Scala analysis: cantonpenta
Canton scale in 13-limit pentacircle (351/350 and 364/363) temperament, 271et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128.413 cents 128.413280 2: 208.118 cents 208.118080 3: 287.823 cents 287.822880 4: 416.236 cents 416.236160 5: 495.941 cents 495.940960 6: 575.646 cents 575.645760 7: 704.059 cents 704.059040 8: 783.764 cents 783.763840 9: 912.177 cents 912.177120 10: 991.882 cents 991.881920 11: 1071.587 cents 1071.586720 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 128.4133 cents 128.4133 1: 128.4133 cents 128.4133 2: 79.7048 cents 79.7048 3: 79.7048 cents 79.7048 4: 128.4133 cents 128.4133 5: 79.7048 cents 79.7048 6: 79.7048 cents 79.7048 7: 128.4133 cents 128.4133 8: 79.7048 cents 79.7048 9: 128.4133 cents 128.4133 10: 79.7048 cents 79.7048 11: 79.7048 cents 79.7048 12: 128.4133 cents 128.4133
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 79.70480 cents 1: 5 128.41328 cents 2: 3 159.40960 cents 2: 8 208.11808 cents 2: 1 256.82656 cents 3: 9 287.82288 cents 3: 3 336.53136 cents 4: 4 367.52768 cents 4: 8 416.23616 cents 5: 1 447.23248 cents 5: 9 495.94096 cents 5: 2 544.64944 cents 6: 6 575.64576 cents 6: 6 624.35424 cents 7: 2 655.35056 cents 7: 9 704.05904 cents 7: 1 752.76752 cents 8: 8 783.76384 cents 8: 4 832.47232 cents 9: 3 863.46864 cents 9: 9 912.17712 cents 10: 1 943.17344 cents 10: 8 991.88192 cents 10: 3 1040.59040 cents 11: 5 1071.58672 cents 11: 7 1120.29520 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.36364 = 26/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 128.4 208.1 287.8 416.2 495.9 575.6 704.1 783.8 912.2 991.9 1071.6 1200.0 128.4 : 79.7 159.4 287.8 367.5 447.2 575.6 655.4 783.8 863.5 943.2 1071.6 1200.0 208.1 : 79.7 208.1 287.8 367.5 495.9 575.6 704.1 783.8 863.5 991.9 1120.3 1200.0 287.8 : 128.4 208.1 287.8 416.2 495.9 624.4 704.1 783.8 912.2 1040.6 1120.3 1200.0 416.2 : 79.7 159.4 287.8 367.5 495.9 575.6 655.4 783.8 912.2 991.9 1071.6 1200.0 495.9 : 79.7 208.1 287.8 416.2 495.9 575.6 704.1 832.5 912.2 991.9 1120.3 1200.0 575.6 : 128.4 208.1 336.5 416.2 495.9 624.4 752.8 832.5 912.2 1040.6 1120.3 1200.0 704.1 : 79.7 208.1 287.8 367.5 495.9 624.4 704.1 783.8 912.2 991.9 1071.6 1200.0 783.8 : 128.4 208.1 287.8 416.2 544.6 624.4 704.1 832.5 912.2 991.9 1120.3 1200.0 912.2 : 79.7 159.4 287.8 416.2 495.9 575.6 704.1 783.8 863.5 991.9 1071.6 1200.0 991.9 : 79.7 208.1 336.5 416.2 495.9 624.4 704.1 783.8 912.2 991.9 1120.3 1200.0 1071.6: 128.4 256.8 336.5 416.2 544.6 624.4 704.1 832.5 912.2 1040.6 1120.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.7048 .. 128.4133 cents 48.70848 cents 79.70480 cents 2: 159.4096 .. 256.8266 cents 97.41696 cents 30.99632 cents 3: 287.8229 .. 336.5314 cents 48.70848 cents 30.99632 cents 4: 367.5277 .. 416.2362 cents 48.70848 cents 30.99632 cents 5: 447.2325 .. 544.6494 cents 97.41696 cents 30.99632 cents 6: 575.6458 .. 624.3542 cents 48.70848 cents 30.99632 cents 7: 655.3506 .. 752.7675 cents 97.41696 cents 30.99632 cents 8: 783.7638 .. 832.4723 cents 48.70848 cents 30.99632 cents 9: 863.4686 .. 912.1771 cents 48.70848 cents 30.99632 cents 10: 943.1734 .. 1040.5904 cents 97.41696 cents 30.99632 cents 11: 1071.5867 .. 1120.2952 cents 48.70848 cents 30.99632 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 79.70480 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 128.41328 cents Average / Smallest step : 1.254630 Largest / Average step : 1.284133 Largest / Smallest step : 1.611111 Median interval of one step : 79.70480 cents, amount: 7 Most common interval of one step : 79.70480 cents, amount: 7 Least squares average step : 99.26313 cents, oct.: 1191.15754 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 271-tone equal temperament with octave 1200.000 cents degrees: 29 47 65 94 112 130 159 177 206 224 242 271 Least number of segments generator : 136 of 602.214 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 159 of 704.059 cents and inv. generated superset size: 15 = 3 more = 125.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABBABABBA Step pattern size order : LSSLSSLSLSSL Scale is a Constant Structure, by a margin of 30.99632 cents Scale diversity : 1.293272 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.391144 Rothenberg efficiency : 0.493519 redundancy: 0.506481 Efficiency x scale size : 5.922222 Number of different interval sizes : 26 = 2.36364 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.36364 = 26/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 30.99632 cents Number of recognisable fifths : 9, average 704.0590 cents Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.3205 c. M: 28.4133 c. Twelve-tone Chromatic (1/11-comma) 17: 2 1 1 2 1 1 2 1 2 1 1 2 P D3 SD: 7.3311 c. M:-12.7632 c. 29: 3 2 2 3 2 2 3 2 3 2 2 3 SP D3 SD: 2.4557 c. M:-4.2753 c. 46: 5 3 3 5 3 3 5 3 5 3 3 5 SP D3 SD: 1.1611 c. M:-2.0215 c. 75: 8 5 5 8 5 5 8 5 8 5 5 8 SP D3 SD: 0.2374 c. M:-0.4133 c. 196: 21 13 13 21 13 13 21 13 21 13 13 21 SP D3 SD: 0.0908 c. M: 0.1581 c. 271: 29 18 18 29 18 18 29 18 29 18 18 29 SP D3 SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 1.0520 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.2993 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.4583 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.7521 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.9033 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 7.9259 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.3050 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 11.0823 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.2305 cents 11:12 x 13:14 x 15 x 17:19 x 20:22 SD: 9.1843 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 5.8445 cents 13:14:15 x x 17:18 x 20:22:23:24:26 SD: 7.2674 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.8267 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.8506 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.1101 cents 21:23:24:25:27:28:29:32:33:36:37:39:42 SD: 4.8729 cents 22:24:25:26:28:29:31:33:35:37:39:41:44 SD: 3.6358 cents 23:25:26:27:29:31:32:35:36:39:41:43:46 SD: 3.5874 cents 26:28:29:31:33:35:36:39:41:44:46:48:52 SD: 3.0077 cents 30:32:34:35:38:40:42:45:47:51:53:56:60 SD: 2.7696 cents 36:39:41:43:46:48:50:54:57:61:64:67:72 SD: 2.7382 cents 37:40:42:44:47:49:52:56:58:63:66:69:74 SD: 2.6990 cents 38:41:43:45:48:51:53:57:60:64:67:71:76 SD: 2.2821 cents 39:42:44:46:50:52:54:59:61:66:69:72:78 SD: 2.2397 cents 40:43:45:47:51:53:56:60:63:68:71:74:80 SD: 1.5450 cents 54:58:61:64:69:72:75:81:85:91:96:100:108 SD: 1.4730 cents 56:60:63:66:71:75:78:84:88:95:99:104:112 SD: 1.4012 cents 63:68:71:74:80:84:88:95:99:107:112:117:126 SD: 1.2166 cents 66:71:74:78:84:88:92:99:104:112:117:123:132 SD: 1.1172 cents 78:84:88:92:99:104:109:117:123:132:138:145:156 SD: 0.7657 cents 115:124:130:136:146:153:160:173:181:195:204:214:230 SD: 0.7584 cents 117:126:132:138:149:156:163:176:184:198:207:217:234 SD: 0.5819 cents 132:142:149:156:168:176:184:198:208:224:234:245:264 SD: 0.5544 cents 133:143:150:157:169:177:185:200:209:225:236:247:266 SD: 0.5441 cents 154:166:174:182:196:205:215:231:242:261:273:286:308 SD: 0.4492 cents 180:194:203:213:229:240:251:270:283:305:319:334:360 SD: 0.4402 cents 187:201:211:221:238:249:261:281:294:317:332:347:374 SD: 0.4370 cents 195:210:220:230:248:260:272:293:307:330:346:362:390 SD: 0.3426 cents 243:262:274:287:309:324:339:365:382:412:431:451:486 SD: 0.3092 cents 259:279:292:306:329:345:361:389:407:439:459:481:518 SD: 0.2792 cents 283:305:319:334:360:377:395:425:445:479:502:526:566 SD: 0.2616 cents 287:309:324:339:365:382:400:431:451:486:509:533:574 SD: 0.2234 cents 299:322:337:353:380:398:417:449:470:506:530:555:598 SD: 0.2232 cents 337:363:380:398:429:449:470:506:530:571:598:626:674 SD: 0.1954 cents 353:380:398:417:449:470:492:530:555:598:626:656:706 SD: 0.1711 cents 398:429:449:470:506:530:555:598:626:674:706:739:796 SD: 0.1621 cents 431:464:486:509:548:574:601:647:678:730:764:800:862 SD: 0.1438 cents 548:590:618:647:697:730:764:823:862:928:972:1018:1096 SD: 0.1033 cents