Scala analysis: syncmt1a
Synchronous meantone tuning for good major triads
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 71.538 cents 71.537700 2: 191.868 cents 191.867920 3: 312.198 cents 312.198130 4: 383.736 cents 383.735830 5: 504.066 cents 504.066040 6: 575.604 cents 575.603750 7: 695.934 cents 695.933960 8: 767.472 cents 767.471660 9: 887.802 cents 887.801870 10: 1008.132 cents 1008.132080 11: 1079.670 cents 1079.669790 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 120.3302 cents 120.3302 1: 71.5377 cents 71.5377 2: 120.3302 cents 120.3302 3: 120.3302 cents 120.3302 4: 71.5377 cents 71.5377 5: 120.3302 cents 120.3302 6: 71.5377 cents 71.5377 7: 120.3302 cents 120.3302 8: 71.5377 cents 71.5377 9: 120.3302 cents 120.3302 10: 120.3302 cents 120.3302 11: 71.5377 cents 71.5377 12: 120.3302 cents 120.3302
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 71.53770 cents 1: 7 120.33022 cents 2: 10 191.86792 cents 2: 2 240.66043 cents 3: 3 263.40562 cents 3: 9 312.19813 cents 4: 8 383.73583 cents 4: 4 432.52834 cents 5: 1 455.27353 cents 5: 11 504.06604 cents 6: 6 575.60375 cents 6: 6 624.39626 cents 7: 11 695.93396 cents 7: 1 744.72647 cents 8: 4 767.47166 cents 8: 8 816.26417 cents 9: 9 887.80187 cents 9: 3 936.59438 cents 10: 2 959.33957 cents 10: 10 1008.13208 cents 11: 7 1079.66979 cents 11: 5 1128.46230 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 : 71.5 191.9 312.2 383.7 504.1 575.6 695.9 767.5 887.8 1008.1 1079.7 1200.0 71.5 : 120.3 240.7 312.2 432.5 504.1 624.4 695.9 816.3 936.6 1008.1 1128.5 1200.0 191.9 : 120.3 191.9 312.2 383.7 504.1 575.6 695.9 816.3 887.8 1008.1 1079.7 1200.0 312.2 : 71.5 191.9 263.4 383.7 455.3 575.6 695.9 767.5 887.8 959.3 1079.7 1200.0 383.7 : 120.3 191.9 312.2 383.7 504.1 624.4 695.9 816.3 887.8 1008.1 1128.5 1200.0 504.1 : 71.5 191.9 263.4 383.7 504.1 575.6 695.9 767.5 887.8 1008.1 1079.7 1200.0 575.6 : 120.3 191.9 312.2 432.5 504.1 624.4 695.9 816.3 936.6 1008.1 1128.5 1200.0 695.9 : 71.5 191.9 312.2 383.7 504.1 575.6 695.9 816.3 887.8 1008.1 1079.7 1200.0 767.5 : 120.3 240.7 312.2 432.5 504.1 624.4 744.7 816.3 936.6 1008.1 1128.5 1200.0 887.8 : 120.3 191.9 312.2 383.7 504.1 624.4 695.9 816.3 887.8 1008.1 1079.7 1200.0 1008.1: 71.5 191.9 263.4 383.7 504.1 575.6 695.9 767.5 887.8 959.3 1079.7 1200.0 1079.7: 120.3 191.9 312.2 432.5 504.1 624.4 695.9 816.3 887.8 1008.1 1128.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.5377 .. 120.3302 cents 48.79252 cents 71.53770 cents 2: 191.8679 .. 240.6604 cents 48.79251 cents 71.53770 cents 3: 263.4056 .. 312.1981 cents 48.79251 cents 22.74519 cents 4: 383.7358 .. 432.5283 cents 48.79251 cents 71.53770 cents 5: 455.2735 .. 504.0660 cents 48.79251 cents 22.74519 cents 6: 575.6037 .. 624.3963 cents 48.79251 cents 71.53771 cents 7: 695.9340 .. 744.7265 cents 48.79251 cents 71.53770 cents 8: 767.4717 .. 816.2642 cents 48.79251 cents 22.74519 cents 9: 887.8019 .. 936.5944 cents 48.79251 cents 71.53770 cents 10: 959.3396 .. 1008.1321 cents 48.79251 cents 22.74519 cents 11: 1079.6698 .. 1128.4623 cents 48.79251 cents 71.53771 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 71.53770 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 120.33022 cents Average / Smallest step : 1.397864 Largest / Average step : 1.203302 Largest / Smallest step : 1.682053 Median interval of one step : 120.33022 cents, amount: 7 Most common interval of one step : 120.33022 cents, amount: 7 Least squares average step : 98.86151 cents, oct.: 1186.33810 cents Scale is strictly proper Scale has Myhill's property chromas: 48.79252 cents and 22.74518 cents, ratio: 2.145181 generators: 5 of 504.06604 cents and 7 of 695.93396 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 2164-tone equal temperament with octave 2/1 degrees: 129 346 563 692 909 1038 1255 1384 1601 1818 1947 2164 generators: 909 and 1255 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 22.74519 cents Ratio Whole / Half tone : 1.594512 Scale diversity : 1.221544 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.552735 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 : 22.74519 cents Most common intervals : 504.06604 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 120.330 695.934 cents Most common triad is 0.0 504.066 695.934 cents, amount: 10 Number of recognisable fifths : 11, average 695.9340 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 -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.3304 c. M:-32.5283 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 5.1024 c. M: 9.5769 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 3.5813 c. M:-6.7219 c. Meantone Chromatic (53/220-comma) 50: 3 5 5 3 5 3 5 3 5 5 3 5 SP M DE SD: 0.2815 c. M:-0.5283 c. Meantone Chromatic (5/18-comma), Eair-12 219: 13 22 22 13 22 13 22 13 22 22 13 22 SP M DE SD: 0.1856 c. M: 0.3484 c. 269: 16 27 27 16 27 16 27 16 27 27 16 27 SP M DE SD: 0.0988 c. M: 0.1854 c. 319: 19 32 32 19 32 19 32 19 32 32 19 32 SP M DE SD: 0.0392 c. M: 0.0735 c. 369: 22 37 37 22 37 22 37 22 37 37 22 37 SP M DE SD: 0.0043 c. M:-0.0080 c. 1795: 107 180 180 107 180 107 180 107 180 180 107 180 SP M DE SD: 0.0035 c. M: 0.0065 c. 2164: 129 217 217 129 217 129 217 129 217 217 129 217 SP M DE SD: 0.0021 c. M: 0.0040 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: 3.0105 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.3120 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.9620 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.5602 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2157 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.9989 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.5069 cents 9 x 10:11 x 12 x 13:14:15:16:17:18 S SD: 8.2434 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.6448 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2076 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.6190 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.9241 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 8.0910 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.8429 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.3390 cents 18:19:20:22 x 24:25:27:28:30:32:34:36 SD: 4.5965 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.7694 cents 24:25:27:29:30:32:33:36:37:40:43:45:48 SD: 3.1923 cents 25:26:28:30:31:33:35:37:39:42:45:47:50 SD: 3.1642 cents 32:33:36:38:40:43:45:48:50:53:57:60:64 SD: 3.1029 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.5080 cents 41:43:46:49:51:55:57:61:64:68:73:76:82 SD: 2.2081 cents 44:46:49:53:55:59:61:66:69:73:79:82:88 SD: 2.0524 cents 45:47:50:54:56:60:63:67:70:75:81:84:90 SD: 1.6276 cents 51:53:57:61:64:68:71:76:79:85:91:95:102 SD: 1.5336 cents 61:64:68:73:76:82:85:91:95:102:109:114:122 SD: 1.3515 cents 66:69:74:79:82:88:92:99:103:110:118:123:132 SD: 1.2764 cents 68:71:76:81:85:91:95:102:106:114:122:127:136 SD: 1.2230 cents 75:78:84:90:94:100:105:112:117:125:134:140:150 SD: 1.2142 cents 76:79:85:91:95:102:106:114:118:127:136:142:152 SD: 0.9766 cents 91:95:102:109:114:122:127:136:142:152:163:170:182 SD: 0.8756 cents 97:101:108:116:121:130:135:145:151:162:174:181:194 SD: 0.7357 cents 121:126:135:145:151:162:169:181:189:202:217:226:242 SD: 0.6122 cents 136:142:152:163:170:182:190:203:212:227:243:254:272 SD: 0.6024 cents 137:143:153:164:171:183:191:205:213:229:245:256:274 SD: 0.5574 cents 142:148:159:170:177:190:198:212:221:237:254:265:284 SD: 0.4674 cents 162:169:181:194:202:217:226:242:252:271:290:302:324 SD: 0.4475 cents 172:179:192:206:215:230:240:257:268:287:308:321:344 SD: 0.3755 cents 213:222:238:255:266:285:297:318:332:356:381:397:426 SD: 0.3091 cents 233:243:260:279:291:312:325:348:363:389:417:435:466 SD: 0.3002 cents 258:269:288:309:322:345:360:386:402:431:462:481:516 SD: 0.2582 cents 263:274:294:315:328:352:367:393:410:439:471:491:526 SD: 0.2551 cents 299:312:334:358:373:400:417:447:466:499:535:558:598 SD: 0.2446 cents 314:327:351:376:392:420:438:469:489:524:562:586:628 SD: 0.2290 cents 334:348:373:400:417:447:466:499:520:558:598:623:668 SD: 0.1814 cents 358:373:400:429:447:479:499:535:558:598:641:668:716 SD: 0.1565 cents 400:417:447:479:499:535:558:598:623:668:716:746:800 SD: 0.1413 cents 497:518:555:595:620:665:693:743:774:830:890:927:994 SD: 0.1377 cents 520:542:581:623:649:696:725:777:810:868:931:970:1040 SD: 0.1225 cents 572:596:639:685:714:765:798:855:891:955:1024:1067:1144 SD: 0.1099 cents 588:613:657:704:734:787:820:879:916:982:1053:1097:1176 SD: 0.0990 cents