Scala analysis: syncmt3
Synchronous Meantone Tuning 3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 74.071 cents 74.070880 2: 192.592 cents 192.591680 3: 311.112 cents 311.112480 4: 385.183 cents 385.183360 5: 503.704 cents 503.704160 6: 577.775 cents 577.775040 7: 696.296 cents 696.295840 8: 770.367 cents 770.366720 9: 888.888 cents 888.887520 10: 1007.408 cents 1007.408320 11: 1081.479 cents 1081.479200 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 118.5208 cents 118.5208 1: 74.0709 cents 74.0709 2: 118.5208 cents 118.5208 3: 118.5208 cents 118.5208 4: 74.0709 cents 74.0709 5: 118.5208 cents 118.5208 6: 74.0709 cents 74.0709 7: 118.5208 cents 118.5208 8: 74.0709 cents 74.0709 9: 118.5208 cents 118.5208 10: 118.5208 cents 118.5208 11: 74.0709 cents 74.0709 12: 118.5208 cents 118.5208
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 74.07088 cents 1: 7 118.52080 cents 2: 10 192.59168 cents 2: 2 237.04160 cents 3: 3 266.66256 cents 3: 9 311.11248 cents 4: 8 385.18336 cents 4: 4 429.63328 cents 5: 1 459.25424 cents 5: 11 503.70416 cents 6: 6 577.77504 cents 6: 6 622.22496 cents 7: 11 696.29584 cents 7: 1 740.74576 cents 8: 4 770.36672 cents 8: 8 814.81664 cents 9: 9 888.88752 cents 9: 3 933.33744 cents 10: 2 962.95840 cents 10: 10 1007.40832 cents 11: 7 1081.47920 cents 11: 5 1125.92912 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 : 74.1 192.6 311.1 385.2 503.7 577.8 696.3 770.4 888.9 1007.4 1081.5 1200.0 74.1 : 118.5 237.0 311.1 429.6 503.7 622.2 696.3 814.8 933.3 1007.4 1125.9 1200.0 192.6 : 118.5 192.6 311.1 385.2 503.7 577.8 696.3 814.8 888.9 1007.4 1081.5 1200.0 311.1 : 74.1 192.6 266.7 385.2 459.3 577.8 696.3 770.4 888.9 963.0 1081.5 1200.0 385.2 : 118.5 192.6 311.1 385.2 503.7 622.2 696.3 814.8 888.9 1007.4 1125.9 1200.0 503.7 : 74.1 192.6 266.7 385.2 503.7 577.8 696.3 770.4 888.9 1007.4 1081.5 1200.0 577.8 : 118.5 192.6 311.1 429.6 503.7 622.2 696.3 814.8 933.3 1007.4 1125.9 1200.0 696.3 : 74.1 192.6 311.1 385.2 503.7 577.8 696.3 814.8 888.9 1007.4 1081.5 1200.0 770.4 : 118.5 237.0 311.1 429.6 503.7 622.2 740.7 814.8 933.3 1007.4 1125.9 1200.0 888.9 : 118.5 192.6 311.1 385.2 503.7 622.2 696.3 814.8 888.9 1007.4 1081.5 1200.0 1007.4: 74.1 192.6 266.7 385.2 503.7 577.8 696.3 770.4 888.9 963.0 1081.5 1200.0 1081.5: 118.5 192.6 311.1 429.6 503.7 622.2 696.3 814.8 888.9 1007.4 1125.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 74.0709 .. 118.5208 cents 44.44992 cents 74.07088 cents 2: 192.5917 .. 237.0416 cents 44.44992 cents 74.07088 cents 3: 266.6626 .. 311.1125 cents 44.44992 cents 29.62096 cents 4: 385.1834 .. 429.6333 cents 44.44992 cents 74.07088 cents 5: 459.2542 .. 503.7042 cents 44.44992 cents 29.62096 cents 6: 577.7750 .. 622.2250 cents 44.44992 cents 74.07088 cents 7: 696.2958 .. 740.7458 cents 44.44992 cents 74.07088 cents 8: 770.3667 .. 814.8166 cents 44.44992 cents 29.62096 cents 9: 888.8875 .. 933.3374 cents 44.44992 cents 74.07088 cents 10: 962.9584 .. 1007.4083 cents 44.44992 cents 29.62096 cents 11: 1081.4792 .. 1125.9291 cents 44.44992 cents 74.07088 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 74.07088 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 118.52080 cents Average / Smallest step : 1.350058 Largest / Average step : 1.185208 Largest / Smallest step : 1.600100 Median interval of one step : 118.52080 cents, amount: 7 Most common interval of one step : 118.52080 cents, amount: 7 Least squares average step : 98.96284 cents, oct.: 1187.55402 cents Scale is strictly proper Scale has Myhill's property chromas: 44.44992 cents and 29.62096 cents, ratio: 1.500624 generators: 5 of 503.70416 cents and 7 of 696.29584 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 81-tone equal temperament with octave 2/1 degrees: 5 13 21 26 34 39 47 52 60 68 73 81 generators: 34 and 47 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : SLLSLSLSLLSL Interval vector is [ 0 0 0 0 5 0 0 7 0 0 0 0 10 0 0 2 0 3 0 0 9 0 0 0 0 8 0 0 4 0 1 0 0 11 0 0 0 0 6 0 ] Scale is a Constant Structure, by a margin of 29.62096 cents Ratio Whole / Half tone : 1.624961 Scale diversity : 1.221910 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.592542 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 : 29.62096 cents Most common intervals : 503.70416 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 118.521 696.296 cents Most common triad is 0.0 503.704 696.296 cents, amount: 10 Number of recognisable fifths : 11, average 696.2958 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: 15.7880 c. M:-29.6333 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 6.6448 c. M: 12.4720 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 2.0389 c. M:-3.8268 c. Meantone Chromatic (53/220-comma) 50: 3 5 5 3 5 3 5 3 5 5 3 5 SP M DE SD: 1.2609 c. M: 2.3667 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: 0.0019 c. M:-0.0037 c. Meantone Chromatic (5/19-comma), Aurus-12
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: 2.8296 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.4161 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.7529 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.9963 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2396 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.5809 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.6012 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.2228 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.3871 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2266 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.5048 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.8798 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 7.8880 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.7766 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.2142 cents 18:19:20:22 x 24:25:27:28:30:32:34:36 SD: 4.5545 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.8974 cents 24:25:27:29:30:32:34:36:37:40:43:45:48 SD: 3.3595 cents 25:26:28:30:31:33:35:37:39:42:45:47:50 SD: 3.1379 cents 32:33:36:38:40:43:45:48:50:53:57:60:64 SD: 3.0571 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.4442 cents 41:43:46:49:51:55:57:61:64:69:73:77:82 SD: 2.1127 cents 44:46:49:53:55:59:61:66:69:74:79:82:88 SD: 2.0657 cents 45:47:50:54:56:60:63:67:70:75:81:84:90 SD: 1.7289 cents 51:53:57:61:64:68:71:76:80:85:91:95:102 SD: 1.5738 cents 60:63:67:72:75:80:84:90:94:100:107:112:120 SD: 1.4962 cents 61:64:68:73:76:82:85:91:95:102:109:114:122 SD: 1.2946 cents 66:69:74:79:82:88:92:99:103:110:118:123:132 SD: 1.2778 cents 68:71:76:81:85:91:95:102:106:114:122:127:136 SD: 1.0503 cents 76:79:85:91:95:102:106:114:119:127:136:142:152 SD: 1.0401 cents 85:89:95:102:106:114:119:127:133:142:152:159:170 SD: 0.9678 cents 91:95:102:109:114:122:127:136:142:152:163:170:182 SD: 0.6984 cents 113:118:126:135:141:151:158:169:176:189:202:211:226 SD: 0.6325 cents 121:126:135:145:151:162:169:181:189:202:217:226:242 SD: 0.6251 cents 136:142:152:163:170:182:190:203:212:227:243:254:272 SD: 0.4659 cents 137:143:153:164:171:183:191:205:214:229:245:256:274 SD: 0.4067 cents 189:197:211:226:236:253:264:283:295:316:338:353:378 SD: 0.4015 cents 204:213:228:244:255:273:285:305:318:341:365:381:408 SD: 0.2410 cents 228:238:255:273:285:305:318:341:356:381:408:426:456 SD: 0.2407 cents 273:285:305:327:341:365:381:408:426:456:489:510:546 SD: 0.2353 cents 305:318:341:365:381:408:426:456:476:510:546:570:610 SD: 0.2228 cents 325:339:363:389:406:435:454:486:507:543:582:607:650 SD: 0.2107 cents 341:356:381:408:426:456:476:510:532:570:610:637:682 SD: 0.1325 cents 477:498:533:571:596:638:666:713:744:797:854:891:954 SD: 0.1293 cents 553:577:618:662:691:740:772:827:863:924:990:1033:1106 SD: 0.1175 cents 598:624:668:716:747:800:835:894:933:999:1070:1117:1196 SD: 0.1161 cents