Scala analysis: xen12-chalmers-tritriadic-mt-11-27-9
Tritriadic M->T scale built from 11:27:9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 243/242 7.139120 neutral third comma, rastma 2: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 4/3 498.044999 perfect fourth 4: 729/484 709.094120 two (neutral third, Zalzal wosta of al-Farabi) 5: 44/27 845.452940 neutral sixth 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: 243/242 7.1391 neutral third comma, rastma 2: 11/9 347.4079 undecimal neutral third 3: 88/81 143.4979 2nd undecimal neutral second 4: 2187/1936 211.0491 5: 21296/19683 136.3588 6: 243/242 7.1391 neutral third comma, rastma 7: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 243/242 7.139 cents neutral third comma, rastma 1: 1 21296/19683 136.359 cents 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 2187/1936 211.049 cents 1: 2 11/9 347.408 cents undecimal neutral third 2: 1 88/81 143.498 cents 2nd undecimal neutral second 2: 1 11/9 347.408 cents undecimal neutral third 2: 4 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 968/729 490.906 cents 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 6561/5324 361.686 cents 3: 2 968/729 490.906 cents 3: 1 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 1 3/2 701.955 cents perfect fifth 4: 2 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 4: 1 10648/6561 838.314 cents 4: 1 44/27 845.453 cents neutral sixth 5: 1 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 5: 4 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 2 18/11 852.592 cents undecimal neutral sixth 6: 1 3872/2187 988.951 cents 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 1 19683/10648 1063.641 cents 6: 2 484/243 1192.861 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 : 7.1 354.5 498.0 709.1 845.5 852.6 1200.0 7.1 : 347.4 490.9 702.0 838.3 845.5 1192.9 1200.0 354.5 : 143.5 354.5 490.9 498.0 845.5 852.6 1200.0 498.0 : 211.0 347.4 354.5 702.0 709.1 1056.5 1200.0 709.1 : 136.4 143.5 490.9 498.0 845.5 989.0 1200.0 845.5 : 7.1 354.5 361.7 709.1 852.6 1063.6 1200.0 852.6 : 347.4 354.5 702.0 845.5 1056.5 1192.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 7.1391 .. 347.4079 cents 2662/2187, 340.2688 cents 243/242, 7.1391 cents 2: 143.4979 .. 490.9059 cents 11/9, 347.4079 cents 8/9,-203.9100 cents 3: 354.5471 .. 701.9550 cents 11/9, 347.4079 cents 19683/21296,-136.3588 cents 4: 498.0450 .. 845.4529 cents 11/9, 347.4079 cents 8/9,-203.9100 cents 5: 709.0941 .. 1056.5021 cents 11/9, 347.4079 cents 19683/21296,-136.3588 cents 6: 852.5921 .. 1192.8609 cents 2662/2187, 340.2688 cents 8/9,-203.9100 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 243/242, 7.1391 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 24.012565 Largest / Average step : 2.026546 Largest / Smallest step : 48.662575 Median interval of one step : 88/81, 143.4979 cents, amount: 1 Least squares average step : 162.78258 cents, oct.: 1139.47809 cents Scale is not proper Step pattern alph. order: ABCDEAB Step pattern size order : AECDBAE Scale is not a Constant Structure Scale diversity : 1.144824 Lumma stability : 0.011899 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 : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 27/22, 354.5471 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 845.453 cents Most common triad is 0.0 354.547 845.453 cents, amount: 3 Number of recognisable fifths : 6, average 705.5246 cents Scale contains a complete diamond : 11 27 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 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.012115 Average absolute harmonicity : 0.195067 Specific harmonicity : 0.066410 Fundamental : 1/13068, -13.6738 octaves, 0.0200 Hz. Guide tone : 32076, 14.9692 octaves, 8391901.633 Hz. Exponens Consonantiae : 4.191692E+08, 28.64296 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 928.5, average 132.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.62958, average 1.37565 Sum of Tenney's harmonic distance : 19.84247, average 2.83464 Vogel's harmonic complexity : 30.57143 Wille's k value : 9841 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 12 Triangular lattice diameter : 9 Lattice compactness : 124.13767, average 4.43349 Lattice compactness (without 2's) : 110.09109, average 3.93182 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.28571 10 1 3: -3 .. 6 1.71429 20 1 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 27 / 7 = 3.85714 Scale is weakly epimorphic with val: <7 10 24| Scale is weakly epimorphic with val: <7 11 25| Scale is weakly epimorphic with val: <7 12 26|
FIT/MODE
7: 0 2 1 1 1 0 2 N T3 SD: 12.8472 c. M: 23.3798 c. 10: 0 3 1 2 1 0 3 N SD: 10.0964 c. M: 18.0450 c. 17: 0 5 2 3 2 0 5 N SD: 4.0086 c. M: 7.1391 c. 88: 1 25 11 15 10 1 25 N SD: 4.2545 c. M:-6.5005 c. 90: 1 26 10 16 10 1 26 N SD: 4.2507 c. M:-6.1942 c. 91: 1 26 11 16 10 1 26 N SD: 3.3818 c. M:-6.0477 c. 94: 1 27 11 17 10 1 27 N SD: 3.5773 c. M:-5.7995 c. 97: 1 28 11 17 11 1 28 N SD: 3.5799 c. M:-5.2320 c. 98: 1 28 12 17 11 1 28 N SD: 3.0377 c. M:-5.1058 c. 101: 1 29 12 18 11 1 29 N SD: 2.7506 c. M:-4.7421 c. 108: 1 31 13 19 12 1 31 N SD: 2.2195 c. M:-3.9720 c. 115: 1 33 14 20 13 1 33 N SD: 2.0191 c. M:-3.2957 c. 118: 1 34 14 21 13 1 34 N SD: 1.8311 c. M:-3.0304 c. 125: 1 36 15 22 14 1 36 N SD: 1.3741 c. M:-2.4609 c. 132: 1 38 16 23 15 1 38 N SD: 1.2788 c. M:-1.9550 c. 135: 1 39 16 24 15 1 39 N SD: 1.1823 c. M:-2.0170 c. 142: 1 41 17 25 16 1 41 N SD: 0.7329 c. M:-1.3116 c. 149: 1 43 18 26 17 1 43 N SD: 0.7462 c. M:-1.2839 c. 159: 1 46 19 28 18 1 46 N SD: 0.2394 c. M:-0.4081 c. 176: 1 51 21 31 20 1 51 N SD: 0.2091 c. M: 0.3209 c. 335: 2 97 40 59 38 2 97 N SD: 0.0925 c. M:-0.1596 c. 501: 3 145 60 88 57 3 145 N SD: 0.0900 c. M:-0.1586 c. 660: 4 191 79 116 75 4 191 N SD: 0.0885 c. M:-0.1368 c. 677: 4 196 81 119 77 4 196 N SD: 0.0450 c. M: 0.0838 c. 836: 5 242 100 147 95 5 242 N SD: 0.0259 c. M:-0.0411 c. 1012: 6 293 121 178 115 6 293 N SD: 0.0151 c. M: 0.0245 c. 1848: 11 535 221 325 210 11 535 N SD: 0.0039 c. M:-0.0069 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: 3.5696 cents 3 x x 4 x x 5:6 S SD: 10.5889 cents 4 x 5 x 6 x 7:8 S SD: 30.1770 cents 5 x 6:7 x 8 x 10 S SD: 24.5681 cents 6 x 7:8:9 x 10:12 S SD: 18.7053 cents 7 x x 9 x 11 x 14 SD: 29.6801 cents 8 x 10:11:12:13 x 16 SD: 12.5257 cents 9 x 11:12:14 x 15:18 SD: 12.9246 cents 10:11:12:13:15:16 x 20 SD: 28.5853 cents 11:12:14:15:17 x 18:22 SD: 27.9153 cents 12:13:15:16:18 x 20:24 SD: 23.1804 cents 13:14:16:17:20:21 x 26 SD: 21.9919 cents 14:15:17:19:21 x 23:28 SD: 19.7120 cents 15:16:18:20:23:24:25:30 SD: 17.7436 cents 16:17:20:21:24:26 x 32 SD: 17.7918 cents 17:18:21:23:26 x 28:34 SD: 16.6869 cents 18:19:22:24:27:29 x 36 SD: 14.8786 cents 19:20:23:25:29:31 x 38 SD: 15.1768 cents 20:21:25:27:30 x 33:40 SD: 14.6332 cents 21:22:26:28:32:34 x 42 SD: 13.0709 cents 22:23:27:29:33 x 36:44 SD: 12.1528 cents 23:24:28:31:35:37:38:46 SD: 11.1281 cents 24:25:29:32:36:39 x 48 SD: 11.5910 cents 25:26:31:33:38 x 41:50 SD: 11.2766 cents 26:27:32:35:39:42:43:52 SD: 9.3746 cents 27:28:33:36:41:44 x 54 SD: 9.6695 cents 28:29:34:37:42 x 46:56 SD: 9.9339 cents 29:30:36:39:44:47 x 58 SD: 9.8891 cents 30:31:37:40:45 x 49:60 SD: 8.4933 cents 31:32:38:41:47 x 51:62 SD: 8.6661 cents 32:33:39:43:48:52 x 64 SD: 8.3842 cents 33:34:41:44:50 x 54:66 SD: 8.4008 cents 34:35:42:45:51:55:56:68 SD: 7.1210 cents 35:36:43:47:53:57 x 70 SD: 7.4079 cents 36:37:44:48:54 x 59:72 SD: 6.9377 cents 37:38:45:49:56:60:61:74 SD: 6.7269 cents 38:39:47:51:57:62 x 76 SD: 7.0634 cents 39:40:48:52:59 x 64:78 SD: 6.3519 cents 40:41:49:53:60:65 x 80 SD: 6.3931 cents 41:42:50:55:62 x 67:82 SD: 6.4116 cents 42:43:52:56:63:68:69:84 SD: 5.6875 cents 43:44:53:57:65:70 x 86 SD: 5.9305 cents 44:45:54:59:66 x 72:88 SD: 5.6674 cents 45:46:55:60:68:73:74:90 SD: 4.8932 cents 46:47:56:61:69:75 x 92 SD: 5.8741 cents 47:48:58:63:71 x 77:94 SD: 5.4371 cents 48:49:59:64:72:78:79:96 SD: 4.5123 cents 49:50:60:65:74:80 x 98 SD: 5.0005 cents 50:51:61:67:75:81:82:100 SD: 4.7126 cents 51:52:63:68:77:83 x 102 SD: 4.8614 cents 52:53:64:69:78 x 85:104 SD: 4.7605 cents 53:54:65:71:80:86:87:106 SD: 4.0473 cents 54:55:66:72:81:88 x 108 SD: 4.4361 cents 55:56:68:73:83 x 90:110 SD: 4.7584 cents 56:57:69:75:84:91:92:112 SD: 3.9926 cents 57:58:70:76:86:93 x 114 SD: 3.8798 cents 58:59:71:77:87 x 95:116 SD: 4.1949 cents 59:60:72:79:89:96:97:118 SD: 3.8120 cents 60:61:74:80:90 x 98:120 SD: 4.0663 cents 61:62:75:81:92:99:100:122 SD: 3.4038 cents 62:63:76:83:93:101 x 124 SD: 3.8259 cents 63:64:77:84:95 x 103:126 SD: 3.5835 cents 65:66:80:87:98:106 x 130 SD: 3.5160 cents 66:67:81:88:99 x 108:132 SD: 3.3664 cents 67:68:82:89:101:109:110:134 SD: 3.0340 cents 68:69:83:91:102:111 x 136 SD: 3.7931 cents 69:70:85:92:104:112:113:138 SD: 2.8869 cents 71:72:87:95:107 x 116:142 SD: 3.0921 cents 72:73:88:96:108:117:118:144 SD: 2.9052 cents 73:74:90:97:110:119 x 146 SD: 3.1963 cents 74:75:91:99:111 x 121:148 SD: 3.1532 cents 75:76:92:100:113:122:123:150 SD: 2.3694 cents 76:77:93:101:114:124 x 152 SD: 3.1335 cents 77:78:95:103:116:125:126:154 SD: 2.8226 cents 78:79:96:104:117:127:128:156 SD: 2.5724 cents 79:80:97:105:119:129 x 158 SD: 2.6728 cents 80:81:98:107:120:130:131:160 SD: 2.5657 cents 81:82:99:108:122:132:133:162 SD: 2.4117 cents 82:83:101:109:124 x 134:164 SD: 2.9414 cents 83:84:102:111:125:135:136:166 SD: 2.1840 cents 84:85:103:112:127:137 x 168 SD: 2.5020 cents 85:86:104:113:128 x 139:170 SD: 2.5124 cents 86:87:106:115:130:140:141:172 SD: 2.4734 cents 87:88:107:116:131:142 x 174 SD: 2.2429 cents 88:89:108:117:133:143:144:176 SD: 2.2038 cents 89:90:109:119:134:145:146:178 SD: 2.0445 cents 90:91:110:120:136 x 147:180 SD: 2.5648 cents 91:92:112:121:137:148:149:182 SD: 2.0178 cents 93:94:114:124:140 x 152:186 SD: 1.9642 cents 95:96:117:127:143:155 x 190 SD: 2.2588 cents 96:97:118:128:145:156:157:192 SD: 1.8763 cents 97:98:119:129:146:158:159:194 SD: 1.7146 cents 98:99:120:131:148:160 x 196 SD: 2.2065 cents 99:100:122:132:149:161:162:198 SD: 1.8647 cents 100:101:123:133:151:163:164:200 SD: 1.8586 cents 101:102:124:135:152 x 165:202 SD: 1.8805 cents 102:103:125:136:154:166:167:204 SD: 1.5959 cents 105:106:129:140:158:171:172:210 SD: 1.4044 cents 106:107:130:141:160:173 x 212 SD: 1.8396 cents 107:108:131:143:161:174:175:214 SD: 1.6399 cents 109:110:134:145:164 x 178:218 SD: 1.7916 cents 110:111:135:147:166:179:180:220 SD: 1.4673 cents 111:112:136:148:167:181:182:222 SD: 1.3970 cents 112:113:137:149:169 x 183:224 SD: 1.9177 cents 113:114:139:151:170:184:185:226 SD: 1.4502 cents 114:115:140:152:172:186:187:228 SD: 1.3977 cents 117:118:144:156:176:191 x 234 SD: 1.6329 cents 118:119:145:157:178:192:193:236 SD: 1.3449 cents 119:120:146:159:179:194:195:238 SD: 1.2703 cents 120:121:147:160:181 x 196:240 SD: 1.4800 cents 121:122:149:161:182:197:198:242 SD: 1.4675 cents 122:123:150:163:184:199:200:244 SD: 1.3491 cents 123:124:151:164:185:200:201:246 SD: 1.2280 cents 124:125:152:165:187:202:203:248 SD: 1.1769 cents 127:128:156:169:191:207:208:254 SD: 1.1477 cents 128:129:157:171:193:209 x 256 SD: 1.3681 cents 129:130:158:172:194:210:211:258 SD: 1.1247 cents 132:133:162:176:199:215:216:264 SD: 0.8856 cents 139:140:171:185:209 x 227:278 SD: 1.4495 cents 140:141:172:187:211:228:229:280 SD: 0.9332 cents 141:142:173:188:212:230:231:282 SD: 0.9310 cents 146:147:179:195:220:238:239:292 SD: 0.8455 cents 154:155:189:205:232:251:252:308 SD: 0.7089 cents 162:163:199:216:244:264:265:324 SD: 0.5572 cents 168:169:206:224:253:274:275:336 SD: 0.5448 cents 184:185:226:245:277:300:301:368 SD: 0.5401 cents 189:190:232:252:285:308:309:378 SD: 0.4612 cents 198:199:243:264:298:323:324:396 SD: 0.3897 cents 219:220:269:292:330:357:358:438 SD: 0.3681 cents 225:226:276:300:339:367:368:450 SD: 0.3036 cents 237:238:291:316:357:386:388:474 SD: 0.2192 cents 423:425:519:564:637:689:692:846 SD: 0.2157 cents 432:434:530:576:651:704:707:864 SD: 0.1955 cents 435:437:534:580:655:709:712:870 SD: 0.1677 cents 462:464:567:616:696:753:756:924 SD: 0.0776 cents