Scala analysis: syndwell3
Syndie #3 in 3~(469762048/11)^(1/16) 5~(176/7)^(1/2) well tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81.398 cents 81.397788 2: 189.058 cents 189.057522 3: 296.717 cents 296.717257 4: 391.246 cents 391.246018 5: 498.906 cents 498.905752 6: 580.304 cents 580.303540 7: 687.963 cents 687.963275 8: 782.492 cents 782.492036 9: 890.152 cents 890.151770 10: 997.812 cents 997.811504 11: 1079.209 cents 1079.209293 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 120.7907 cents 120.7907 1: 81.3978 cents 81.3978 2: 107.6597 cents 107.6597 3: 107.6597 cents 107.6597 4: 94.5288 cents 94.5288 5: 107.6597 cents 107.6597 6: 81.3978 cents 81.3978 7: 107.6597 cents 107.6597 8: 94.5288 cents 94.5288 9: 107.6597 cents 107.6597 10: 107.6597 cents 107.6597 11: 81.3978 cents 81.3978 12: 120.7907 cents 120.7907
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 : 81.4 189.1 296.7 391.2 498.9 580.3 688.0 782.5 890.2 997.8 1079.2 1200.0 81.4 : 107.7 215.3 309.8 417.5 498.9 606.6 701.1 808.8 916.4 997.8 1118.6 1200.0 189.1 : 107.7 202.2 309.8 391.2 498.9 593.4 701.1 808.8 890.2 1010.9 1092.3 1200.0 296.7 : 94.5 202.2 283.6 391.2 485.8 593.4 701.1 782.5 903.3 984.7 1092.3 1200.0 391.2 : 107.7 189.1 296.7 391.2 498.9 606.6 688.0 808.8 890.2 997.8 1105.5 1200.0 498.9 : 81.4 189.1 283.6 391.2 498.9 580.3 701.1 782.5 890.2 997.8 1092.3 1200.0 580.3 : 107.7 202.2 309.8 417.5 498.9 619.7 701.1 808.8 916.4 1010.9 1118.6 1200.0 688.0 : 94.5 202.2 309.8 391.2 512.0 593.4 701.1 808.8 903.3 1010.9 1092.3 1200.0 782.5 : 107.7 215.3 296.7 417.5 498.9 606.6 714.2 808.8 916.4 997.8 1105.5 1200.0 890.2 : 107.7 189.1 309.8 391.2 498.9 606.6 701.1 808.8 890.2 997.8 1092.3 1200.0 997.8 : 81.4 202.2 283.6 391.2 498.9 593.4 701.1 782.5 890.2 984.7 1092.3 1200.0 1079.2: 120.8 202.2 309.8 417.5 512.0 619.7 701.1 808.8 903.3 1010.9 1118.6 1200.0 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 68.26681 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 68.26681 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 : 98.81148 cents, oct.: 1185.73774 cents Scale is strictly proper Scale is a mode of a 457-tone equal temperament with octave 1200.000 cents degrees: 31 72 113 149 190 221 262 298 339 380 411 457 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: ABBCBABCBBAD Step pattern size order : ACCBCACBCCAD 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 : 1 = 8.3333% Limited transpositions with margin 39.3929 cents: 3 5 10 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: 12.6747 c. M:-20.7907 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 12.6091 c. M: 24.5973 c. Meantone Chromatic (1/3-comma) 28: 2 2 3 2 3 1 3 2 3 2 2 3 SP D3 SD: 11.4567 c. M: 23.1607 c. 29: 2 3 2 2 3 2 3 2 3 2 2 3 SP M ME SD: 10.9005 c. M:-20.1931 c. 30: 2 3 2 3 2 3 2 3 2 3 2 3 SP B ME SD: 11.9079 c. M:-19.6965 c. 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 6.3434 c. M:-12.9602 c. Meantone Chromatic (53/220-comma) 40: 3 3 4 3 4 2 4 3 4 3 3 4 SP D3 SD: 6.8715 c. M:-11.0942 c. 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 5.9840 c. M:-10.2595 c. Meantone Chromatic (1/5-comma) 46: 3 4 4 4 4 3 4 4 4 4 3 5 SP D3 SD: 6.0404 c. M: 9.7607 c. 49: 3 5 4 4 4 4 4 4 4 5 3 5 SP D3 SD: 5.6121 c. M: 9.1098 c. 58: 4 5 5 5 5 4 5 5 5 5 4 6 SP D3 SD: 3.4681 c. M: 7.0621 c. 70: 5 6 6 6 6 5 6 6 6 6 5 7 SP D3 SD: 3.1939 c. M:-6.0794 c. 77: 5 7 7 6 7 5 7 6 7 7 5 8 SP SD: 2.3682 c. M: 3.8846 c. 89: 6 8 8 7 8 6 8 7 8 8 6 9 SP SD: 0.3399 c. M: 0.5576 c. 279: 19 25 25 22 25 19 25 22 25 25 19 28 SP SD: 0.2198 c. M:-0.3606 c. 368: 25 33 33 29 33 25 33 29 33 33 25 37 SP SD: 0.0845 c. M:-0.1385 c. 457: 31 41 41 36 41 31 41 36 41 41 31 46 SP SD: 0.0018 c. M:-0.0030 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: 6.9959 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: 8.1404 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.3127 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.4753 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.9366 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.5382 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.1842 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.9588 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2269 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.1065 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 9.1964 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.4149 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.5225 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.2001 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.8116 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 4.7818 cents 21:22:23:25:26:28:29:31:33:35:37:39:42 SD: 4.1868 cents 23:24:26:27:29:31:32:34:36:38:41:43:46 SD: 3.8131 cents 27:28:30:32:34:36:38:40:42:45:48:50:54 SD: 2.8120 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.7844 cents 35:37:39:42:44:47:49:52:55:59:62:65:70 SD: 2.7121 cents 36:38:40:43:45:48:50:54:57:60:64:67:72 SD: 2.4842 cents 37:39:41:44:46:49:52:55:58:62:66:69:74 SD: 2.2471 cents 42:44:47:50:53:56:59:62:66:70:75:78:84 SD: 1.9909 cents 43:45:48:51:54:57:60:64:68:72:77:80:86 SD: 1.6970 cents 58:61:65:69:73:77:81:86:91:97:103:108:116 SD: 1.4557 cents 59:62:66:70:74:79:82:88:93:99:105:110:118 SD: 1.3901 cents 60:63:67:71:75:80:84:89:94:100:107:112:120 SD: 1.1069 cents 80:84:89:95:100:107:112:119:126:134:142:149:160 SD: 0.9494 cents 86:90:96:102:108:115:120:128:135:144:153:160:172 SD: 0.7398 cents 103:108:115:122:129:137:144:153:162:172:183:192:206 SD: 0.6987 cents 119:125:133:141:149:159:166:177:187:199:212:222:238 SD: 0.6864 cents 123:129:137:146:154:164:172:183:193:206:219:229:246 SD: 0.5055 cents 149:156:166:177:187:199:208:222:234:249:265:278:298 SD: 0.4919 cents 150:157:167:178:188:200:210:223:236:251:267:280:300 SD: 0.4703 cents 182:191:203:216:228:243:254:271:286:304:324:339:364 SD: 0.4601 cents 186:195:207:221:233:248:260:277:292:311:331:347:372 SD: 0.4254 cents 189:198:211:224:237:252:264:281:297:316:336:353:378 SD: 0.4097 cents 201:211:224:239:252:268:281:299:316:336:358:375:402 SD: 0.4011 cents 208:218:232:247:261:277:291:309:327:348:370:388:416 SD: 0.3957 cents 209:219:233:248:262:279:292:311:328:350:372:390:418 SD: 0.3379 cents 236:247:263:280:296:315:330:351:371:395:420:440:472 SD: 0.3228 cents 252:264:281:299:316:336:352:375:396:421:448:470:504 SD: 0.2793 cents 268:281:299:318:336:358:375:399:421:448:477:500:536 SD: 0.2667 cents 269:282:300:319:337:359:376:400:423:450:479:502:538 SD: 0.2581 cents 311:326:347:369:390:415:435:463:489:520:553:580:622 SD: 0.2004 cents 332:348:370:394:416:443:464:494:522:555:591:619:664 SD: 0.1976 cents 336:352:375:399:421:448:470:500:528:562:598:627:672 SD: 0.1918 cents 354:371:395:420:444:472:495:527:556:592:630:660:708 SD: 0.1833 cents 422:442:471:501:529:563:590:628:663:706:751:787:844 SD: 0.1629 cents 434:455:484:515:544:579:607:646:682:726:772:810:868 SD: 0.1480 cents 476:499:531:565:597:635:666:708:748:796:847:888:952 SD: 0.1390 cents 518:543:578:615:649:691:724:771:814:866:922:966:1036 SD: 0.1387 cents 563:590:628:668:706:751:787:838:885:941:1002:1050:1126 SD: 0.1350 cents 580:608:647:688:727:774:811:863:911:970:1032:1082:1160 SD: 0.1326 cents 599:628:668:711:751:799:838:891:941:1002:1066:1117:1198 SD: 0.1279 cents