Scala analysis: ratwolf
Eleven fifths of (418/5)^(1/11) and one 20/13 wolf
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70.863 cents 70.863424 2: 191.675 cents 191.675263 3: 312.487 cents 312.487105 4: 383.351 cents 383.350528 5: 504.162 cents 504.162369 6: 575.026 cents 575.025791 7: 695.838 cents 695.837632 8: 766.701 cents 766.701055 9: 887.513 cents 887.512896 10: 1008.325 cents 1008.324736 11: 1079.188 cents 1079.188160 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 120.8118 cents 120.8118 1: 70.8634 cents 70.8634 2: 120.8118 cents 120.8118 3: 120.8118 cents 120.8118 4: 70.8634 cents 70.8634 5: 120.8118 cents 120.8118 6: 70.8634 cents 70.8634 7: 120.8118 cents 120.8118 8: 70.8634 cents 70.8634 9: 120.8118 cents 120.8118 10: 120.8118 cents 120.8118 11: 70.8634 cents 70.8634 12: 120.8118 cents 120.8118
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 70.86342 cents 1: 7 120.81184 cents 2: 10 191.67526 cents 2: 2 241.62368 cents 3: 3 262.53869 cents 3: 9 312.48710 cents 4: 8 383.35053 cents 4: 4 433.29894 cents 5: 1 454.21395 cents 5: 11 504.16237 cents 6: 6 575.02579 cents 6: 6 624.97421 cents 7: 11 695.83763 cents 7: 1 745.78605 cents 8: 4 766.70105 cents 8: 8 816.64947 cents 9: 9 887.51290 cents 9: 3 937.46131 cents 10: 2 958.37632 cents 10: 10 1008.32474 cents 11: 7 1079.18816 cents 11: 5 1129.13658 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 0.0 : 70.9 191.7 312.5 383.4 504.2 575.0 695.8 766.7 887.5 1008.3 1079.2 1200.0 70.9 : 120.8 241.6 312.5 433.3 504.2 625.0 695.8 816.6 937.5 1008.3 1129.1 1200.0 191.7 : 120.8 191.7 312.5 383.4 504.2 575.0 695.8 816.6 887.5 1008.3 1079.2 1200.0 312.5 : 70.9 191.7 262.5 383.4 454.2 575.0 695.8 766.7 887.5 958.4 1079.2 1200.0 383.4 : 120.8 191.7 312.5 383.4 504.2 625.0 695.8 816.6 887.5 1008.3 1129.1 1200.0 504.2 : 70.9 191.7 262.5 383.4 504.2 575.0 695.8 766.7 887.5 1008.3 1079.2 1200.0 575.0 : 120.8 191.7 312.5 433.3 504.2 625.0 695.8 816.6 937.5 1008.3 1129.1 1200.0 695.8 : 70.9 191.7 312.5 383.4 504.2 575.0 695.8 816.6 887.5 1008.3 1079.2 1200.0 766.7 : 120.8 241.6 312.5 433.3 504.2 625.0 745.8 816.6 937.5 1008.3 1129.1 1200.0 887.5 : 120.8 191.7 312.5 383.4 504.2 625.0 695.8 816.6 887.5 1008.3 1079.2 1200.0 1008.3: 70.9 191.7 262.5 383.4 504.2 575.0 695.8 766.7 887.5 958.4 1079.2 1200.0 1079.2: 120.8 191.7 312.5 433.3 504.2 625.0 695.8 816.6 887.5 1008.3 1129.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.8634 .. 120.8118 cents 49.94841 cents 70.86342 cents 2: 191.6753 .. 241.6237 cents 49.94842 cents 70.86342 cents 3: 262.5387 .. 312.4871 cents 49.94842 cents 20.91501 cents 4: 383.3505 .. 433.2989 cents 49.94842 cents 70.86342 cents 5: 454.2140 .. 504.1624 cents 49.94842 cents 20.91501 cents 6: 575.0258 .. 624.9742 cents 49.94842 cents 70.86342 cents 7: 695.8376 .. 745.7860 cents 49.94842 cents 70.86342 cents 8: 766.7011 .. 816.6495 cents 49.94842 cents 20.91501 cents 9: 887.5129 .. 937.4613 cents 49.94842 cents 70.86342 cents 10: 958.3763 .. 1008.3247 cents 49.94842 cents 20.91501 cents 11: 1079.1882 .. 1129.1366 cents 49.94842 cents 70.86342 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 70.86342 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 120.81184 cents Average / Smallest step : 1.411165 Largest / Average step : 1.208118 Largest / Smallest step : 1.704855 Median interval of one step : 120.81184 cents, amount: 7 Most common interval of one step : 120.81184 cents, amount: 7 Least squares average step : 98.83454 cents, oct.: 1186.01444 cents Scale is strictly proper Scale has Myhill's property chromas: 49.94841 cents and 20.91501 cents, ratio: 2.388161 generators: 5 of 504.16237 cents and 7 of 695.83763 cents ET pair of linear temperament : 12&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1033-tone equal temperament with octave 1200.000 cents degrees: 61 165 269 330 434 495 599 660 764 868 929 1033 generators: 434 and 599 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : SLLSLSLSLLSL Scale is a Constant Structure, by a margin of 20.91501 cents Ratio Whole / Half tone : 1.586560 Scale diversity : 1.220569 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.542140 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 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 : 20.91501 cents Most common intervals : 504.16237 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 120.812 695.838 cents Most common triad is 0.0 504.162 695.838 cents, amount: 10 Number of recognisable fifths : 11, average 695.8376 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.7410 c. M:-33.2989 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 4.6918 c. M: 8.8063 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 3.9918 c. M:-7.4925 c. Meantone Chromatic (53/220-comma) 50: 3 5 5 3 5 3 5 3 5 5 3 5 SP M DE SD: 0.6921 c. M:-1.2989 c. Meantone Chromatic (5/18-comma), Eair-12 119: 7 12 12 7 12 7 12 7 12 12 7 12 SP M DE SD: 0.1676 c. M: 0.3145 c. Meantone Chromatic (2/7-comma), Zarlino 169: 10 17 17 10 17 10 17 10 17 17 10 17 SP M DE SD: 0.0868 c. M:-0.1629 c. 288: 17 29 29 17 29 17 29 17 29 29 17 29 SP M DE SD: 0.0183 c. M: 0.0344 c. 745: 44 75 75 44 75 44 75 44 75 75 44 75 SP M DE SD: 0.0055 c. M:-0.0104 c. 1033: 61 104 104 61 104 61 104 61 104 104 61 104 SP M DE SD: 0.0011 c. M: 0.0021 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: 3.0587 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.2942 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.0199 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.7151 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2123 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.1132 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.4854 cents 9 x 10:11 x 12 x 13:14:15:16:17:18 S SD: 8.2330 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.7160 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2054 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.6528 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.9396 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 8.1486 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.8661 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.3779 cents 18:19:20:22 x 24:25:27:28:30:32:34:36 SD: 4.6156 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.7435 cents 24:25:27:29:30:32:33:36:37:40:43:45:48 SD: 3.1382 cents 32:33:36:38:40:43:45:48:50:53:57:60:64 SD: 3.1257 cents 33:34:37:40:41:44:46:49:51:55:59:62:66 SD: 3.1200 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.5379 cents 41:43:46:49:51:55:57:61:64:68:73:76:82 SD: 2.2080 cents 44:46:49:53:55:59:61:66:69:73:79:82:88 SD: 2.0516 cents 45:47:50:54:56:60:63:67:70:75:81:84:90 SD: 1.6203 cents 51:53:57:61:64:68:71:76:79:85:91:95:102 SD: 1.4955 cents 61:64:68:73:76:82:85:91:95:102:109:114:122 SD: 1.3904 cents 66:69:74:79:82:88:92:99:103:110:118:123:132 SD: 1.3020 cents 68:71:76:81:85:91:95:102:106:114:122:127:136 SD: 1.2911 cents 71:74:79:85:89:95:99:106:111:119:127:132:142 SD: 1.2877 cents 75:78:84:90:94:100:105:112:117:125:134:140:150 SD: 1.2564 cents 76:79:85:91:95:102:106:114:118:127:136:142:152 SD: 0.9544 cents 91:95:102:109:114:122:127:136:142:152:163:170:182 SD: 0.9527 cents 95:99:106:114:119:127:132:142:148:159:170:177:190 SD: 0.8875 cents 97:101:108:116:121:130:135:145:151:162:174:181:194 SD: 0.6914 cents 101:105:113:121:126:135:141:151:157:169:181:188:202 SD: 0.6906 cents 121:126:135:145:151:162:169:181:188:202:217:226:242 SD: 0.5832 cents 142:148:159:170:177:190:198:212:221:237:254:265:284 SD: 0.4640 cents 162:169:181:194:202:217:226:242:252:270:290:302:324 SD: 0.4420 cents 172:179:192:206:215:230:240:257:268:287:308:321:344 SD: 0.3885 cents 213:222:238:255:266:285:297:318:332:356:381:397:426 SD: 0.3511 cents 237:247:265:284:296:317:330:354:369:396:424:442:474 SD: 0.3213 cents 239:249:267:286:298:320:333:357:372:399:428:446:478 SD: 0.2567 cents 267:278:298:320:333:357:372:399:416:446:478:498:534 SD: 0.2512 cents 287:299:321:344:358:384:400:429:447:479:514:535:574 SD: 0.2422 cents 307:320:343:368:383:411:428:459:478:513:550:573:614 SD: 0.2403 cents 314:327:351:376:392:420:438:469:489:524:562:586:628 SD: 0.2377 cents 334:348:373:400:417:447:466:499:520:558:598:623:668 SD: 0.1941 cents 358:373:400:429:447:479:499:535:557:598:641:668:716 SD: 0.1857 cents 384:400:429:460:479:514:535:574:598:641:688:716:768 SD: 0.1627 cents 429:447:479:514:535:574:598:641:668:716:768:800:858 SD: 0.1496 cents 485:505:542:581:605:649:676:725:755:810:868:905:970 SD: 0.1489 cents 497:518:555:595:620:665:693:743:774:830:890:927:994 SD: 0.1365 cents 505:526:564:605:630:676:704:755:786:843:904:942:1010 SD: 0.1229 cents 556:579:621:666:694:744:775:831:866:928:995:1037:1112 SD: 0.1198 cents