Scala analysis: pure7-6mnt
Meantone with pure 7:6, based on 836.75 TU for 64:63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 74.233 cents 74.232960 2: 192.638 cents 192.637990 3: 311.043 cents 311.043020 4: 385.276 cents 385.275980 5: 503.681 cents 503.681010 6: 577.914 cents 577.913960 7: 696.319 cents 696.318990 8: 770.552 cents 770.551950 9: 888.957 cents 888.956980 10: 1007.362 cents 1007.362010 11: 1081.595 cents 1081.594970 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 118.4050 cents 118.4050 1: 74.2330 cents 74.2330 2: 118.4050 cents 118.4050 3: 118.4050 cents 118.4050 4: 74.2330 cents 74.2330 5: 118.4050 cents 118.4050 6: 74.2330 cents 74.2330 7: 118.4050 cents 118.4050 8: 74.2330 cents 74.2330 9: 118.4050 cents 118.4050 10: 118.4050 cents 118.4050 11: 74.2330 cents 74.2330 12: 118.4050 cents 118.4050
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 74.23296 cents 1: 7 118.40503 cents 2: 10 192.63799 cents 2: 2 236.81006 cents 3: 3 266.87094 cents 3: 9 311.04302 cents 4: 8 385.27598 cents 4: 4 429.44805 cents 5: 1 459.50893 cents 5: 11 503.68101 cents 6: 6 577.91396 cents 6: 6 622.08603 cents 7: 11 696.31899 cents 7: 1 740.49107 cents 8: 4 770.55195 cents 8: 8 814.72402 cents 9: 9 888.95698 cents 9: 3 933.12905 cents 10: 2 963.18994 cents 10: 10 1007.36201 cents 11: 7 1081.59497 cents 11: 5 1125.76704 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 : 74.2 192.6 311.0 385.3 503.7 577.9 696.3 770.6 889.0 1007.4 1081.6 1200.0 74.2 : 118.4 236.8 311.0 429.4 503.7 622.1 696.3 814.7 933.1 1007.4 1125.8 1200.0 192.6 : 118.4 192.6 311.0 385.3 503.7 577.9 696.3 814.7 889.0 1007.4 1081.6 1200.0 311.0 : 74.2 192.6 266.9 385.3 459.5 577.9 696.3 770.6 889.0 963.2 1081.6 1200.0 385.3 : 118.4 192.6 311.0 385.3 503.7 622.1 696.3 814.7 889.0 1007.4 1125.8 1200.0 503.7 : 74.2 192.6 266.9 385.3 503.7 577.9 696.3 770.6 889.0 1007.4 1081.6 1200.0 577.9 : 118.4 192.6 311.0 429.4 503.7 622.1 696.3 814.7 933.1 1007.4 1125.8 1200.0 696.3 : 74.2 192.6 311.0 385.3 503.7 577.9 696.3 814.7 889.0 1007.4 1081.6 1200.0 770.6 : 118.4 236.8 311.0 429.4 503.7 622.1 740.5 814.7 933.1 1007.4 1125.8 1200.0 889.0 : 118.4 192.6 311.0 385.3 503.7 622.1 696.3 814.7 889.0 1007.4 1081.6 1200.0 1007.4: 74.2 192.6 266.9 385.3 503.7 577.9 696.3 770.6 889.0 963.2 1081.6 1200.0 1081.6: 118.4 192.6 311.0 429.4 503.7 622.1 696.3 814.7 889.0 1007.4 1125.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 74.2330 .. 118.4050 cents 44.17207 cents 74.23296 cents 2: 192.6380 .. 236.8101 cents 44.17207 cents 74.23296 cents 3: 266.8709 .. 311.0430 cents 44.17208 cents 30.06088 cents 4: 385.2760 .. 429.4481 cents 44.17207 cents 74.23296 cents 5: 459.5089 .. 503.6810 cents 44.17208 cents 30.06088 cents 6: 577.9140 .. 622.0860 cents 44.17207 cents 74.23295 cents 7: 696.3190 .. 740.4911 cents 44.17208 cents 74.23296 cents 8: 770.5520 .. 814.7240 cents 44.17207 cents 30.06088 cents 9: 888.9570 .. 933.1291 cents 44.17207 cents 74.23296 cents 10: 963.1899 .. 1007.3620 cents 44.17207 cents 30.06089 cents 11: 1081.5950 .. 1125.7670 cents 44.17207 cents 74.23296 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 74.23295 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 118.40503 cents Average / Smallest step : 1.347111 Largest / Average step : 1.184050 Largest / Smallest step : 1.595047 Median interval of one step : 118.40503 cents, amount: 7 Most common interval of one step : 118.40503 cents, amount: 7 Least squares average step : 98.96932 cents, oct.: 1187.63182 cents Scale is strictly proper Scale has Myhill's property chromas: 44.17207 cents and 30.06089 cents, ratio: 1.469420 generators: 5 of 503.68101 cents and 7 of 696.31899 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 1277-tone equal temperament with octave 2/1 degrees: 79 205 331 410 536 615 741 820 946 1072 1151 1277 generators: 536 and 741 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 30.06088 cents Ratio Whole / Half tone : 1.626941 Scale diversity : 1.221756 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.595089 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 : 30.06088 cents Most common intervals : 503.68101 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 118.405 696.319 cents Most common triad is 0.0 503.681 696.319 cents, amount: 10 Number of recognisable fifths : 11, average 696.3190 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: 15.6893 c. M:-29.4480 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 6.7435 c. M: 12.6572 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 1.9402 c. M:-3.6416 c. Meantone Chromatic (53/220-comma) 50: 3 5 5 3 5 3 5 3 5 5 3 5 SP M DE SD: 1.3596 c. M: 2.5520 c. Meantone Chromatic (5/18-comma), Eair-12 81: 5 8 8 5 8 5 8 5 8 8 5 8 SP M DE SD: 0.0967 c. M: 0.1816 c. Meantone Chromatic (5/19-comma), Aurus-12 355: 22 35 35 22 35 22 35 22 35 35 22 35 SP M DE SD: 0.0811 c. M:-0.1523 c. 436: 27 43 43 27 43 27 43 27 43 43 27 43 SP M DE SD: 0.0481 c. M:-0.0903 c. 517: 32 51 51 32 51 32 51 32 51 51 32 51 SP M DE SD: 0.0254 c. M:-0.0477 c. 598: 37 59 59 37 59 37 59 37 59 59 37 59 SP M DE SD: 0.0088 c. M:-0.0166 c. 679: 42 67 67 42 67 42 67 42 67 67 42 67 SP M DE SD: 0.0037 c. M: 0.0070 c. 1277: 79 126 126 79 126 79 126 79 126 126 79 126 SP M DE SD: 0.0022 c. M:-0.0040 c. 1956: 121 193 193 121 193 121 193 121 193 193 121 193 SP M DE SD: 0.0001 c. M:-0.0002 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: 2.8180 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.4246 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.7400 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.9612 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2417 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.5548 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.6080 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.2127 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.3711 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2284 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.4982 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.8777 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 7.8758 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.7735 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.2074 cents 18:19:20:22 x 24:25:27:28:30:32:34:36 SD: 4.5534 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.9072 cents 24:25:27:29:30:32:34:36:37:40:43:45:48 SD: 3.3613 cents 25:26:28:30:31:33:35:37:39:42:45:47:50 SD: 3.1383 cents 32:33:36:38:40:43:45:48:50:53:57:60:64 SD: 3.0564 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.4428 cents 41:43:46:49:51:55:57:61:64:69:73:77:82 SD: 2.1053 cents 44:46:49:53:55:59:61:66:69:74:79:82:88 SD: 2.0676 cents 45:47:50:54:56:60:63:67:70:75:81:84:90 SD: 1.7391 cents 51:53:57:61:64:68:71:76:80:85:91:95:102 SD: 1.5742 cents 60:63:67:72:75:80:84:90:94:100:107:112:120 SD: 1.4804 cents 61:64:68:73:76:82:85:91:95:102:109:114:122 SD: 1.2961 cents 66:69:74:79:82:88:92:99:103:110:118:123:132 SD: 1.2832 cents 68:71:76:81:85:91:95:102:106:114:122:127:136 SD: 1.0448 cents 76:79:85:91:95:102:106:114:119:127:136:142:152 SD: 1.0412 cents 85:89:95:102:106:114:119:127:133:142:152:159:170 SD: 0.9535 cents 91:95:102:109:114:122:127:136:142:152:163:170:182 SD: 0.6953 cents 113:118:126:135:141:151:158:169:176:189:202:211:226 SD: 0.6337 cents 136:142:152:163:170:182:190:203:212:227:243:254:272 SD: 0.4703 cents 137:143:153:164:171:183:191:205:214:229:245:256:274 SD: 0.4066 cents 189:197:211:226:236:253:264:283:295:316:338:353:378 SD: 0.4038 cents 204:213:228:244:255:273:285:305:318:341:365:381:408 SD: 0.2387 cents 228:238:255:273:285:305:318:341:356:381:408:426:456 SD: 0.2369 cents 305:318:341:365:381:408:426:456:476:510:546:570:610 SD: 0.2229 cents 325:339:363:389:406:435:454:486:507:543:582:607:650 SD: 0.2216 cents 341:356:381:408:426:456:476:510:532:570:610:637:682 SD: 0.1298 cents 432:451:483:517:540:578:603:646:674:722:773:807:864 SD: 0.1276 cents 553:577:618:662:691:740:772:827:863:924:990:1033:1106 SD: 0.1258 cents 569:594:636:681:711:761:794:851:888:951:1018:1063:1138 SD: 0.1196 cents