Scala analysis: xen10-chalmers-tritriadic-17-5-25
Tritriadic scale built from 17:5:25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 625/578 135.344036 2: 20/17 281.358304 septendecimal augmented second 3: 34/25 532.327982 4: 25/17 667.672018 5: 8/5 813.686286 minor sixth 6: 500/289 949.030323 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 289/250 250.9697 1: 625/578 135.3440 2: 136/125 146.0143 3: 289/250 250.9697 4: 625/578 135.3440 5: 136/125 146.0143 6: 625/578 135.3440 7: 289/250 250.9697
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 625/578 135.344 cents 1: 2 136/125 146.014 cents 1: 2 289/250 250.970 cents 2: 3 20/17 281.358 cents septendecimal augmented second 2: 3 5/4 386.314 cents major third 2: 1 19652/15625 396.984 cents 3: 1 6250/4913 416.702 cents 3: 1 3125/2312 521.658 cents 3: 5 34/25 532.328 cents 4: 5 25/17 667.672 cents 4: 1 4624/3125 678.342 cents 4: 1 4913/3125 783.298 cents 5: 1 15625/9826 803.016 cents 5: 3 8/5 813.686 cents minor sixth 5: 3 17/10 918.642 cents septendecimal diminished seventh 6: 2 500/289 949.030 cents 6: 2 125/68 1053.986 cents 6: 3 1156/625 1064.656 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 : 135.3 281.4 532.3 667.7 813.7 949.0 1200.0 135.3 : 146.0 397.0 532.3 678.3 813.7 1064.7 1200.0 281.4 : 251.0 386.3 532.3 667.7 918.6 1054.0 1200.0 532.3 : 135.3 281.4 416.7 667.7 803.0 949.0 1200.0 667.7 : 146.0 281.4 532.3 667.7 813.7 1064.7 1200.0 813.7 : 135.3 386.3 521.7 667.7 918.6 1054.0 1200.0 949.0 : 251.0 386.3 532.3 783.3 918.6 1064.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 135.3440 .. 250.9697 cents 83521/78125, 115.6256 cents 625/578, 135.3440 cents 2: 281.3583 .. 396.9839 cents 83521/78125, 115.6256 cents 5000/4913, 30.3886 cents 3: 416.7023 .. 532.3280 cents 83521/78125, 115.6256 cents 48828125/48275138, 19.7184 cents 4: 667.6720 .. 783.2977 cents 83521/78125, 115.6256 cents 625/578, 135.3440 cents 5: 803.0161 .. 918.6417 cents 83521/78125, 115.6256 cents 48828125/48275138, 19.7184 cents 6: 949.0303 .. 1064.6560 cents 83521/78125, 115.6256 cents 5000/4913, 30.3886 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 625/578, 135.3440 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 289/250, 250.9697 cents Average / Smallest step : 1.266613 Largest / Average step : 1.463990 Largest / Smallest step : 1.854309 Median interval of one step : 136/125, 146.0143 cents, amount: 2 Most common interval of one step : 625/578, 135.3440 cents, amount: 3 Least squares average step : 165.20247 cents, oct.: 1156.41730 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : SMLSMSL Scale is a Constant Structure, by a margin of 19.71840 cents Scale diversity : 1.258667 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.421872 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 : 78608/78125, 10.6702 cents Most common intervals : 34/25, 532.3280 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 281.358 667.672 cents Most common triad is 0.0 532.328 667.672 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Scale contains a complete diamond : 17 25 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 115.6256 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.007533 Average absolute harmonicity : 0.171744 Specific harmonicity : 0.041566 Fundamental : 1/14450, -13.8188 octaves, 0.0181 Hz. Guide tone : 85000, 16.3752 octaves, 22238173.051 Hz. Exponens Consonantiae : 1.228250E+09, 30.19396 octaves Euler's gradus suavitatis : 77 Sum of Mann's harmonic distance : 1073.0, average 153.28571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.98208, average 1.42601 Sum of Tenney's harmonic distance : 20.71005, average 2.95858 Vogel's harmonic complexity : 39.00000 Wille's k value : 7812 Wilson's harmonic complexity : 81 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 95.97858, average 3.42781 Lattice compactness (without 2's) : 78.26340, average 2.79512 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.14286 10 1 5: -2 .. 4 1.00000 13 1 17: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 15 28| Scale is JI-epimorphic with val: <7 16 28| Scale is weakly epimorphic with val: <7 17 28| Scale is weakly epimorphic with val: <7 18 28|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 44.6422 c. M:-79.5411 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 9.6778 c. M: 15.6970 c. Pseudo Pelog, Pelogic-7, Antiionian 25: 3 3 5 3 3 3 5 SP M DE S SD: 6.3492 c. M:-10.9697 c. Antiionian 34: 4 4 7 4 4 4 7 SP M DE S SD: 3.1848 c. M:-5.8324 c. 43: 5 5 9 5 5 5 9 SP M DE S SD: 2.6949 c. M: 4.3840 c. 63: 7 8 13 7 8 7 13 SP T3 SD: 3.0475 c. M:-5.3613 c. 72: 8 9 15 8 9 8 15 SP T3 SD: 1.6813 c. M:-2.9804 c. 81: 9 10 17 9 10 9 17 SP T3 SD: 1.0778 c. M: 2.0107 c. 106: 12 13 22 12 13 12 22 SP T3 SD: 1.1201 c. M:-1.9131 c. 115: 13 14 24 13 14 13 24 SP T3 SD: 0.2988 c. M:-0.5349 c. 239: 27 29 50 27 29 27 50 SP T3 SD: 0.1699 c. M: 0.2972 c. 354: 40 43 74 40 43 40 74 SP T3 SD: 0.1332 c. M:-0.2492 c. 435: 49 53 91 49 53 49 91 SP T3 SD: 0.0928 c. M: 0.1716 c. 550: 62 67 115 62 67 62 115 SP T3 SD: 0.0736 c. M:-0.1319 c. 674: 76 82 141 76 82 76 141 SP T3 SD: 0.0386 c. M: 0.0689 c. 789: 89 96 165 89 96 89 165 SP T3 SD: 0.0115 c. M:-0.0191 c. 1463: 165 178 306 165 178 165 306 SP T3 SD: 0.0125 c. M: 0.0214 c. 2252: 254 274 471 254 274 254 471 SP T3 SD: 0.0056 c. M: 0.0096 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: 17.1415 cents 3 x x 4 x x 5:6 S SD: 24.3989 cents 4 x 5 x 6 x 7:8 S SD: 28.0433 cents 5 x 6:7 x 8:9:10 S SD: 18.3249 cents 6 x 7:8:9 x 10:12 S SD: 16.4231 cents 7 x 8 x 10:11:12:14 S SD: 15.8276 cents 8:9 x 11:12:13:14:16 SD: 14.2883 cents 10:11:12:14:15:16:17:20 SD: 11.6692 cents 11:12:13:15:16:18:19:22 SD: 6.6994 cents 17:18:20:23:25:27:29:34 SD: 6.6461 cents 22:24:26:30:32:35:38:44 SD: 3.9971 cents 23:25:27:31:34:37:40:46 SD: 3.4643 cents 34:37:40:46:50:54:59:68 SD: 2.8331 cents 38:41:45:52:56:61:66:76 SD: 2.6663 cents 40:43:47:54:59:64:69:80 SD: 2.5707 cents 45:49:53:61:66:72:78:90 SD: 2.0880 cents 47:51:55:64:69:75:81:94 SD: 2.0290 cents 51:55:60:69:75:82:88:102 SD: 1.9978 cents 58:63:68:79:85:93:100:116 SD: 1.9648 cents 61:66:72:83:90:98:106:122 SD: 1.8831 cents 62:67:73:84:91:99:107:124 SD: 1.3433 cents 74:80:87:101:109:118:128:148 SD: 1.2941 cents 75:81:88:102:110:120:130:150 SD: 1.0842 cents 85:92:100:116:125:136:147:170 SD: 0.8922 cents 97:105:114:132:143:155:168:194 SD: 0.8386 cents 100:108:118:136:147:160:173:200 SD: 0.8059 cents 108:117:127:147:159:173:187:216 SD: 0.6802 cents 125:135:147:170:184:200:216:250 SD: 0.4972 cents 147:159:173:200:216:235:254:294 SD: 0.4554 cents 170:184:200:231:250:272:294:340 SD: 0.3345 cents 233:252:274:317:343:373:403:466 SD: 0.3319 cents 255:276:300:347:375:408:441:510 SD: 0.2940 cents 272:294:320:370:400:435:471:544 SD: 0.2690 cents 283:306:333:385:416:453:490:566 SD: 0.2604 cents 295:319:347:401:434:472:510:590 SD: 0.2474 cents 345:373:406:469:507:552:597:690 SD: 0.2222 cents 370:400:435:503:544:592:640:740 SD: 0.2149 cents 397:429:467:540:584:635:687:794 SD: 0.2080 cents 408:441:480:555:600:653:706:816 SD: 0.1417 cents 442:478:520:601:650:707:765:884 SD: 0.1315 cents 555:600:653:755:816:888:960:1110 SD: 0.1156 cents 567:613:667:771:834:907:981:1134 SD: 0.0977 cents 578:625:680:786:850:925:1000:1156 SD: 0.0591 cents