Scala analysis: thrush15
Thrush[15] hobbit 7&9 limit minimax tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 79.869 cents 79.868940 2: 159.738 cents 159.737880 3: 231.174 cents 231.174090 4: 311.043 cents 311.043030 5: 390.912 cents 390.911970 6: 498.045 cents 498.045000 7: 577.914 cents 577.913940 8: 622.086 cents 622.086060 9: 701.955 cents 701.955000 10: 809.088 cents 809.088030 11: 888.957 cents 888.956970 12: 968.826 cents 968.825910 13: 1040.262 cents 1040.262120 14: 1120.131 cents 1120.131060 15: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 79.8689 cents 79.8689 1: 79.8689 cents 79.8689 2: 79.8689 cents 79.8689 3: 71.4362 cents 71.4362 4: 79.8689 cents 79.8689 5: 79.8689 cents 79.8689 6: 107.1330 cents 107.1330 7: 79.8689 cents 79.8689 8: 44.1721 cents 44.1721 9: 79.8689 cents 79.8689 10: 107.1330 cents 107.1330 11: 79.8689 cents 79.8689 12: 79.8689 cents 79.8689 13: 71.4362 cents 71.4362 14: 79.8689 cents 79.8689 15: 79.8689 cents 79.8689
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 44.17212 cents 1: 2 71.43621 cents 1: 10 79.86894 cents 1: 2 107.13303 cents 2: 2 124.04106 cents 2: 4 151.30515 cents 2: 5 159.73788 cents 2: 4 187.00197 cents 3: 1 203.91000 cents 3: 8 231.17409 cents 3: 2 239.60682 cents 3: 4 266.87091 cents 4: 10 311.04303 cents 4: 1 319.47576 cents 4: 2 338.30712 cents 4: 2 346.73985 cents 5: 10 390.91197 cents 5: 5 418.17606 cents 6: 3 462.34818 cents 6: 6 470.78091 cents 6: 6 498.04500 cents 7: 6 542.21712 cents 7: 2 550.64985 cents 7: 7 577.91394 cents 8: 7 622.08606 cents 8: 2 649.35015 cents 8: 6 657.78288 cents 9: 6 701.95500 cents 9: 6 729.21909 cents 9: 3 737.65182 cents 10: 5 781.82394 cents 10: 10 809.08803 cents 11: 2 853.26015 cents 11: 2 861.69288 cents 11: 1 880.52424 cents 11: 10 888.95697 cents 12: 4 933.12909 cents 12: 2 960.39318 cents 12: 8 968.82591 cents 12: 1 996.09000 cents 13: 4 1012.99803 cents 13: 5 1040.26212 cents 13: 4 1048.69485 cents 13: 2 1075.95894 cents 14: 2 1092.86697 cents 14: 10 1120.13106 cents 14: 2 1128.56379 cents 14: 1 1155.82788 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.42857 = 24/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 79.9 159.7 231.2 311.0 390.9 498.0 577.9 622.1 702.0 809.1 889.0 968.8 1040.3 1120.1 1200.0 79.9 : 79.9 151.3 231.2 311.0 418.2 498.0 542.2 622.1 729.2 809.1 889.0 960.4 1040.3 1120.1 1200.0 159.7 : 71.4 151.3 231.2 338.3 418.2 462.3 542.2 649.4 729.2 809.1 880.5 960.4 1040.3 1120.1 1200.0 231.2 : 79.9 159.7 266.9 346.7 390.9 470.8 577.9 657.8 737.7 809.1 889.0 968.8 1048.7 1128.6 1200.0 311.0 : 79.9 187.0 266.9 311.0 390.9 498.0 577.9 657.8 729.2 809.1 889.0 968.8 1048.7 1120.1 1200.0 390.9 : 107.1 187.0 231.2 311.0 418.2 498.0 577.9 649.4 729.2 809.1 889.0 968.8 1040.3 1120.1 1200.0 498.0 : 79.9 124.0 203.9 311.0 390.9 470.8 542.2 622.1 702.0 781.8 861.7 933.1 1013.0 1092.9 1200.0 577.9 : 44.2 124.0 231.2 311.0 390.9 462.3 542.2 622.1 702.0 781.8 853.3 933.1 1013.0 1120.1 1200.0 622.1 : 79.9 187.0 266.9 346.7 418.2 498.0 577.9 657.8 737.7 809.1 889.0 968.8 1076.0 1155.8 1200.0 702.0 : 107.1 187.0 266.9 338.3 418.2 498.0 577.9 657.8 729.2 809.1 889.0 996.1 1076.0 1120.1 1200.0 809.1 : 79.9 159.7 231.2 311.0 390.9 470.8 550.6 622.1 702.0 781.8 889.0 968.8 1013.0 1092.9 1200.0 889.0 : 79.9 151.3 231.2 311.0 390.9 470.8 542.2 622.1 702.0 809.1 889.0 933.1 1013.0 1120.1 1200.0 968.8 : 71.4 151.3 231.2 311.0 390.9 462.3 542.2 622.1 729.2 809.1 853.3 933.1 1040.3 1120.1 1200.0 1040.3: 79.9 159.7 239.6 319.5 390.9 470.8 550.6 657.8 737.7 781.8 861.7 968.8 1048.7 1128.6 1200.0 1120.1: 79.9 159.7 239.6 311.0 390.9 470.8 577.9 657.8 702.0 781.8 889.0 968.8 1048.7 1120.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.1721 .. 107.1330 cents 62.96091 cents 44.17212 cents 2: 124.0411 .. 187.0020 cents 62.96091 cents 16.90803 cents 3: 203.9100 .. 266.8709 cents 62.96091 cents 16.90803 cents 4: 311.0430 .. 346.7399 cents 35.69682 cents 44.17212 cents 5: 390.9120 .. 418.1761 cents 27.26409 cents 44.17212 cents 6: 462.3482 .. 498.0450 cents 35.69682 cents 44.17212 cents 7: 542.2171 .. 577.9139 cents 35.69682 cents 44.17212 cents 8: 622.0861 .. 657.7829 cents 35.69682 cents 44.17212 cents 9: 701.9550 .. 737.6518 cents 35.69682 cents 44.17212 cents 10: 781.8239 .. 809.0880 cents 27.26409 cents 44.17212 cents 11: 853.2601 .. 888.9570 cents 35.69682 cents 44.17212 cents 12: 933.1291 .. 996.0900 cents 62.96091 cents 44.17212 cents 13: 1012.9980 .. 1075.9589 cents 62.96091 cents 16.90803 cents 14: 1092.8670 .. 1155.8279 cents 62.96091 cents 16.90803 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 44.17212 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 107.13303 cents Average / Smallest step : 1.811097 Largest / Average step : 1.339163 Largest / Smallest step : 2.425354 Median interval of one step : 79.86894 cents, amount: 10 Most common interval of one step : 79.86894 cents, amount: 10 Least squares average step : 80.09686 cents, oct.: 1201.45295 cents Scale is strictly proper Step pattern alph. order: AABAACADACAABAA Step pattern size order : CCBCCDCACDCCBCC Scale is a Constant Structure, by a margin of 16.90803 cents Scale diversity : 1.345238 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.461271 Number of different interval sizes : 48 = 3.42857 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.42857 = 24/7 Median interval variety : 2.5 Lowest interval variety : 2 Smallest interval difference : 8.43273 cents Number of recognisable fifths : 6, average 701.9550 cents Best minor thirds form a closed circle Formal octave complements present : 15 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties --
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.8771 c. M: 18.0450 c. 27: 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 SP B ME I SD: 9.3337 c. M: 18.0399 c. 31: 2 2 2 2 2 3 2 1 2 3 2 2 2 2 2 P D3 I SD: 3.3045 c. M: 5.1808 c. 46: 3 3 3 3 3 4 3 2 3 4 3 3 3 3 3 SP D3 I SD: 2.6291 c. M:-4.0009 c. 77: 5 5 5 5 5 7 5 3 5 7 5 5 5 5 5 SP D3 I SD: 1.9959 c. M: 3.8937 c. 89: 6 6 5 6 6 8 6 3 6 8 6 6 5 6 6 SP I SD: 1.3750 c. M: 2.0599 c. 104: 7 7 6 7 7 9 7 4 7 9 7 7 6 7 7 SP I SD: 1.2093 c. M:-1.8912 c. 135: 9 9 8 9 9 12 9 5 9 12 9 9 8 9 9 SP I SD: 0.1729 c. M:-0.2672 c. 436: 29 29 26 29 29 39 29 16 29 39 29 29 26 29 29 SP I SD: 0.0746 c. M:-0.1201 c. 571: 38 38 34 38 38 51 38 21 38 51 38 38 34 38 38 SP I SD: 0.0165 c. M:-0.0286 c. 1277: 85 85 76 85 85 114 85 47 85 114 85 85 76 85 85 SP I SD: 0.0058 c. M: 0.0115 c. 1848: 123 123 110 123 123 165 123 68 123 165 123 123 110 123 123 SP I SD: 0.0048 c. M:-0.0081 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 1.5328 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 1.1496 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 4.8049 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 6.1874 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 10.0432 cents 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.3692 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 7.9561 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 5.9051 cents 11 x 12 x 13:14:15 x 16:17 x 18:19:20:21:22 S SD: 8.1422 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 4.1104 cents 13 x 14:15 x 16:17:18:19:20:21:22:23:24:25:26 S SD: 7.1359 cents 14:15 x 16:17:18:19 x 20:21:22:23:25:26:27:28 SD: 7.3711 cents 15:16 x 17:18:19:20:21 x 23:24:25:26:27:29:30 SD: 5.0619 cents 16:17 x 18:19:20:21:22:23:24:26:27:28:29:31:32 SD: 5.0883 cents 17:18:19 x 20:21:23:24 x 26:27:28:30:31:32:34 SD: 6.2590 cents 18:19:20:21:22:23:24:25:26:27:29:30:32:33:34:36 SD: 5.2495 cents 19:20:21:22:23:24:25 x 27:29:30:32:33:35:36:38 SD: 4.6003 cents 20:21:22:23:24:25:27:28:29:30:32:33:35:36:38:40 SD: 3.1540 cents 24:25:26:27:29:30:32 x 34:36:38:40:42:44:46:48 SD: 3.3968 cents 27:28:30:31:32:34:36:38:39:41:43:45:47:49:52:54 SD: 3.3117 cents 28:29:31:32:34:35:37:39:40:42:45:47:49:51:53:56 SD: 2.9980 cents 30:31:33:34:36:38:40:42:43:45:48:50:53:55:57:60 SD: 2.6876 cents 35:37:38:40:42:44:47:49:50:53:56:58:61:64:67:70 SD: 2.4946 cents 36:38:39:41:43:45:48:50:52:54:57:60:63:66:69:72 SD: 2.4284 cents 39:41:43:45:47:49:52:54:56:59:62:65:68:71:74:78 SD: 2.3613 cents 40:42:44:46:48:50:53:56:57:60:64:67:70:73:76:80 SD: 1.5563 cents 56:59:61:64:67:70:75:78:80:84:89:94:98:102:107:112 SD: 1.4619 cents 60:63:66:69:72:75:80:84:86:90:96:100:105:109:115:120 SD: 1.2572 cents 63:66:69:72:75:79:84:88:90:95:101:105:110:115:120:126 SD: 1.1938 cents 64:67:70:73:77:80:85:89:92:96:102:107:112:117:122:128 SD: 1.1622 cents 72:75:79:82:86:90:96:101:103:108:115:120:126:131:138:144 SD: 1.1592 cents 76:80:83:87:91:95:101:106:109:114:121:127:133:139:145:152 SD: 1.0457 cents 83:87:91:95:99:104:111:116:119:125:132:139:145:151:159:166 SD: 1.0057 cents 84:88:92:96:101:105:112:117:120:126:134:140:147:153:160:168 SD: 0.8887 cents 86:90:94:98:103:108:115:120:123:129:137:144:151:157:164:172 SD: 0.8688 cents 91:95:100:104:109:114:121:127:130:137:145:152:159:166:174:182 SD: 0.8105 cents 102:107:112:117:122:128:136:142:146:153:163:170:179:186:195:204 SD: 0.7929 cents 104:109:114:119:124:130:139:145:149:156:166:174:182:190:199:208 SD: 0.7279 cents 106:111:116:121:127:133:141:148:152:159:169:177:186:193:202:212 SD: 0.6441 cents 126:132:138:144:151:158:168:176:180:189:201:211:221:230:241:252 SD: 0.5630 cents 134:140:147:153:160:168:179:187:192:201:214:224:235:244:256:268 SD: 0.5608 cents 146:153:160:167:175:183:195:204:209:219:233:244:256:266:279:292 SD: 0.4153 cents 174:182:191:199:208:218:232:243:249:261:278:291:305:317:332:348 SD: 0.3995 cents 188:197:206:215:225:236:251:263:269:282:300:314:329:343:359:376 SD: 0.3830 cents 189:198:207:216:226:237:252:264:271:284:302:316:331:345:361:378 SD: 0.3770 cents 208:218:228:238:249:261:277:290:298:312:332:348:364:379:397:416 SD: 0.3664 cents 210:220:230:240:251:263:280:293:301:315:335:351:368:383:401:420 SD: 0.3092 cents 240:251:263:274:287:301:320:335:344:360:383:401:420:438:458:480 SD: 0.2877 cents 252:264:276:288:302:316:336:352:361:378:402:421:441:460:481:504 SD: 0.2679 cents 280:293:307:320:335:351:373:391:401:420:447:468:490:511:535:560 SD: 0.1828 cents 300:314:329:343:359:376:400:419:430:450:479:501:525:547:573:600 SD: 0.1549 cents 426:446:467:487:510:534:568:595:610:639:680:712:746:777:814:852 SD: 0.1387 cents 504:528:553:576:603:632:672:704:722:756:804:842:882:919:963:1008 SD: 0.1351 cents 532:557:583:608:637:667:709:743:762:798:849:889:931:970:1016:1064 SD: 0.1284 cents 568:595:623:649:680:712:757:793:814:852:906:949:994:1036:1085:1136 SD: 0.1170 cents 588:616:645:672:704:737:784:821:842:882:938:983:1029:1072:1123:1176 SD: 0.1042 cents