Scala analysis: meantop
TOP 5&7 limit meantone
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.157 cents 76.156642 2: 193.430 cents 193.430258 3: 310.704 cents 310.703874 4: 386.861 cents 386.860515 5: 504.134 cents 504.134131 6: 580.291 cents 580.290773 7: 697.564 cents 697.564389 8: 773.721 cents 773.721031 9: 890.995 cents 890.994647 10: 1008.268 cents 1008.268263 11: 1084.425 cents 1084.424904 12: 1201.699 cents 1201.698520
SHOW/INTERVAL
0: 117.2736 cents 117.2736 1: 76.1566 cents 76.1566 2: 117.2736 cents 117.2736 3: 117.2736 cents 117.2736 4: 76.1566 cents 76.1566 5: 117.2736 cents 117.2736 6: 76.1566 cents 76.1566 7: 117.2736 cents 117.2736 8: 76.1566 cents 76.1566 9: 117.2736 cents 117.2736 10: 117.2736 cents 117.2736 11: 76.1566 cents 76.1566 12: 117.2736 cents 117.2736
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 76.15664 cents 1: 7 117.27362 cents 2: 10 193.43026 cents 2: 2 234.54723 cents 3: 3 269.58690 cents 3: 9 310.70387 cents 4: 8 386.86051 cents 4: 4 427.97749 cents 5: 1 463.01716 cents 5: 11 504.13413 cents 6: 6 580.29077 cents 6: 6 621.40775 cents 7: 11 697.56439 cents 7: 1 738.68136 cents 8: 4 773.72103 cents 8: 8 814.83801 cents 9: 9 890.99465 cents 9: 3 932.11162 cents 10: 2 967.15129 cents 10: 10 1008.26826 cents 11: 7 1084.42490 cents 11: 5 1125.54188 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 : 76.2 193.4 310.7 386.9 504.1 580.3 697.6 773.7 891.0 1008.3 1084.4 1201.7 76.2 : 117.3 234.5 310.7 428.0 504.1 621.4 697.6 814.8 932.1 1008.3 1125.5 1201.7 193.4 : 117.3 193.4 310.7 386.9 504.1 580.3 697.6 814.8 891.0 1008.3 1084.4 1201.7 310.7 : 76.2 193.4 269.6 386.9 463.0 580.3 697.6 773.7 891.0 967.2 1084.4 1201.7 386.9 : 117.3 193.4 310.7 386.9 504.1 621.4 697.6 814.8 891.0 1008.3 1125.5 1201.7 504.1 : 76.2 193.4 269.6 386.9 504.1 580.3 697.6 773.7 891.0 1008.3 1084.4 1201.7 580.3 : 117.3 193.4 310.7 428.0 504.1 621.4 697.6 814.8 932.1 1008.3 1125.5 1201.7 697.6 : 76.2 193.4 310.7 386.9 504.1 580.3 697.6 814.8 891.0 1008.3 1084.4 1201.7 773.7 : 117.3 234.5 310.7 428.0 504.1 621.4 738.7 814.8 932.1 1008.3 1125.5 1201.7 891.0 : 117.3 193.4 310.7 386.9 504.1 621.4 697.6 814.8 891.0 1008.3 1084.4 1201.7 1008.3: 76.2 193.4 269.6 386.9 504.1 580.3 697.6 773.7 891.0 967.2 1084.4 1201.7 1084.4: 117.3 193.4 310.7 428.0 504.1 621.4 697.6 814.8 891.0 1008.3 1125.5 1201.7 1201.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.1566 .. 117.2736 cents 41.11697 cents 76.15664 cents 2: 193.4303 .. 234.5472 cents 41.11697 cents 76.15664 cents 3: 269.5869 .. 310.7039 cents 41.11698 cents 35.03967 cents 4: 386.8605 .. 427.9775 cents 41.11697 cents 76.15664 cents 5: 463.0172 .. 504.1341 cents 41.11697 cents 35.03967 cents 6: 580.2908 .. 621.4077 cents 41.11697 cents 76.15664 cents 7: 697.5644 .. 738.6814 cents 41.11697 cents 76.15664 cents 8: 773.7210 .. 814.8380 cents 41.11697 cents 35.03967 cents 9: 890.9946 .. 932.1116 cents 41.11697 cents 76.15664 cents 10: 967.1513 .. 1008.2683 cents 41.11698 cents 35.03967 cents 11: 1084.4249 .. 1125.5419 cents 41.11697 cents 76.15664 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 76.15664 cents, class 1 Average step (divided formal octave): 100.1415 cents Largest one step interval : 117.27362 cents Average / Smallest step : 1.314942 Largest / Average step : 1.171079 Largest / Smallest step : 1.539900 Median interval of one step : 117.27362 cents, amount: 7 Most common interval of one step : 117.27362 cents, amount: 7 Least squares average step : 99.18215 cents, oct.: 1190.18577 cents Scale is strictly proper Scale has Myhill's property chromas: 41.11697 cents and 35.03967 cents, ratio: 1.173441 generators: 5 of 504.13413 cents and 7 of 697.56439 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 789-tone equal temperament with octave 1201.699 cents degrees: 50 127 204 254 331 381 458 508 585 662 712 789 generators: 331 and 458 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 35.03967 cents Scale diversity : 1.217080 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.623627 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 : 35.03967 cents Most common intervals : 504.13413 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 117.274 697.564 cents Most common triad is 0.0 504.134 697.564 cents, amount: 10 Number of recognisable fifths : 11, average 697.5644 cents Number of recognisable fourths : 11, average 504.1341 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% 2/1 octave complements present : 0 = 0.0000% 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: 14.6042 c. M:-27.4113 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 7.8604 c. M: 14.7535 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 0.8356 c. M:-1.5683 c. Meantone Chromatic (53/220-comma) 112: 7 11 11 7 11 7 11 7 11 11 7 11 SP M DE SD: 0.6396 c. M: 1.2006 c. Meantone Chromatic (7/27-comma), Meanpop-12 143: 9 14 14 9 14 9 14 9 14 14 9 14 SP M DE SD: 0.3198 c. M: 0.6003 c. Meantone Chromatic (19/75-comma) 174: 11 17 17 11 17 11 17 11 17 17 11 17 SP M DE SD: 0.1140 c. M: 0.2139 c. Meantone Chromatic (1/4-comma), Milliet de Chales-12 205: 13 20 20 13 20 13 20 13 20 20 13 20 SP M DE SD: 0.0296 c. M:-0.0556 c. 584: 37 57 57 37 57 37 57 37 57 57 37 57 SP M DE SD: 0.0132 c. M: 0.0247 c. 789: 50 77 77 50 77 50 77 50 77 77 50 77 SP M DE SD: 0.0021 c. M: 0.0039 c. 1783: 113 174 174 113 174 113 174 113 174 174 113 174 SP M DE SD: 0.0016 c. M:-0.0030 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 1.6985 cents 2 x x x x x x 3 x x x x 4 S SD: 2.3539 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.0550 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.9315 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.2860 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5072 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.0803 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.9172 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.0335 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.0728 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2577 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.5338 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.9805 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.1363 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.8039 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.1226 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 4.1100 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.2689 cents 25:26:28:30:31:33:35:37:39:42:45:47:50 SD: 3.1716 cents 32:33:36:38:40:43:45:48:50:54:57:60:64 SD: 3.0019 cents 35:37:39:42:44:47:49:52:55:59:63:65:70 SD: 2.9355 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.6093 cents 40:42:45:48:50:54:56:60:63:67:72:75:80 SD: 2.2599 cents 41:43:46:49:51:55:57:61:64:69:73:77:82 SD: 2.0759 cents 44:46:49:53:55:59:62:66:69:74:79:82:88 SD: 2.0019 cents 45:47:50:54:56:60:63:67:70:75:81:84:90 SD: 1.9637 cents 48:50:54:57:60:64:67:72:75:80:86:90:96 SD: 1.7555 cents 51:53:57:61:64:68:71:76:80:85:91:95:102 SD: 1.7538 cents 52:54:58:62:65:70:73:78:81:87:93:97:104 SD: 1.7193 cents 60:63:67:72:75:80:84:90:94:100:107:112:120 SD: 1.3967 cents 65:68:73:78:81:87:91:97:102:109:116:122:130 SD: 1.3595 cents 67:70:75:80:84:90:94:100:105:112:120:125:134 SD: 1.1255 cents 68:71:76:81:85:91:95:102:106:114:122:127:136 SD: 1.0208 cents 83:87:93:99:104:111:116:124:130:139:149:155:166 SD: 0.9833 cents 85:89:95:102:106:114:119:127:133:142:152:159:170 SD: 0.8383 cents 91:95:102:109:114:122:127:136:142:152:163:170:182 SD: 0.7848 cents 92:96:103:110:115:123:129:138:144:154:165:172:184 SD: 0.7261 cents 128:134:143:153:160:171:179:192:200:214:229:239:256 SD: 0.6529 cents 133:139:149:159:166:178:186:199:208:223:238:249:266 SD: 0.5439 cents 153:160:171:183:191:205:214:229:239:256:274:286:306 SD: 0.4158 cents 204:213:228:244:255:273:285:305:319:341:365:382:408 SD: 0.3367 cents 248:259:277:297:310:332:347:371:388:415:444:464:496 SD: 0.3115 cents 264:276:295:316:330:353:369:395:413:442:473:494:529 SD: 0.2794 cents 296:309:331:354:370:396:414:443:463:495:530:554:593 SD: 0.2371 cents 311:325:348:372:389:416:435:465:486:520:557:582:623 SD: 0.2352 cents 355:371:397:425:444:475:496:531:555:594:636:664:711 SD: 0.1858 cents 397:415:444:475:496:531:555:594:621:664:711:743:795 SD: 0.1852 cents 423:442:473:506:529:566:591:633:661:708:757:791:847 SD: 0.1816 cents 447:467:500:535:559:598:625:669:699:748:800:836:895 SD: 0.1158 cents 550:575:615:658:688:736:769:823:860:920:985:1029:1101 SD: 0.1121 cents 600:627:671:718:750:803:839:898:938:1004:1074:1123:1201 SD: 0.1078 cents