Scala analysis: xen12-chalmers-tritriadic-mt-25-27-11
Tritriadic M->T scale built from 25:27:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 729/625 266.475150 two (large limma, BP small semitone, Zarlino semitone) 3: 44/27 845.452940 neutral sixth 4: 44/25 978.690515 undecimal grave minor seventh 5: 50/27 1066.762425 grave major seventh 6: 1188/625 1111.928090 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 625/594 88.0719 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 27500/19683 578.9778 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 625/594 88.0719 6: 16038/15625 45.1657 7: 625/594 88.0719
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16038/15625 45.166 cents 1: 2 625/594 88.072 cents 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 27500/19683 578.978 cents 2: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 2 25/22 221.309 cents undecimal acute whole tone 2: 1 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 2: 2 1100/729 712.215 cents 3: 1 25/22 221.309 cents undecimal acute whole tone 3: 2 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 31250/19683 800.287 cents 3: 2 44/27 845.453 cents neutral sixth 4: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 1 19683/15625 399.713 cents 4: 1 44/27 845.453 cents neutral sixth 4: 2 1250/729 933.525 cents 4: 1 44/25 978.691 cents undecimal grave minor seventh 5: 2 729/550 487.785 cents 5: 1 1250/729 933.525 cents 5: 2 44/25 978.691 cents undecimal grave minor seventh 5: 2 50/27 1066.762 cents grave major seventh 6: 1 19683/13750 621.022 cents 6: 3 50/27 1066.762 cents grave major seventh 6: 2 1188/625 1111.928 cents 6: 1 15625/8019 1154.834 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 133.2 266.5 845.5 978.7 1066.8 1111.9 1200.0 133.2 : 133.2 712.2 845.5 933.5 978.7 1066.8 1200.0 266.5 : 579.0 712.2 800.3 845.5 933.5 1066.8 1200.0 845.5 : 133.2 221.3 266.5 354.5 487.8 621.0 1200.0 978.7 : 88.1 133.2 221.3 354.5 487.8 1066.8 1200.0 1066.8: 45.2 133.2 266.5 399.7 978.7 1111.9 1200.0 1111.9: 88.1 221.3 354.5 933.5 1066.8 1154.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 45.1657 .. 578.9778 cents 19531250/14348907, 533.8121 cents 16038/15625, 45.1657 cents 2: 133.2376 .. 712.2154 cents 27500/19683, 578.9778 cents 531441/687500,-445.7402 cents 3: 221.3095 .. 845.4529 cents 968/675, 624.1435 cents 729/968,-490.9059 cents 4: 354.5471 .. 978.6905 cents 968/675, 624.1435 cents 729/968,-490.9059 cents 5: 487.7846 .. 1066.7624 cents 27500/19683, 578.9778 cents 729/968,-490.9059 cents 6: 621.0222 .. 1154.8343 cents 19531250/14348907, 533.8121 cents 531441/687500,-445.7402 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16038/15625, 45.1657 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 27500/19683, 578.9778 cents Average / Smallest step : 3.795551 Largest / Average step : 3.377370 Largest / Smallest step : 12.818981 Median interval of one step : 27/25, 133.2376 cents, amount: 3 Most common interval of one step : 27/25, 133.2376 cents, amount: 3 Least squares average step : 196.59064 cents, oct.: 1376.13447 cents Scale is not proper Step pattern alph. order: AABACDC Step pattern size order : CCDCBAB Scale is not a Constant Structure Scale diversity : 1.454556 Lumma stability : 0.075276 Lumma impropriety factor : 0.777937 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 : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 387420489/378125000, 42.0444 cents Most common intervals : 27/25, 133.2376 cents & inv., amount: 5 Most common triad is 0.0 133.238 1066.762 cents, amount: 3 Number of recognisable fifths : 2, average 712.2154 cents Scale contains a complete diamond : 25 27 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 11 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.012109 Average absolute harmonicity : 0.171769 Specific harmonicity : 0.062577 Fundamental : 1/16875, -14.0426 octaves, 0.0155 Hz. Guide tone : 801900, 19.6131 octaves, 209797540.815 Hz. Exponens Consonantiae : 1.353206E+10, 33.65566 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 1719.5, average 245.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.35064, average 1.62152 Sum of Tenney's harmonic distance : 23.90618, average 3.41517 Vogel's harmonic complexity : 30.28571 Wille's k value : 9841 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 16 Triangular lattice diameter : 9 Lattice compactness : 139.78462, average 4.99231 Lattice compactness (without 2's) : 133.04011, average 4.75143 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.14286 8 1 3: -3 .. 6 0.85714 18 5: -4 .. 2 -1.42857 14 3 11: 0 .. 1 0.42857 3 3 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 35 / 7 = 5.00000 Scale is weakly epimorphic with val: <7 10 16 24| Scale is weakly epimorphic with val: <7 10 17 25| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 17 23| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 12 15 26|
FIT/MODE
7: 1 1 3 1 0 1 0 N SD: 52.2805 c. M:-88.0719 c. 8: 1 1 4 1 0 1 0 N SD: 50.0042 c. M:-88.0719 c. 9: 1 1 4 1 1 0 1 N T3 SD: 29.6934 c. M: 45.4529 c. 10: 1 1 5 1 1 0 1 N T3 SD: 18.7078 c. M: 31.9281 c. 16: 2 2 7 2 1 1 1 N SD: 18.0819 c. M:-33.5249 c. 17: 2 2 8 2 1 1 1 N SD: 10.5392 c. M:-17.4837 c. 26: 3 3 12 3 2 1 2 N SD: 8.3391 c. M: 14.6837 c. 27: 3 3 13 3 2 1 2 N SD: 0.6062 c. M: 1.0085 c. 217: 24 24 105 24 16 8 16 N SD: 0.5593 c. M: 1.0374 c. 234: 26 26 113 26 17 9 17 N SD: 0.5315 c. M:-0.8924 c. 244: 27 27 118 27 18 9 18 N SD: 0.4818 c. M: 0.9014 c. 261: 29 29 126 29 19 10 19 N SD: 0.4185 c. M:-0.7156 c. 288: 32 32 139 32 21 11 21 N SD: 0.3281 c. M:-0.5719 c. 315: 35 35 152 35 23 12 23 N SD: 0.2552 c. M:-0.4529 c. 342: 38 38 165 38 25 13 25 N SD: 0.1969 c. M:-0.3526 c. 369: 41 41 178 41 27 14 27 N SD: 0.1518 c. M:-0.2670 c. 396: 44 44 191 44 29 15 29 N SD: 0.1206 c. M:-0.1931 c. 423: 47 47 204 47 31 16 31 N SD: 0.1046 c. M:-0.1915 c. 450: 50 50 217 50 33 17 33 N SD: 0.1036 c. M:-0.1915 c. 721: 80 80 348 80 53 27 53 N SD: 0.1007 c. M: 0.1783 c. 748: 83 83 361 83 55 28 55 N SD: 0.1029 c. M: 0.1650 c. 775: 86 86 374 86 57 29 57 N SD: 0.1087 c. M: 0.1862 c. 873: 97 97 421 97 64 33 64 N SD: 0.1024 c. M:-0.1915 c. 982: 109 109 474 109 72 37 72 N SD: 0.0942 c. M:-0.1682 c. 1009: 112 112 487 112 74 38 74 N SD: 0.0764 c. M:-0.1368 c. 1036: 115 115 500 115 76 39 76 N SD: 0.0599 c. M:-0.1069 c. 1063: 118 118 513 118 78 40 78 N SD: 0.0451 c. M:-0.0786 c. 1090: 121 121 526 121 80 41 80 N SD: 0.0328 c. M: 0.0531 c. 1117: 124 124 539 124 82 42 82 N SD: 0.0253 c. M: 0.0472 c. 1144: 127 127 552 127 84 43 84 N SD: 0.0255 c. M: 0.0416 c. 1513: 168 168 730 168 111 57 111 N SD: 0.0196 c. M:-0.0349 c. 1540: 171 171 743 171 113 58 113 N SD: 0.0121 c. M:-0.0200 c. 1567: 174 174 756 174 115 59 115 N SD: 0.0119 c. M:-0.0213 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 71.7490 cents 3 x 4:5 x x x 6 S SD: 78.2718 cents 4 x 5 x 7 x x 8 SD: 40.0813 cents 5 x 6:8:9 x x 10 S SD: 17.5714 cents 6 x 7:10 x 11 x 12 SD: 10.6553 cents 7 x 8:11:12:13 x 14 SD: 17.1003 cents 8 x 9:13:14:15 x 16 SD: 13.4142 cents 9:10:11:15:16 x 17:18 SD: 17.4023 cents 10:11:12:16:18 x 19:20 S SD: 12.8558 cents 11:12:13:18:19:20:21:22 SD: 7.8147 cents 12:13:14:20:21:22:23:24 SD: 6.6232 cents 13:14:15:21:23:24:25:26 SD: 4.7889 cents 16:17:19:26:28:30 x 32 SD: 8.0749 cents 17:18:20:28:30:31:32:34 SD: 7.4975 cents 18:19:21:29:32:33:34:36 SD: 7.4044 cents 19:21:22:31:33:35:36:38 SD: 7.0089 cents 20:22:23:33:35:37:38:40 SD: 6.6600 cents 21:23:24:34:37:39:40:42 SD: 6.3929 cents 22:24:26:36:39:41:42:44 SD: 4.9560 cents 24:26:28:39:42:44:46:48 SD: 3.6702 cents 25:27:29:41:44:46:48:50 SD: 3.6073 cents 29:31:34:47:51:54:55:58 SD: 3.4807 cents 35:38:41:57:62:65:67:70 SD: 2.9964 cents 36:39:42:59:63:67:68:72 SD: 2.9107 cents 37:40:43:60:65:69:70:74 SD: 2.6293 cents 38:41:44:62:67:70:72:76 SD: 2.4384 cents 41:44:48:67:72:76:78:82 SD: 2.0434 cents 48:52:56:78:84:89:91:96 SD: 1.8919 cents 49:53:57:80:86:91:93:98 SD: 1.3793 cents 60:65:70:98:106:111:114:120 SD: 1.3586 cents 62:67:72:101:109:115:118:124 SD: 1.2416 cents 84:91:98:137:148:156:160:168 SD: 1.2079 cents 88:95:103:143:155:163:167:176 SD: 1.2010 cents 89:96:104:145:157:165:169:178 SD: 0.8758 cents 100:108:117:163:176:185:190:200 SD: 0.8100 cents 113:122:132:184:199:209:215:226 SD: 0.5973 cents 138:149:161:225:243:256:262:276 SD: 0.5549 cents 149:161:174:243:262:276:283:298 SD: 0.4787 cents 151:163:176:246:266:280:287:302 SD: 0.4573 cents 162:175:189:264:285:300:308:324 SD: 0.1429 cents 451:487:526:735:794:835:857:902 SD: 0.1286 cents 475:513:554:774:836:880:903:950 SD: 0.1131 cents