Scala analysis: xen10-chalmers-tritriadic-5-17-27
Tritriadic scale built from 5:17:27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 459/400 238.192984 2: 34/27 399.090407 septendecimal major third 3: 27/20 519.551289 acute fourth 4: 40/27 680.448711 grave fifth 5: 17/10 918.641696 septendecimal diminished seventh 6: 729/400 1039.102577 acute minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 800/729 160.8974 grave whole tone 1: 459/400 238.1930 2: 800/729 160.8974 grave whole tone 3: 729/680 120.4609 4: 800/729 160.8974 grave whole tone 5: 459/400 238.1930 6: 729/680 120.4609 7: 800/729 160.8974 grave whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 729/680 120.461 cents 1: 3 800/729 160.897 cents grave whole tone 1: 2 459/400 238.193 cents 2: 3 20/17 281.358 cents septendecimal augmented second 2: 1 19683/16000 358.654 cents 2: 3 34/27 399.090 cents septendecimal major third 3: 1 16000/12393 442.256 cents 3: 5 27/20 519.551 cents acute fourth 3: 1 27200/19683 559.988 cents 4: 1 19683/13600 640.012 cents 4: 5 40/27 680.449 cents grave fifth 4: 1 12393/8000 757.744 cents 5: 3 27/17 800.910 cents septendecimal minor sixth 5: 1 32000/19683 841.346 cents 5: 3 17/10 918.642 cents septendecimal diminished seventh 6: 2 800/459 961.807 cents 6: 3 729/400 1039.103 cents acute minor seventh 6: 2 1360/729 1079.539 cents 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 : 238.2 399.1 519.6 680.4 918.6 1039.1 1200.0 238.2 : 160.9 281.4 442.3 680.4 800.9 961.8 1200.0 399.1 : 120.5 281.4 519.6 640.0 800.9 1039.1 1200.0 519.6 : 160.9 399.1 519.6 680.4 918.6 1079.5 1200.0 680.4 : 238.2 358.7 519.6 757.7 918.6 1039.1 1200.0 918.6 : 120.5 281.4 519.6 680.4 800.9 961.8 1200.0 1039.1: 160.9 399.1 560.0 680.4 841.3 1079.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 120.4609 .. 238.1930 cents 289/270, 117.7321 cents 729/680, 120.4609 cents 2: 281.3583 .. 399.0904 cents 289/270, 117.7321 cents 8000/7803, 43.1653 cents 3: 442.2557 .. 559.9878 cents 289/270, 117.7321 cents 8000/7803, 43.1653 cents 4: 640.0122 .. 757.7443 cents 289/270, 117.7321 cents 387420489/369920000, 80.0243 cents 5: 800.9096 .. 918.6417 cents 289/270, 117.7321 cents 8000/7803, 43.1653 cents 6: 961.8070 .. 1079.5391 cents 289/270, 117.7321 cents 8000/7803, 43.1653 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 729/680, 120.4609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 459/400, 238.1930 cents Average / Smallest step : 1.423106 Largest / Average step : 1.389459 Largest / Smallest step : 1.977347 Median interval of one step : 800/729, 160.8974 cents, amount: 3 Most common interval of one step : 800/729, 160.8974 cents, amount: 3 Least squares average step : 175.31890 cents, oct.: 1227.23232 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : LMSMLSM Scale is a Constant Structure, by a margin of 43.16532 cents Scale diversity : 1.433252 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.411339 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 : 544000/531441, 40.4365 cents Most common intervals : 27/20, 519.5513 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 399.090 680.449 cents Most common triad is 0.0 519.551 680.449 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Scale contains a complete diamond : 5 27 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 17 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.012451 Average absolute harmonicity : 0.174194 Specific harmonicity : 0.062029 Fundamental : 1/10800, -13.3987 octaves, 0.0242 Hz. Guide tone : 495720, 18.9192 octaves, 129693025.231 Hz. Exponens Consonantiae : 5.353776E+09, 32.31791 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 1096.5, average 156.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.04908, average 1.57844 Sum of Tenney's harmonic distance : 21.98880, average 3.14126 Vogel's harmonic complexity : 28.42857 Wille's k value : 9841 Wilson's harmonic complexity : 59 Rectangular lattice diameter : 13 Triangular lattice diameter : 9 Lattice compactness : 145.73477, average 5.20481 Lattice compactness (without 2's) : 114.83671, average 4.10131 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.85714 16 1 3: -3 .. 6 0.85714 18 5: -2 .. 1 -0.71429 7 3 17: 0 .. 1 0.42857 3 3 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 28 / 7 = 4.00000 Scale is weakly epimorphic with val: <7 10 15 26| Scale is weakly epimorphic with val: <7 10 17 27| Scale is weakly epimorphic with val: <7 10 18 31| Scale is weakly epimorphic with val: <7 11 15 31| Scale is JI-epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 17 32| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 12 16 26| Scale is weakly epimorphic with val: <7 12 17 30| Scale is weakly epimorphic with val: <7 12 18 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 40.6521 c. M: 66.7644 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 17.5950 c. M:-28.4737 c. 14: 3 2 1 2 3 1 2 P T3 SD: 16.8225 c. M:-29.4810 c. 16: 3 2 2 2 3 2 2 SP M ME S SD: 13.5227 c. M: 24.0904 c. Antiphrygian 21: 4 3 2 3 4 2 3 SP T3 SD: 6.3102 c. M: 10.5311 c. 30: 6 4 3 4 6 3 4 SP T3 SD: 1.0104 c. M:-1.8070 c. 111: 22 15 11 15 22 11 15 SP T3 SD: 0.7000 c. M: 1.2647 c. 141: 28 19 14 19 28 14 19 SP T3 SD: 0.5434 c. M:-0.9096 c. 171: 34 23 17 23 34 17 23 SP T3 SD: 0.5079 c. M:-0.9096 c. 201: 40 27 20 27 40 20 27 SP T3 SD: 0.5230 c. M:-0.9096 c. 217: 43 29 22 29 43 22 29 SP T3 SD: 0.5214 c. M: 0.9337 c. 231: 46 31 23 31 46 23 31 SP T3 SD: 0.5543 c. M:-0.9096 c. 247: 49 33 25 33 49 25 33 SP T3 SD: 0.4132 c. M: 0.7098 c. 277: 55 37 28 37 55 28 37 SP T3 SD: 0.3585 c. M:-0.6086 c. 298: 59 40 30 40 59 30 40 SP T3 SD: 0.3538 c. M: 0.6091 c. 307: 61 41 31 41 61 31 41 SP T3 SD: 0.3439 c. M:-0.6368 c. 328: 65 44 33 44 65 33 44 SP T3 SD: 0.2323 c. M: 0.3881 c. 358: 71 48 36 48 71 36 48 SP T3 SD: 0.1348 c. M: 0.2077 c. 388: 77 52 39 52 77 39 52 SP T3 SD: 0.0679 c. M: 0.1213 c. 806: 160 108 81 108 160 81 108 SP T3 SD: 0.0589 c. M:-0.1034 c. 887: 176 119 89 119 176 89 119 SP T3 SD: 0.0569 c. M: 0.0947 c. 917: 182 123 92 123 182 92 123 SP T3 SD: 0.0335 c. M: 0.0622 c. 947: 188 127 95 127 188 95 127 SP T3 SD: 0.0363 c. M:-0.0648 c. 1275: 253 171 128 171 253 128 171 SP T3 SD: 0.0421 c. M: 0.0753 c. 1305: 259 175 131 175 259 131 175 SP T3 SD: 0.0181 c. M: 0.0321 c. 1335: 265 179 134 179 265 134 179 SP T3 SD: 0.0066 c. M:-0.0107 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: 10.7531 cents 3 x x 4 x 5 x 6 S SD: 13.4901 cents 4 x 5 x 6:7 x 8 S SD: 14.0183 cents 5:6 x 7 x x 9:10 SD: 25.5255 cents 6:7 x 8:9:10:11:12 S SD: 9.1713 cents 7:8:9 x 10:12:13:14 S SD: 13.5211 cents 8:9:10:11:12:14:15:16 S SD: 12.5730 cents 11:13:14:15:16:19:20:22 SD: 10.1316 cents 12:14:15:16:18:20:22:24 S SD: 8.0702 cents 14:16:18:19:21:24:26:28 SD: 8.0349 cents 15:17:19:20:22:26:27:30 SD: 7.7242 cents 19:22:24:26:28:32:35:38 SD: 5.5521 cents 20:23:25:27:30:34:36:40 SD: 4.7434 cents 23:26:29:31:34:39:42:46 SD: 3.8624 cents 27:31:34:36:40:46:49:54 SD: 3.2925 cents 34:39:43:46:50:58:62:68 SD: 2.3492 cents 40:46:50:54:59:68:73:80 SD: 2.2163 cents 46:53:58:62:68:78:84:92 SD: 1.4821 cents 54:62:68:73:80:92:98:108 SD: 1.2314 cents 69:79:87:93:102:117:126:138 SD: 1.2224 cents 74:85:93:100:110:126:135:148 SD: 1.1295 cents 89:102:112:120:132:151:162:178 SD: 0.7945 cents 100:115:126:135:148:170:182:200 SD: 0.6981 cents 108:124:136:146:160:184:197:216 SD: 0.6854 cents 123:141:155:166:182:209:224:246 SD: 0.4885 cents 143:164:180:193:212:243:261:286 SD: 0.4536 cents 177:203:223:239:262:301:323:354 SD: 0.4337 cents 197:226:248:266:292:335:359:394 SD: 0.1824 cents 243:279:306:328:360:413:443:486 SD: 0.1732 cents 320:367:403:432:474:544:583:640 SD: 0.1654 cents 366:420:461:494:542:622:667:732 SD: 0.1513 cents 440:505:554:594:652:748:802:880 SD: 0.0872 cents 563:646:709:760:834:957:1026:1126 SD: 0.0459 cents