harmonicity : 0.163706 Specific harmonicity : 0.040281 Fundamental : 1/4046, -11.9823 octaves, 0.0647 Hz. Guide tone : 99960, 16.6091 octaves, 26152091.507 Hz. Exponens Consonantiae : 4.044382E+08, 28.59134 octaves Euler's gradus suavitatis : 77 Sum of Mann's harmonic distance : 772.5, average 110.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.78923, average 1.39846 Sum of Tenney's harmonic distance : 20.52333, average 2.93190 Vogel's harmonic complexity : 36.28571 Wille's k value : 2456 Wilson's harmonic complexity : 80 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 80.02799, average 2.85814 Lattice compactness (without 2's) : 60.28697, average 2.15311 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 11 1 3: 0 .. 1 0.42857 3 5: 0 .. 1 0.42857 3 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: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 15 19 31| Scale is weakly epimorphic with val: <7 10 15 20 30| Scale is weakly epimorphic with val: <7 10 15 21 29| Scale is weakly epimorphic with val: <7 10 15 22 28| Scale is JI-epimorphic with val: <7 10 16 18 27| Scale is weakly epimorphic with val: <7 10 16 20 32| Scale is weakly epimorphic with val: <7 10 16 21 31| Scale is weakly epimorphic with val: <7 10 16 22 30| Scale is weakly epimorphic with val: <7 10 17 18 29| Scale is JI-epimorphic with val: <7 10 17 19 28| Scale is weakly epimorphic with val: <7 10 17 21 26| Scale is weakly epimorphic with val: <7 10 17 22 32| Scale is weakly epimorphic with val: <7 10 18 18 31| Scale is weakly epimorphic with val: <7 10 18 19 30| Scale is JI-epimorphic with val: <7 10 18 20 29| Scale is weakly epimorphic with val: <7 10 18 22 27| Scale is JI-epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 21 31| Scale is weakly epimorphic with val: <7 11 15 22 30| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is JI-epimorphic with val: <7 11 16 19 28| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 22 32| Scale is weakly epimorphic with val: <7 11 17 18 31| Scale is weakly epimorphic with val: <7 11 17 19 30| Scale is JI-epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 22 27| Scale is weakly epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 19 32| Scale is weakly epimorphic with val: <7 11 18 20 31| Scale is JI-epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 12 15 18 29| Scale is JI-epimorphic with val: <7 12 15 19 28| Scale is weakly epimorphic with val: <7 12 15 21 26| Scale is weakly epimorphic with val: <7 12 15 22 32| Scale is weakly epimorphic with val: <7 12 16 18 31| Scale is weakly epimorphic with val: <7 12 16 19 30| Scale is JI-epimorphic with val: <7 12 16 20 29| Scale is weakly epimorphic with val: <7 12 16 22 27| Scale is weakly epimorphic with val: <7 12 17 18 26| Scale is weakly epimorphic with val: <7 12 17 19 32| Scale is weakly epimorphic with val: <7 12 17 20 31| Scale is JI-epimorphic with val: <7 12 17 21 30| Scale is weakly epimorphic with val: <7 12 18 18 28| Scale is weakly epimorphic with val: <7 12 18 19 27| Scale is weakly epimorphic with val: <7 12 18 20 26| Scale is weakly epimorphic with val: <7 12 18 21 32| Scale is JI-epimorphic with val: <7 12 18 22 31|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 30.4888 c. M:-51.9858 c. Lebeng 10: 1 2 1 1 2 1 2 P M ME S SD: 29.7344 c. M: 47.7410 c. 11: 1 2 2 1 2 1 2 P M ME S SD: 9.5187 c. M:-17.7136 c. Orgone-7 18: 2 3 3 2 3 2 3 SP M ME S SD: 11.3256 c. M:-19.4829 c. Dicot-7 21: 2 4 3 2 4 2 4 SP T3 SD: 10.5953 c. M: 18.6124 c. 28: 3 5 4 3 5 3 5 SP T3 SD: 7.3619 c. M: 13.4553 c. 29: 3 5 5 3 5 3 5 SP M DE S SD: 8.4110 c. M:-14.8852 c. 32: 3 6 5 3 6 3 6 SP T3 SD: 5.6361 c. M: 9.6838 c. 39: 4 7 6 4 7 4 7 SP T3 SD: 2.6347 c. M: 4.6641 c. 50: 5 9 8 5 9 5 9 SP T3 SD: 0.4704 c. M:-0.8162 c. 232: 23 42 37 23 42 23 42 SP T3 SD: 0.3724 c. M: 0.6321 c. 282: 28 51 45 28 51 28 51 SP T3 SD: 0.2233 c. M: 0.3753 c. 332: 33 60 53 33 60 33 60 SP T3 SD: 0.1194 c. M: 0.1959 c. 382: 38 69 61 38 69 38 69 SP T3 SD: 0.0442 c. M: 0.0711 c. 432: 43 78 69 43 78 43 78 SP T3 SD: 0.0236 c. M:-0.0384 c. 814: 81 147 130 81 147 81 147 SP T3 SD: 0.0185 c. M: 0.0325 c. 1246: 124 225 199 124 225 124 225 SP T3 SD: 0.0155 c. M:-0.0279 c. 2060: 205 372 329 205 372 205 372 SP T3 SD: 0.0161 c. M:-0.0260 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: 27.3856 cents 3 x x 4 x 5 x 6 S SD: 12.0260 cents 4 x 5 x 6 x 7:8 S SD: 18.9213 cents 5 x 6:7 x 8:9:10 S SD: 16.8682 cents 6 x 7:8:9:10:11:12 S SD: 19.3368 cents 7 x x x 10 x 12:14 SD: 19.4374 cents 8:9:10:11:12:13:14:16 S SD: 16.8812 cents 9:10:11:12:13:15:16:18 SD: 10.7550 cents 11:12:13:15:16:18:19:22 SD: 9.8629 cents 13:14:16:18:19:21:23:26 SD: 8.0044 cents 14:15:17:19:20:23:25:28 SD: 5.1943 cents 25:27:30:34:36:41:44:50 SD: 4.4277 cents 28:30:34:38:41:46:49:56 SD: 2.8597 cents 42:45:51:57:61:69:74:84 SD: 0.7717 cents 126:135:153:171:183:208:222:252 SD: 0.7143 cents 141:151:171:191:205:232:249:282 SD: 0.5665 cents 154:165:187:209:224:254:272:308 SD: 0.4777 cents 196:210:238:266:285:323:346:392 SD: 0.2488 cents 238:255:289:323:346:392:420:476 SD: 0.1592 cents 505:541:613:685:734:832:891:1010 SD: 0.1296 cents 547:586:664:742:795:901:965:1094 SD: 0.1172 cents