Scala analysis: syncmt4
Synchronous meantone tuning 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 73.001 cents 73.001305 2: 192.286 cents 192.286087 3: 311.571 cents 311.570869 4: 384.572 cents 384.572174 5: 503.857 cents 503.856956 6: 576.858 cents 576.858262 7: 696.143 cents 696.143044 8: 769.144 cents 769.144349 9: 888.429 cents 888.429131 10: 1007.714 cents 1007.713913 11: 1080.715 cents 1080.715218 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 119.2848 cents 119.2848 1: 73.0013 cents 73.0013 2: 119.2848 cents 119.2848 3: 119.2848 cents 119.2848 4: 73.0013 cents 73.0013 5: 119.2848 cents 119.2848 6: 73.0013 cents 73.0013 7: 119.2848 cents 119.2848 8: 73.0013 cents 73.0013 9: 119.2848 cents 119.2848 10: 119.2848 cents 119.2848 11: 73.0013 cents 73.0013 12: 119.2848 cents 119.2848
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 73.00131 cents 1: 7 119.28478 cents 2: 10 192.28609 cents 2: 2 238.56956 cents 3: 3 265.28739 cents 3: 9 311.57087 cents 4: 8 384.57217 cents 4: 4 430.85565 cents 5: 1 457.57348 cents 5: 11 503.85696 cents 6: 6 576.85826 cents 6: 6 623.14174 cents 7: 11 696.14304 cents 7: 1 742.42652 cents 8: 4 769.14435 cents 8: 8 815.42783 cents 9: 9 888.42913 cents 9: 3 934.71261 cents 10: 2 961.43044 cents 10: 10 1007.71391 cents 11: 7 1080.71522 cents 11: 5 1126.99869 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 : 73.0 192.3 311.6 384.6 503.9 576.9 696.1 769.1 888.4 1007.7 1080.7 1200.0 73.0 : 119.3 238.6 311.6 430.9 503.9 623.1 696.1 815.4 934.7 1007.7 1127.0 1200.0 192.3 : 119.3 192.3 311.6 384.6 503.9 576.9 696.1 815.4 888.4 1007.7 1080.7 1200.0 311.6 : 73.0 192.3 265.3 384.6 457.6 576.9 696.1 769.1 888.4 961.4 1080.7 1200.0 384.6 : 119.3 192.3 311.6 384.6 503.9 623.1 696.1 815.4 888.4 1007.7 1127.0 1200.0 503.9 : 73.0 192.3 265.3 384.6 503.9 576.9 696.1 769.1 888.4 1007.7 1080.7 1200.0 576.9 : 119.3 192.3 311.6 430.9 503.9 623.1 696.1 815.4 934.7 1007.7 1127.0 1200.0 696.1 : 73.0 192.3 311.6 384.6 503.9 576.9 696.1 815.4 888.4 1007.7 1080.7 1200.0 769.1 : 119.3 238.6 311.6 430.9 503.9 623.1 742.4 815.4 934.7 1007.7 1127.0 1200.0 888.4 : 119.3 192.3 311.6 384.6 503.9 623.1 696.1 815.4 888.4 1007.7 1080.7 1200.0 1007.7: 73.0 192.3 265.3 384.6 503.9 576.9 696.1 769.1 888.4 961.4 1080.7 1200.0 1080.7: 119.3 192.3 311.6 430.9 503.9 623.1 696.1 815.4 888.4 1007.7 1127.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.0013 .. 119.2848 cents 46.28348 cents 73.00131 cents 2: 192.2861 .. 238.5696 cents 46.28348 cents 73.00131 cents 3: 265.2874 .. 311.5709 cents 46.28348 cents 26.71783 cents 4: 384.5722 .. 430.8557 cents 46.28348 cents 73.00131 cents 5: 457.5735 .. 503.8570 cents 46.28348 cents 26.71783 cents 6: 576.8583 .. 623.1417 cents 46.28348 cents 73.00131 cents 7: 696.1430 .. 742.4265 cents 46.28348 cents 73.00131 cents 8: 769.1443 .. 815.4278 cents 46.28348 cents 26.71783 cents 9: 888.4291 .. 934.7126 cents 46.28348 cents 73.00131 cents 10: 961.4304 .. 1007.7139 cents 46.28348 cents 26.71783 cents 11: 1080.7152 .. 1126.9987 cents 46.28348 cents 73.00131 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 73.00131 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 119.28478 cents Average / Smallest step : 1.369839 Largest / Average step : 1.192848 Largest / Smallest step : 1.634009 Median interval of one step : 119.28478 cents, amount: 7 Most common interval of one step : 119.28478 cents, amount: 7 Least squares average step : 98.92005 cents, oct.: 1187.04063 cents Scale is strictly proper Scale has Myhill's property chromas: 46.28348 cents and 26.71783 cents, ratio: 1.732307 generators: 5 of 503.85696 cents and 7 of 696.14304 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 674-tone equal temperament with octave 2/1 degrees: 41 108 175 216 283 324 391 432 499 566 607 674 generators: 283 and 391 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 26.71783 cents Ratio Whole / Half tone : 1.611992 Scale diversity : 1.222392 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.575735 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 : 26.71783 cents Most common intervals : 503.85696 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 119.285 696.143 cents Most common triad is 0.0 503.857 696.143 cents, amount: 10 Number of recognisable fifths : 11, average 696.1430 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: 16.4393 c. M:-30.8557 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 5.9936 c. M: 11.2496 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 2.6901 c. M:-5.0492 c. Meantone Chromatic (53/220-comma) 50: 3 5 5 3 5 3 5 3 5 5 3 5 SP M DE SD: 0.6097 c. M: 1.1443 c. Meantone Chromatic (5/18-comma), Eair-12 131: 8 13 13 8 13 8 13 8 13 13 8 13 SP M DE SD: 0.1712 c. M:-0.3213 c. Golden Meantone Chromatic 181: 11 18 18 11 18 11 18 11 18 18 11 18 SP M DE SD: 0.0445 c. M: 0.0836 c. 493: 30 49 49 30 49 30 49 30 49 49 30 49 SP M DE SD: 0.0128 c. M:-0.0240 c. 674: 41 67 67 41 67 41 67 41 67 67 41 67 SP M DE SD: 0.0026 c. M: 0.0049 c. 1841: 112 183 183 112 183 112 183 112 183 183 112 183 SP M DE SD: 0.0015 c. M:-0.0029 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: 2.9060 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.3652 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.8396 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.2308 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2273 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.7551 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.5587 cents 9 x 10:11 x 12 x 13:14:15:16:17:18 S SD: 8.2715 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.4940 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2165 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.5506 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.8957 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 7.9710 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.8005 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.2626 cents 18:19:20:22 x 24:25:27:28:30:32:34:36 SD: 4.5664 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.8376 cents 24:25:27:29:30:32:33:36:37:40:43:45:48 SD: 3.3212 cents 25:26:28:30:31:33:35:37:39:42:45:47:50 SD: 3.1413 cents 32:33:36:38:40:43:45:48:50:53:57:60:64 SD: 3.0687 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.4615 cents 41:43:46:49:51:55:57:61:64:68:73:77:82 SD: 2.1620 cents 44:46:49:53:55:59:61:66:69:74:79:82:88 SD: 2.0633 cents 45:47:50:54:56:60:63:67:70:75:81:84:90 SD: 1.6725 cents 51:53:57:61:64:68:71:76:80:85:91:95:102 SD: 1.5840 cents 61:64:68:73:76:82:85:91:95:102:109:114:122 SD: 1.3004 cents 66:69:74:79:82:88:92:99:103:110:118:123:132 SD: 1.2582 cents 68:71:76:81:85:91:95:102:106:114:122:127:136 SD: 1.1048 cents 76:79:85:91:95:102:106:114:119:127:136:142:152 SD: 1.0522 cents 86:90:96:103:107:115:120:129:134:144:154:161:172 SD: 1.0308 cents 91:95:102:109:114:122:127:136:142:152:163:170:182 SD: 0.7464 cents 112:117:125:134:140:150:156:167:175:187:200:209:224 SD: 0.7406 cents 113:118:126:135:141:151:158:169:176:189:202:211:226 SD: 0.6562 cents 121:126:135:145:151:162:169:181:189:202:217:226:242 SD: 0.5793 cents 136:142:152:163:170:182:190:203:212:227:243:254:272 SD: 0.4799 cents 137:143:153:164:171:183:191:205:214:229:245:256:274 SD: 0.4547 cents 186:194:208:223:232:249:260:278:290:311:333:347:372 SD: 0.4272 cents 204:213:228:244:255:273:285:305:318:341:365:381:408 SD: 0.3256 cents 213:222:238:255:266:285:297:318:332:356:381:398:426 SD: 0.3100 cents 257:268:287:308:321:344:359:384:401:429:460:480:514 SD: 0.3075 cents 258:269:288:309:322:345:360:386:402:431:462:482:516 SD: 0.2893 cents 273:285:305:327:341:365:381:408:426:456:489:510:546 SD: 0.2601 cents 299:312:334:358:373:400:417:447:466:500:535:558:598 SD: 0.2525 cents 323:337:361:387:403:432:451:483:504:540:578:603:646 SD: 0.2484 cents 325:339:363:389:406:435:454:486:507:543:582:607:650 SD: 0.2324 cents 329:343:368:394:411:440:459:492:513:550:589:614:658 SD: 0.2197 cents 349:364:390:418:436:467:487:522:544:583:625:652:698 SD: 0.1895 cents 374:390:418:448:467:500:522:559:583:625:669:698:748 SD: 0.1818 cents 390:407:436:467:487:522:544:583:608:652:698:728:780 SD: 0.1747 cents 442:461:494:529:552:591:617:661:689:738:791:825:884 SD: 0.1512 cents 467:487:522:559:583:625:652:698:728:780:836:872:934 SD: 0.1378 cents 486:507:543:582:607:650:678:727:758:812:870:907:972 SD: 0.1351 cents 538:561:601:644:672:720:751:804:839:899:963:1004:1076 SD: 0.1348 cents 562:586:628:673:702:752:784:840:876:939:1006:1049:1124 SD: 0.1199 cents