Scala analysis: duowell
Ellis duodene well-tuned to fifth=(7168/11)^(1/16) third=(11/7)^(1/2)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 107.660 cents 107.659734 2: 202.188 cents 202.188496 3: 309.848 cents 309.848230 4: 391.246 cents 391.246018 5: 498.906 cents 498.905752 6: 593.435 cents 593.434513 7: 701.094 cents 701.094248 8: 808.754 cents 808.753982 9: 890.152 cents 890.151770 10: 1010.942 cents 1010.942478 11: 1092.340 cents 1092.340266 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 107.6597 cents 107.6597 1: 107.6597 cents 107.6597 2: 94.5288 cents 94.5288 3: 107.6597 cents 107.6597 4: 81.3978 cents 81.3978 5: 107.6597 cents 107.6597 6: 94.5288 cents 94.5288 7: 107.6597 cents 107.6597 8: 107.6597 cents 107.6597 9: 81.3978 cents 81.3978 10: 120.7907 cents 120.7907 11: 81.3978 cents 81.3978 12: 107.6597 cents 107.6597
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 81.39779 cents 1: 2 94.52876 cents 1: 6 107.65973 cents 1: 1 120.79071 cents 2: 4 189.05752 cents 2: 6 202.18850 cents 2: 2 215.31947 cents 3: 3 283.58628 cents 3: 3 296.71726 cents 3: 6 309.84823 cents 4: 8 391.24602 cents 4: 4 417.50796 cents 5: 1 485.77478 cents 5: 9 498.90575 cents 5: 2 512.03673 cents 6: 2 580.30354 cents 6: 4 593.43451 cents 6: 4 606.56549 cents 6: 2 619.69646 cents 7: 2 687.96327 cents 7: 9 701.09425 cents 7: 1 714.22522 cents 8: 4 782.49204 cents 8: 8 808.75398 cents 9: 6 890.15177 cents 9: 3 903.28274 cents 9: 3 916.41372 cents 10: 2 984.68053 cents 10: 6 997.81150 cents 10: 4 1010.94248 cents 11: 1 1079.20929 cents 11: 6 1092.34027 cents 11: 2 1105.47124 cents 11: 3 1118.60221 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 107.7 202.2 309.8 391.2 498.9 593.4 701.1 808.8 890.2 1010.9 1092.3 1200.0 107.7 : 94.5 202.2 283.6 391.2 485.8 593.4 701.1 782.5 903.3 984.7 1092.3 1200.0 202.2 : 107.7 189.1 296.7 391.2 498.9 606.6 688.0 808.8 890.2 997.8 1105.5 1200.0 309.8 : 81.4 189.1 283.6 391.2 498.9 580.3 701.1 782.5 890.2 997.8 1092.3 1200.0 391.2 : 107.7 202.2 309.8 417.5 498.9 619.7 701.1 808.8 916.4 1010.9 1118.6 1200.0 498.9 : 94.5 202.2 309.8 391.2 512.0 593.4 701.1 808.8 903.3 1010.9 1092.3 1200.0 593.4 : 107.7 215.3 296.7 417.5 498.9 606.6 714.2 808.8 916.4 997.8 1105.5 1200.0 701.1 : 107.7 189.1 309.8 391.2 498.9 606.6 701.1 808.8 890.2 997.8 1092.3 1200.0 808.8 : 81.4 202.2 283.6 391.2 498.9 593.4 701.1 782.5 890.2 984.7 1092.3 1200.0 890.2 : 120.8 202.2 309.8 417.5 512.0 619.7 701.1 808.8 903.3 1010.9 1118.6 1200.0 1010.9: 81.4 189.1 296.7 391.2 498.9 580.3 688.0 782.5 890.2 997.8 1079.2 1200.0 1092.3: 107.7 215.3 309.8 417.5 498.9 606.6 701.1 808.8 916.4 997.8 1118.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 81.3978 .. 120.7907 cents 39.39292 cents 81.39779 cents 2: 189.0575 .. 215.3195 cents 26.26195 cents 68.26681 cents 3: 283.5863 .. 309.8482 cents 26.26195 cents 68.26681 cents 4: 391.2460 .. 417.5080 cents 26.26195 cents 81.39779 cents 5: 485.7748 .. 512.0367 cents 26.26195 cents 68.26682 cents 6: 580.3035 .. 619.6965 cents 39.39292 cents 68.26681 cents 7: 687.9633 .. 714.2252 cents 26.26195 cents 68.26681 cents 8: 782.4920 .. 808.7540 cents 26.26195 cents 68.26681 cents 9: 890.1518 .. 916.4137 cents 26.26195 cents 81.39779 cents 10: 984.6805 .. 1010.9425 cents 26.26195 cents 68.26682 cents 11: 1079.2093 .. 1118.6022 cents 39.39292 cents 68.26681 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 81.39779 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 120.79071 cents Average / Smallest step : 1.228535 Largest / Average step : 1.207907 Largest / Smallest step : 1.483956 Median interval of one step : 107.65973 cents, amount: 6 Most common interval of one step : 107.65973 cents, amount: 6 Least squares average step : 99.96296 cents, oct.: 1199.55557 cents Scale is strictly proper Scale is a mode of a 457-tone equal temperament with octave 1200.000 cents degrees: 41 77 118 149 190 226 267 308 339 385 416 457 Least number of segments generator : 229 of 601.313 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 267 of 701.094 cents and inv. generated superset size: 20 = 8 more = 166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABAACDCA Step pattern size order : CBCACBCCADAC Scale is a Constant Structure, by a margin of 68.26681 cents Scale diversity : 1.223951 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.726438 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 13.13097 cents Most common intervals : 498.90575 cents & inv., amount: 9 Most common triad is 0.0 498.906 701.094 cents, amount: 6 Number of recognisable fifths : 12, average 700.0000 cents Number of appreciable fifths : 10, average 702.4073 cents Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% Limited transpositions with margin 26.2619 cents: 2 5 7 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: 7.2722 c. M: 10.9425 c. Twelve-tone Chromatic (1/11-comma) 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 6.2827 c. M: 12.7894 c. Genus diatonico-chromaticum 34: 3 3 3 2 3 3 3 3 2 4 2 3 SP D3 SD: 6.3586 c. M:-12.5869 c. 43: 4 3 4 3 4 3 4 4 3 4 3 4 SP M ME SD: 4.2123 c. M: 7.3880 c. Genus diatonico-chromaticum 46: 4 4 4 3 4 4 4 4 3 5 3 4 SP D3 SD: 3.9851 c. M:-6.5655 c. 55: 5 4 5 4 5 4 5 5 4 5 4 5 SP M ME SD: 3.7664 c. M: 7.3061 c. Genus diatonico-chromaticum 58: 5 5 5 4 5 5 5 5 4 6 4 5 SP D3 SD: 3.2576 c. M:-6.5655 c. 65: 6 5 6 4 6 5 6 6 4 7 4 6 SP SD: 2.9522 c. M:-4.4421 c. 77: 7 6 7 5 7 6 7 7 5 8 5 7 SP SD: 1.3588 c. M:-2.0445 c. 89: 8 7 8 6 8 7 8 8 6 9 6 8 SP SD: 0.1950 c. M:-0.2935 c. 279: 25 22 25 19 25 22 25 25 19 28 19 25 SP SD: 0.1261 c. M: 0.1898 c. 368: 33 29 33 25 33 29 33 33 25 37 25 33 SP SD: 0.0485 c. M: 0.0729 c. 457: 41 36 41 31 41 36 41 41 31 46 31 41 SP SD: 0.0010 c. M: 0.0016 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: 0.4304 cents 3 x x x x 4 x x x 5 x x 6 S SD: 1.9522 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.6033 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 2.9763 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.6584 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.3418 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.4796 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.5486 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9062 cents 11:12 x 13:14:15 x 16 x 18:20:21:22 S SD: 11.0454 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.8985 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.0590 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.0549 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.0763 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.3520 cents 30:32:34:36:38:40:42:45:48:50:54:56:60 SD: 2.5632 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2904 cents 40:43:45:48:50:53:56:60:64:67:72:75:80 SD: 2.2348 cents 42:45:47:50:53:56:59:63:67:70:75:79:84 SD: 1.8705 cents 47:50:53:56:59:63:66:70:75:79:84:88:94 SD: 1.8047 cents 48:51:54:57:60:64:68:72:77:80:86:90:96 SD: 1.7095 cents 56:60:63:67:70:75:79:84:89:94:100:105:112 SD: 1.6126 cents 62:66:70:74:78:83:87:93:99:104:111:117:124 SD: 1.4136 cents 64:68:72:77:80:85:90:96:102:107:115:120:128 SD: 1.3001 cents 66:70:74:79:83:88:93:99:105:110:118:124:132 SD: 1.0811 cents 82:87:92:98:103:109:116:123:131:137:147:154:164 SD: 1.0128 cents 91:97:102:109:114:121:128:136:145:152:163:171:182 SD: 0.9119 cents 96:102:108:115:120:128:135:144:153:161:172:180:192 SD: 0.8373 cents 98:104:110:117:123:131:138:147:156:164:176:184:196 SD: 0.7595 cents 106:113:119:127:133:141:149:159:169:177:190:199:212 SD: 0.7334 cents 107:114:120:128:134:143:151:160:171:179:192:201:214 SD: 0.7024 cents 122:130:137:146:153:163:172:183:195:204:219:229:244 SD: 0.5054 cents 168:179:189:201:211:224:237:252:268:281:301:316:336 SD: 0.4529 cents 174:185:196:208:218:232:245:261:278:291:312:327:348 SD: 0.4405 cents 188:200:211:225:236:251:265:282:300:314:337:353:376 SD: 0.4102 cents 201:214:226:240:252:268:283:301:321:336:360:378:402 SD: 0.4068 cents 216:230:243:258:271:288:304:324:345:361:387:406:432 SD: 0.3959 cents 218:232:245:261:273:291:307:327:348:365:391:410:436 SD: 0.3345 cents 233:248:262:279:292:311:328:349:372:390:418:438:466 SD: 0.3334 cents 249:265:280:298:312:332:351:373:397:416:446:468:498 SD: 0.3129 cents 260:277:292:311:326:347:366:390:415:435:466:489:520 SD: 0.2958 cents 266:283:299:318:333:355:375:399:424:445:477:500:532 SD: 0.2874 cents 281:299:316:336:352:375:396:421:448:470:504:528:562 SD: 0.2196 cents 296:315:333:354:371:395:417:444:472:495:531:556:592 SD: 0.2133 cents 347:369:390:415:435:463:489:520:554:580:622:652:694 SD: 0.1880 cents 403:429:453:482:505:538:568:604:643:674:723:757:806 SD: 0.1872 cents 435:463:489:520:545:580:613:652:694:727:780:818:870 SD: 0.1866 cents 437:465:491:523:548:583:616:655:697:731:784:821:874 SD: 0.1840 cents 450:479:506:538:564:600:634:675:718:753:807:846:900 SD: 0.1778 cents 455:484:511:544:570:607:641:682:726:761:816:855:910 SD: 0.1680 cents 469:499:527:561:588:626:661:703:748:784:841:881:938 SD: 0.1534 cents 470:500:528:562:589:627:662:705:750:786:843:883:940 SD: 0.1426 cents 485:516:545:580:608:647:683:727:774:811:870:912:970 SD: 0.1314 cents 531:565:597:635:666:708:748:796:847:888:952:998:1062 SD: 0.1291 cents 541:576:608:647:678:722:762:811:863:905:970:1017:1082 SD: 0.1281 cents