Scala analysis: xen10-chalmers-tritriadic-21-1-23
Tritriadic scale built from 21:1:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/21 157.493440 2: 529/441 314.986880 3: 32/23 571.725653 23rd subharmonic 4: 32/21 729.219093 wide fifth 5: 736/441 886.712533 6: 42/23 1042.506560 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/21 157.4934 1: 23/21 157.4934 2: 23/21 157.4934 3: 14112/12167 256.7388 4: 23/21 157.4934 5: 23/21 157.4934 6: 9261/8464 155.7940 7: 23/21 157.4934
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9261/8464 155.794 cents 1: 5 23/21 157.493 cents 1: 1 14112/12167 256.739 cents 2: 2 441/368 313.287 cents 2: 3 529/441 314.987 cents 2: 2 672/529 414.232 cents 3: 3 21/16 470.781 cents narrow fourth 3: 1 12167/9261 472.480 cents 3: 3 32/23 571.726 cents 23rd subharmonic 4: 3 23/16 628.274 cents 23rd harmonic 4: 1 18522/12167 727.520 cents 4: 3 32/21 729.219 cents wide fifth 5: 2 529/336 785.768 cents 5: 3 882/529 885.013 cents 5: 2 736/441 886.713 cents 6: 1 12167/7056 943.261 cents 6: 5 42/23 1042.507 cents 6: 1 16928/9261 1044.206 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 : 157.5 315.0 571.7 729.2 886.7 1042.5 1200.0 157.5 : 157.5 414.2 571.7 729.2 885.0 1042.5 1200.0 315.0 : 256.7 414.2 571.7 727.5 885.0 1042.5 1200.0 571.7 : 157.5 315.0 470.8 628.3 785.8 943.3 1200.0 729.2 : 157.5 313.3 470.8 628.3 785.8 1042.5 1200.0 886.7 : 155.8 313.3 470.8 628.3 885.0 1042.5 1200.0 1042.5: 157.5 315.0 472.5 729.2 886.7 1044.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 155.7940 .. 256.7388 cents 512/483, 100.9447 cents 9261/8464, 155.7940 cents 2: 313.2875 .. 414.2322 cents 512/483, 100.9447 cents 529/512, 56.5487 cents 3: 470.7809 .. 571.7257 cents 512/483, 100.9447 cents 529/512, 56.5487 cents 4: 628.2743 .. 729.2191 cents 512/483, 100.9447 cents 529/512, 56.5487 cents 5: 785.7678 .. 886.7125 cents 512/483, 100.9447 cents 529/512, 56.5487 cents 6: 943.2612 .. 1044.2060 cents 512/483, 100.9447 cents 529/512, 56.5487 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 9261/8464, 155.7940 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 14112/12167, 256.7388 cents Average / Smallest step : 1.100354 Largest / Average step : 1.497643 Largest / Smallest step : 1.647937 Median interval of one step : 23/21, 157.4934 cents, amount: 5 Most common interval of one step : 23/21, 157.4934 cents, amount: 5 Least squares average step : 175.05802 cents, oct.: 1225.40613 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : MMLMMSM Scale is a Constant Structure, by a margin of 56.54869 cents Scale diversity : 1.261602 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.495276 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 : 194672/194481, 1.6994 cents Most common intervals : 23/21, 157.4934 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 571.726 1042.507 cents Most common triad is 0.0 157.493 1042.507 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best major thirds form a closed circle Scale contains a complete diamond : 21 23 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 100.9447 cents: 5 -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.005878 Average absolute harmonicity : 0.162248 Specific harmonicity : 0.032664 Fundamental : 1/10143, -13.3082 octaves, 0.0258 Hz. Guide tone : 355488, 18.4394 octaves, 93004748.958 Hz. Exponens Consonantiae : 3.605715E+09, 31.74764 octaves Euler's gradus suavitatis : 96 Sum of Mann's harmonic distance : 1183.5, average 169.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.77530, average 1.53933 Sum of Tenney's harmonic distance : 22.54341, average 3.22049 Vogel's harmonic complexity : 44.85714 Wille's k value : 6083 Wilson's harmonic complexity : 99 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 111.00045, average 3.96430 Lattice compactness (without 2's) : 63.54627, average 2.26951 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 5 2.42857 17 1 3: -2 .. 1 -0.71429 7 7: -2 .. 1 -0.71429 7 1 23: -1 .. 2 0.28571 6 5 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 19 34| Scale is weakly epimorphic with val: <7 10 20 33| Scale is JI-epimorphic with val: <7 10 21 32| Scale is weakly epimorphic with val: <7 10 22 31| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 19 33| Scale is JI-epimorphic with val: <7 11 20 32| = patent Scale is weakly epimorphic with val: <7 11 21 31| Scale is weakly epimorphic with val: <7 11 22 30| Scale is weakly epimorphic with val: <7 12 18 33| Scale is JI-epimorphic with val: <7 12 19 32| Scale is weakly epimorphic with val: <7 12 20 31| Scale is weakly epimorphic with val: <7 12 21 30| Scale is weakly epimorphic with val: <7 12 22 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.1414 c. M: 57.4399 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 15.7877 c. M:-28.2743 c. 15: 2 2 3 2 2 2 2 SP M ME S SD: 6.6034 c. M: 11.7257 c. 23: 3 3 5 3 3 3 3 SP M DE S SD: 1.3086 c. M:-2.1874 c. 61: 8 8 13 8 8 8 8 SP M DE S SD: 0.8927 c. M: 1.4666 c. 84: 11 11 18 11 11 11 11 SP M DE S SD: 0.5659 c. M: 0.9982 c. 107: 14 14 23 14 14 14 14 SP M DE S SD: 0.5422 c. M: 0.9682 c. 191: 25 25 41 25 25 25 25 SP M DE S SD: 0.5325 c. M: 0.8508 c. 298: 39 39 64 39 39 39 39 SP M DE S SD: 0.5323 c. M: 0.8929 c. 365: 48 48 78 48 48 47 48 SP T3 SD: 0.5394 c. M:-0.9587 c. 380: 50 50 81 50 50 49 50 SP T3 SD: 0.4602 c. M:-0.8026 c. 388: 51 51 83 51 51 50 51 SP T3 SD: 0.5118 c. M:-0.9163 c. 403: 53 53 86 53 53 52 53 SP T3 SD: 0.4003 c. M:-0.6459 c. 426: 56 56 91 56 56 55 56 SP T3 SD: 0.3581 c. M:-0.6114 c. 441: 58 58 94 58 58 57 58 SP T3 SD: 0.3531 c. M:-0.6594 c. 449: 59 59 96 59 59 58 59 SP T3 SD: 0.3328 c. M:-0.5926 c. 464: 61 61 99 61 61 60 61 SP T3 SD: 0.2897 c. M:-0.5304 c. 472: 62 62 101 62 62 61 62 SP T3 SD: 0.3227 c. M:-0.5756 c. 487: 64 64 104 64 64 63 64 SP T3 SD: 0.2404 c. M:-0.4135 c. 510: 67 67 109 67 67 66 67 SP T3 SD: 0.2071 c. M:-0.3463 c. 533: 70 70 114 70 70 69 70 SP T3 SD: 0.1914 c. M:-0.3419 c. 548: 72 72 117 72 72 71 72 SP T3 SD: 0.1832 c. M:-0.3416 c. 556: 73 73 119 73 73 72 73 SP T3 SD: 0.1927 c. M:-0.3378 c. 571: 75 75 122 75 75 74 75 SP T3 SD: 0.1346 c. M:-0.2495 c. 594: 78 78 127 78 78 77 78 SP T3 SD: 0.1004 c. M:-0.1646 c. 617: 81 81 132 81 81 80 81 SP T3 SD: 0.0890 c. M:-0.1594 c. 655: 86 86 140 86 86 85 86 SP T3 SD: 0.0783 c. M:-0.1276 c. 678: 89 89 145 89 89 88 89 SP T3 SD: 0.0323 c. M:-0.0574 c. 701: 92 92 150 92 92 91 92 SP T3 SD: 0.0169 c. M:-0.0290 c. 1379: 181 181 295 181 181 179 181 SP T3 SD: 0.0132 c. M:-0.0240 c. 2080: 273 273 445 273 273 270 273 SP T3 SD: 0.0104 c. M:-0.0182 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: 13.6320 cents 3 x x 4 x 5 x 6 S SD: 24.5727 cents 4 x 5 x 6 x 7:8 S SD: 26.5279 cents 5 x 6:7 x 8:9:10 S SD: 15.5822 cents 6 x 7:8:9:10:11:12 S SD: 15.4019 cents 7:8 x 10:11:12:13:14 S SD: 19.2699 cents 8:9:10:11:12:13:15:16 SD: 16.0541 cents 9:10:11:13:14:15:16:18 SD: 13.7892 cents 10:11:12:14:15:17:18:20 SD: 7.2231 cents 18:20:22:25:27:30:33:36 SD: 7.1093 cents 19:21:23:26:29:32:35:38 SD: 6.0736 cents 21:23:25:29:32:35:38:42 SD: 3.4824 cents 30:33:36:42:46:50:55:60 SD: 2.6422 cents 40:44:48:56:61:67:73:80 SD: 2.0973 cents 51:56:61:71:78:85:93:102 SD: 1.4113 cents 61:67:73:85:93:102:111:122 SD: 1.4063 cents 74:81:89:103:113:124:135:148 SD: 1.3333 cents 75:82:90:104:114:125:137:150 SD: 1.1741 cents 84:92:101:117:128:140:153:168 SD: 0.9638 cents 94:103:113:131:143:157:172:188 SD: 0.9593 cents 105:115:126:146:160:175:192:210 SD: 0.5065 cents 115:126:138:160:175:192:210:230 SD: 0.3732 cents 166:182:199:231:253:277:303:332 SD: 0.3290 cents 220:241:264:306:335:367:402:440 SD: 0.2918 cents 271:297:325:377:413:452:495:542 SD: 0.2411 cents 281:308:337:391:428:469:513:562 SD: 0.2376 cents 317:347:380:441:483:529:579:634 SD: 0.2261 cents 345:378:414:480:526:576:630:690 SD: 0.2104 cents 386:423:463:537:588:644:705:772 SD: 0.1868 cents 401:439:481:558:611:669:732:802 SD: 0.1711 cents 432:473:518:601:658:721:789:864 SD: 0.1692 cents 460:504:552:640:701:768:840:920 SD: 0.1628 cents 462:506:554:643:704:771:844:924 SD: 0.1576 cents 516:565:619:718:786:861:942:1032 SD: 0.1419 cents 546:598:655:760:832:911:997:1092 SD: 0.1320 cents 586:642:703:815:893:978:1070:1172 SD: 0.1226 cents