Scala analysis: xen15-oconnell-golden-section-11
11-note scale in 25 parts of Golden Section
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.647 cents 66.647224 2: 166.618 cents 166.618059 3: 233.265 cents 233.265283 4: 299.913 cents 299.912507 5: 366.560 cents 366.559730 6: 466.531 cents 466.530566 7: 533.178 cents 533.177790 8: 599.825 cents 599.825013 9: 666.472 cents 666.472237 10: 766.443 cents 766.443073 11: 833.090 cents 833.090296
SHOW/INTERVAL
0: 66.6472 cents 66.6472 1: 66.6472 cents 66.6472 2: 99.9708 cents 99.9708 3: 66.6472 cents 66.6472 4: 66.6472 cents 66.6472 5: 66.6472 cents 66.6472 6: 99.9708 cents 99.9708 7: 66.6472 cents 66.6472 8: 66.6472 cents 66.6472 9: 66.6472 cents 66.6472 10: 99.9708 cents 99.9708 11: 66.6472 cents 66.6472
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 66.64722 cents 1: 3 99.97083 cents 2: 5 133.29445 cents 2: 6 166.61806 cents 3: 2 199.94167 cents 3: 9 233.26528 cents 4: 10 299.91251 cents 4: 1 333.23612 cents 5: 7 366.55973 cents 5: 4 399.88334 cents 6: 4 433.20695 cents 6: 7 466.53057 cents 7: 1 499.85418 cents 7: 10 533.17779 cents 8: 9 599.82501 cents 8: 2 633.14863 cents 9: 6 666.47224 cents 9: 5 699.79585 cents 10: 3 733.11946 cents 10: 8 766.44307 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 66.6 166.6 233.3 299.9 366.6 466.5 533.2 599.8 666.5 766.4 833.1 66.6 : 100.0 166.6 233.3 299.9 399.9 466.5 533.2 599.8 699.8 766.4 833.1 166.6: 66.6 133.3 199.9 299.9 366.6 433.2 499.9 599.8 666.5 733.1 833.1 233.3: 66.6 133.3 233.3 299.9 366.6 433.2 533.2 599.8 666.5 766.4 833.1 299.9: 66.6 166.6 233.3 299.9 366.6 466.5 533.2 599.8 699.8 766.4 833.1 366.6: 100.0 166.6 233.3 299.9 399.9 466.5 533.2 633.1 699.8 766.4 833.1 466.5: 66.6 133.3 199.9 299.9 366.6 433.2 533.2 599.8 666.5 733.1 833.1 533.2: 66.6 133.3 233.3 299.9 366.6 466.5 533.2 599.8 666.5 766.4 833.1 599.8: 66.6 166.6 233.3 299.9 399.9 466.5 533.2 599.8 699.8 766.4 833.1 666.5: 100.0 166.6 233.3 333.2 399.9 466.5 533.2 633.1 699.8 766.4 833.1 766.4: 66.6 133.3 233.3 299.9 366.6 433.2 533.2 599.8 666.5 733.1 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6472 .. 99.9708 cents 33.32361 cents 66.64722 cents 2: 133.2944 .. 166.6181 cents 33.32361 cents 33.32361 cents 3: 199.9417 .. 233.2653 cents 33.32361 cents 33.32361 cents 4: 299.9125 .. 333.2361 cents 33.32361 cents 66.64722 cents 5: 366.5597 .. 399.8833 cents 33.32361 cents 33.32361 cents 6: 433.2070 .. 466.5306 cents 33.32361 cents 33.32361 cents 7: 499.8542 .. 533.1778 cents 33.32361 cents 33.32361 cents 8: 599.8250 .. 633.1486 cents 33.32361 cents 66.64722 cents 9: 666.4722 .. 699.7958 cents 33.32361 cents 33.32361 cents 10: 733.1195 .. 766.4431 cents 33.32361 cents 33.32361 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 66.64722 cents, class 1 Average step (divided formal octave): 75.7355 cents Largest one step interval : 99.97083 cents Average / Smallest step : 1.136364 Largest / Average step : 1.320000 Largest / Smallest step : 1.500000 Median interval of one step : 66.64722 cents, amount: 8 Most common interval of one step : 66.64722 cents, amount: 8 Least squares average step : 75.66962 cents, oct.: 832.36587 cents Scale is strictly proper Scale has Myhill's property chromas: 33.32361 cents and 33.32361 cents, ratio: 1.000000 generators: 4 of 299.91251 cents and 7 of 533.17779 cents Scale is maximally even in 25-tone equal temperament ET pair of linear temperament : 11&25 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 25-tone equal temperament with octave 833.090 cents degrees: 2 5 7 9 11 14 16 18 20 23 25 generators: 9 and 16 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAAABA Step pattern size order : SLSSSLSSSLS Interval vector is [ 0 8 3 5 6 2 9 0 10 1 7 4 ] Scale is a Constant Structure, by a margin of 33.32361 cents Scale diversity : 0.971381 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.600000 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 33.32361 cents Most common intervals : 299.91251 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 299.913 599.825 cents Most common triad is 0.0 299.913 533.178 cents, amount: 9 Number of recognisable fifths : 5, average 699.7958 cents Number of recognisable fourths : 1, average 499.8542 cents Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 11 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.5799 c. M: 15.1471 c. 14: 1 2 1 1 1 2 1 1 1 2 1 P M ME I SD: 7.5270 c. M: 11.9013 c. 25: 2 3 2 2 2 3 2 2 2 3 2 SP M ME I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 366.9097 cents 2 x x x x x x x x 3 x x S SD: 35.4828 cents 3 x x x x x 4 x x x x 5 S SD: 30.0899 cents 4 x x x x 5 x x x 6 x x S SD: 20.3055 cents 5 x x x 6 x x x 7 x x 8 S SD: 10.1305 cents 6 x x x 7 x 8 x x 9 x 10 S SD: 19.3203 cents 7 x x 8 x x 9 x 10 x 11 x S SD: 9.8831 cents 8 x x 9 x 10 x 11 x 12 x 13 S SD: 10.7617 cents 9 x 10 x x 11:12 x x 13:14:15 S SD: 11.9388 cents 10 x 11 x 12 x 13 x 14:15 x 16 S SD: 8.0570 cents 11 x 12 x 13 x 14:15 x 16:17:18 S SD: 8.6286 cents 12 x 13 x 14:15:16 x 17:18:19 x S SD: 10.4769 cents 13 x 14:15 x 16:17:18 x 19:20:21 S SD: 7.0375 cents 14 x 15:16 x 17:18:19:20:21:22:23 S SD: 9.0869 cents 15:16 x 17:18:19:20 x 21:22:23:24 S SD: 9.1333 cents 16:17 x 18:19:20:21:22:23:24:25:26 S SD: 7.2349 cents 17:18:19 x 20:21:22:23:24:25:26:28 S SD: 6.6897 cents 18:19:20 x 21:22:24 x 25:26:28:29 S SD: 8.1225 cents 19:20:21:22:23 x 25:26:27:28:30:31 SD: 5.4539 cents 20:21:22:23:24:25:26:27:28:29:31:32 SD: 4.6757 cents 21:22:23:24:25:26:27:29:30:31:33:34 SD: 4.6095 cents 22:23:24:25:26:27:29:30:31:32:34:36 SD: 3.8712 cents 26:27:29:30:31:32:34:35:37:38:40:42 SD: 3.8360 cents 27:28:30:31:32:33:35:37:38:40:42:44 SD: 3.5955 cents 29:30:32:33:34:36:38:39:41:43:45:47 SD: 3.5509 cents 34:35:37:39:40:42:45:46:48:50:53:55 SD: 3.5274 cents 36:37:40:41:43:44:47:49:51:53:56:58 SD: 3.1650 cents 39:41:43:45:46:48:51:53:55:57:61:63 SD: 2.9523 cents 41:43:45:47:49:51:54:56:58:60:64:66 SD: 2.5611 cents 42:44:46:48:50:52:55:57:59:62:65:68 SD: 2.2545 cents 47:49:52:54:56:58:62:64:66:69:73:76 SD: 2.0462 cents 48:50:53:55:57:59:63:65:68:71:75:78 SD: 1.9431 cents 55:57:61:63:65:68:72:75:78:81:86:89 SD: 1.8410 cents 58:60:64:66:69:72:76:79:82:85:90:94 SD: 1.5748 cents 68:71:75:78:81:84:89:93:96:100:106:110 SD: 1.2689 cents 77:80:85:88:92:95:101:105:109:113:120:125 SD: 1.1841 cents 81:84:89:93:96:100:106:110:115:119:126:131 SD: 1.1537 cents 97:101:107:111:115:120:127:132:137:143:151:157 SD: 0.8471 cents 111:115:122:127:132:137:145:151:157:163:173:180 SD: 0.8048 cents 126:131:139:144:150:156:165:171:178:185:196:204 SD: 0.6994 cents 147:153:162:168:175:182:192:200:208:216:229:238 SD: 0.6335 cents 149:155:164:170:177:184:195:203:211:219:232:241 SD: 0.6113 cents 152:158:167:174:181:188:199:207:215:223:237:246 SD: 0.5720 cents 158:164:174:181:188:195:207:215:223:232:246:256 SD: 0.5364 cents 178:185:196:204:212:220:233:242:252:262:277:288 SD: 0.4951 cents 181:188:199:207:215:224:237:246:256:266:282:293 SD: 0.4420 cents 200:208:220:229:238:247:262:272:283:294:311:324 SD: 0.4122 cents 207:215:228:237:246:256:271:282:293:304:322:335 SD: 0.3675 cents 249:259:274:285:296:308:326:339:352:366:388:403 SD: 0.2885 cents 275:286:303:315:327:340:360:374:389:404:428:445 SD: 0.2720 cents 285:296:314:326:339:352:373:388:403:419:444:461 SD: 0.2467 cents 355:369:391:406:422:439:465:483:502:522:553:574 SD: 0.2363 cents 386:401:425:442:459:477:505:525:546:567:601:625 SD: 0.2343 cents 407:423:448:466:484:503:533:554:576:598:634:659 SD: 0.2304 cents 408:424:449:467:485:504:534:555:577:600:635:660 SD: 0.1941 cents 458:476:504:524:545:566:600:623:648:673:713:741 SD: 0.1941 cents 466:484:513:533:554:576:610:634:659:685:726:754 SD: 0.1721 cents 485:504:534:555:577:599:635:660:686:713:755:785 SD: 0.1527 cents 513:533:565:587:610:634:672:698:725:754:799:830 SD: 0.1503 cents 534:555:588:611:635:660:699:727:755:785:831:864 SD: 0.1356 cents 582:605:641:666:692:719:762:792:823:855:906:942 SD: 0.1178 cents