Scala analysis: xen12-chalmers-tritriadic-mt-7-17-23
Tritriadic M->T scale built from 7:17:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/14 336.129503 supraminor third 2: 23/17 523.318938 3: 289/196 672.259006 two (supraminor third) 4: 23/14 859.448441 5: 28/17 863.870497 submajor sixth 6: 391/196 1195.577944 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 392/391 4.4221 1: 17/14 336.1295 supraminor third 2: 322/289 187.1894 3: 4913/4508 148.9401 4: 322/289 187.1894 5: 392/391 4.4221 6: 6647/5488 331.7074 7: 392/391 4.4221
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 392/391 4.422 cents 1: 1 4913/4508 148.940 cents 1: 2 322/289 187.189 cents 1: 1 6647/5488 331.707 cents 1: 1 17/14 336.130 cents supraminor third 2: 1 5488/4913 191.611 cents 2: 4 17/14 336.130 cents supraminor third 2: 1 28/23 340.552 cents 2: 1 23/17 523.319 cents 3: 2 28/23 340.552 cents 3: 2 23/17 523.319 cents 3: 1 392/289 527.741 cents 3: 2 289/196 672.259 cents two (supraminor third) 4: 2 392/289 527.741 cents 4: 1 289/196 672.259 cents two (supraminor third) 4: 2 34/23 676.681 cents 4: 2 23/14 859.448 cents 5: 1 34/23 676.681 cents 5: 1 23/14 859.448 cents 5: 4 28/17 863.870 cents submajor sixth 5: 1 4913/2744 1008.389 cents 6: 1 28/17 863.870 cents submajor sixth 6: 1 10976/6647 868.293 cents 6: 2 289/161 1012.811 cents 6: 1 9016/4913 1051.060 cents 6: 2 391/196 1195.578 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 : 336.1 523.3 672.3 859.4 863.9 1195.6 1200.0 336.1 : 187.2 336.1 523.3 527.7 859.4 863.9 1200.0 523.3 : 148.9 336.1 340.6 672.3 676.7 1012.8 1200.0 672.3 : 187.2 191.6 523.3 527.7 863.9 1051.1 1200.0 859.4 : 4.4 336.1 340.6 676.7 863.9 1012.8 1200.0 863.9 : 331.7 336.1 672.3 859.4 1008.4 1195.6 1200.0 1195.6: 4.4 340.6 527.7 676.7 863.9 868.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 4.4221 .. 336.1295 cents 6647/5488, 331.7074 cents 392/391, 4.4221 cents 2: 191.6115 .. 523.3189 cents 6647/5488, 331.7074 cents 76832/83521,-144.5180 cents 3: 340.5516 .. 672.2590 cents 6647/5488, 331.7074 cents 476/529,-182.7674 cents 4: 527.7410 .. 859.4484 cents 6647/5488, 331.7074 cents 76832/83521,-144.5180 cents 5: 676.6811 .. 1008.3885 cents 6647/5488, 331.7074 cents 476/529,-182.7674 cents 6: 863.8705 .. 1195.5779 cents 6647/5488, 331.7074 cents 76832/83521,-144.5180 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 392/391, 4.4221 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 38.766711 Largest / Average step : 1.960755 Largest / Smallest step : 76.012038 Median interval of one step : 322/289, 187.1894 cents, amount: 2 Least squares average step : 190.92970 cents, oct.: 1336.50792 cents Scale is not proper Step pattern alph. order: ABCBDED Step pattern size order : ECBCADA Scale is not a Constant Structure Scale diversity : 1.092464 Lumma stability : 0.007370 Lumma impropriety factor : 0.665907 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 : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 392/391, 4.4221 cents Most common intervals : 17/14, 336.1295 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 523.319 863.870 cents Most common triad is 0.0 336.130 863.870 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 7 17 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 6647 (O: 6647 U: 6647) Highest odd numerator or denominator: 391 Scale harmonicity : 0.005977 Average absolute harmonicity : 0.157564 Specific harmonicity : 0.031033 Fundamental : 1/3332, -11.7022 octaves, 0.0785 Hz. Guide tone : 186116, 17.5058 octaves, 48692703.712 Hz. Exponens Consonantiae : 6.201385E+08, 29.20802 octaves Euler's gradus suavitatis : 93 Sum of Mann's harmonic distance : 614.0, average 87.71429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.23743, average 1.46249 Sum of Tenney's harmonic distance : 20.09283, average 2.87040 Vogel's harmonic complexity : 42.28571 Wille's k value : 3323 Wilson's harmonic complexity : 95 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 75.82199, average 2.70793 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.42857 9 1 7: -2 .. 1 -0.71429 7 17: -1 .. 2 0.28571 6 3 23: 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 18 26 29| Scale is weakly epimorphic with val: <7 18 27 33| Scale is weakly epimorphic with val: <7 18 28 30| Scale is weakly epimorphic with val: <7 18 29 34| Scale is weakly epimorphic with val: <7 18 30 31| Scale is weakly epimorphic with val: <7 18 31 35| Scale is weakly epimorphic with val: <7 19 27 30| Scale is weakly epimorphic with val: <7 19 28 34| Scale is weakly epimorphic with val: <7 19 29 31| Scale is weakly epimorphic with val: <7 19 30 35| Scale is weakly epimorphic with val: <7 19 31 32| Scale is weakly epimorphic with val: <7 20 26 30| Scale is weakly epimorphic with val: <7 20 28 31| Scale is weakly epimorphic with val: <7 20 29 35| Scale is weakly epimorphic with val: <7 20 30 32| Scale is weakly epimorphic with val: <7 20 32 33| Scale is weakly epimorphic with val: <7 21 26 34| Scale is weakly epimorphic with val: <7 21 27 31| Scale is weakly epimorphic with val: <7 21 29 32| Scale is weakly epimorphic with val: <7 21 31 33| Scale is weakly epimorphic with val: <7 22 26 31| Scale is weakly epimorphic with val: <7 22 27 35| Scale is weakly epimorphic with val: <7 22 28 32| Scale is weakly epimorphic with val: <7 22 30 33| Scale is weakly epimorphic with val: <7 22 32 34|
FIT/MODE
7: 2 1 1 1 0 2 0 N T3 SD: 7.3488 c. M:-13.4553 c. 18: 5 3 2 3 0 5 0 N SD: 5.5915 c. M:-10.0144 c. 25: 7 4 3 4 0 7 0 N SD: 2.9829 c. M:-4.6811 c. 32: 9 5 4 5 0 9 0 N SD: 2.4774 c. M:-4.4221 c. 89: 25 14 11 14 0 25 0 N SD: 2.4897 c. M:-4.4221 c. 96: 27 15 12 15 0 27 0 N SD: 2.4774 c. M:-4.4221 c. 103: 29 16 13 16 0 29 0 N SD: 2.5562 c. M:-4.4221 c. 114: 32 18 14 18 0 32 0 N SD: 2.5451 c. M:-4.4221 c. 121: 34 19 15 19 0 34 0 N SD: 2.4755 c. M:-4.4221 c. 136: 38 21 17 21 1 37 1 N SD: 2.4995 c. M: 4.4015 c. 140: 39 22 17 22 1 38 1 N SD: 2.4826 c. M: 4.1494 c. 143: 40 22 18 22 1 39 1 N SD: 2.3474 c. M: 3.9696 c. 147: 41 23 18 23 1 40 1 N SD: 2.1526 c. M: 3.7412 c. 150: 42 23 19 23 1 41 1 N SD: 2.2618 c. M: 3.5779 c. 151: 42 24 19 23 1 41 1 N SD: 2.2919 c. M: 3.5250 c. 154: 43 24 19 24 1 42 1 N SD: 1.8903 c. M: 3.3702 c. 161: 45 25 20 25 1 44 1 N SD: 1.6971 c. M: 3.0314 c. 168: 47 26 21 26 1 46 1 N SD: 1.5733 c. M: 2.7208 c. 172: 48 27 21 27 1 47 1 N SD: 1.5836 c. M: 2.5547 c. 175: 49 27 22 27 1 48 1 N SD: 1.5157 c. M: 2.4351 c. 179: 50 28 22 28 1 49 1 N SD: 1.3325 c. M: 2.2819 c. 186: 52 29 23 29 1 51 1 N SD: 1.1390 c. M: 2.0296 c. 193: 54 30 24 30 1 53 1 N SD: 1.0121 c. M: 1.7956 c. 200: 56 31 25 31 1 55 1 N SD: 0.9583 c. M: 1.5779 c. 211: 59 33 26 33 1 58 1 N SD: 0.7675 c. M: 1.2651 c. 218: 61 34 27 34 1 60 1 N SD: 0.6082 c. M: 1.0825 c. 225: 63 35 28 35 1 62 1 N SD: 0.5302 c. M: 0.9113 c. 232: 65 36 29 36 1 64 1 N SD: 0.5482 c. M: 0.9051 c. 243: 68 38 30 38 1 67 1 N SD: 0.3709 c. M: 0.6541 c. 250: 70 39 31 39 1 69 1 N SD: 0.2136 c. M: 0.3779 c. 257: 72 40 32 40 1 71 1 N SD: 0.2085 c. M: 0.3617 c. 275: 77 43 34 43 1 76 1 N SD: 0.1852 c. M:-0.3174 c. 282: 79 44 35 44 1 78 1 N SD: 0.0933 c. M:-0.1667 c. 532: 149 83 66 83 2 147 2 N SD: 0.0532 c. M: 0.0892 c. 814: 228 127 101 127 3 225 3 N SD: 0.0143 c. M: 0.0231 c. 2167: 607 338 269 338 8 599 8 N SD: 0.0083 c. M: 0.0148 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: 14.8480 cents 3 x 4 x x 5 x 6 S SD: 10.8451 cents 4:5 x 6 x 7 x 8 S SD: 30.0166 cents 5:6:7 x 8 x x 10 S SD: 19.3936 cents 6:7:8:9 x 10 x 12 S SD: 16.4160 cents 7 x 9:10 x 12 x 14 SD: 31.2070 cents 8:10:11:12:13 x x 16 SD: 13.4792 cents 9:11:12:13 x 15 x 18 SD: 9.9117 cents 10:12:14:15:16 x x 20 S SD: 16.6128 cents 11:13:15:16:18 x x 22 SD: 10.9365 cents 12:15:16:18 x 20 x 24 S SD: 13.3549 cents 13:16:18:19:21 x x 26 SD: 11.3765 cents 14:17:19:21:23 x x 28 SD: 6.0355 cents 15:18:20:22 x 25 x 30 SD: 7.9073 cents 16:19:22:24:26 x x 32 SD: 11.8575 cents 17:21:23:25 x 28 x 34 SD: 6.0096 cents 18:22:24:27 x 30 x 36 SD: 9.0942 cents 19:23:26:28:31 x x 38 SD: 4.7323 cents 20:24:27:29 x 33 x 40 SD: 7.1673 cents 21:26:28:31 x 35 x 42 SD: 9.3651 cents 22:27:30:32:36 x x 44 SD: 6.7169 cents 23:28:31:34 x 38 x 46 SD: 2.1065 cents 24:29:32:35:39:40 x 48 SD: 7.1739 cents 25:30:34:37:41 x x 50 SD: 4.6977 cents 26:32:35:38 x 43 x 52 SD: 6.0156 cents 27:33:37:40:44 x x 54 SD: 5.9371 cents 28:34:38:41:46 x x 56 SD: 2.6333 cents 29:35:39:43 x 48 x 58 SD: 3.9304 cents 30:36:41:44:49 x x 60 SD: 6.0374 cents 31:38:42:46 x 51 x 62 SD: 3.9884 cents 32:39:43:47 x 53 x 64 SD: 3.5667 cents 33:40:45:49:54 x x 66 SD: 3.9460 cents 34:41:46:50 x 56 x 68 SD: 2.5736 cents 35:43:47:52 x 58 x 70 SD: 5.8713 cents 36:44:49:53:59 x x 72 SD: 3.2278 cents 37:45:50:55 x 61 x 74 SD: 2.9072 cents 38:46:51:56:62:63 x 76 SD: 3.7067 cents 39:47:53:58:64 x x 78 SD: 4.2657 cents 40:49:54:59 x 66 x 80 SD: 3.1962 cents 41:50:55:60:67:68 x 82 SD: 4.3220 cents 42:51:57:62:69 x x 84 SD: 1.1454 cents 43:52:58:63 x 71 x 86 SD: 2.9585 cents 44:53:60:65:72 x x 88 SD: 4.1852 cents 45:55:61:66:74 x x 90 SD: 3.0066 cents 46:56:62:68 x 76 x 92 SD: 2.1065 cents 47:57:64:69:77 x x 94 SD: 2.8949 cents 48:58:65:71 x 79 x 96 SD: 2.0645 cents 49:60:66:72 x 81 x 98 SD: 3.7138 cents 50:61:68:74:82 x x 100 SD: 2.8143 cents 51:62:69:75 x 84 x 102 SD: 1.0005 cents 52:63:70:77:85:86 x 104 SD: 2.7478 cents 53:64:72:78:87 x x 106 SD: 2.4965 cents 54:66:73:80 x 89 x 108 SD: 2.8109 cents 55:67:74:81:90:91 x 110 SD: 2.5603 cents 56:68:76:83:92 x x 112 SD: 2.0894 cents 57:69:77:84 x 94 x 114 SD: 1.2868 cents 58:70:78:86:95:96 x 116 SD: 3.3880 cents 59:72:80:87:97 x x 118 SD: 1.9012 cents 60:73:81:88 x 99 x 120 SD: 2.1914 cents 61:74:83:90:100 x x 122 SD: 2.1409 cents 62:75:84:91 x 102 x 124 SD: 2.1565 cents 63:77:85:93 x 104 x 126 SD: 2.6036 cents 64:78:87:94:105 x x 128 SD: 2.5216 cents 65:79:88:96 x 107 x 130 SD: 0.7168 cents 66:80:89:97:108:109 x 132 SD: 1.9918 cents 67:81:91:99:110 x x 134 SD: 2.1720 cents 68:83:92:100 x 112 x 136 SD: 2.0136 cents 69:84:93:102:113:114 x 138 SD: 1.9775 cents 70:85:95:103:115 x x 140 SD: 1.2925 cents 71:86:96:105 x 117 x 142 SD: 1.3690 cents 72:87:97:106:118:119 x 144 SD: 2.2779 cents 73:89:99:108:120 x x 146 SD: 2.0032 cents 74:90:100:109 x 122 x 148 SD: 0.8408 cents 75:91:101:111:123:124 x 150 SD: 2.1129 cents 76:92:103:112:125 x x 152 SD: 1.3030 cents 77:94:104:114 x 127 x 154 SD: 2.4461 cents 78:95:106:115:128 x x 156 SD: 1.9003 cents 79:96:107:116 x 130 x 158 SD: 1.5473 cents 80:97:108:118:131:132 x 160 SD: 1.3182 cents 81:98:110:119:133 x x 162 SD: 2.2122 cents 82:100:111:121 x 135 x 164 SD: 1.5287 cents 83:101:112:122:136:137 x 166 SD: 1.6498 cents 84:102:114:124:138 x x 168 SD: 1.1454 cents 85:103:115:125 x 140 x 170 SD: 1.1660 cents 86:104:116:127:141:142 x 172 SD: 1.7965 cents 87:106:118:128:143 x x 174 SD: 1.6484 cents 88:107:119:130 x 145 x 176 SD: 0.8302 cents 89:108:120:131:146:147 x 178 SD: 1.4501 cents 90:109:122:133:148 x x 180 SD: 1.4053 cents 91:111:123:134 x 150 x 182 SD: 1.6851 cents 92:112:124:136:151:152 x 184 SD: 1.7765 cents 93:113:126:137 x 153 x 186 SD: 0.7393 cents 94:114:127:139:154:155 x 188 SD: 1.3140 cents 95:115:129:140:156 x x 190 SD: 1.6778 cents 96:117:130:142 x 158 x 192 SD: 1.7267 cents 97:118:131:143:159:160 x 194 SD: 1.0702 cents 98:119:133:145:161 x x 196 SD: 1.6072 cents 99:120:134:146 x 163:197:198 SD: 0.9047 cents 101:123:137:149:166 x 201:202 SD: 1.3335 cents 102:124:138:150 x 168:203:204 SD: 1.0764 cents 103:125:139:152:169:170:205:206 SD: 1.0704 cents 104:126:141:153:171 x 207:208 SD: 1.3048 cents 105:128:142:155 x 173:209:210 SD: 1.3490 cents 106:129:143:156:174:175:211:212 SD: 1.3022 cents 107:130:145:158:176 x 213:214 SD: 0.9602 cents 108:131:146:159:177:178:215:216 SD: 0.9528 cents 110:134:149:162 x 181:219:220 SD: 1.2260 cents 111:135:150:164:182:183:221:222 SD: 1.0083 cents 112:136:152:165:184 x 223:224 SD: 1.0815 cents 113:137:153:167 x 186:225:226 SD: 1.0091 cents 115:140:156:170:189 x 229:230 SD: 1.3966 cents 116:141:157:171 x 191:231:232 SD: 0.6077 cents 118:143:160:174:194 x 235:236 SD: 1.0107 cents 119:145:161:175 x 196:237:238 SD: 1.3440 cents 120:146:162:177:197:198:239:240 SD: 0.9588 cents 121:147:164:178:199 x 241:242 SD: 1.0207 cents 122:148:165:180:200:201:243:244 SD: 0.7221 cents 124:151:168:183 x 204:247:248 SD: 1.0940 cents 125:152:169:184:205:206:249:250 SD: 0.8128 cents 127:154:172:187 x 209:253:254 SD: 0.7937 cents 129:157:175:190:212 x 257:258 SD: 1.1370 cents 130:158:176:192 x 214:259:260 SD: 0.7053 cents 131:159:177:193:215:216:261:262 SD: 0.6272 cents 132:160:179:195:217 x 263:264 SD: 1.0802 cents 133:162:180:196 x 219:265:266 SD: 0.9786 cents 134:163:181:198:220:221:267:268 SD: 0.9183 cents 135:164:183:199:222 x 269:270 SD: 0.7223 cents 138:168:187:203:227 x 275:276 SD: 1.2006 cents 139:169:188:205:228:229:277:278 SD: 0.5734 cents 141:171:191:208 x 232:281:282 SD: 0.6661 cents 144:175:195:212 x 237:287:288 SD: 0.6620 cents 145:176:196:214:238:239:289:290 SD: 0.4950 cents 146:177:198:215:240 x 291:292 SD: 0.9581 cents 147:179:199:217 x 242:293:294 SD: 0.9335 cents 148:180:200:218:243:244:295:296 SD: 0.6511 cents 149:181:202:220:245 x 297:298 SD: 0.7960 cents 150:182:203:221:246:247:299:300 SD: 0.5540 cents 152:185:206:224:250 x 303:304 SD: 0.9338 cents 153:186:207:226:251:252:305:306 SD: 0.6569 cents 154:187:208:227:253:254:307:308 SD: 0.5744 cents 155:188:210:229 x 255:309:310 SD: 0.8651 cents 156:189:211:230:256:257:311:312 SD: 0.6517 cents 158:192:214:233 x 260:315:316 SD: 0.4980 cents 161:196:218:237 x 265:321:322 SD: 0.9428 cents 162:197:219:239:266:267:323:324 SD: 0.4994 cents 163:198:221:240:268 x 325:326 SD: 0.7959 cents 164:199:222:242:269:270:327:328 SD: 0.5156 cents 166:202:225:245:273 x 331:332 SD: 0.9168 cents 167:203:226:246:274:275:333:334 SD: 0.4991 cents 169:205:229:249 x 278:337:338 SD: 0.6962 cents 170:206:230:251:279:280:339:340 SD: 0.6692 cents 172:209:233:254 x 283:343:344 SD: 0.6830 cents 173:210:234:255:284:285:345:346 SD: 0.2500 cents 175:213:237:258 x 288:349:350 SD: 0.7791 cents 176:214:238:260:289:290:351:352 SD: 0.6097 cents 179:217:242:264:294:295:357:358 SD: 0.4805 cents 180:219:244:265:296 x 359:360 SD: 0.9534 cents 181:220:245:267:297:298:361:362 SD: 0.4297 cents 183:222:248:270:301 x 365:366 SD: 0.6781 cents 184:223:249:271:302:303:367:368 SD: 0.6046 cents 185:225:250:273:304:305:369:370 SD: 0.5832 cents 186:226:252:274 x 306:371:372 SD: 0.6174 cents 187:227:253:276:307:308:373:374 SD: 0.3091 cents 189:230:256:279 x 311:377:378 SD: 0.8307 cents 190:231:257:280:312:313:379:380 SD: 0.3613 cents 196:238:265:289:322:323:391:392 SD: 0.2130 cents 197:239:267:290:324 x 393:394 SD: 0.8061 cents 198:240:268:292:325:326:395:396 SD: 0.5134 cents 200:243:271:295 x 329:399:400 SD: 0.6014 cents 201:244:272:296:330:331:401:402 SD: 0.3644 cents 203:247:275:299 x 334:405:406 SD: 0.8178 cents 204:248:276:301:335:336:407:408 SD: 0.3481 cents 210:255:284:310:345:346:419:420 SD: 0.3172 cents 214:260:290:316:352 x 427:428 SD: 0.7404 cents 215:261:291:317:353:354:429:430 SD: 0.2171 cents 217:264:294:320 x 357:433:434 SD: 0.7613 cents 218:265:295:321:358:359:435:436 SD: 0.4508 cents 219:266:296:323:360:361:437:438 SD: 0.3686 cents 221:268:299:326:363:364:441:442 SD: 0.3562 cents 224:272:303:330:368:369:447:448 SD: 0.2365 cents 231:281:313:341 x 380:461:462 SD: 0.8386 cents 232:282:314:342:381:382:463:464 SD: 0.3146 cents 238:289:322:351:391:392:475:476 SD: 0.1224 cents 411:499:556:606:675:677:820:822 SD: 0.0972 cents