Scala analysis: xen09-chalmers-tritriadic-14-15-17
Tritriadic scale built from 14:15:17
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: 255/196 455.572311 4: 289/196 672.259006 two (supraminor third) 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: 15/14 119.4428 major diatonic semitone 4: 17/15 216.6867 septendecimal whole tone 5: 5488/4913 191.6115 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 : 119.4 336.1 455.6 672.3 863.9 983.3 1200.0 119.4 : 216.7 336.1 552.8 744.4 863.9 1080.6 1200.0 336.1 : 119.4 336.1 527.7 647.2 863.9 983.3 1200.0 455.6 : 216.7 408.3 527.7 744.4 863.9 1080.6 1200.0 672.3 : 191.6 311.1 527.7 647.2 863.9 983.3 1200.0 863.9 : 119.4 336.1 455.6 672.3 791.7 1008.4 1200.0 983.3 : 216.7 336.1 552.8 672.3 888.9 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 : 167.61919 cents, oct.: 1173.33435 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : SLSLMSL 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: 1 -- 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 : 0.164289 Specific harmonicity : 0.040764 Fundamental : 1/3332, -11.7022 octaves, 0.0785 Hz. Guide tone : 121380, 16.8892 octaves, 31756111.116 Hz. Exponens Consonantiae : 4.044382E+08, 28.59134 octaves Euler's gradus suavitatis : 77 Sum of Mann's harmonic distance : 545.5, average 77.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.73488, average 1.39070 Sum of Tenney's harmonic distance : 19.83695, average 2.83385 Vogel's harmonic complexity : 36.00000 Wille's k value : 2456 Wilson's harmonic complexity : 80 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 80.71137, average 2.88255 Lattice compactness (without 2's) : 60.28697, average 2.15311 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.28571 10 1 3: 0 .. 1 0.42857 3 5: 0 .. 1 0.42857 3 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: 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: 34.7843 c. M:-58.7134 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 25.5212 c. M:-47.7410 c. 11: 1 2 1 2 2 1 2 P M ME S SD: 11.6437 c. M: 19.2087 c. 18: 2 3 2 3 3 2 3 SP M ME S SD: 9.5722 c. M:-16.6867 c. 21: 2 4 2 4 3 2 4 SP T3 SD: 7.9451 c. M:-13.4553 c. 28: 3 5 3 5 4 3 5 SP T3 SD: 9.3510 c. M:-15.8563 c. 29: 3 5 3 5 5 3 5 SP M DE S SD: 6.2542 c. M: 10.1900 c. 32: 3 6 3 6 5 3 6 SP T3 SD: 4.7754 c. M: 8.3133 c. 39: 4 7 4 7 6 4 7 SP T3 SD: 3.4461 c. M:-5.9662 c. 50: 5 9 5 9 8 5 9 SP T3 SD: 0.3902 c. M:-0.6867 c. 232: 23 42 23 42 37 23 42 SP T3 SD: 0.3232 c. M: 0.5547 c. 282: 28 51 28 51 45 28 51 SP T3 SD: 0.1972 c. M: 0.3346 c. 332: 33 60 33 60 53 33 60 SP T3 SD: 0.1097 c. M: 0.1808 c. 382: 38 69 38 69 61 38 69 SP T3 SD: 0.0467 c. M: 0.0749 c. 432: 43 78 43 78 69 43 78 SP T3 SD: 0.0197 c. M: 0.0368 c. 1246: 124 225 124 225 199 124 225 SP T3 SD: 0.0201 c. M: 0.0346 c. 1678: 167 303 167 303 268 167 303 SP T3 SD: 0.0188 c. M: 0.0302 c. 2110: 210 381 210 381 337 210 381 SP T3 SD: 0.0185 c. M: 0.0315 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: 15.7187 cents 4 x 5 x 6 x 7:8 S SD: 15.0212 cents 5 x 6 x 7:8:9:10 S SD: 22.0618 cents 6 x 7:8:9:10:11:12 S SD: 18.4578 cents 7 x x 9:10 x 12:14 SD: 19.2648 cents 8:9:10 x 12:13:14:16 S SD: 17.7089 cents 9:10:11:12:13:15:16:18 SD: 12.5751 cents 10:11:12:13:15:16:18:20 SD: 12.0145 cents 11:12:13:14:16:18:19:22 SD: 11.6796 cents 12:13:15:16:18:20:21:24 SD: 11.2484 cents 13:14:16:17:19:21:23:26 SD: 6.5228 cents 14:15:17:18:21:23:25:28 SD: 5.9607 cents 17:18:21:22:25:28:30:34 SD: 5.3595 cents 23:25:28:30:34:38:41:46 SD: 4.5476 cents 26:28:32:34:38:43:46:52 SD: 4.5296 cents 27:29:33:35:40:44:48:54 SD: 3.9243 cents 29:31:35:38:43:48:51:58 SD: 3.1372 cents 40:43:49:52:59:66:71:80 SD: 2.7761 cents 42:45:51:55:62:69:74:84 SD: 1.7974 cents 56:60:68:73:83:92:99:112 SD: 1.5709 cents 57:61:69:74:84:94:101:114 SD: 1.4442 cents 69:74:84:90:102:114:122:138 SD: 1.4389 cents 70:75:85:91:103:115:124:140 SD: 1.2591 cents 80:86:97:104:118:132:141:160 SD: 1.0701 cents 84:90:102:109:124:138:148:168 SD: 1.0266 cents 93:100:113:121:137:153:164:186 SD: 0.9865 cents 97:104:118:126:143:160:171:194 SD: 0.7634 cents 99:106:120:129:146:163:175:198 SD: 0.7424 cents 116:124:141:151:171:191:205:232 SD: 0.7349 cents 127:136:154:165:187:209:224:254 SD: 0.6573 cents 139:149:169:181:205:229:245:278 SD: 0.5044 cents 182:195:221:237:268:300:321:364 SD: 0.4633 cents 183:196:222:238:270:301:323:366 SD: 0.4619 cents 196:210:238:255:289:323:346:392 SD: 0.1592 cents 462:495:561:601:681:761:815:924 SD: 0.1235 cents 518:555:629:674:764:853:914:1036 SD: 0.0956 cents