Scala analysis: xen09-chalmers-tritriadic-7-9-11
Tritriadic scale built from 7:9:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99/98 17.576131 small undecimal comma 2: 121/98 364.984072 3: 14/11 417.507964 undecimal diminished fourth or major third 4: 9/7 435.084095 septimal major third, BP third 5: 11/7 782.492036 undecimal augmented fifth 6: 18/11 852.592059 undecimal neutral sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 99/98 17.5761 small undecimal comma 2: 11/9 347.4079 undecimal neutral third 3: 1372/1331 52.5239 4: 99/98 17.5761 small undecimal comma 5: 11/9 347.4079 undecimal neutral third 6: 126/121 70.1000 7: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 99/98 17.576 cents small undecimal comma 1: 1 1372/1331 52.524 cents 1: 1 126/121 70.100 cents 1: 3 11/9 347.408 cents undecimal neutral third 2: 1 126/121 70.100 cents 2: 3 121/98 364.984 cents 2: 1 1372/1089 399.932 cents 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 3 14/11 417.508 cents undecimal diminished fourth or major third 3: 2 9/7 435.084 cents septimal major third, BP third 3: 1 1331/882 712.392 cents 3: 1 14/9 764.916 cents septimal minor sixth 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 1764/1331 487.608 cents 4: 2 14/9 764.916 cents septimal minor sixth 4: 3 11/7 782.492 cents undecimal augmented fifth 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 1089/686 800.068 cents 5: 3 196/121 835.016 cents two (undecimal diminished fourth or major third) 5: 1 121/63 1129.900 cents 6: 3 18/11 852.592 cents undecimal neutral sixth 6: 1 121/63 1129.900 cents 6: 1 1331/686 1147.476 cents 6: 2 196/99 1182.424 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 17.6 365.0 417.5 435.1 782.5 852.6 1200.0 17.6 : 347.4 399.9 417.5 764.9 835.0 1182.4 1200.0 365.0 : 52.5 70.1 417.5 487.6 835.0 852.6 1200.0 417.5 : 17.6 365.0 435.1 782.5 800.1 1147.5 1200.0 435.1 : 347.4 417.5 764.9 782.5 1129.9 1182.4 1200.0 782.5 : 70.1 417.5 435.1 782.5 835.0 852.6 1200.0 852.6 : 347.4 365.0 712.4 764.9 782.5 1129.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.5761 .. 347.4079 cents 98/81, 329.8318 cents 99/98, 17.5761 cents 2: 70.1000 .. 417.5080 cents 11/9, 347.4079 cents 1134/1331,-277.3079 cents 3: 417.5080 .. 764.9159 cents 11/9, 347.4079 cents 1/1, 0.0000 cents 4: 435.0841 .. 782.4920 cents 11/9, 347.4079 cents 81/98,-329.8318 cents 5: 782.4920 .. 1129.9000 cents 11/9, 347.4079 cents 1/1, 0.0000 cents 6: 852.5921 .. 1182.4239 cents 98/81, 329.8318 cents 1134/1331,-277.3079 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 99/98, 17.5761 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 9.753487 Largest / Average step : 2.026546 Largest / Smallest step : 19.765894 Median interval of one step : 126/121, 70.1000 cents, amount: 1 Most common interval of one step : 11/9, 347.4079 cents, amount: 3 Least squares average step : 151.20298 cents, oct.: 1058.42085 cents Scale is not proper Step pattern alph. order: ABCABDB Step pattern size order : ADBADCD Scale is not a Constant Structure Scale diversity : 0.970616 Lumma stability : 0.029294 Lumma impropriety factor : 0.737040 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 99/98, 17.5761 cents Most common intervals : 14/11, 417.5080 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 435.084 782.492 cents Most common triad is 0.0 417.508 782.492 cents, amount: 3 Number of recognisable fifths : 1, average 712.3920 cents Scale contains a complete diamond : 7 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% -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.010783 Average absolute harmonicity : 0.173331 Specific harmonicity : 0.058976 Fundamental : 1/1078, -10.0741 octaves, 0.2427 Hz. Guide tone : 15246, 13.8961 octaves, 3988743.369 Hz. Exponens Consonantiae : 1.643519E+07, 23.97028 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 253.5, average 36.21429 Mersenne's string divisions : 1501376400 Sum of van Prooijen's expressibility: 8.15684, average 1.16526 Sum of Tenney's harmonic distance : 16.53192, average 2.36170 Vogel's harmonic complexity : 26.85714 Wille's k value : 665 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 74.05592, average 2.64485 Lattice compactness (without 2's) : 66.59060, average 2.37824 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.14286 5 1 3: 0 .. 2 0.85714 6 7: -2 .. 1 -0.71429 7 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 18 22| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 10 22 25| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 20 24| = patent Scale is weakly epimorphic with val: <7 11 21 23| Scale is weakly epimorphic with val: <7 12 18 23| Scale is weakly epimorphic with val: <7 12 19 22| Scale is weakly epimorphic with val: <7 12 22 26|
FIT/MODE
7: 0 2 0 0 2 1 2 N SD: 58.8748 c. M: 96.7778 c. 8: 0 2 1 0 2 1 2 N T3 SD: 36.0819 c. M: 64.9841 c. 9: 0 3 0 0 3 0 3 N M DE S SD: 29.6284 c. M: 52.5921 c. 11: 0 3 1 0 3 1 3 N T3 SD: 20.1750 c. M: 37.7113 c. 14: 0 4 1 0 4 1 4 N T3 SD: 12.5723 c. M: 22.1269 c. 17: 0 5 1 0 5 1 5 N T3 SD: 9.9326 c. M: 17.5761 c. 20: 0 6 1 0 6 1 6 N T3 SD: 10.2279 c. M: 17.5761 c. 34: 0 10 2 0 10 2 10 N T3 SD: 9.9326 c. M: 17.5761 c. 35: 1 10 1 1 10 2 10 N SD: 9.5220 c. M:-16.7096 c. 37: 0 11 2 0 11 2 11 N T3 SD: 9.8495 c. M: 17.5761 c. 38: 1 11 1 1 11 2 11 N SD: 8.7655 c. M:-14.0028 c. 41: 1 11 2 1 12 2 12 N SD: 8.2497 c. M: 13.7646 c. 43: 1 12 2 1 12 3 12 N SD: 7.5724 c. M:-12.5242 c. 45: 1 13 2 0 13 3 13 N SD: 7.4787 c. M:-9.1587 c. 46: 1 13 2 1 13 3 13 N SD: 5.4967 c. M:-8.5108 c. 49: 1 14 2 1 14 3 14 N SD: 3.9595 c. M:-6.9137 c. 52: 1 15 2 1 15 3 15 N SD: 3.1688 c. M:-5.5008 c. 63: 1 18 3 1 18 4 18 N SD: 2.5681 c. M:-4.5508 c. 66: 1 19 3 1 19 4 19 N SD: 1.1048 c. M:-1.9534 c. 69: 1 20 3 1 20 4 20 N SD: 0.2335 c. M: 0.4181 c. 204: 3 59 9 3 59 12 59 N SD: 0.2025 c. M:-0.3491 c. 273: 4 79 12 4 79 16 79 N SD: 0.0955 c. M:-0.1552 c. 342: 5 99 15 5 99 20 99 N SD: 0.0384 c. M: 0.0718 c. 411: 6 119 18 6 119 24 119 N SD: 0.0330 c. M: 0.0579 c. 753: 11 218 33 11 218 44 218 N SD: 0.0283 c. M: 0.0463 c. 1164: 17 337 51 17 337 68 337 N SD: 0.0286 c. M: 0.0504 c. 1575: 23 456 69 23 456 92 456 N SD: 0.0293 c. M: 0.0523 c. 1848: 27 535 81 27 535 108 535 N SD: 0.0290 c. M: 0.0490 c. 1917: 28 555 84 28 555 112 555 N SD: 0.0283 c. M: 0.0487 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: 40.2685 cents 3 x x x 4 x 5:6 S SD: 23.5070 cents 4 x 5 x x 6:7:8 S SD: 35.7522 cents 5 x 6 x x 8 x 10 S SD: 19.4588 cents 6 x 7 x 8:9:10:12 S SD: 29.0418 cents 7 x x x 9:11 x 14 SD: 0.0000 cents 8 x 10 x x x 13:16 SD: 8.1684 cents 9:10:11 x 12:14:15:18 S SD: 30.1658 cents 10:11:12 x 13:16 x 20 SD: 31.9429 cents 11:12 x 14 x 17:18:22 SD: 27.2307 cents 12:13:15 x x 19:20:24 SD: 25.5147 cents 13:14:16 x 17:20:21:26 SD: 20.4105 cents 14:15:17 x 18:22:23:28 SD: 17.6827 cents 15:16 x 19 x 24:25:30 SD: 20.8956 cents 16:17:20 x 21:25:26:32 SD: 16.3361 cents 17:18:21 x 22:27:28:34 SD: 14.1586 cents 18:19:22:23 x 28:29:36 SD: 14.1125 cents 19:20:23:24 x 30:31:38 SD: 13.4462 cents 20:21:25 x 26:31:33:40 SD: 12.9816 cents 21:22:26 x 27:33:34:42 SD: 10.9620 cents 22:23:27:28 x 35:36:44 SD: 10.6587 cents 23:24:28:29:30:36:38:46 SD: 10.0528 cents 24:25:30 x 31:38:39:48 SD: 10.0752 cents 25:26:31 x 32:39:41:50 SD: 8.8531 cents 26:27:32:33 x 41:43:52 SD: 8.6750 cents 27:28:33:34:35:42:44:54 SD: 8.1681 cents 28:29:35 x 36:44:46:56 SD: 8.1070 cents 29:30:36:37 x 46:47:58 SD: 8.0558 cents 30:31:37:38:39:47:49:60 SD: 6.4074 cents 32:33:40 x 41:50:52:64 SD: 7.4691 cents 33:34:41:42 x 52:54:66 SD: 6.0154 cents 34:35:42:43:44:53:56:68 SD: 5.7722 cents 35:36:43 x 45:55:57:70 SD: 5.5663 cents 36:37:44:46 x 57:59:72 SD: 6.2921 cents 37:38:46:47:48:58:61:74 SD: 5.3421 cents 38:39:47:48:49:60:62:76 SD: 4.6285 cents 39:40:48 x 50:61:64:78 SD: 4.8126 cents 40:41:49:51 x 63:65:80 SD: 5.2451 cents 41:42:51:52:53:64:67:82 SD: 4.5433 cents 42:43:52:53:54:66:69:84 SD: 4.1025 cents 43:44:53:55 x 68:70:86 SD: 4.6465 cents 44:45:54:56:57:69:72:88 SD: 3.9056 cents 46:47:57 x 59:72:75:92 SD: 3.8332 cents 47:48:58:60 x 74:77:94 SD: 3.3332 cents 50:51:62 x 64:79:82:100 SD: 3.7162 cents 51:52:63:65:66:80:83:102 SD: 3.1624 cents 52:53:64:66:67:82:85:104 SD: 2.6490 cents 54:55:67:69 x 85:88:108 SD: 3.2462 cents 55:56:68:70:71:86:90:110 SD: 2.5303 cents 56:57:69:71:72:88:92:112 SD: 2.3673 cents 57:58:70 x 73:90:93:114 SD: 3.2639 cents 58:59:72:74:75:91:95:116 SD: 2.7050 cents 59:60:73:75:76:93:97:118 SD: 2.2832 cents 60:61:74:76:77:94:98:120 SD: 2.2224 cents 61:62:75:78 x 96:100:122 SD: 2.6190 cents 63:64:78:80:81:99:103:126 SD: 1.6557 cents 68:69:84 x 87:107:111:136 SD: 2.0799 cents 69:70:85:88:89:108:113:138 SD: 1.8189 cents 73:74:90:93:94:115:119:146 SD: 1.5263 cents 77:78:95:98:99:121:126:154 SD: 0.7053 cents 102:103:126:130:131:160:167:204 SD: 0.6553 cents 175:177:216:223:225:275:286:350 SD: 0.5355 cents 179:181:221:228:230:281:293:358 SD: 0.4335 cents 217:219:268:276:279:341:355:434 SD: 0.3056 cents 294:297:363:374:378:462:481:588 SD: 0.1290 cents