Scala analysis: xen12-chalmers-tritriadic-mt-27-21-19
Tritriadic M->T scale built from 27:21:19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 266/243 156.563918 2: 98/81 329.831809 3: 9/7 435.084095 septimal major third, BP third 4: 38/27 591.648014 5: 14/9 764.915905 septimal minor sixth 6: 38/21 1026.732109 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/19 173.2679 1: 266/243 156.5639 2: 21/19 173.2679 3: 729/686 105.2523 4: 266/243 156.5639 5: 21/19 173.2679 6: 57/49 261.8162 7: 21/19 173.2679
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 729/686 105.252 cents 1: 2 266/243 156.564 cents 1: 3 21/19 173.268 cents 1: 1 57/49 261.816 cents 2: 1 57/49 261.816 cents 2: 1 2187/1862 278.520 cents 2: 3 98/81 329.832 cents 2: 2 9/7 435.084 cents septimal major third, BP third 3: 3 9/7 435.084 cents septimal major third, BP third 3: 1 686/513 503.100 cents 3: 2 38/27 591.648 cents 3: 1 27/19 608.352 cents 4: 1 38/27 591.648 cents 4: 2 27/19 608.352 cents 4: 1 513/343 696.900 cents 4: 3 14/9 764.916 cents septimal minor sixth 5: 2 14/9 764.916 cents septimal minor sixth 5: 3 81/49 870.168 cents two (septimal major third, BP third) 5: 1 3724/2187 921.480 cents 5: 1 98/57 938.184 cents 6: 1 98/57 938.184 cents 6: 3 38/21 1026.732 cents 6: 2 243/133 1043.436 cents 6: 1 1372/729 1094.748 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 : 156.6 329.8 435.1 591.6 764.9 1026.7 1200.0 156.6 : 173.3 278.5 435.1 608.4 870.2 1043.4 1200.0 329.8 : 105.3 261.8 435.1 696.9 870.2 1026.7 1200.0 435.1 : 156.6 329.8 591.6 764.9 921.5 1094.7 1200.0 591.6 : 173.3 435.1 608.4 764.9 938.2 1043.4 1200.0 764.9 : 261.8 435.1 591.6 764.9 870.2 1026.7 1200.0 1026.7: 173.3 329.8 503.1 608.4 764.9 938.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 105.2523 .. 261.8162 cents 266/243, 156.5639 cents 729/686, 105.2523 cents 2: 261.8162 .. 435.0841 cents 21/19, 173.2679 cents 1/1, 0.0000 cents 3: 435.0841 .. 608.3520 cents 21/19, 173.2679 cents 1/1, 0.0000 cents 4: 591.6480 .. 764.9159 cents 21/19, 173.2679 cents 722/729,-16.7040 cents 5: 764.9159 .. 938.1838 cents 21/19, 173.2679 cents 1/1, 0.0000 cents 6: 938.1838 .. 1094.7477 cents 266/243, 156.5639 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 729/686, 105.2523 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 57/49, 261.8162 cents Average / Smallest step : 1.628740 Largest / Average step : 1.527261 Largest / Smallest step : 2.487511 Median interval of one step : 21/19, 173.2679 cents, amount: 3 Most common interval of one step : 21/19, 173.2679 cents, amount: 3 Least squares average step : 163.37889 cents, oct.: 1143.65220 cents Scale is not proper Step pattern alph. order: ABCABDB Step pattern size order : BCABCDC Scale is not a Constant Structure Scale diversity : 1.387110 Lumma stability : 0.175420 Lumma impropriety factor : 0.013920 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 : 729/722, 16.7040 cents Most common intervals : 9/7, 435.0841 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 591.648 764.916 cents Most common triad is 0.0 435.084 764.916 cents, amount: 3 Number of recognisable fifths : 1, average 696.9003 cents Scale contains a complete diamond : 7 9 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.011816 Average absolute harmonicity : 0.173750 Specific harmonicity : 0.059042 Fundamental : 1/1701, -10.7322 octaves, 0.1538 Hz. Guide tone : 16758, 14.0326 octaves, 4384321.223 Hz. Exponens Consonantiae : 2.850536E+07, 24.76473 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 427.0, average 61.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.95616, average 1.27945 Sum of Tenney's harmonic distance : 18.82409, average 2.68916 Vogel's harmonic complexity : 27.42857 Wille's k value : 1093 Wilson's harmonic complexity : 61 Rectangular lattice diameter : 11 Triangular lattice diameter : 7 Lattice compactness : 94.57826, average 3.37780 Lattice compactness (without 2's) : 92.02134, average 3.28648 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.85714 6 1 3: -5 .. 2 -1.85714 17 7: -1 .. 2 0.28571 6 3 19: 0 .. 1 0.42857 3 3 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 26 / 7 = 3.71429 Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 10 19 33| Scale is weakly epimorphic with val: <7 10 21 27| Scale is weakly epimorphic with val: <7 10 22 31| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 20 32| Scale is weakly epimorphic with val: <7 11 21 29| Scale is weakly epimorphic with val: <7 12 18 33| Scale is weakly epimorphic with val: <7 12 19 30| Scale is weakly epimorphic with val: <7 12 20 27| Scale is weakly epimorphic with val: <7 12 21 31| Scale is weakly epimorphic with val: <7 12 22 28|
FIT/MODE
7: 1 1 0 1 1 2 1 N T3 SD: 54.9774 c. M: 92.2270 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 16.8571 c. M: 29.8318 c. 14: 2 2 1 2 2 3 2 P T3 SD: 8.8526 c. M:-14.8647 c. 22: 3 3 2 3 3 5 3 P T3 SD: 5.6362 c. M:-9.6315 c. 36: 5 5 3 5 5 8 5 P T3 SD: 5.7791 c. M:-10.1027 c. 46: 6 7 4 6 6 10 7 N SD: 7.4104 c. M: 9.3408 c. 47: 6 7 4 6 7 10 7 N SD: 3.0967 c. M: 5.4555 c. 55: 7 8 5 7 8 12 8 N SD: 2.1618 c. M: 3.8366 c. 69: 9 10 6 9 10 15 10 N SD: 0.3931 c. M: 0.6452 c. 215: 28 31 19 28 31 47 31 N SD: 0.2833 c. M: 0.5295 c. 284: 37 41 25 37 41 62 41 N SD: 0.1505 c. M: 0.2543 c. 353: 46 51 31 46 51 77 51 N SD: 0.1066 c. M: 0.1900 c. 513: 67 74 45 67 74 112 74 N SD: 0.1080 c. M:-0.1685 c. 582: 76 84 51 76 84 127 84 N SD: 0.0768 c. M:-0.1371 c. 651: 85 94 57 85 94 142 94 N SD: 0.0752 c. M:-0.1221 c. 797: 104 115 70 104 115 174 115 N SD: 0.0689 c. M:-0.1186 c. 866: 113 125 76 113 125 189 125 N SD: 0.0326 c. M:-0.0577 c. 935: 122 135 82 122 135 204 135 N SD: 0.0076 c. M:-0.0136 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: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 45.0070 cents 4 x x 5 x 6:7:8 S SD: 24.6168 cents 5 x 6 x 7:8:9:10 S SD: 10.4821 cents 6 x 7:8 x 9:11:12 SD: 22.2750 cents 7:8 x 9:10:11:13:14 SD: 15.4251 cents 8:9 x 10:11:12:14:16 S SD: 19.4107 cents 9:10:11:12:13:14:16:18 S SD: 12.6989 cents 10:11:12:13:14:16:18:20 S SD: 8.0610 cents 12:13 x 15:17:19:22:24 SD: 10.9064 cents 13:14:16:17:18:20:24:26 S SD: 10.0074 cents 14:15:17:18:20:22:25:28 SD: 7.7197 cents 18:20:22:23:25:28:33:36 SD: 6.5923 cents 20:22:24:26:28:31:36:40 SD: 4.1499 cents 29:32:35:37:41:45:52:58 SD: 3.8235 cents 32:35:39:41:45:50:58:64 SD: 2.3383 cents 42:46:51:54:59:65:76:84 SD: 1.6260 cents 52:57:63:67:73:81:94:104 SD: 1.0391 cents 94:103:114:121:132:146:170:188 SD: 0.9811 cents 95:104:115:122:134:148:172:190 SD: 0.7472 cents 105:115:127:135:148:163:190:210 SD: 0.6451 cents 115:126:139:148:162:179:208:230 SD: 0.5042 cents 147:161:178:189:207:229:266:294 SD: 0.4555 cents 157:172:190:202:221:244:284:314 SD: 0.3668 cents 252:276:305:324:355:392:456:504 SD: 0.2824 cents 263:288:318:338:370:409:476:526 SD: 0.2444 cents 315:345:381:405:443:490:570:630 SD: 0.2397 cents 319:349:386:410:449:496:577:638 SD: 0.2243 cents 329:360:398:423:463:512:595:658 SD: 0.2032 cents 371:406:449:477:522:577:671:742 SD: 0.1811 cents 410:449:496:527:577:638:742:820 SD: 0.1585 cents 434:475:525:558:611:675:785:868 SD: 0.1470 cents 486:532:588:625:684:756:879:972 SD: 0.1332 cents 567:621:686:729:798:882:1026:1134 SD: 0.1328 cents 592:648:716:761:833:921:1071:1184 SD: 0.1285 cents