Scala analysis: xen12-chalmers-tritriadic-dm-5-17-25
Tritriadic D->M scale built from 5:17:25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 289/250 250.969677 2: 5/4 386.313714 major third 3: 34/25 532.327982 4: 25/17 667.672018 5: 17/10 918.641696 septendecimal diminished seventh 6: 125/68 1053.985732 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 136/125 146.0143 1: 289/250 250.9697 2: 625/578 135.3440 3: 136/125 146.0143 4: 625/578 135.3440 5: 289/250 250.9697 6: 625/578 135.3440 7: 136/125 146.0143
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 : 251.0 386.3 532.3 667.7 918.6 1054.0 1200.0 251.0 : 135.3 281.4 416.7 667.7 803.0 949.0 1200.0 386.3 : 146.0 281.4 532.3 667.7 813.7 1064.7 1200.0 532.3 : 135.3 386.3 521.7 667.7 918.6 1054.0 1200.0 667.7 : 251.0 386.3 532.3 783.3 918.6 1064.7 1200.0 918.6 : 135.3 281.4 532.3 667.7 813.7 949.0 1200.0 1054.0: 146.0 397.0 532.3 678.3 813.7 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 : 175.77423 cents, oct.: 1230.41960 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : LSMSLSM 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 Scale contains two identical disjunct tetrachords 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: 5 -- Rational properties -- Prime limit : 17 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 289 Scale harmonicity : 0.007590 Average absolute harmonicity : 0.174813 Specific harmonicity : 0.042689 Fundamental : 1/8500, -13.0532 octaves, 0.0308 Hz. Guide tone : 72250, 16.1407 octaves, 18902447.093 Hz. Exponens Consonantiae : 6.141250E+08, 29.19396 octaves Euler's gradus suavitatis : 76 Sum of Mann's harmonic distance : 436.0, average 62.28571 Mersenne's string divisions : 331430022 Sum of van Prooijen's expressibility: 9.28311, average 1.32616 Sum of Tenney's harmonic distance : 18.17857, average 2.59694 Vogel's harmonic complexity : 38.28571 Wille's k value : 7812 Wilson's harmonic complexity : 81 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 92.92017, average 3.31858 Lattice compactness (without 2's) : 76.95355, average 2.74834 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.57143 8 1 5: -3 .. 3 0.00000 12 1 17: -1 .. 2 0.28571 6 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 18 / 7 = 2.57143 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: 43.5797 c. M: 79.5411 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 10.7729 c. M:-15.6970 c. 25: 5 3 3 3 5 3 3 SP M DE S SD: 5.4944 c. M: 10.9697 c. Antiphrygian 34: 7 4 4 4 7 4 4 SP M DE S SD: 2.9372 c. M:-4.8378 c. 43: 9 5 5 5 9 5 5 SP M DE S SD: 3.2789 c. M:-6.4794 c. 63: 13 7 8 7 13 7 8 SP T3 SD: 3.8079 c. M: 6.3667 c. 65: 14 7 8 7 14 7 8 P T3 SD: 3.7645 c. M:-7.4919 c. 72: 15 8 9 8 15 8 9 SP T3 SD: 2.1257 c. M: 3.9857 c. 81: 17 9 10 9 17 9 10 SP T3 SD: 1.1111 c. M: 2.1339 c. 106: 22 12 13 12 22 12 13 SP T3 SD: 1.1870 c. M: 1.9131 c. 115: 24 13 14 13 24 13 14 SP T3 SD: 0.2765 c. M: 0.5349 c. 239: 50 27 29 27 50 27 29 SP T3 SD: 0.2136 c. M:-0.4076 c. 320: 67 36 39 36 67 36 39 SP T3 SD: 0.1728 c. M:-0.2803 c. 354: 74 40 43 40 74 40 43 SP T3 SD: 0.1338 c. M:-0.2516 c. 435: 91 49 53 49 91 49 53 SP T3 SD: 0.0985 c. M: 0.1926 c. 550: 115 62 67 62 115 62 67 SP T3 SD: 0.0933 c. M: 0.1676 c. 665: 139 75 81 75 139 75 81 SP T3 SD: 0.1111 c. M: 0.1511 c. 674: 141 76 82 76 141 76 82 SP T3 SD: 0.0374 c. M:-0.0689 c. 789: 165 89 96 89 165 89 96 SP T3 SD: 0.0098 c. M: 0.0191 c. 2252: 471 254 274 254 471 254 274 SP T3 SD: 0.0069 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: 17.1415 cents 3 x x 4 x 5 x 6 S SD: 16.1612 cents 4 x 5 x 6:7 x 8 S SD: 15.1941 cents 5:6 x 7 x x 9:10 SD: 22.3957 cents 6:7 x 8:9:10:11:12 S SD: 10.2743 cents 7:8:9 x 10:12:13:14 S SD: 12.7067 cents 8:9:10:11:12:14:15:16 S SD: 12.3258 cents 11:13:14:15:16:19:20:22 SD: 8.9638 cents 12:14:15:16:18:20:22:24 S SD: 8.8065 cents 13:15:16:18:19:22:24:26 SD: 6.2702 cents 17:20:21:23:25:29:31:34 SD: 5.8091 cents 19:22:24:26:28:32:35:38 SD: 3.8818 cents 31:36:39:42:46:53:57:62 SD: 3.4073 cents 32:37:40:44:47:54:59:64 SD: 3.3673 cents 36:42:45:49:53:61:66:72 SD: 2.5235 cents 44:51:55:60:65:75:81:88 SD: 1.6418 cents 64:74:80:87:94:109:118:128 SD: 0.9309 cents 100:116:125:136:147:170:184:200 SD: 0.8922 cents 116:134:145:158:171:197:213:232 SD: 0.8160 cents 117:135:146:159:172:199:215:234 SD: 0.6755 cents 128:148:160:174:188:218:235:256 SD: 0.6430 cents 136:157:170:185:200:231:250:272 SD: 0.4053 cents 180:208:225:245:265:306:331:360 SD: 0.3647 cents 200:231:250:272:294:340:368:400 SD: 0.3345 cents 217:251:271:295:319:369:399:434 SD: 0.3167 cents 236:273:295:321:347:401:434:472 SD: 0.2363 cents 308:356:385:419:453:524:566:616 SD: 0.2209 cents 340:393:425:462:500:578:625:680 SD: 0.2155 cents 353:408:441:480:519:600:649:706 SD: 0.1715 cents 444:513:555:604:653:755:816:888 SD: 0.1677 cents 480:555:600:653:706:816:882:960 SD: 0.1417 cents 500:578:625:680:735:850:919:1000 SD: 0.1039 cents 544:629:680:740:800:925:1000:1088 SD: 0.0926 cents