Scala analysis: xen09-chalmers-tritriadic-1-11-13
Tritriadic scale built from 1:11:13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 143/128 191.845604 2: 16/13 359.472338 tridecimal neutral third 3: 169/128 481.055324 4: 11/8 551.317942 undecimal semi-augmented fourth 5: 13/8 840.527662 tridecimal neutral sixth 6: 22/13 910.790281 tridecimal major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 143/128 191.8456 2: 2048/1859 167.6267 3: 2197/2048 121.5830 4: 176/169 70.2626 5: 13/11 289.2097 tridecimal minor third 6: 176/169 70.2626 7: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 176/169 70.263 cents 1: 1 2197/2048 121.583 cents 1: 1 2048/1859 167.627 cents 1: 1 143/128 191.846 cents 1: 2 13/11 289.210 cents tridecimal minor third 2: 1 143/128 191.846 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 4 16/13 359.472 cents tridecimal neutral third 2: 1 169/128 481.055 cents 3: 1 16/13 359.472 cents tridecimal neutral third 3: 1 2816/2197 429.735 cents 3: 2 169/128 481.055 cents 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 2 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 2 256/169 718.945 cents two (tridecimal neutral third) 4: 1 2197/1408 770.265 cents 4: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 256/169 718.945 cents two (tridecimal neutral third) 5: 4 13/8 840.528 cents tridecimal neutral sixth 5: 1 22/13 910.790 cents tridecimal major sixth 5: 1 256/143 1008.154 cents 6: 2 22/13 910.790 cents tridecimal major sixth 6: 1 256/143 1008.154 cents 6: 1 1859/1024 1032.373 cents 6: 1 4096/2197 1078.417 cents 6: 2 169/88 1129.737 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 191.8 359.5 481.1 551.3 840.5 910.8 1200.0 191.8 : 167.6 289.2 359.5 648.7 718.9 1008.2 1200.0 359.5 : 121.6 191.8 481.1 551.3 840.5 1032.4 1200.0 481.1 : 70.3 359.5 429.7 718.9 910.8 1078.4 1200.0 551.3 : 289.2 359.5 648.7 840.5 1008.2 1129.7 1200.0 840.5 : 70.3 359.5 551.3 718.9 840.5 910.8 1200.0 910.8 : 289.2 481.1 648.7 770.3 840.5 1129.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.2626 .. 289.2097 cents 2197/1936, 218.9471 cents 176/169, 70.2626 cents 2: 191.8456 .. 481.0553 cents 13/11, 289.2097 cents 121/128,-97.3641 cents 3: 359.4723 .. 648.6821 cents 13/11, 289.2097 cents 2048/2197,-121.5830 cents 4: 551.3179 .. 840.5277 cents 13/11, 289.2097 cents 121/128,-97.3641 cents 5: 718.9447 .. 1008.1544 cents 13/11, 289.2097 cents 2048/2197,-121.5830 cents 6: 910.7903 .. 1129.7374 cents 2197/1936, 218.9471 cents 121/128,-97.3641 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 176/169, 70.2626 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 2.439826 Largest / Average step : 1.687057 Largest / Smallest step : 4.116125 Median interval of one step : 2048/1859, 167.6267 cents, amount: 1 Least squares average step : 161.61863 cents, oct.: 1131.33040 cents Scale is not proper Step pattern alph. order: ABCDEDE Step pattern size order : DCBAEAE Scale is not a Constant Structure Scale diversity : 1.461005 Lumma stability : 0.117104 Lumma impropriety factor : 0.446049 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 : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 265837/262144, 24.2189 cents Most common intervals : 16/13, 359.4723 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 551.318 840.528 cents Most common triad is 0.0 359.472 840.528 cents, amount: 3 Number of recognisable fifths : 3, average 718.9447 cents Number of appreciable fifths : 0 Scale contains a complete diamond : 1 13 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 169 Scale harmonicity : 0.010456 Average absolute harmonicity : 0.170001 Specific harmonicity : 0.055269 Fundamental : 1/1664, -10.7004 octaves, 0.1572 Hz. Guide tone : 29744, 14.8603 octaves, 7781790.814 Hz. Exponens Consonantiae : 4.949402E+07, 25.56075 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 337.5, average 48.21429 Mersenne's string divisions : 1552191795 Sum of van Prooijen's expressibility: 8.76645, average 1.25235 Sum of Tenney's harmonic distance : 17.63462, average 2.51923 Vogel's harmonic complexity : 26.42857 Wille's k value : 1098 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 142.33928, average 5.08355 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 4 -2.00000 26 1 11: 0 .. 1 0.42857 3 1 13: -1 .. 2 0.28571 6 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 23 25| Scale is weakly epimorphic with val: <7 24 27| Scale is weakly epimorphic with val: <7 25 29|
FIT/MODE
7: 1 1 1 0 2 0 2 N T3 SD: 30.0539 c. M: 53.6474 c. 10: 2 1 1 1 2 1 2 N D3 SD: 31.8749 c. M:-49.2097 c. 11: 2 1 1 1 3 0 3 N G SD: 29.8753 c. M: 44.6917 c. 12: 2 2 1 1 2 1 3 N SD: 29.7532 c. M:-48.6821 c. 13: 2 2 1 1 3 1 3 N SD: 10.5627 c. M: 19.5169 c. 17: 3 2 2 1 4 1 4 N SD: 11.2056 c. M:-19.9191 c. 20: 3 3 2 1 5 1 5 N SD: 7.4308 c. M: 11.8456 c. 30: 5 4 3 2 7 2 7 N SD: 5.7117 c. M:-9.2097 c. 37: 6 5 4 2 9 2 9 N SD: 2.9032 c. M:-5.4312 c. 50: 8 7 5 3 12 3 12 N SD: 0.7194 c. M:-1.2097 c. 137: 22 19 14 8 33 8 33 N SD: 0.4987 c. M:-0.8551 c. 187: 30 26 19 11 45 11 45 N SD: 0.3824 c. M:-0.6678 c. 207: 33 29 21 12 50 12 50 N SD: 0.3924 c. M: 0.6454 c. 237: 38 33 24 14 57 14 57 N SD: 0.3809 c. M:-0.6021 c. 257: 41 36 26 15 62 15 62 N SD: 0.2351 c. M: 0.4059 c. 307: 49 43 31 18 74 18 74 N SD: 0.1869 c. M: 0.3147 c. 394: 63 55 40 23 95 23 95 N SD: 0.0928 c. M:-0.1630 c. 444: 71 62 45 26 107 26 107 N SD: 0.0258 c. M:-0.0463 c. 1589: 254 222 161 93 383 93 383 N SD: 0.0182 c. M: 0.0288 c. 1639: 262 229 166 96 395 96 395 N SD: 0.0167 c. M: 0.0303 c. 2033: 325 284 206 119 490 119 490 N SD: 0.0102 c. M: 0.0180 c. 2083: 333 291 211 122 502 122 502 N SD: 0.0099 c. M: 0.0184 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 69.2863 cents 3 x x 4 x x 5:6 S SD: 10.4737 cents 4 x 5 x x x 7:8 SD: 21.3140 cents 5 x 6 x 7:8 x 10 S SD: 15.0306 cents 6:7 x 8 x x 10:12 S SD: 20.3348 cents 7:8 x 9:10:11:12:14 S SD: 18.1855 cents 8:9:10 x 11:13:14:16 SD: 10.8450 cents 9:10:11:12 x x 15:18 S SD: 6.9914 cents 11:12:14 x 15:18:19:22 SD: 13.6135 cents 12:13:15:16:17 x 20:24 SD: 14.1586 cents 13:15:16:17:18:21:22:26 SD: 8.6330 cents 16:18:20:21:22:26:27:32 SD: 4.5081 cents 25:28:31:33:34:41:42:50 SD: 4.4258 cents 26:29:32:34:36:42:44:52 SD: 3.3056 cents 34:38:42:45:47:55:58:68 SD: 2.8458 cents 35:39:43:46:48:57:59:70 SD: 1.8789 cents 43:48:53:57:59:70:73:86 SD: 1.4907 cents 69:77:85:91:95:112:117:138 SD: 0.7893 cents 104:116:128:137:143:169:176:208 SD: 0.6907 cents 144:161:177:190:198:234:244:288 SD: 0.5144 cents 147:164:181:194:202:239:249:294 SD: 0.4820 cents 178:199:219:235:245:289:301:356 SD: 0.4287 cents 213:238:262:281:293:346:360:426 SD: 0.4266 cents 221:247:272:292:304:359:374:442 SD: 0.2450 cents 256:286:315:338:352:416:433:512 SD: 0.1450 cents 325:363:400:429:447:528:550:650 SD: 0.1227 cents 546:610:672:721:751:887:924:1092 SD: 0.1144 cents 581:649:715:767:799:944:983:1162 SD: 0.0938 cents