Scala analysis: 12throotofphi
12th root pf phi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69.421 cents 69.421160 2: 138.842 cents 138.842320 3: 208.263 cents 208.263480 4: 277.685 cents 277.684640 5: 347.106 cents 347.105800 6: 416.527 cents 416.526960 7: 485.948 cents 485.948130 8: 555.369 cents 555.369290 9: 624.790 cents 624.790450 10: 694.212 cents 694.211610 11: 763.633 cents 763.632770
SHOW/INTERVAL
0: 69.4212 cents 69.4212 1: 69.4212 cents 69.4212 2: 69.4212 cents 69.4212 3: 69.4212 cents 69.4212 4: 69.4212 cents 69.4212 5: 69.4212 cents 69.4212 6: 69.4212 cents 69.4212 7: 69.4212 cents 69.4212 8: 69.4212 cents 69.4212 9: 69.4212 cents 69.4212 10: 69.4212 cents 69.4212 11: 69.4212 cents 69.4212
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 69.42116 cents 2: 11 138.84232 cents 3: 11 208.26348 cents 4: 11 277.68464 cents 5: 11 347.10580 cents 6: 11 416.52696 cents 7: 11 485.94813 cents 8: 11 555.36929 cents 9: 11 624.79045 cents 10: 11 694.21161 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 69.4 : 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 138.8: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 208.3: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 277.7: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 347.1: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 416.5: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 485.9: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 555.4: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 624.8: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 694.2: 69.4 138.8 208.3 277.7 347.1 416.5 485.9 555.4 624.8 694.2 763.6 763.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.4212 .. 69.4212 cents 1/1, 0.0000 cents 69.42116 cents 2: 138.8423 .. 138.8423 cents 1/1, 0.0000 cents 69.42116 cents 3: 208.2635 .. 208.2635 cents 1/1, 0.0000 cents 69.42116 cents 4: 277.6846 .. 277.6846 cents 1/1, 0.0000 cents 69.42116 cents 5: 347.1058 .. 347.1058 cents 1/1, 0.0000 cents 69.42116 cents 6: 416.5270 .. 416.5270 cents 1/1, 0.0000 cents 69.42116 cents 7: 485.9481 .. 485.9481 cents 1/1, 0.0000 cents 69.42117 cents 8: 555.3693 .. 555.3693 cents 1/1, 0.0000 cents 69.42116 cents 9: 624.7905 .. 624.7905 cents 1/1, 0.0000 cents 69.42116 cents 10: 694.2116 .. 694.2116 cents 1/1, 0.0000 cents 69.42116 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 69.42116 cents, class 1 Average step (divided formal octave): 69.4212 cents Largest one step interval : 69.42116 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 69.42116 cents, amount: 11 Most common interval of one step : 69.42116 cents, amount: 11 Least squares average step : 69.42116 cents, oct.: 763.63277 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 69.42116 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.090909 redundancy: 0.909091 Efficiency x scale size : 1.000000 Number of different interval sizes : 10 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 11, average 694.2116 cents Number of recognisable fourths : 11, average 485.9481 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B 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: 436.3672 cents 2 x x x x x x x x x 3 x S SD: 7.7434 cents 3 x x x x x x 4 x x x 5 S SD: 60.6652 cents 4 x x x x x 5 x x x 6 x S SD: 15.5949 cents 5 x x x x 6 x x 7 x x 8 S SD: 21.6849 cents 6 x x x 7 x x 8 x x 9 x S SD: 5.9929 cents 7 x x 8 x x 9 x x 10 x 11 S SD: 8.9382 cents 8 x x 9 x x 10 x 11 x 12 x S SD: 7.9379 cents 9 x x 10 x 11 x 12 x 13 x 14 S SD: 6.1861 cents 10 x 11 x x 12 x 13:14 x 15:16 S SD: 12.8923 cents 11 x 12 x 13 x 14 x 15:16 x 17 S SD: 5.9695 cents 12 x 13 x 14 x 15:16 x 17:18:19 S SD: 7.4644 cents 13 x 14 x 15:16 x 17:18:19 x 20 S SD: 7.8806 cents 14 x 15:16 x 17:18 x 19:20:21:22 S SD: 6.3085 cents 15 x 16:17 x 18:19:20:21 x 22:23 S SD: 8.1599 cents 16 x 17:18:19 x 20:21:22:23:24:25 S SD: 5.9553 cents 17:18 x 19:20:21:22 x 23:24:25:26 S SD: 8.3624 cents 18:19 x 20:21:22:23:24:25:26:27:28 S SD: 4.4249 cents 19:20:21 x 22:23:24:25:26:27:28:30 S SD: 6.5912 cents 20:21:22:23 x 24:25:26:28:29:30:31 S SD: 7.8220 cents 21:22:23:24:25:26:27:28:29:30:31:33 SD: 5.3028 cents 22:23:24:25:26:27:28:29:30:32:33:34 S SD: 3.7309 cents 32:33:35:36:38:39:41:42:44:46:48:50 SD: 3.5402 cents 34:35:37:38:40:42:43:45:47:49:51:53 SD: 3.2914 cents 37:39:40:42:43:45:47:49:51:53:55:58 SD: 3.2454 cents 39:41:42:44:46:48:50:52:54:56:58:61 SD: 3.1355 cents 40:42:43:45:47:49:51:53:55:57:60:62 SD: 2.4147 cents 45:47:49:51:53:55:57:60:62:65:67:70 SD: 2.1855 cents 47:49:51:53:55:57:60:62:65:67:70:73 SD: 1.9854 cents 58:60:63:65:68:71:74:77:80:83:87:90 SD: 1.8348 cents 63:66:68:71:74:77:80:83:87:90:94:98 SD: 1.6317 cents 69:72:75:78:81:84:88:91:95:99:103:107 SD: 1.2701 cents 71:74:77:80:83:87:90:94:98:102:106:110 SD: 1.1769 cents 92:96:100:104:108:112:117:122:127:132:137:143 SD: 1.0980 cents 95:99:103:107:112:116:121:126:131:136:142:148 SD: 0.9622 cents 99:103:107:112:116:121:126:131:136:142:148:154 SD: 0.9012 cents 103:107:112:116:121:126:131:136:142:148:154:160 SD: 0.8988 cents 108:112:117:122:127:132:137:143:149:155:161:168 SD: 0.8835 cents 117:122:127:132:137:143:149:155:161:168:175:182 SD: 0.7266 cents 132:137:143:149:155:161:168:175:182:189:197:205 SD: 0.7035 cents 143:149:155:161:168:175:182:189:197:205:214:222 SD: 0.6526 cents 148:154:160:167:174:181:188:196:204:212:221:230 SD: 0.5533 cents 166:173:180:187:195:203:211:220:229:238:248:258 SD: 0.4229 cents 195:203:211:220:229:238:248:258:269:280:291:303 SD: 0.3954 cents 217:226:235:245:255:265:276:287:299:311:324:337 SD: 0.3919 cents 225:234:244:254:264:275:286:298:310:323:336:350 SD: 0.3304 cents 265:276:287:299:311:324:337:351:365:380:396:412 SD: 0.2430 cents 346:360:375:390:406:423:440:458:477:496:517:538 SD: 0.2394 cents 361:376:391:407:424:441:459:478:498:518:539:561 SD: 0.2297 cents 368:383:399:415:432:450:468:487:507:528:550:572 SD: 0.2287 cents 391:407:424:441:459:478:497:518:539:561:584:608 SD: 0.2188 cents 420:437:455:474:493:513:534:556:579:603:627:653 SD: 0.2178 cents 442:460:479:499:519:540:562:585:609:634:660:687 SD: 0.1986 cents 444:462:481:501:521:543:565:588:612:637:663:690 SD: 0.1932 cents 460:479:498:519:540:562:585:609:634:660:687:715 SD: 0.1652 cents 518:539:561:584:608:633:659:686:714:743:774:805 SD: 0.1602 cents 540:562:585:609:634:660:687:715:744:775:806:839 SD: 0.1422 cents 563:586:610:635:661:688:716:745:776:808:841:875 SD: 0.1298 cents