Scala analysis: xen12-chalmers-tritriadic-dm-15-11-5
Tritriadic D->M scale built from 15:11:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 40/33 333.040771 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 121/75 828.053456 6: 20/11 1034.995772 large minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 400/363 168.0365 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 1500/1331 206.9423 7: 11/10 165.0042 Ptolemy's second, 4/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 400/363 168.037 cents 1: 1 1500/1331 206.942 cents 2: 3 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 2: 2 40/33 333.041 cents 2: 2 150/121 371.947 cents 3: 1 1331/1000 495.013 cents 3: 3 4/3 498.045 cents perfect fourth 3: 3 15/11 536.951 cents undecimal augmented fourth 4: 3 22/15 663.049 cents undecimal diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 2000/1331 704.987 cents 5: 2 121/75 828.053 cents 5: 2 33/20 866.959 cents 5: 3 200/121 869.992 cents 6: 1 1331/750 993.058 cents 6: 1 363/200 1031.963 cents 6: 5 20/11 1034.996 cents large minor seventh 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 : 165.0 333.0 498.0 663.0 828.1 1035.0 1200.0 165.0 : 168.0 333.0 498.0 663.0 870.0 1035.0 1200.0 333.0 : 165.0 330.0 495.0 702.0 867.0 1032.0 1200.0 498.0 : 165.0 330.0 537.0 702.0 867.0 1035.0 1200.0 663.0 : 165.0 371.9 537.0 702.0 870.0 1035.0 1200.0 828.1 : 206.9 371.9 537.0 705.0 870.0 1035.0 1200.0 1035.0: 165.0 330.0 498.0 663.0 828.1 993.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 206.9423 cents 15000/14641, 41.9381 cents 11/10, 165.0042 cents 2: 330.0085 .. 371.9465 cents 15000/14641, 41.9381 cents 161051/150000, 123.0661 cents 3: 495.0127 .. 536.9508 cents 15000/14641, 41.9381 cents 161051/150000, 123.0661 cents 4: 663.0492 .. 704.9873 cents 15000/14641, 41.9381 cents 242/225, 126.0985 cents 5: 828.0535 .. 869.9915 cents 15000/14641, 41.9381 cents 161051/150000, 123.0661 cents 6: 993.0577 .. 1034.9958 cents 15000/14641, 41.9381 cents 161051/150000, 123.0661 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1500/1331, 206.9423 cents Average / Smallest step : 1.038934 Largest / Average step : 1.207164 Largest / Smallest step : 1.254164 Median interval of one step : 11/10, 165.0042 cents, amount: 5 Most common interval of one step : 11/10, 165.0042 cents, amount: 5 Least squares average step : 169.48328 cents, oct.: 1186.38298 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : SMSSSLS Scale is a Constant Structure, by a margin of 123.06614 cents Scale diversity : 1.197508 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.790310 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 : 4000/3993, 3.0323 cents Most common intervals : 11/10, 165.0042 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 536.951 1034.996 cents Most common triad is 0.0 165.004 1034.996 cents, amount: 3 Number of recognisable fifths : 4, average 702.7131 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 5 11 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 n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 41.9381 cents: 4 -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.012436 Average absolute harmonicity : 0.196964 Specific harmonicity : 0.069380 Fundamental : 1/1650, -10.6883 octaves, 0.1586 Hz. Guide tone : 4840, 12.2408 octaves, 1266267.736 Hz. Exponens Consonantiae : 7.986000E+06, 22.92904 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 184.0, average 26.28571 Mersenne's string divisions : 49233828 Sum of van Prooijen's expressibility: 7.33730, average 1.04819 Sum of Tenney's harmonic distance : 15.36096, average 2.19442 Vogel's harmonic complexity : 26.14286 Wille's k value : 907 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 74.26570, average 2.65235 Lattice compactness (without 2's) : 55.11067, average 1.96824 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.14286 10 1 3: -1 .. 0 -0.57143 4 1 5: -2 .. 1 -0.28571 6 11: -1 .. 2 0.28571 6 5 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 17 23| Scale is weakly epimorphic with val: <7 10 18 24| Scale is JI-epimorphic with val: <7 11 15 23| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is JI-epimorphic with val: <7 11 17 25| Scale is JI-epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 12 15 25| Scale is weakly epimorphic with val: <7 12 16 26|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 16.0471 c. M:-29.0894 c. Lebeng 15: 2 2 2 2 2 3 2 SP M ME S SD: 16.3184 c. M: 28.0535 c. 17: 2 3 2 2 3 3 2 SP D3 S SD: 19.5613 c. M: 27.7551 c. Dastgah-e Sehgah 20: 3 3 2 3 3 3 3 SP M ME S SD: 15.3725 c. M:-26.9592 c. 22: 3 3 3 3 3 4 3 SP M ME S SD: 6.0674 c. M: 9.8716 c. 29: 4 4 4 4 4 5 4 SP M ME S SD: 1.0664 c. M: 2.0063 c. 94: 13 13 13 13 13 16 13 SP M DE S SD: 0.9805 c. M:-1.7338 c. 123: 17 17 17 17 17 21 17 SP M DE S SD: 0.8506 c. M: 1.3335 c. 152: 21 21 21 21 21 26 21 SP M DE S SD: 0.8141 c. M: 1.4618 c. 181: 25 25 25 25 25 31 25 SP M DE S SD: 0.8118 c. M: 1.5491 c. 210: 29 29 29 29 29 36 29 SP M DE S SD: 0.8217 c. M: 1.6122 c. 219: 30 31 30 30 30 38 30 SP T3 SD: 0.6545 c. M:-1.2058 c. 226: 31 32 31 31 31 39 31 SP T3 SD: 0.7703 c. M:-1.4725 c. 248: 34 35 34 34 34 43 34 SP T3 SD: 0.4937 c. M:-0.8302 c. 255: 35 36 35 35 35 44 35 SP T3 SD: 0.5616 c. M:-1.0769 c. 277: 38 39 38 38 38 48 38 SP T3 SD: 0.3846 c. M: 0.6166 c. 284: 39 40 39 39 39 49 39 SP T3 SD: 0.3956 c. M:-0.7620 c. 306: 42 43 42 42 42 53 42 SP T3 SD: 0.3205 c. M: 0.6025 c. 313: 43 44 43 43 43 54 43 SP T3 SD: 0.2605 c. M:-0.5056 c. 342: 47 48 47 47 47 59 47 SP T3 SD: 0.1487 c. M:-0.2926 c. 371: 51 52 51 51 51 64 51 SP T3 SD: 0.0565 c. M:-0.1129 c. 400: 55 56 55 55 55 69 55 SP T3 SD: 0.0359 c. M: 0.0535 c. 771: 106 108 106 106 106 133 106 SP T3 SD: 0.0238 c. M: 0.0379 c. 1171: 161 164 161 161 161 202 161 SP T3 SD: 0.0216 c. M: 0.0432 c. 1571: 216 220 216 216 216 271 216 SP T3 SD: 0.0235 c. M: 0.0458 c. 1942: 267 272 267 267 267 335 267 SP T3 SD: 0.0215 c. M: 0.0411 c. 2378: 327 333 327 327 327 410 327 SP T3 SD: 0.0205 c. M:-0.0374 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: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 18.7684 cents 4 x 5 x 6 x 7:8 S SD: 23.3588 cents 5 x 6 x 7:8:9:10 S SD: 17.0858 cents 6 x 7:8:9:10:11:12 S SD: 16.0458 cents 7:8 x 9:10:11:13:14 SD: 19.6083 cents 8:9:10:11:12:13:15:16 SD: 15.4503 cents 9:10:11:12:13:15:16:18 SD: 10.9654 cents 10:11:12:13:15:16:18:20 SD: 9.3096 cents 13:14:16:17:19:21:24:26 SD: 8.9401 cents 15:17:18:20:22:24:27:30 SD: 8.4310 cents 17:19:21:23:25:27:31:34 SD: 8.1526 cents 18:20:22:24:26:29:33:36 SD: 5.3831 cents 21:23:25:28:31:34:38:42 SD: 5.0726 cents 23:25:28:31:34:37:42:46 SD: 4.7386 cents 28:31:34:37:41:45:51:56 SD: 2.9896 cents 38:42:46:51:56:61:69:76 SD: 2.6773 cents 39:43:47:52:57:63:71:78 SD: 1.8245 cents 51:56:62:68:75:82:93:102 SD: 1.5481 cents 60:66:73:80:88:97:109:120 SD: 1.0770 cents 81:89:98:108:119:131:147:162 SD: 1.0180 cents 90:99:109:120:132:145:164:180 SD: 0.6783 cents 99:109:120:132:145:160:180:198 SD: 0.5961 cents 150:165:182:200:220:242:273:300 SD: 0.3496 cents 231:254:280:308:339:373:420:462 SD: 0.2754 cents 240:264:291:320:352:387:436:480 SD: 0.2546 cents 279:307:338:372:409:450:507:558 SD: 0.2467 cents 321:353:389:428:471:518:584:642 SD: 0.2152 cents 330:363:400:440:484:532:600:660 SD: 0.1859 cents 390:429:473:520:572:629:709:780 SD: 0.1659 cents 411:452:498:548:603:663:747:822 SD: 0.1641 cents 429:472:520:572:629:692:780:858 SD: 0.1038 cents 561:617:680:748:823:905:1020:1122 SD: 0.0755 cents