Scala analysis: xen15-oconnell-golden-section-14
14-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: 133.294 cents 133.294447 3: 166.618 cents 166.618059 4: 233.265 cents 233.265283 5: 299.913 cents 299.912507 6: 366.560 cents 366.559730 7: 433.207 cents 433.206954 8: 466.531 cents 466.530566 9: 533.178 cents 533.177790 10: 599.825 cents 599.825013 11: 666.472 cents 666.472237 12: 733.119 cents 733.119461 13: 766.443 cents 766.443073 14: 833.090 cents 833.090296
SHOW/INTERVAL
0: 66.6472 cents 66.6472 1: 66.6472 cents 66.6472 2: 66.6472 cents 66.6472 3: 33.3236 cents 33.3236 4: 66.6472 cents 66.6472 5: 66.6472 cents 66.6472 6: 66.6472 cents 66.6472 7: 66.6472 cents 66.6472 8: 33.3236 cents 33.3236 9: 66.6472 cents 66.6472 10: 66.6472 cents 66.6472 11: 66.6472 cents 66.6472 12: 66.6472 cents 66.6472 13: 33.3236 cents 33.3236 14: 66.6472 cents 66.6472
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 33.32361 cents 1: 11 66.64722 cents 2: 6 99.97083 cents 2: 8 133.29445 cents 3: 9 166.61806 cents 3: 5 199.94167 cents 4: 12 233.26528 cents 4: 2 266.58889 cents 5: 1 266.58889 cents 5: 13 299.91251 cents 6: 4 333.23612 cents 6: 10 366.55973 cents 7: 7 399.88334 cents 7: 7 433.20695 cents 8: 10 466.53057 cents 8: 4 499.85418 cents 9: 13 533.17779 cents 9: 1 566.50140 cents 10: 2 566.50140 cents 10: 12 599.82501 cents 11: 5 633.14863 cents 11: 9 666.47224 cents 12: 8 699.79585 cents 12: 6 733.11946 cents 13: 11 766.44307 cents 13: 3 799.76668 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 12 13 14 0.0 : 66.6 133.3 166.6 233.3 299.9 366.6 433.2 466.5 533.2 599.8 666.5 733.1 766.4 833.1 66.6 : 66.6 100.0 166.6 233.3 299.9 366.6 399.9 466.5 533.2 599.8 666.5 699.8 766.4 833.1 133.3: 33.3 100.0 166.6 233.3 299.9 333.2 399.9 466.5 533.2 599.8 633.1 699.8 766.4 833.1 166.6: 66.6 133.3 199.9 266.6 299.9 366.6 433.2 499.9 566.5 599.8 666.5 733.1 799.8 833.1 233.3: 66.6 133.3 199.9 233.3 299.9 366.6 433.2 499.9 533.2 599.8 666.5 733.1 766.4 833.1 299.9: 66.6 133.3 166.6 233.3 299.9 366.6 433.2 466.5 533.2 599.8 666.5 699.8 766.4 833.1 366.6: 66.6 100.0 166.6 233.3 299.9 366.6 399.9 466.5 533.2 599.8 633.1 699.8 766.4 833.1 433.2: 33.3 100.0 166.6 233.3 299.9 333.2 399.9 466.5 533.2 566.5 633.1 699.8 766.4 833.1 466.5: 66.6 133.3 199.9 266.6 299.9 366.6 433.2 499.9 533.2 599.8 666.5 733.1 799.8 833.1 533.2: 66.6 133.3 199.9 233.3 299.9 366.6 433.2 466.5 533.2 599.8 666.5 733.1 766.4 833.1 599.8: 66.6 133.3 166.6 233.3 299.9 366.6 399.9 466.5 533.2 599.8 666.5 699.8 766.4 833.1 666.5: 66.6 100.0 166.6 233.3 299.9 333.2 399.9 466.5 533.2 599.8 633.1 699.8 766.4 833.1 733.1: 33.3 100.0 166.6 233.3 266.6 333.2 399.9 466.5 533.2 566.5 633.1 699.8 766.4 833.1 766.4: 66.6 133.3 199.9 233.3 299.9 366.6 433.2 499.9 533.2 599.8 666.5 733.1 799.8 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3236 .. 66.6472 cents 33.32361 cents 33.32361 cents 2: 99.9708 .. 133.2944 cents 33.32361 cents 33.32361 cents 3: 166.6181 .. 199.9417 cents 33.32361 cents 33.32361 cents 4: 233.2653 .. 266.5889 cents 33.32361 cents 33.32361 cents 5: 266.5889 .. 299.9125 cents 33.32361 cents -0.00000 cents 6: 333.2361 .. 366.5597 cents 33.32361 cents 33.32361 cents 7: 399.8833 .. 433.2070 cents 33.32361 cents 33.32361 cents 8: 466.5306 .. 499.8542 cents 33.32361 cents 33.32361 cents 9: 533.1778 .. 566.5014 cents 33.32361 cents 33.32361 cents 10: 566.5014 .. 599.8250 cents 33.32361 cents -0.00000 cents 11: 633.1486 .. 666.4722 cents 33.32361 cents 33.32361 cents 12: 699.7958 .. 733.1195 cents 33.32361 cents 33.32361 cents 13: 766.4431 .. 799.7667 cents 33.32361 cents 33.32361 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 33.32361 cents, class 1 Average step (divided formal octave): 59.5064 cents Largest one step interval : 66.64722 cents Average / Smallest step : 1.785714 Largest / Average step : 1.120000 Largest / Smallest step : 2.000000 Median interval of one step : 66.64722 cents, amount: 11 Most common interval of one step : 66.64722 cents, amount: 11 Least squares average step : 59.88401 cents, oct.: 838.37611 cents Scale is proper Scale has Myhill's property chromas: 33.32361 cents and 1/1, 0.0000 cents generators: 5 of 299.91251 cents and 9 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 4 5 7 9 11 13 14 16 18 20 22 23 25 generators: 9 and 16 Number of contiguous 1-step segments: 3 Step pattern alph. order: AABAAAABAAAABA Step pattern size order : LLSLLLLSLLLLSL Interval vector is [ 3 11 6 8 9 5 12 3 13 4 10 7 ] Scale is not a Constant Structure Scale diversity : 0.839753 Rothenberg stability : 0.967033 = 88/91 Lumma stability : 0.480000 Number of different interval sizes : 24 = 1.84615 / 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: 13 Scale is a chain of 7 triads 0.0 133.294 533.178 cents Most common triad is 0.0 299.913 533.178 cents, amount: 12 Number of recognisable fifths : 8, average 699.7958 cents Number of recognisable fourths : 4, average 499.8542 cents Formal octave complements present : 11 = 78.5714% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 7-8 -- Rational properties --
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.2379 c. M: 19.0421 c. 23: 2 2 1 1 2 2 2 1 2 2 1 2 1 2 P D3 SD: 10.1789 c. M:-15.9374 c. 24: 2 2 1 2 2 2 1 1 2 2 2 2 1 2 P D3 SD: 10.0194 c. M: 16.6618 c. 25: 2 2 1 2 2 2 2 1 2 2 2 2 1 2 P M ME SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x 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 x x x 3 x x S SD: 31.1645 cents 3 x x x x x x x 4 x x x x x 5 S SD: 30.0899 cents 4 x x x x x 5 x x x x x 6 x x S SD: 18.4489 cents 5 x x x x 6 x x x x 7 x x x 8 S SD: 10.1305 cents 6 x x x x 7 x x 8 x x x 9 x 10 S SD: 18.8490 cents 7 x x x 8 x x 9 x x 10 x x 11 x S SD: 6.0075 cents 8 x x x 9 x 10 x x 11 x x 12 x 13 S SD: 10.2128 cents 9 x x 10 x x 11 x 12 x x 13 x 14:15 S SD: 11.9388 cents 10 x x 11 x 12 x x 13 x 14 x 15 x 16 S SD: 7.5446 cents 11 x x 12 x 13 x 14 x 15 x 16 x 17:18 S SD: 5.5170 cents 12 x 13 x x 14:15 x 16 x 17 x 18:19 x S SD: 9.4025 cents 13 x 14 x 15 x 16 x 17:18 x 19:20 x 21 S SD: 4.7762 cents 14 x 15 x 16 x 17:18 x 19:20 x 21:22:23 S SD: 6.4611 cents 15 x 16 x 17:18 x 19:20 x 21:22:23 x 24 S SD: 6.3731 cents 16 x 17 x 18:19:20 x 21:22:23 x 24:25:26 S SD: 6.5438 cents 17:18 x 19 x 20:21:22 x 23:24:25:26 x 28 S SD: 5.7398 cents 18:19 x 20 x 21:22:23:24 x 25:26:27:28:29 S SD: 7.2689 cents 19:20 x 21:22:23 x 24:25:26:27:28:29:30:31 S SD: 5.1391 cents 20:21 x 22:23:24:25 x 26:27:28:29 x 31:32 SD: 4.6757 cents 21:22 x 23:24:25:26:27 x 29:30:31:32:33:34 SD: 3.3342 cents 22:23 x 24:25:26:27:28:29:30:31:32 x 34:36 S SD: 3.7821 cents 23:24:25 x 26:27:28 x 30:31:33:34:35:36:37 SD: 4.6114 cents 24:25:26 x 27:29:30:31 x 33:34:35:37 x 39 SD: 4.9768 cents 25:26:27:28:29:30:31:32:33:34:35:37:38:39:40 SD: 3.8191 cents 26:27:28:29:30:31:32:33:34:35:37:38:40 x 42 SD: 3.4037 cents 27:28:29:30:31:32:33:35 x 37:38:40:41:42:44 SD: 3.1855 cents 30:31:32:33:34:36:37 x 39:41:42:44:46:47:49 SD: 3.4830 cents 32:33 x 35:37:38:40:41:42:44:45:47:49:50:52 SD: 3.0817 cents 33:34 x 36:38:39:41:42:43:45:47:48:50:51:53 SD: 3.5402 cents 34:35:37 x 39:40:42:44:45:46:48:50:52:53:55 SD: 2.9260 cents 36:37:39:40:41:43:44:46:47:49:51:53:55:56:58 SD: 2.5937 cents 37:38:40:41:42:44:46 x 48:50:52:54:57:58:60 S SD: 3.3300 cents 38:39:41:42:43:45:47:49:50:52:54:56:58:59:61 SD: 2.7376 cents 39:41:42:43:45:46:48:50:51:53:55:57:60:61:63 SD: 2.5248 cents 41:43:44:45:47:49:51:53:54:56:58:60:63:64:66 SD: 2.4256 cents 42:44:45:46:48:50:52:54:55:57:59:62:64:65:68 SD: 2.0524 cents 44:46 x 48:50:52:54:57:58:60:62:65:67:69:71 SD: 2.9410 cents 45:47:49:50:51:54:56:58:59:61:64:66:69:70:73 SD: 2.7269 cents 46:48:50:51:53:55:57:59:60:63:65:68:70:72:74 SD: 2.3422 cents 47:49:51:52:54:56:58:60:62:64:66:69:72:73:76 SD: 1.9024 cents 48:50:52:53:55:57:59:62:63:65:68:71:73:75:78 SD: 1.8003 cents 49:51:53:54:56:58:61:63:64:67:69:72:75:76:79 SD: 1.5755 cents 63:65:68:69:72:75:78:81:82:86:89:93:96:98:102 SD: 1.5668 cents 68:71:73:75:78:81:84:87:89:93:96:100:104:106:110 SD: 1.3444 cents 70:73:76:77:80:83:87:90:92:95:99:103:107:109:113 SD: 1.3127 cents 74:77:80:81:85:88:91:95:97:101:105:109:113:115:120 SD: 1.3112 cents 75:78:81:83:86:89:93:96:98:102:106:110:115:117:121 SD: 1.2043 cents 77:80:83:85:88:92:95:99:101:105:109:113:118:120:125 SD: 1.0585 cents 97:101:105:107:111:115:120:125:127:132:137:143:148:151:157 SD: 0.8420 cents 102:106:110:112:117:121:126:131:134:139:144:150:156:159:165 SD: 0.8031 cents 110:114:119:121:126:131:136:141:144:150:156:162:168:171:178 SD: 0.7702 cents 123:128:133:135:141:146:152:158:161:167:174:181:188:192:199 SD: 0.7202 cents 126:131:136:139:144:150:156:162:165:171:178:185:192:196:204 SD: 0.6352 cents 147:153:159:162:168:175:182:189:192:200:208:216:225:229:238 SD: 0.6109 cents 149:155:161:164:170:177:184:191:195:203:211:219:228:232:241 SD: 0.5886 cents 152:158:164:167:174:181:188:195:199:207:215:223:232:237:246 SD: 0.4920 cents 178:185:192:196:204:212:220:229:233:242:252:262:272:277:288 SD: 0.4751 cents 186:193:201:205:213:221:230:239:244:253:263:273:284:290:301 SD: 0.4497 cents 200:208:216:220:229:238:247:257:262:272:283:294:305:311:324 SD: 0.3772 cents 228:237:246:251:261:271:282:293:299:310:322:335:348:355:369 SD: 0.3449 cents 249:259:269:274:285:296:308:320:326:339:352:366:380:388:403 SD: 0.2593 cents 275:286:297:303:315:327:340:353:360:374:389:404:420:428:445 SD: 0.2237 cents 285:296:308:314:326:339:352:366:373:388:403:419:435:444:461 SD: 0.2217 cents 375:390:405:413:429:446:463:482:491:510:530:551:573:584:607 SD: 0.2200 cents 377:392:407:415:431:448:466:484:494:513:533:554:576:587:610 SD: 0.2068 cents 408:424:441:449:467:485:504:524:534:555:577:600:623:635:660 SD: 0.1822 cents 437:454:472:481:500:520:540:561:572:595:618:642:667:680:707 SD: 0.1814 cents 485:504:524:534:555:577:599:623:635:660:686:713:741:755:785 SD: 0.1377 cents 560:582:605:617:641:666:692:719:733:762:792:823:855:872:906 SD: 0.1253 cents