Scala analysis: xen12-chalmers-tritriadic-dm-13-9-5
Tritriadic D->M scale built from 13:9:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 81/65 380.978628 3: 18/13 563.382340 tridecimal augmented fourth 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 200/117 928.189764 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 729/650 198.5749 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 10/9 182.4037 minor whole tone 6: 1053/1000 89.4065 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1053/1000 89.407 cents 1: 5 10/9 182.404 cents minor whole tone 1: 1 729/650 198.575 cents 2: 2 117/100 271.810 cents 2: 3 100/81 364.807 cents grave major third 2: 2 81/65 380.979 cents 3: 3 13/10 454.214 cents tridecimal semi-diminished fourth 3: 1 1000/729 547.211 cents 3: 3 18/13 563.382 cents tridecimal augmented fourth 4: 3 13/9 636.618 cents tridecimal diminished fifth 4: 1 729/500 652.789 cents 4: 3 20/13 745.786 cents tridecimal semi-augmented fifth 5: 2 130/81 819.021 cents 5: 3 81/50 835.193 cents acute minor sixth 5: 2 200/117 928.190 cents 6: 1 1300/729 1001.425 cents 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 2000/1053 1110.593 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 : 182.4 381.0 563.4 745.8 928.2 1017.6 1200.0 182.4 : 198.6 381.0 563.4 745.8 835.2 1017.6 1200.0 381.0 : 182.4 364.8 547.2 636.6 819.0 1001.4 1200.0 563.4 : 182.4 364.8 454.2 636.6 819.0 1017.6 1200.0 745.8 : 182.4 271.8 454.2 636.6 835.2 1017.6 1200.0 928.2 : 89.4 271.8 454.2 652.8 835.2 1017.6 1200.0 1017.6: 182.4 364.8 563.4 745.8 928.2 1110.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.4065 .. 198.5749 cents 180/169, 109.1684 cents 1053/1000, 89.4065 cents 2: 271.8102 .. 380.9786 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 3: 454.2139 .. 563.3823 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 4: 636.6177 .. 745.7861 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 5: 819.0214 .. 928.1898 cents 180/169, 109.1684 cents 169/162, 73.2353 cents 6: 1001.4251 .. 1110.5935 cents 180/169, 109.1684 cents 169/162, 73.2353 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1053/1000, 89.4065 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 729/650, 198.5749 cents Average / Smallest step : 1.917406 Largest / Average step : 1.158354 Largest / Smallest step : 2.221034 Median interval of one step : 10/9, 182.4037 cents, amount: 5 Most common interval of one step : 10/9, 182.4037 cents, amount: 5 Least squares average step : 176.88699 cents, oct.: 1238.20894 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : MLMMMSM Scale is a Constant Structure, by a margin of 73.23532 cents Scale diversity : 1.390251 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.454158 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 : 6561/6500, 16.1712 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 454.214 1017.596 cents Most common triad is 0.0 182.404 1017.596 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 5 9 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% Limited inverse transpositions with margin 109.1684 cents: 4 -- Rational properties -- Prime limit : 13 Odd number limit : 1053 (O: 1053 U: 1053) Highest odd numerator or denominator: 117 Scale harmonicity : 0.016569 Average absolute harmonicity : 0.182884 Specific harmonicity : 0.081280 Fundamental : 1/585, -9.1923 octaves, 0.4472 Hz. Guide tone : 16200, 13.9837 octaves, 4238334.158 Hz. Exponens Consonantiae : 9.477000E+06, 23.17600 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 281.5, average 40.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.11304, average 1.15901 Sum of Tenney's harmonic distance : 16.78329, average 2.39761 Vogel's harmonic complexity : 20.85714 Wille's k value : 526 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 93.87753, average 3.35277 Lattice compactness (without 2's) : 83.60828, average 2.98601 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.14286 8 1 3: -2 .. 4 0.57143 12 5: -1 .. 2 0.28571 6 2 13: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 15 28| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 12 16 27| Scale is JI-epimorphic with val: <7 12 18 28|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 42.6965 c. M: 71.0469 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 35.8912 c. M:-69.0214 c. 9: 1 2 1 2 1 1 1 N D3 S SD: 35.9487 c. M:-54.2139 c. 12: 2 2 2 1 2 1 2 P D3 S SD: 27.2893 c. M: 45.7861 c. Lydian Dominant, Mela Vacaspati, Raga Bhusavati, Bhusavali, Vachaspati, Overtone, Lydian-Mixolydian, Bartok 13: 2 2 2 2 2 1 2 SP M ME S SD: 6.7456 c. M: 11.7479 c. Karakalian 32: 5 5 5 5 5 2 5 SP M DE S SD: 5.2496 c. M:-9.3102 c. 40: 6 7 6 6 6 3 6 SP T3 SD: 4.7475 c. M:-9.0214 c. 45: 7 7 7 7 7 3 7 SP M DE S SD: 4.3666 c. M: 7.6453 c. 53: 8 9 8 8 8 4 8 SP T3 SD: 1.9869 c. M:-3.9270 c. 66: 10 11 10 10 10 5 10 SP T3 SD: 0.5863 c. M: 0.9170 c. 145: 22 24 22 22 22 11 22 SP T3 SD: 0.6853 c. M: 1.2932 c. 164: 25 27 25 25 25 12 25 SP T3 SD: 0.5683 c. M:-1.0785 c. 211: 32 35 32 32 32 16 32 SP T3 SD: 0.5893 c. M: 1.1755 c. 217: 33 36 33 33 33 16 33 SP T3 SD: 0.5474 c. M:-0.8425 c. 230: 35 38 35 35 35 17 35 SP T3 SD: 0.2540 c. M:-0.5059 c. 296: 45 49 45 45 45 22 45 SP T3 SD: 0.1137 c. M:-0.1886 c. 605: 92 100 92 92 92 45 92 SP T3 SD: 0.0811 c. M: 0.1522 c. 671: 102 111 102 102 102 50 102 SP T3 SD: 0.0311 c. M: 0.0546 c. 967: 147 160 147 147 147 72 147 SP T3 SD: 0.0210 c. M:-0.0419 c. 1638: 249 271 249 249 249 122 249 SP T3 SD: 0.0145 c. M: 0.0262 c. 1704: 259 282 259 259 259 127 259 SP T3 SD: 0.0106 c. M: 0.0208 c. 2000: 304 331 304 304 304 149 304 SP T3 SD: 0.0125 c. M:-0.0214 c. 2375: 361 393 361 361 361 177 361 SP T3 SD: 0.0125 c. M: 0.0213 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: 21.9155 cents 3 x x 4 x 5 x 6 S SD: 26.2258 cents 4 x 5 x 6:7 x 8 S SD: 15.0019 cents 5 x 6:7:8 x 9:10 S SD: 19.2306 cents 6:7 x 8:9:10:11:12 S SD: 21.2493 cents 7:8:9:10:11:12:13:14 H SD: 15.9927 cents 8:9:10:11:12:14 x 16 S SD: 10.8128 cents 11:12:14:15:17:19:20:22 SD: 8.7257 cents 15:17:19:21:23:26:27:30 SD: 7.7630 cents 16:18:20:22:25:27:29:32 SD: 6.3871 cents 20:22:25:28:31:34:36:40 SD: 4.4162 cents 24:27:30:33:37:41:43:48 SD: 3.8205 cents 28:31:35:39:43:48:50:56 SD: 2.8452 cents 37:41:46:51:57:63:67:74 SD: 2.2972 cents 44:49:55:61:68:75:79:88 SD: 1.7713 cents 45:50:56:62:69:77:81:90 SD: 1.5354 cents 65:72:81:90:100:111:117:130 SD: 0.8013 cents 89:99:111:123:137:152:160:178 SD: 0.7061 cents 117:130:146:162:180:200:211:234 SD: 0.5789 cents 135:150:168:187:208:231:243:270 SD: 0.5664 cents 145:161:181:201:223:248:261:290 SD: 0.5593 cents 154:171:192:213:237:263:277:308 SD: 0.4520 cents 171:190:213:237:263:292:308:342 SD: 0.4104 cents 206:229:257:285:317:352:371:412 SD: 0.4054 cents 216:240:269:299:332:369:389:432 SD: 0.3476 cents 244:271:304:338:375:417:439:488 SD: 0.3249 cents 260:289:324:360:400:444:468:520 SD: 0.2651 cents 325:361:405:450:500:556:585:650 SD: 0.2119 cents 369:410:460:511:568:631:664:738 SD: 0.2034 cents 395:439:492:547:608:675:711:790 SD: 0.2009 cents 406:451:506:562:625:694:731:812 SD: 0.1923 cents 414:460:516:573:637:708:745:828 SD: 0.1695 cents 431:479:537:597:663:737:776:862 SD: 0.1614 cents 468:520:583:648:720:800:842:936 SD: 0.1449 cents 496:551:618:687:763:848:893:992 SD: 0.1266 cents 520:578:648:720:800:889:936:1040 SD: 0.1000 cents 585:650:729:810:900:1000:1053:1170 SD: 0.0000 cents