Scala analysis: xen09-chalmers-tritriadic-11-15-20
Tritriadic scale built from 11:15:20
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: 150/121 371.946544 3: 15/11 536.950772 undecimal augmented fourth 4: 3/2 701.955001 perfect fifth 5: 200/121 869.991543 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: 1500/1331 206.9423 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 400/363 168.0365 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 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 : 165.0 371.9 537.0 702.0 870.0 1035.0 1200.0 165.0 : 206.9 371.9 537.0 705.0 870.0 1035.0 1200.0 371.9 : 165.0 330.0 498.0 663.0 828.1 993.1 1200.0 537.0 : 165.0 333.0 498.0 663.0 828.1 1035.0 1200.0 702.0 : 168.0 333.0 498.0 663.0 870.0 1035.0 1200.0 870.0 : 165.0 330.0 495.0 702.0 867.0 1032.0 1200.0 1035.0: 165.0 330.0 537.0 702.0 867.0 1035.0 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 : 173.48216 cents, oct.: 1214.37510 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : SLSSMSS 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 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: 3 -- 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 : 0.203462 Specific harmonicity : 0.067555 Fundamental : 1/1210, -10.2408 octaves, 0.2162 Hz. Guide tone : 6600, 12.6883 octaves, 1726728.731 Hz. Exponens Consonantiae : 7.986000E+06, 22.92904 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 339.0, average 48.42857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.90157, average 1.12880 Sum of Tenney's harmonic distance : 16.32317, average 2.33188 Vogel's harmonic complexity : 25.71429 Wille's k value : 907 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 77.19971, average 2.75713 Lattice compactness (without 2's) : 56.20705, average 2.00739 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.71429 9 1 3: 0 .. 1 0.42857 3 1 5: -1 .. 2 0.71429 7 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 17 / 7 = 2.42857 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: 16.3502 c. M: 29.0894 c. Lebeng 15: 2 3 2 2 2 2 2 SP M ME S SD: 16.0095 c. M:-28.0535 c. Miller's Porcupine-7 Major 22: 3 4 3 3 3 3 3 SP M ME S SD: 5.7559 c. M:-9.8716 c. Miller's Porcupine-7 Major 29: 4 5 4 4 4 4 4 SP M ME S SD: 0.8442 c. M:-1.4933 c. Miller's Porcupine-7 Major 152: 21 26 21 21 21 21 21 SP M DE S SD: 0.8425 c. M: 1.5705 c. 181: 25 31 25 25 25 25 25 SP M DE S SD: 0.7940 c. M: 1.4833 c. 197: 27 34 27 27 28 27 27 SP T3 SD: 0.8276 c. M: 1.4474 c. 210: 29 36 29 29 29 29 29 SP M DE S SD: 0.7694 c. M: 1.4201 c. 219: 30 38 30 30 31 30 30 SP T3 SD: 0.6639 c. M:-1.2413 c. 226: 31 39 31 31 32 31 31 SP T3 SD: 0.6133 c. M: 1.0700 c. 248: 34 43 34 34 35 34 34 SP T3 SD: 0.5305 c. M:-0.9762 c. 255: 35 44 35 35 36 35 35 SP T3 SD: 0.4478 c. M: 0.7785 c. 277: 38 48 38 38 39 38 38 SP T3 SD: 0.4373 c. M:-0.7666 c. 284: 39 49 39 39 40 39 39 SP T3 SD: 0.3163 c. M: 0.5466 c. 313: 43 54 43 43 44 43 43 SP T3 SD: 0.2094 c. M: 0.3576 c. 342: 47 59 47 47 48 47 47 SP T3 SD: 0.1213 c. M: 0.2006 c. 371: 51 64 51 51 52 51 51 SP T3 SD: 0.0502 c. M:-0.0893 c. 400: 55 69 55 55 56 55 55 SP T3 SD: 0.0325 c. M:-0.0535 c. 771: 106 133 106 106 108 106 106 SP T3 SD: 0.0270 c. M:-0.0474 c. 1171: 161 202 161 161 164 161 161 SP T3 SD: 0.0250 c. M:-0.0432 c. 1571: 216 271 216 216 220 216 216 SP T3 SD: 0.0256 c. M:-0.0458 c. 1942: 267 335 267 267 272 267 267 SP T3 SD: 0.0253 c. M:-0.0411 c. 2378: 327 410 327 327 333 327 327 SP T3 SD: 0.0210 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 13.8246 cents 4 x 5 x 6 x 7:8 S SD: 16.9279 cents 5 x 6:7 x 8:9:10 S SD: 18.6753 cents 6:7 x 8:9:10:11:12 S SD: 18.4867 cents 8:9:10:11:12:13:15:16 SD: 10.7215 cents 11:12:14:15:17:18:20:22 SD: 10.3570 cents 12:13:15:16:18:20:22:24 SD: 7.6017 cents 16:18:20:22:24:26:29:32 SD: 7.5916 cents 17:19:21:23:26:28:31:34 SD: 6.6638 cents 20:22:25:27:30:33:36:40 SD: 4.0935 cents 22:24:27:30:33:36:40:44 S SD: 4.0706 cents 28:31:35:38:42:46:51:56 SD: 3.2607 cents 30:33:37:41:45:50:55:60 SD: 3.2144 cents 38:42:47:52:57:63:69:76 SD: 1.7685 cents 50:55:62:68:75:83:91:100 SD: 1.2758 cents 72:79:89:98:108:119:131:144 SD: 1.0660 cents 80:88:99:109:120:132:145:160 SD: 1.0085 cents 88:97:109:120:132:145:160:176 SD: 0.9499 cents 100:110:124:136:150:165:182:200 SD: 0.8302 cents 110:121:136:150:165:182:200:220 SD: 0.7051 cents 130:143:161:177:195:215:236:260 SD: 0.6070 cents 138:152:171:188:207:228:251:276 SD: 0.4409 cents 170:187:211:232:255:281:309:340 SD: 0.3650 cents 220:242:273:300:330:364:400:440 SD: 0.3496 cents 230:253:285:314:345:380:418:460 SD: 0.3418 cents 242:266:300:330:363:400:440:484 SD: 0.1859 cents 280:308:347:382:420:463:509:560 SD: 0.1789 cents 380:418:471:518:570:628:691:760 SD: 0.1079 cents 550:605:682:750:825:909:1000:1100 SD: 0.0704 cents