Scala analysis: akjmagic
TOP tuned magic tempering of akj.scl
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.890 cents 58.889588 2: 204.127 cents 204.126953 3: 263.017 cents 263.016542 4: 439.685 cents 439.685307 5: 498.575 cents 498.574895 6: 643.812 cents 643.812260 7: 702.702 cents 702.701848 8: 761.591 cents 761.591437 9: 906.829 cents 906.828801 10: 997.150 cents 997.149791 11: 1142.387 cents 1142.387155 12: 1201.277 cents 1201.276744
SHOW/INTERVAL
0: 58.8896 cents 58.8896 1: 58.8896 cents 58.8896 2: 145.2374 cents 145.2374 3: 58.8896 cents 58.8896 4: 176.6688 cents 176.6688 5: 58.8896 cents 58.8896 6: 145.2374 cents 145.2374 7: 58.8896 cents 58.8896 8: 58.8896 cents 58.8896 9: 145.2374 cents 145.2374 10: 90.3210 cents 90.3210 11: 145.2374 cents 145.2374 12: 58.8896 cents 58.8896
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 58.88959 cents 1: 1 90.32099 cents 1: 4 145.23736 cents 1: 1 176.66876 cents 2: 2 117.77918 cents 2: 6 204.12695 cents 2: 4 235.55835 cents 3: 6 263.01654 cents 3: 3 294.44794 cents 3: 3 380.79572 cents 4: 2 321.90613 cents 4: 2 353.33753 cents 4: 2 408.25391 cents 4: 6 439.68531 cents 5: 2 467.14349 cents 5: 9 498.57490 cents 5: 1 584.92267 cents 6: 6 557.46448 cents 6: 6 643.81226 cents 7: 1 616.35407 cents 7: 9 702.70185 cents 7: 2 734.13325 cents 8: 6 761.59144 cents 8: 2 793.02284 cents 8: 2 847.93921 cents 8: 2 879.37061 cents 9: 3 820.48103 cents 9: 3 906.82880 cents 9: 6 938.26020 cents 10: 4 965.71839 cents 10: 6 997.14979 cents 10: 2 1083.49757 cents 11: 1 1024.60798 cents 11: 4 1056.03938 cents 11: 1 1110.95575 cents 11: 6 1142.38715 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 58.9 204.1 263.0 439.7 498.6 643.8 702.7 761.6 906.8 997.1 1142.4 1201.3 58.9 : 145.2 204.1 380.8 439.7 584.9 643.8 702.7 847.9 938.3 1083.5 1142.4 1201.3 204.1 : 58.9 235.6 294.4 439.7 498.6 557.5 702.7 793.0 938.3 997.1 1056.0 1201.3 263.0 : 176.7 235.6 380.8 439.7 498.6 643.8 734.1 879.4 938.3 997.1 1142.4 1201.3 439.7 : 58.9 204.1 263.0 321.9 467.1 557.5 702.7 761.6 820.5 965.7 1024.6 1201.3 498.6 : 145.2 204.1 263.0 408.3 498.6 643.8 702.7 761.6 906.8 965.7 1142.4 1201.3 643.8 : 58.9 117.8 263.0 353.3 498.6 557.5 616.4 761.6 820.5 997.1 1056.0 1201.3 702.7 : 58.9 204.1 294.4 439.7 498.6 557.5 702.7 761.6 938.3 997.1 1142.4 1201.3 761.6 : 145.2 235.6 380.8 439.7 498.6 643.8 702.7 879.4 938.3 1083.5 1142.4 1201.3 906.8 : 90.3 235.6 294.4 353.3 498.6 557.5 734.1 793.0 938.3 997.1 1056.0 1201.3 997.1 : 145.2 204.1 263.0 408.3 467.1 643.8 702.7 847.9 906.8 965.7 1111.0 1201.3 1142.4: 58.9 117.8 263.0 321.9 498.6 557.5 702.7 761.6 820.5 965.7 1056.0 1201.3 1201.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.8896 .. 176.6688 cents 117.77918 cents 58.88959 cents 2: 117.7792 .. 235.5584 cents 117.77918 cents -58.88959 cents 3: 263.0165 .. 380.7957 cents 117.77918 cents 27.45819 cents 4: 321.9061 .. 439.6853 cents 117.77918 cents -58.88959 cents 5: 467.1435 .. 584.9227 cents 117.77918 cents 27.45819 cents 6: 557.4645 .. 643.8123 cents 86.34778 cents -27.45819 cents 7: 616.3541 .. 734.1332 cents 117.77918 cents -27.45819 cents 8: 761.5914 .. 879.3706 cents 117.77918 cents 27.45819 cents 9: 820.4810 .. 938.2602 cents 117.77918 cents -58.88959 cents 10: 965.7184 .. 1083.4976 cents 117.77918 cents 27.45819 cents 11: 1024.6080 .. 1142.3872 cents 117.77918 cents -58.88959 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 58.88959 cents, class 1 Average step (divided formal octave): 100.1064 cents Largest one step interval : 176.66876 cents Average / Smallest step : 1.699900 Largest / Average step : 1.764810 Largest / Smallest step : 3.000000 Median interval of one step : 74.60529 cents, amount: 0 Most common interval of one step : 58.88959 cents, amount: 6 Least squares average step : 100.76441 cents, oct.: 1209.17287 cents Scale is not proper Step pattern alph. order: ABACABAABDBA Step pattern size order : ACADACAACBCA Scale is a Constant Structure, by a margin of 27.45819 cents Scale diversity : 1.419386 Lumma stability : 0.189475 Lumma impropriety factor : 0.241805 Rothenberg efficiency : 0.415278 redundancy: 0.584722 Efficiency x scale size : 4.983333 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 27.45819 cents Most common intervals : 498.57490 cents & inv., amount: 9 Most common triad is 0.0 498.575 702.702 cents, amount: 6 Number of recognisable fifths : 9, average 702.7018 cents Number of recognisable fourths : 9, average 498.5749 cents Formal octave complements present : 9 = 75.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 28.5898 c. M: 43.1739 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 2 0 2 1 0 2 1 1 1 N D3 SD: 24.4442 c. M:-36.5454 c. 15: 1 1 1 2 1 2 1 0 2 1 2 1 N D3 SD: 27.6811 c. M: 43.9567 c. 17: 1 2 1 2 1 2 1 1 2 1 2 1 P M ME SD: 11.2225 c. M:-19.6368 c. 19: 1 2 1 3 1 2 1 1 2 2 2 1 N D3 SD: 10.3374 c. M: 21.6775 c. 22: 1 3 1 3 1 3 1 1 3 1 3 1 N M DE SD: 10.2196 c. M:-21.4305 c. 24: 1 3 1 4 1 3 1 1 3 2 3 1 N SD: 7.4824 c. M: 12.7506 c. 36: 2 4 2 5 2 4 2 2 4 3 4 2 N SD: 5.6049 c. M: 9.8051 c. 41: 2 5 2 6 2 5 2 2 5 3 5 2 N SD: 0.6932 c. M:-1.4536 c. 183: 9 22 9 27 9 22 9 9 22 14 22 9 N SD: 0.4521 c. M: 0.9480 c. 224: 11 27 11 33 11 27 11 11 27 17 27 11 N SD: 0.2424 c. M: 0.5084 c. 265: 13 32 13 39 13 32 13 13 32 20 32 13 N SD: 0.0977 c. M: 0.2048 c. 306: 15 37 15 45 15 37 15 15 37 23 37 15 N SD: 0.0083 c. M:-0.0174 c. 1795: 88 217 88 264 88 217 88 88 217 135 217 88 N SD: 0.0074 c. M: 0.0154 c. 2101: 103 254 103 309 103 254 103 103 254 158 254 103 N SD: 0.0051 c. M: 0.0107 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 1.2767 cents 2 x x x x x x 3 x x x x 4 S SD: 0.7396 cents 3 x x x x 4 x x x 5 x x 6 S SD: 7.5042 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 15.1099 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 19.6577 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.4992 cents 7 x 8 x 9 x 10 x 11:12 x x 14 S SD: 8.4588 cents 8 x 9 x 10:11 x 12 x x 14:15:16 S SD: 13.8237 cents 9 x 10 x x 12:13 x 14:15:16:17:18 S SD: 6.5572 cents 10 x 11:12:13 x x 15:16:17:18:19:20 SD: 10.3979 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 9.5436 cents 12 x x 14:15:16:17:18:19:20:21:23:24 SD: 8.5150 cents 13:14 x 15:17 x 19 x 20:22:23:25:26 SD: 8.8178 cents 14:15:16 x 18:19:20:21:22:24:25:27:28 SD: 7.7260 cents 15:16:17 x 19:20:22 x 23:25:27:29:30 SD: 7.5091 cents 16:17:18:19 x 21:23:24:25:27:28:31:32 SD: 6.5934 cents 17:18:19:20:22:23:25 x 26:29:30:33:34 SD: 6.1142 cents 18:19:20:21:23:24:26:27:28:30:32:35:36 SD: 4.2295 cents 20:21 x 23:26:27:29:30:31:34:36:39:40 SD: 4.5517 cents 21:22:24 x 27:28:30:32:33:35:37:41:42 SD: 5.8131 cents 22:23:25:26:28:29:32:33:34:37:39:43:44 SD: 4.3308 cents 24:25:27:28:31:32:35:36:37:41:43:46:48 SD: 2.9202 cents 31:32:35:36:40:41:45:47:48:52:55:60:62 SD: 2.3177 cents 38:39:43:44:49:51:55:57:59:64:68:74:76 SD: 2.3050 cents 42:43:47:49:54:56:61:63:65:71:75:81:84 SD: 1.9886 cents 48:50:54:56:62:64:70:72:75:81:85:93:96 SD: 1.7613 cents 49:51:55:57:63:65:71:74:76:83:87:95:98 SD: 1.7078 cents 54:56:61:63:70:72:78:81:84:91:96:104:108 SD: 1.4628 cents 56:58:63:65:72:75:81:84:87:95:100:108:112 SD: 1.3631 cents 62:64:70:72:80:83:90:93:96:105:110:120:124 SD: 1.1395 cents 78:81:88:91:101:104:113:117:121:132:139:151:156 SD: 1.0970 cents 80:83:90:93:103:107:116:120:124:135:142:155:160 SD: 0.7924 cents 96:99:108:112:124:128:139:144:149:162:171:186:192 SD: 0.7605 cents 114:118:128:133:147:152:165:171:177:192:203:221:228 SD: 0.7452 cents 118:122:133:137:152:157:171:177:183:199:210:228:236 SD: 0.6886 cents 120:124:135:140:155:160:174:180:186:203:213:232:240 SD: 0.6883 cents 122:126:137:142:157:163:177:183:189:206:217:236:244 SD: 0.6216 cents 135:140:152:157:174:180:196:203:210:228:240:261:270 SD: 0.5980 cents 144:149:162:168:186:192:209:216:224:243:256:279:288 SD: 0.5910 cents 152:157:171:177:196:203:220:228:236:257:270:294:304 SD: 0.5402 cents 166:172:187:193:214:221:241:249:258:280:295:321:332 SD: 0.5270 cents 170:176:191:198:219:227:247:255:264:287:302:329:340 SD: 0.4638 cents 176:182:198:205:227:235:255:264:273:297:313:340:352 SD: 0.3887 cents 200:207:225:233:258:267:290:300:311:338:356:387:400 SD: 0.3742 cents 208:215:234:242:268:277:302:312:323:351:370:402:416 SD: 0.3731 cents 225:233:253:262:290:300:326:338:349:380:400:435:450 SD: 0.3535 cents 231:239:260:269:298:308:335:347:359:390:411:447:462 SD: 0.2718 cents 288:298:324:335:371:384:418:432:447:486:512:557:576 SD: 0.2588 cents 311:322:350:362:401:415:451:467:483:525:553:602:622 SD: 0.2305 cents 318:329:358:370:410:424:461:477:494:537:566:615:636 SD: 0.2251 cents 353:365:397:411:455:471:512:530:548:596:628:683:707 SD: 0.1784 cents 408:422:459:475:526:544:592:612:633:689:726:789:817 SD: 0.1779 cents 440:455:495:512:567:587:638:660:683:743:783:851:881 SD: 0.1653 cents 456:472:513:531:588:608:661:684:708:770:811:882:913 SD: 0.1642 cents 488:505:549:568:629:651:708:732:758:824:868:944:977 SD: 0.1208 cents 519:537:584:604:669:692:753:779:806:876:923:1004:1039 SD: 0.1124 cents