Scala analysis: xen12-chalmers-tritriadic-mt-3-7-19
Tritriadic M->T scale built from 3:7:19
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: 19/14 528.687110 3: 49/36 533.741811 Arabic lute acute fourth 4: 19/12 795.558015 undevicesimal minor sixth 5: 12/7 933.129094 septimal major sixth 6: 133/72 1062.428921 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 144/133 137.5711 1: 7/6 266.8709 septimal minor third 2: 57/49 261.8162 3: 343/342 5.0547 4: 57/49 261.8162 5: 144/133 137.5711 6: 931/864 129.2998 7: 144/133 137.5711
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 343/342 5.055 cents 1: 1 931/864 129.300 cents 1: 2 144/133 137.571 cents 1: 2 57/49 261.816 cents 1: 1 7/6 266.871 cents septimal minor third 2: 4 7/6 266.871 cents septimal minor third 2: 1 432/343 399.387 cents 2: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 19/14 528.687 cents 3: 2 24/19 404.442 cents smaller undevicesimal major third 3: 2 19/14 528.687 cents 3: 2 49/36 533.742 cents Arabic lute acute fourth 3: 1 72/49 666.258 cents Arabic lute grave fifth 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 2 72/49 666.258 cents Arabic lute grave fifth 4: 2 28/19 671.313 cents 4: 2 19/12 795.558 cents undevicesimal minor sixth 5: 1 28/19 671.313 cents 5: 1 19/12 795.558 cents undevicesimal minor sixth 5: 1 343/216 800.613 cents 5: 4 12/7 933.129 cents septimal major sixth 6: 1 12/7 933.129 cents septimal major sixth 6: 2 98/57 938.184 cents 6: 2 133/72 1062.429 cents 6: 1 1728/931 1070.700 cents 6: 1 684/343 1194.945 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 : 266.9 528.7 533.7 795.6 933.1 1062.4 1200.0 266.9 : 261.8 266.9 528.7 666.3 795.6 933.1 1200.0 528.7 : 5.1 266.9 404.4 533.7 671.3 938.2 1200.0 533.7 : 261.8 399.4 528.7 666.3 933.1 1194.9 1200.0 795.6 : 137.6 266.9 404.4 671.3 933.1 938.2 1200.0 933.1 : 129.3 266.9 533.7 795.6 800.6 1062.4 1200.0 1062.4: 137.6 404.4 666.3 671.3 933.1 1070.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 5.0547 .. 266.8709 cents 57/49, 261.8162 cents 343/342, 5.0547 cents 2: 266.8709 .. 528.6871 cents 57/49, 261.8162 cents 1/1, 0.0000 cents 3: 404.4420 .. 666.2582 cents 57/49, 261.8162 cents 336/361,-124.2451 cents 4: 533.7418 .. 795.5580 cents 57/49, 261.8162 cents 2401/2592,-132.5164 cents 5: 671.3129 .. 933.1291 cents 57/49, 261.8162 cents 336/361,-124.2451 cents 6: 933.1291 .. 1194.9453 cents 57/49, 261.8162 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 343/342, 5.0547 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 33.914677 Largest / Average step : 1.556747 Largest / Smallest step : 52.796570 Median interval of one step : 144/133, 137.5711 cents, amount: 2 Least squares average step : 182.48515 cents, oct.: 1277.39608 cents Scale is not proper Step pattern alph. order: ABCBDED Step pattern size order : EDADCBC Scale is not a Constant Structure Scale diversity : 1.177461 Lumma stability : 0.008425 Lumma impropriety factor : 0.317506 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 : 343/342, 5.0547 cents Most common intervals : 7/6, 266.8709 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 528.687 933.129 cents Most common triad is 0.0 266.871 933.129 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 3 7 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% -- Rational properties -- Prime limit : 19 Odd number limit : 931 (O: 931 U: 931) Highest odd numerator or denominator: 133 Scale harmonicity : 0.012827 Average absolute harmonicity : 0.177311 Specific harmonicity : 0.063327 Fundamental : 1/504, -8.9773 octaves, 0.5191 Hz. Guide tone : 11172, 13.4476 octaves, 2922880.816 Hz. Exponens Consonantiae : 5.630688E+06, 22.42488 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 194.5, average 27.78571 Mersenne's string divisions : 880593285 Sum of van Prooijen's expressibility: 8.06175, average 1.15168 Sum of Tenney's harmonic distance : 15.85906, average 2.26558 Vogel's harmonic complexity : 23.14286 Wille's k value : 465 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 83.01325, average 2.96476 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.85714 12 1 3: -2 .. 1 -0.71429 7 7: -1 .. 2 0.28571 6 3 19: 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 18 28| Scale is weakly epimorphic with val: <7 10 19 32| Scale is weakly epimorphic with val: <7 10 20 29| Scale is weakly epimorphic with val: <7 10 21 33| Scale is weakly epimorphic with val: <7 10 22 30| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 20 33| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <7 12 20 30| Scale is weakly epimorphic with val: <7 12 21 27| Scale is weakly epimorphic with val: <7 12 22 31|
FIT/MODE
7: 2 1 0 2 0 1 1 N T3 SD: 49.3859 c. M: 75.9862 c. 9: 2 2 0 2 1 1 1 N T3 SD: 2.9161 c. M:-4.6462 c. 68: 15 15 0 15 8 7 8 N SD: 2.4992 c. M: 4.3300 c. 77: 17 17 0 17 9 8 9 N SD: 2.1274 c. M: 3.8717 c. 86: 19 19 0 19 10 9 10 N SD: 1.8808 c. M: 3.5093 c. 95: 21 21 0 21 11 10 11 N SD: 1.7254 c. M: 3.2155 c. 104: 23 23 0 23 12 11 12 N SD: 1.6361 c. M: 2.9726 c. 113: 25 25 0 25 13 12 13 N SD: 1.5933 c. M: 2.7684 c. 121: 27 26 1 26 14 13 14 N SD: 1.7141 c. M: 3.0673 c. 122: 27 27 0 27 14 13 14 N SD: 1.5821 c. M: 2.5943 c. 130: 29 28 1 28 15 14 15 N SD: 1.4237 c. M: 2.5333 c. 139: 31 30 1 30 16 15 16 N SD: 1.1793 c. M: 2.0684 c. 148: 33 32 1 32 17 16 17 N SD: 0.9759 c. M: 1.6601 c. 157: 35 34 1 34 18 17 18 N SD: 0.8115 c. M: 1.2986 c. 166: 37 36 1 36 19 18 19 N SD: 0.6863 c. M:-1.1979 c. 175: 39 38 1 38 20 19 20 N SD: 0.6022 c. M:-1.1153 c. 184: 41 40 1 40 21 20 21 N SD: 0.5597 c. M:-1.0408 c. 193: 43 42 1 42 22 21 22 N SD: 0.5553 c. M:-0.9732 c. 202: 45 44 1 44 23 22 23 N SD: 0.5804 c. M:-0.9374 c. 225: 50 49 1 49 26 24 26 N SD: 0.6230 c. M: 1.0956 c. 234: 52 51 1 51 27 25 27 N SD: 0.4995 c. M: 0.8905 c. 243: 54 53 1 53 28 26 28 N SD: 0.3914 c. M: 0.7005 c. 252: 56 55 1 55 29 27 29 N SD: 0.3025 c. M: 0.5242 c. 261: 58 57 1 57 30 28 30 N SD: 0.2410 c. M: 0.4085 c. 270: 60 59 1 59 31 29 31 N SD: 0.2183 c. M: 0.4085 c. 427: 95 93 2 93 49 46 49 N SD: 0.1960 c. M: 0.3499 c. 436: 97 95 2 95 50 47 50 N SD: 0.1443 c. M: 0.2467 c. 445: 99 97 2 97 51 48 51 N SD: 0.1076 c. M:-0.1908 c. 454: 101 99 2 99 52 49 52 N SD: 0.0986 c. M:-0.1789 c. 697: 155 152 3 152 80 75 80 N SD: 0.0986 c. M: 0.1621 c. 706: 157 154 3 154 81 76 81 N SD: 0.0615 c. M: 0.1060 c. 715: 159 156 3 156 82 77 82 N SD: 0.0290 c. M: 0.0513 c. 724: 161 158 3 158 83 78 83 N SD: 0.0259 c. M:-0.0422 c. 1169: 260 255 5 255 134 126 134 N SD: 0.0259 c. M:-0.0478 c. 1439: 320 314 6 314 165 155 165 N SD: 0.0206 c. M: 0.0379 c. 1884: 419 411 8 411 216 203 216 N SD: 0.0139 c. M: 0.0247 c. 1893: 421 413 8 413 217 204 217 N SD: 0.0081 c. M:-0.0141 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: 46.8015 cents 3 x 4 x x 5 x 6 S SD: 19.1992 cents 4:5 x x 6:7 x 8 S SD: 38.9730 cents 5:6 x 7:8 x 9:10 S SD: 16.8472 cents 6:7:8 x x 10:11:12 S SD: 11.8122 cents 7:8 x 10:11:12:13:14 S SD: 15.4060 cents 8:9 x 11:13:14:15:16 SD: 15.1265 cents 9:11:12 x 14:15:17:18 SD: 18.4345 cents 10:12 x 14:16:17:18:20 S SD: 14.2455 cents 11:13 x 15:17:19:20:22 SD: 9.4133 cents 12:14:16 x 19:21:22:24 SD: 8.1376 cents 13:15 x 18:21:22:24:26 SD: 9.0497 cents 14:16:19 x 22:24:26:28 SD: 6.5213 cents 15:18:20 x 24:26:28:30 S SD: 10.9807 cents 16:19 x 22:25:27:30:32 SD: 9.4055 cents 17:20:23 x 27:29:31:34 SD: 4.8281 cents 19:22 x 26:30:33:35:38 SD: 4.7580 cents 20:23:27 x 32:34:37:40 SD: 5.8908 cents 21:25 x 29:33:36:39:42 SD: 7.6517 cents 22:26 x 30:35:38:41:44 SD: 5.2252 cents 23:27:31 x 36:39:42:46 SD: 6.2560 cents 24:28 x 33:38:41:44:48 SD: 3.7856 cents 25:29 x 34:40:43:46:50 SD: 3.7574 cents 26:30:35 x 41:45:48:52 SD: 4.9689 cents 27:32 x 37:43:46:50:54 SD: 5.5695 cents 28:33:38 x 44:48:52:56 SD: 3.9638 cents 29:34:39 x 46:50:54:58 SD: 4.1559 cents 30:35 x 41:48:51:55:60 SD: 4.5916 cents 31:36:42 x 49:53:57:62 SD: 2.1532 cents 33:39 x 45:52:57:61:66 SD: 4.5655 cents 34:40:46 x 54:58:63:68 SD: 3.1988 cents 35:41 x 48:55:60:65:70 SD: 3.6414 cents 36:42 x 49:57:62:67:72 SD: 2.5392 cents 37:43:50 x 59:63:68:74 SD: 3.5968 cents 38:44 x 52:60:65:70:76 SD: 2.9687 cents 39:46:53 x 62:67:72:78 SD: 3.4441 cents 40:47:54 x 63:69:74:80 SD: 3.5035 cents 41:48 x 56:65:70:76:82 SD: 2.1308 cents 42:49:57 x 67:72:78:84 SD: 2.6571 cents 44:51 x 60:70:75:81:88 SD: 3.0652 cents 45:53:61 x 71:77:83:90 SD: 3.0162 cents 46:54:62:63:73:79:85:92 SD: 2.8495 cents 47:55 x 64:74:81:87:94 SD: 2.4718 cents 48:56:65 x 76:82:89:96 SD: 1.6065 cents 49:57 x 67:78:84:91:98 SD: 2.6882 cents 50:58 x 68:79:86:92:100 SD: 2.3150 cents 51:60:69 x 81:87:94:102 SD: 3.1376 cents 52:61 x 71:82:89:96:104 SD: 2.2204 cents 53:62:72 x 84:91:98:106 SD: 1.0270 cents 55:64 x 75:87:94:102:110 SD: 1.7308 cents 56:65:76 x 89:96:103:112 SD: 2.2122 cents 58:68 x 79:92:99:107:116 SD: 2.0047 cents 59:69:80 x 93:101:109:118 SD: 1.5442 cents 61:71 x 83:97:105:113:122 SD: 2.0174 cents 62:72:84 x 98:106:115:124 SD: 2.0664 cents 63:74 x 86:100:108:116:126 SD: 2.4334 cents 64:75 x 87:101:110:118:128 SD: 1.8839 cents 65:76:88 x 103:111:120:130 SD: 1.4874 cents 66:77 x 90:105:113:122:132 SD: 1.5345 cents 67:78:91 x 106:115:124:134 SD: 0.9556 cents 69:81 x 94:109:118:127:138 SD: 2.2939 cents 70:82:95 x 111:120:129:140 SD: 1.4267 cents 72:84 x 98:114:123:133:144 SD: 1.0036 cents 73:85:99 x 116:125:135:146 SD: 1.2869 cents 75:88 x 102:119:129:139:150 SD: 2.2264 cents 76:89:103 x 120:130:140:152 SD: 1.7363 cents 77:90 x 105:122:132:142:154 SD: 0.9169 cents 78:91:106 x 124:134:144:156 SD: 1.3848 cents 80:93 x 109:127:137:148:160 SD: 1.4163 cents 81:95:110 x 128:139:150:162 SD: 1.8111 cents 82:96:111:112:130:141:151:164 SD: 1.7743 cents 83:97 x 113:131:142:153:166 SD: 1.3377 cents 84:98:114 x 133:144:155:168 SD: 0.3101 cents 86:100 x 117:136:147:159:172 SD: 1.3545 cents 87:102:118 x 138:149:161:174 SD: 1.6324 cents 88:103:119:120:139:151:163:176 SD: 1.5827 cents 89:104 x 121:141:153:164:178 SD: 1.2283 cents 91:106 x 124:144:156:168:182 SD: 0.6048 cents 92:107:125 x 146:158:170:184 SD: 1.2771 cents 94:110 x 128:149:161:174:188 SD: 1.1453 cents 95:111:129 x 150:163:175:190 SD: 1.2485 cents 96:112:130:131:152:165:177:192 SD: 1.1498 cents 97:113 x 132:154:166:179:194 SD: 1.0614 cents 98:114:133 x 155:168:181:196 SD: 0.8988 cents 100:117 x 136:158:171:185:200 SD: 1.3463 cents 101:118:137 x 160:173:187:202 SD: 0.8430 cents 103:120 x 140:163:177:190:206 SD: 0.9961 cents 105:123 x 143:166:180:194:210 SD: 1.2657 cents 106:124:144 x 168:182:196:212 SD: 1.0270 cents 108:126 x 147:171:185:200:216 SD: 0.7558 cents 109:127:148 x 173:187:201:218 SD: 0.9713 cents 111:130 x 151:176:190:205:222 SD: 1.2733 cents 112:131:152 x 177:192:207:224 SD: 0.9269 cents 113:132:153:154:179:194:209:226 SD: 0.8784 cents 114:133 x 155:181:195:211:228 SD: 1.2082 cents 115:134:156:157:182:197:212:230 SD: 0.9793 cents 117:137:159 x 185:201:216:234 SD: 1.3503 cents 118:138:160:161:187:202:218:236 SD: 0.9675 cents 119:139 x 162:188:204:220:238 SD: 0.7658 cents 120:140:163 x 190:206:222:240 SD: 0.6422 cents 122:142 x 166:193:209:225:244 SD: 0.8843 cents 123:144:167 x 195:211:227:246 SD: 1.1259 cents 124:145:168:169:196:213:229:248 SD: 1.0173 cents 125:146 x 170:198:214:231:250 SD: 0.5847 cents 128:149 x 174:203:219:236:256 SD: 1.1786 cents 129:151:175:176:204:221:238:258 SD: 1.1116 cents 130:152:176:177:206:223:240:260 SD: 0.8650 cents 131:153:178 x 207:225:242:262 SD: 0.9270 cents 132:154:179:180:209:226:244:264 SD: 0.6126 cents 133:155 x 181:211:228:246:266 SD: 0.7510 cents 134:156:182 x 212:230:248:268 SD: 0.9556 cents 136:159 x 185:215:233:251:272 SD: 0.8325 cents 137:160:186 x 217:235:253:274 SD: 0.3899 cents 139:162 x 189:220:238:257:278 SD: 0.6150 cents 142:166 x 193:225:243:262:284 SD: 0.9622 cents 143:167:194:195:226:245:264:286 SD: 0.7268 cents 144:168:195:196:228:247:266:288 SD: 0.5615 cents 145:169:197 x 230:249:268:290 SD: 0.8529 cents 146:170:198:199:231:250:270:292 SD: 0.7589 cents 147:172 x 200:233:252:272:294 SD: 1.0261 cents 148:173:201 x 234:254:273:296 SD: 0.8914 cents 149:174:202:203:236:255:275:298 SD: 0.6374 cents 150:175 x 204:238:257:277:300 SD: 0.6760 cents 151:176:205:206:239:259:279:302 SD: 0.6436 cents 153:179 x 208:242:262:283:306 SD: 1.0515 cents 154:180:209:210:244:264:284:308 SD: 0.7859 cents 155:181:210:211:245:266:286:310 SD: 0.7437 cents 156:182:212 x 247:267:288:312 SD: 0.6273 cents 157:183:213:214:249:269:290:314 SD: 0.6094 cents 159:186:216 x 252:273:294:318 SD: 1.0270 cents 160:187:217:218:253:274:296:320 SD: 0.7716 cents 161:188 x 219:255:276:297:322 SD: 0.5106 cents 164:191 x 223:260:281:303:328 SD: 0.7050 cents 167:195 x 227:264:286:308:334 SD: 0.8418 cents 168:196:228:229:266:288:310:336 SD: 0.4477 cents 170:198:231 x 269:291:314:340 SD: 0.7589 cents 171:200:232:233:271:293:316:342 SD: 0.7320 cents 173:202:235 x 274:297:320:346 SD: 0.6769 cents 174:203:236:237:276:298:321:348 SD: 0.6426 cents 175:204 x 238:277:300:323:350 SD: 0.4173 cents 178:208 x 242:282:305:329:356 SD: 0.6326 cents 179:209:243:244:283:307:331:358 SD: 0.6256 cents 180:210:244:245:285:309:333:360 SD: 0.5828 cents 181:211:246 x 287:310:334:362 SD: 0.7509 cents 182:212:247:248:288:312:336:364 SD: 0.5184 cents 184:215:250 x 291:315:340:368 SD: 0.7624 cents 185:216:251:252:293:317:342:370 SD: 0.3628 cents 189:221 x 257:299:324:349:378 SD: 0.7581 cents 190:222:258:259:301:326:351:380 SD: 0.6010 cents 191:223:259:260:302:327:353:382 SD: 0.5603 cents 192:224 x 261:304:329:355:384 SD: 0.4741 cents 195:228:265 x 309:334:360:390 SD: 0.8342 cents 196:229:266:267:310:336:362:392 SD: 0.4942 cents 197:230:267:268:312:338:364:394 SD: 0.4586 cents 199:232:270:271:315:341:368:398 SD: 0.3745 cents 203:237 x 276:321:348:375:406 SD: 0.5323 cents 204:238:277:278:323:350:377:408 SD: 0.3963 cents 206:240 x 280:326:353:381:412 SD: 0.6958 cents 207:242:281:282:328:355:382:414 SD: 0.6466 cents 208:243:282:283:329:357:384:416 SD: 0.5990 cents 209:244:284 x 331:358:386:418 SD: 0.4813 cents 210:245:285:286:333:360:388:420 SD: 0.4021 cents 216:252:293:294:342:370:399:432 SD: 0.2258 cents 217:253 x 295:344:372:401:434 SD: 0.5432 cents 218:254:296:297:345:374:403:436 SD: 0.5081 cents 220:257:299 x 348:377:406:440 SD: 0.6900 cents 221:258:300:301:350:379:408:442 SD: 0.2953 cents 231:270 x 314:366:396:427:462 SD: 0.7143 cents 232:271:315:316:367:398:429:464 SD: 0.5322 cents 233:272:316:317:369:399:430:466 SD: 0.4360 cents 235:274:319:320:372:403:434:470 SD: 0.2259 cents 245:286 x 333:388:420:453:490 SD: 0.5240 cents 246:287:334:335:390:422:454:492 SD: 0.4545 cents 247:288:335:336:391:423:456:494 SD: 0.3898 cents 252:294:342:343:399:432:466:504 SD: 0.2655 cents 269:314:365:366:426:461:497:538 SD: 0.1973 cents 288:336:391:392:456:494:532:576 SD: 0.1692 cents 420:490:570:572:665:720:776:840 SD: 0.1536 cents 437:510:593:595:692:749:807:874 SD: 0.1493 cents 451:526:612:614:714:773:833:902 SD: 0.1177 cents 504:588:684:686:798:864:931:1008 SD: 0.0000 cents