Scala analysis: xen09-chalmers-tritriadic-26-30-39
Tritriadic scale built from 26:30:39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 20/13 745.786052 tridecimal semi-augmented fifth 6: 45/26 949.696054 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 52/45 250.3039 1: 9/8 203.9100 major whole tone 2: 40/39 43.8311 tridecimal minor diesis 3: 52/45 250.3039 4: 9/8 203.9100 major whole tone 5: 40/39 43.8311 tridecimal minor diesis 6: 9/8 203.9100 major whole tone 7: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 40/39 43.831 cents tridecimal minor diesis 1: 3 9/8 203.910 cents major whole tone 1: 2 52/45 250.304 cents 2: 3 15/13 247.741 cents tridecimal 5/4-tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 13/10 454.214 cents tridecimal semi-diminished fourth 3: 1 135/104 451.651 cents 3: 5 4/3 498.045 cents perfect fourth 3: 1 117/80 658.124 cents 4: 1 160/117 541.876 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 208/135 748.349 cents 5: 3 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 45/26 949.696 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 39/20 1156.169 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 : 203.9 247.7 498.0 702.0 745.8 949.7 1200.0 203.9 : 43.8 294.1 498.0 541.9 745.8 996.1 1200.0 247.7 : 250.3 454.2 498.0 702.0 952.3 1156.2 1200.0 498.0 : 203.9 247.7 451.7 702.0 905.9 949.7 1200.0 702.0 : 43.8 247.7 498.0 702.0 745.8 996.1 1200.0 745.8 : 203.9 454.2 658.1 702.0 952.3 1156.2 1200.0 949.7 : 250.3 454.2 498.0 748.3 952.3 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 250.3039 cents 169/150, 206.4729 cents 40/39, 43.8311 cents 2: 247.7411 .. 454.2139 cents 169/150, 206.4729 cents 675/676,-2.5629 cents 3: 451.6511 .. 658.1239 cents 169/150, 206.4729 cents 675/676,-2.5629 cents 4: 541.8761 .. 748.3489 cents 169/150, 206.4729 cents 12800/13689,-116.2479 cents 5: 745.7861 .. 952.2589 cents 169/150, 206.4729 cents 675/676,-2.5629 cents 6: 949.6961 .. 1156.1689 cents 169/150, 206.4729 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 3.911122 Largest / Average step : 1.460106 Largest / Smallest step : 5.710654 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 163.06038 cents, oct.: 1141.42268 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MSLMSML Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.221723 Lumma stability : 0.073052 Lumma impropriety factor : 0.105416 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 : 676/675, 2.5629 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 247.741 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Scale contains a complete diamond : 1 3 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% Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.242919 Specific harmonicity : 0.110795 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 82.0, average 11.71429 Mersenne's string divisions : 5576340 Sum of van Prooijen's expressibility: 5.85173, average 0.83596 Sum of Tenney's harmonic distance : 11.78889, average 1.68413 Vogel's harmonic complexity : 17.71429 Wille's k value : 175 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 76.80430, average 2.74301 Lattice compactness (without 2's) : 47.16374, average 1.68442 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 10 1 3: -1 .. 2 0.71429 7 3 5: 0 .. 1 0.42857 3 13: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 15 27| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 17 29| Scale is JI-epimorphic with val: <7 11 15 24| Scale is JI-epimorphic with val: <7 11 16 25| Scale is JI-epimorphic with val: <7 11 17 26| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 12 15 28| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 18 24|
FIT/MODE
7: 1 0 2 1 0 1 2 N T3 SD: 52.8892 c. M: 92.5532 c. 9: 2 0 2 1 1 1 2 N T3 SD: 37.7851 c. M:-62.7567 c. 10: 2 0 2 2 0 2 2 N M DE S SD: 19.9455 c. M:-36.0900 c. 14: 2 1 3 2 1 2 3 P T3 SD: 18.4208 c. M: 32.4814 c. 16: 3 0 4 2 1 3 3 N SD: 20.9528 c. M:-26.9550 c. 17: 3 1 3 3 1 3 3 N M DE S SD: 23.0445 c. M:-38.5392 c. Seventeen-tone Natural Minor 18: 3 0 4 3 1 3 4 N SD: 26.5846 c. M: 47.7411 c. 19: 3 1 4 3 1 3 4 N T3 SD: 8.3544 c. M: 14.4363 c. 24: 4 1 5 4 1 4 5 N T3 SD: 2.5603 c. M:-4.2139 c. 29: 5 1 6 5 1 5 6 N T3 SD: 1.6343 c. M:-2.9865 c. 53: 9 2 11 9 2 9 11 N T3 SD: 0.8643 c. M:-1.3838 c. 82: 14 3 17 14 3 14 17 N T3 SD: 0.8549 c. M:-1.5235 c. 135: 23 5 28 23 5 23 28 N T3 SD: 0.8039 c. M:-1.4151 c. 188: 32 7 39 32 7 32 39 N T3 SD: 0.8039 c. M:-1.3678 c. 241: 41 9 50 41 9 41 50 N T3 SD: 0.8099 c. M:-1.3413 c. 248: 42 9 52 42 9 42 52 N T3 SD: 0.7310 c. M: 1.3090 c. 253: 43 9 53 43 9 43 53 N T3 SD: 0.7210 c. M: 1.1220 c. 272: 46 10 57 46 10 46 57 N T3 SD: 0.6839 c. M: 1.1666 c. 277: 47 10 58 47 10 47 58 N T3 SD: 0.5537 c. M: 0.9596 c. 301: 51 11 63 51 11 51 63 N T3 SD: 0.4853 c. M: 0.8588 c. 306: 52 11 64 52 11 52 64 N T3 SD: 0.4467 c. M: 0.6880 c. 330: 56 12 69 56 12 56 69 N T3 SD: 0.3397 c. M: 0.6051 c. 354: 60 13 74 60 13 60 74 N T3 SD: 0.3343 c. M: 0.5435 c. 359: 61 13 75 61 13 61 75 N T3 SD: 0.2536 c. M: 0.3924 c. 383: 65 14 80 65 14 65 80 N T3 SD: 0.1989 c. M: 0.3488 c. 412: 70 15 86 70 15 70 86 N T3 SD: 0.1110 c. M: 0.1815 c. 465: 79 17 97 79 17 79 97 N T3 SD: 0.0209 c. M: 0.0390 c. 1424: 242 52 297 242 52 242 297 N T3 SD: 0.0143 c. M:-0.0230 c. 1889: 321 69 394 321 69 321 394 N T3 SD: 0.0071 c. M:-0.0128 c. 2354: 400 86 491 400 86 400 491 N T3 SD: 0.0050 c. M:-0.0083 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: 0.0000 cents 3 x x 4 x x 5:6 S SD: 21.7791 cents 4 x x 5:6 x 7:8 S SD: 28.3393 cents 5 x 6:7 x 8:9:10 S SD: 28.9593 cents 6 x 7:8:9 x 10:12 S SD: 13.6160 cents 7 x 8:9 x 11:12:14 SD: 15.3106 cents 8:9 x 11:12 x 14:16 SD: 11.3207 cents 9:10 x 12 x 14:16:18 S SD: 10.9195 cents 10:11:12:13:15 x 17:20 SD: 15.8198 cents 11:12:13:15 x 17:19:22 SD: 13.0652 cents 12 x 14:16:18 x 21:24 S SD: 5.4107 cents 13 x 15:17 x 20:23:26 SD: 10.1547 cents 14 x 16:19:21:22:24:28 SD: 8.8744 cents 15:17 x 20 x 23:26:30 SD: 2.8511 cents 16:18 x 21:24:25:28:32 SD: 7.1292 cents 17:19:20:23 x 26:29:34 SD: 8.5486 cents 18:20:21:24:27:28:31:36 SD: 5.0867 cents 19:21:22:25 x 29:33:38 SD: 6.9254 cents 20 x 23:27:30:31:35:40 SD: 5.3469 cents 21 x 24:28 x 32:36:42 S SD: 5.7390 cents 22:25 x 29:33:34:38:44 SD: 4.6192 cents 23:26:27:31 x 35:40:46 SD: 6.9492 cents 24:27:28:32:36:37:42:48 SD: 3.8989 cents 25:28:29:33 x 38:43:50 SD: 5.2721 cents 26:29:30:35:39:40:45:52 SD: 3.1793 cents 28 x 32:37:42:43:48:56 SD: 4.7128 cents 29:33 x 39:44:45:50:58 SD: 5.9367 cents 30:34:35:40:45:46:52:60 SD: 3.4082 cents 32:36:37:43:48:49:55:64 SD: 2.8792 cents 39:44:45:52:59:60:68:78 SD: 2.8735 cents 40:45:46:53:60:62:69:80 SD: 2.6801 cents 46:52:53:61:69:71:80:92 SD: 2.3313 cents 48:54:55:64:72:74:83:96 SD: 1.8132 cents 63:71:73:84:95:97:109:126 SD: 1.7409 cents 64:72:74:85:96:98:111:128 SD: 1.6784 cents 66:74:76:88:99:102:114:132 SD: 1.5666 cents 72:81:83:96:108:111:125:144 SD: 0.9478 cents 78:88:90:104:117:120:135:156 SD: 0.7036 cents 104:117:120:139:156:160:180:208 SD: 0.5938 cents 150:169:173:200:225:231:260:300 SD: 0.5842 cents 162:182:187:216:243:249:280:324 SD: 0.5416 cents 168:189:194:224:252:258:291:336 SD: 0.5219 cents 182:205:210:243:273:280:315:364 SD: 0.4542 cents 208:234:240:277:312:320:360:416 SD: 0.2974 cents 234:263:270:312:351:360:405:468 SD: 0.2350 cents 312:351:360:416:468:480:540:624 SD: 0.0000 cents