Scala analysis: tritriad3d
From 1/1 7/6 5/3, a variant of the 3.5.7 triad
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 6/5 315.641287 minor third 3: 25/18 568.717426 classic augmented fourth 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 5/3 884.358713 major sixth, BP sixth 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 7/6 266.8709 septimal minor third 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 125/108 253.0761 semi-augmented whole tone 4: 126/125 13.7948 septimal semicomma, Starling comma 5: 25/21 301.8465 BP second, quasi-equal minor third 6: 7/6 266.8709 septimal minor third 7: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 126/125 13.795 cents septimal semicomma, Starling comma 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 125/108 253.076 cents semi-augmented whole tone 1: 2 7/6 266.871 cents septimal minor third 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 7/6 266.871 cents septimal minor third 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 4 6/5 315.641 cents minor third 2: 1 25/18 568.717 cents classic augmented fourth 3: 1 6/5 315.641 cents minor third 3: 1 216/175 364.412 cents 3: 2 25/18 568.717 cents classic augmented fourth 3: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 10/7 617.488 cents Euler's tritone 4: 2 36/25 631.283 cents classic diminished fifth 4: 1 175/108 835.588 cents 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 36/25 631.283 cents classic diminished fifth 5: 4 5/3 884.359 cents major sixth, BP sixth 5: 1 42/25 898.153 cents quasi-equal major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 42/25 898.153 cents quasi-equal major sixth 6: 2 12/7 933.129 cents septimal major sixth 6: 1 216/125 946.924 cents semi-augmented sixth 6: 2 35/18 1151.230 cents septimal semi-diminished octave 6: 1 125/63 1186.205 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 : 266.9 315.6 568.7 582.5 884.4 1151.2 1200.0 266.9 : 48.8 301.8 315.6 617.5 884.4 933.1 1200.0 315.6 : 253.1 266.9 568.7 835.6 884.4 1151.2 1200.0 568.7 : 13.8 315.6 582.5 631.3 898.2 946.9 1200.0 582.5 : 301.8 568.7 617.5 884.4 933.1 1186.2 1200.0 884.4 : 266.9 315.6 582.5 631.3 884.4 898.2 1200.0 1151.2: 48.8 315.6 364.4 617.5 631.3 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 13.7948 .. 301.8465 cents 3125/2646, 288.0518 cents 126/125, 13.7948 cents 2: 266.8709 .. 568.7174 cents 25/21, 301.8465 cents 49/50,-34.9756 cents 3: 315.6413 .. 617.4878 cents 25/21, 301.8465 cents 108/125,-253.0761 cents 4: 582.5122 .. 884.3587 cents 25/21, 301.8465 cents 49/50,-34.9756 cents 5: 631.2826 .. 933.1291 cents 25/21, 301.8465 cents 108/125,-253.0761 cents 6: 898.1535 .. 1186.2052 cents 3125/2646, 288.0518 cents 49/50,-34.9756 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 126/125, 13.7948 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 25/21, 301.8465 cents Average / Smallest step : 12.427073 Largest / Average step : 1.760771 Largest / Smallest step : 21.881234 Median interval of one step : 125/108, 253.0761 cents, amount: 1 Least squares average step : 176.16804 cents, oct.: 1233.17629 cents Scale is not proper Scale is a mode of a 1304-tone equal temperament with octave 2/1 degrees: 290 343 618 633 961 1251 1304 Least number of segments generator : 653 of 600.920 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1077 of 991.104 cents and inv. generated superset size: 70 = 63 more = 1000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEAB Step pattern size order : DBCAEDB Scale is not a Constant Structure Scale diversity : 1.070454 Lumma stability : 0.022991 Lumma impropriety factor : 0.509233 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 : 126/125, 13.7948 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 266.871 884.359 cents Most common triad is 0.0 315.641 884.359 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 3 5 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 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 175 (O: 175 U: 175) Highest odd numerator or denominator: 35 Scale harmonicity : 0.025326 Average absolute harmonicity : 0.205277 Specific harmonicity : 0.130023 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 1050, 10.0362 octaves, 274706.844 Hz. Exponens Consonantiae : 9.450000E+04, 16.52803 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 71.5, average 10.21429 Mersenne's string divisions : 7821528 Sum of van Prooijen's expressibility: 6.03014, average 0.86145 Sum of Tenney's harmonic distance : 11.57411, average 1.65344 Vogel's harmonic complexity : 14.14286 Wille's k value : 87 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 65.24844, average 2.33030 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.14286 5 1 3: -2 .. 1 -0.71429 7 5: -1 .. 2 0.28571 6 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 16 20| Scale is weakly epimorphic with val: <7 10 18 21| Scale is weakly epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 1 0 2 0 2 1 1 N T3 SD: 87.2680 c. M: 144.2127 c. 8: 2 0 2 0 2 2 0 N M DE S SD: 27.3856 c. M:-48.7704 c. 15: 3 1 3 0 4 3 1 N SD: 18.1978 c. M: 31.2296 c. 18: 4 1 4 0 4 4 1 N SD: 17.8516 c. M:-31.2826 c. 19: 4 1 4 0 5 4 1 N SD: 9.3232 c. M: 14.3875 c. 23: 5 1 5 0 6 5 1 N SD: 4.8113 c. M: 8.5991 c. 45: 10 2 9 1 11 10 2 N SD: 4.6616 c. M: 8.7174 c. 49: 11 2 10 1 12 11 2 N SD: 3.3478 c. M: 5.4521 c. 53: 12 2 11 1 13 12 2 N SD: 3.4696 c. M:-6.1671 c. 68: 15 3 14 1 17 15 3 N SD: 2.5704 c. M: 4.1708 c. 72: 16 3 15 1 18 16 3 N SD: 1.1043 c. M: 2.0508 c. 76: 17 3 16 1 19 17 3 N SD: 1.0271 c. M:-1.6983 c. 95: 21 4 20 1 24 21 4 N SD: 1.0644 c. M: 1.7559 c. 99: 22 4 21 1 25 22 4 N SD: 0.5404 c. M:-0.9795 c. 171: 38 7 36 2 43 38 7 N SD: 0.2073 c. M: 0.3524 c. 270: 60 11 57 3 68 60 11 N SD: 0.1621 c. M: 0.2900 c. 346: 77 14 73 4 87 77 14 N SD: 0.1241 c. M:-0.2155 c. 441: 98 18 93 5 111 98 18 N SD: 0.1338 c. M: 0.2092 c. 517: 115 21 109 6 130 115 21 N SD: 0.0448 c. M:-0.0797 c. 787: 175 32 166 9 198 175 32 N SD: 0.0263 c. M: 0.0471 c. 1133: 252 46 239 13 285 252 46 N SD: 0.0288 c. M:-0.0502 c. 1304: 290 53 275 15 328 290 53 N SD: 0.0031 c. M: 0.0058 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: 59.7214 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6:7 x 8 S SD: 40.6170 cents 5 x 6 x 7:8 x 10 S SD: 17.6681 cents 6:7 x 8 x 10 x 12 S SD: 17.6681 cents 7:8 x x 10:12 x 14 S SD: 17.4573 cents 8:9:10:11 x 13 x 16 SD: 21.1495 cents 9 x 11 x 13:15 x 18 SD: 15.6854 cents 10 x 12 x 14:17:19:20 SD: 10.5409 cents 11:13 x 15 x 18:21:22 SD: 11.8767 cents 12:14 x x 17:20:23:24 SD: 6.4507 cents 13:15:16:18 x 22:25:26 SD: 9.6898 cents 15 x 18 x 21:25:29:30 SD: 1.9842 cents 16 x 19:22 x 27:31:32 SD: 6.7298 cents 17:20 x x 24:28:33:34 SD: 5.8241 cents 18:21:22:25 x 30:35:36 SD: 5.2944 cents 20:23:24 x 28:33:39:40 SD: 5.1307 cents 21 x 25:29 x 35:41:42 SD: 3.6794 cents 22:26 x x 31:37:43:44 SD: 6.1661 cents 23:27:28:32 x 38:45:46 SD: 5.4975 cents 24:28:29:33:34:40:47:48 SD: 4.5578 cents 25:29:30 x 35:42:49:50 SD: 3.6478 cents 26:30:31:36 x 43:51:52 SD: 5.0736 cents 27 x 32 x 38:45:53:54 SD: 5.7106 cents 28:33:34:39 x 47:54:56 SD: 5.5435 cents 29:34:35:40:41:48:56:58 SD: 4.2607 cents 30:35:36 x 42:50:58:60 SD: 1.6535 cents 31:36:37:43 x 52:60:62 SD: 3.0909 cents 33:39:40:46 x 55:64:66 SD: 4.8920 cents 34:40:41:47:48:57:66:68 SD: 3.6970 cents 35:41:42 x 49:58:68:70 SD: 2.0423 cents 36:42:43:50 x 60:70:72 SD: 1.3389 cents 38:44:46 x 53:63:74:76 SD: 3.8445 cents 39:46:47:54:55:65:76:78 SD: 3.5430 cents 40:47:48 x 56:67:78:80 SD: 2.6394 cents 41:48:49:57 x 68:80:82 SD: 2.3379 cents 43:50:52 x 60:72:84:86 SD: 3.2240 cents 44:51:53:61:62:73:86:88 SD: 3.0244 cents 45:53:54 x 63:75:88:90 SD: 3.1911 cents 46:54:55:64 x 77:89:92 SD: 2.8589 cents 47:55:56:65:66:78:91:94 SD: 2.7500 cents 48:56:58 x 67:80:93:96 SD: 2.4068 cents 49:57:59:68:69:82:95:98 SD: 2.2071 cents 51:60:61:71 x 85:99:102 SD: 2.7235 cents 52:61:62:72:73:87:101:104 SD: 2.5264 cents 53:62:64 x 74:88:103:106 SD: 2.3867 cents 54:63:65:75:76:90:105:108 SD: 1.5114 cents 56:65:67:78 x 93:109:112 SD: 2.1790 cents 58:68:70 x 81:97:113:116 SD: 2.5613 cents 59:69:71:82:83:98:115:118 SD: 1.8339 cents 60:70:72:83:84:100:117:120 SD: 1.2168 cents 61:71:73:85 x 102:119:122 SD: 1.9383 cents 63:74:76 x 88:105:123:126 SD: 2.8206 cents 64:75:77:89:90:107:124:128 SD: 2.0772 cents 65:76:78:90:91:108:126:130 SD: 1.4274 cents 66:77:79:92 x 110:128:132 SD: 1.4806 cents 70:82:84:97:98:117:136:140 SD: 1.3689 cents 71:83:85:99 x 118:138:142 SD: 1.6619 cents 72:84:86:100:101:120:140:144 SD: 1.2480 cents 76:89:91 x 106:127:148:152 SD: 1.8755 cents 77:90:92:107:108:128:150:154 SD: 1.4873 cents 78:91:94:108:109:130:152:156 SD: 1.4811 cents 80:93:96:111:112:133:156:160 SD: 1.3135 cents 81:95:97 x 113:135:158:162 SD: 2.1325 cents 82:96:98:114:115:137:159:164 SD: 1.6846 cents 83:97:100:115:116:138:161:166 SD: 1.5534 cents 84:98:101:117:118:140:163:168 SD: 1.3034 cents 85:99:102:118:119:142:165:170 SD: 0.8352 cents 90:105:108:125:126:150:175:180 SD: 0.0000 cents