Scala analysis: secor12_2
George Secor's 12-tone well-temperament #2, with 7 just fifths
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 194.868 cents 194.868280 3: 32/27 294.134997 Pythagorean minor third 4: 388.025 cents 388.025140 5: 4/3 498.044999 perfect fourth 6: 1024/729 588.269995 Pythagorean diminished fifth 7: 698.290 cents 698.289850 8: 128/81 792.179997 Pythagorean minor sixth 9: 891.447 cents 891.446710 10: 16/9 996.089998 Pythagorean minor seventh 11: 4096/2187 1086.314994 Pythagorean diminished octave 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 2187/2048 113.6850 apotome 1: 256/243 90.2250 limma, Pythagorean minor second 2: 104.6433 cents 104.6433 3: 99.2667 cents 99.2667 4: 93.8901 cents 93.8901 5: 110.0199 cents 110.0199 6: 256/243 90.2250 limma, Pythagorean minor second 7: 110.0199 cents 110.0199 8: 93.8901 cents 93.8901 9: 99.2667 cents 99.2667 10: 104.6433 cents 104.6433 11: 256/243 90.2250 limma, Pythagorean minor second 12: 2187/2048 113.6850 apotome
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 256/243 90.225 cents limma, Pythagorean minor second 1: 2 93.89014 cents 1: 2 99.26672 cents 1: 2 104.64328 cents 1: 2 110.01986 cents 1: 1 2187/2048 113.685 cents apotome 2: 2 193.15686 cents 2: 2 194.86828 cents 2: 2 200.24485 cents 2: 6 9/8 203.910 cents major whole tone 3: 5 32/27 294.135 cents Pythagorean minor third 3: 2 297.80014 cents 3: 2 303.17672 cents 3: 2 308.55329 cents 3: 1 310.26471 cents 4: 2 388.02514 cents 4: 2 393.40171 cents 4: 2 398.77829 cents 4: 2 404.15485 cents 4: 4 81/64 407.820 cents Pythagorean major third 5: 7 4/3 498.045 cents perfect fourth 5: 2 501.71015 cents 5: 3 503.42157 cents 6: 2 1024/729 588.270 cents Pythagorean diminished fifth 6: 2 591.93515 cents 6: 2 597.31172 cents 6: 2 602.68828 cents 6: 2 608.06485 cents 6: 2 729/512 611.730 cents Pythagorean tritone 7: 3 696.57843 cents 7: 2 698.28985 cents 7: 7 3/2 701.955 cents perfect fifth 8: 4 128/81 792.180 cents Pythagorean minor sixth 8: 2 795.84515 cents 8: 2 801.22171 cents 8: 2 806.59829 cents 8: 2 811.97486 cents 9: 1 889.73529 cents 9: 2 891.44671 cents 9: 2 896.82328 cents 9: 2 902.19986 cents 9: 5 27/16 905.865 cents Pythagorean major sixth 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 2 999.75515 cents 10: 2 1005.13172 cents 10: 2 1006.84314 cents 11: 1 4096/2187 1086.315 cents Pythagorean diminished octave 11: 2 1089.98014 cents 11: 2 1095.35672 cents 11: 2 1100.73328 cents 11: 2 1106.10986 cents 11: 3 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.72727 = 52/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 90.2 194.9 294.1 388.0 498.0 588.3 698.3 792.2 891.4 996.1 1086.3 1200.0 90.2 : 104.6 203.9 297.8 407.8 498.0 608.1 702.0 801.2 905.9 996.1 1109.8 1200.0 194.9 : 99.3 193.2 303.2 393.4 503.4 597.3 696.6 801.2 891.4 1005.1 1095.4 1200.0 294.1 : 93.9 203.9 294.1 404.2 498.0 597.3 702.0 792.2 905.9 996.1 1100.7 1200.0 388.0 : 110.0 200.2 310.3 404.2 503.4 608.1 698.3 812.0 902.2 1006.8 1106.1 1200.0 498.0 : 90.2 200.2 294.1 393.4 498.0 588.3 702.0 792.2 896.8 996.1 1090.0 1200.0 588.3 : 110.0 203.9 303.2 407.8 498.0 611.7 702.0 806.6 905.9 999.8 1109.8 1200.0 698.3 : 93.9 193.2 297.8 388.0 501.7 591.9 696.6 795.8 889.7 999.8 1090.0 1200.0 792.2 : 99.3 203.9 294.1 407.8 498.0 602.7 702.0 795.8 905.9 996.1 1106.1 1200.0 891.4 : 104.6 194.9 308.6 398.8 503.4 602.7 696.6 806.6 896.8 1006.8 1100.7 1200.0 996.1 : 90.2 203.9 294.1 398.8 498.0 591.9 702.0 792.2 902.2 996.1 1095.4 1200.0 1086.3: 113.7 203.9 308.6 407.8 501.7 611.7 702.0 812.0 905.9 1005.1 1109.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 113.6850 cents 531441/524288, 23.4600 cents 256/243, 90.2250 cents 2: 193.1569 .. 203.9100 cents 10.75314 cents 79.47185 cents 3: 294.1350 .. 310.2647 cents 16.12971 cents 256/243, 90.2250 cents 4: 388.0251 .. 407.8200 cents 19.79486 cents 77.76043 cents 5: 498.0450 .. 503.4216 cents 5.37657 cents 256/243, 90.2250 cents 6: 588.2700 .. 611.7300 cents 531441/524288, 23.4600 cents 84.84842 cents 7: 696.5784 .. 701.9550 cents 5.37657 cents 84.84842 cents 8: 792.1800 .. 811.9749 cents 19.79486 cents 256/243, 90.2250 cents 9: 889.7353 .. 905.8650 cents 16.12971 cents 77.76043 cents 10: 996.0900 .. 1006.8431 cents 10.75314 cents 256/243, 90.2250 cents 11: 1086.3150 .. 1109.7750 cents 531441/524288, 23.4600 cents 79.47185 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 2187/2048, 113.6850 cents Average / Smallest step : 1.108340 Largest / Average step : 1.136850 Largest / Smallest step : 1.260017 Median interval of one step : 99.26672 cents, amount: 2 Most common interval of one step : 256/243, 90.2250 cents, amount: 3 Least squares average step : 99.22026 cents, oct.: 1190.64307 cents Scale is strictly proper Step pattern alph. order: ABCDEAEDCBAF Step pattern size order : ADCBEAEBCDAF Scale is a Constant Structure, by a margin of 77.76043 cents Scale diversity : 1.121267 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.854593 Rothenberg efficiency : 0.281602 redundancy: 0.718398 Efficiency x scale size : 3.379221 Number of different interval sizes : 52 = 4.72727 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.72727 = 52/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1.71142 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 3 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 23.4600 cents: 2 3 5 7 9 10 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.0669 c. M:-13.6850 c. Twelve-tone Chromatic (1/11-comma) 39: 3 3 4 3 3 3 4 3 3 3 3 4 SP D3 SD: 8.4316 c. M:-13.5573 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 5.6754 c. M: 13.3979 c. Schismic-12 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 6.0177 c. M:-12.8417 c. Meantone Chromatic (1/5-comma) 50: 4 4 4 4 5 4 4 4 4 5 3 5 SP D3 SD: 6.2407 c. M:-11.9100 c. 52: 4 4 5 4 5 3 5 4 5 4 4 5 SP D3 SD: 6.8762 c. M: 11.3469 c. 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 3.8041 c. M:-8.9053 c. Schismic-12 63: 5 5 5 5 6 5 6 5 5 5 5 6 SP D3 SD: 5.2233 c. M: 8.4207 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.2958 c. M:-8.2086 c. 74: 6 6 6 6 7 5 7 6 6 6 6 7 SP D3 SD: 3.5703 c. M:-7.0723 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.4331 c. M:-7.7291 c. 82: 6 7 7 6 8 6 8 6 7 7 6 8 SP D3 SD: 3.2881 c. M: 7.5373 c. 83: 6 7 7 7 7 7 7 7 7 7 6 8 SP D3 SD: 4.1891 c. M: 6.9165 c. 84: 6 8 7 6 8 6 8 6 7 8 6 8 SP D3 SD: 3.9792 c. M: 6.4657 c. 86: 6 8 7 7 8 6 8 7 7 7 7 8 SP D3 S SD: 3.1675 c. M: 6.5041 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 3.7705 c. M:-7.3789 c. 92: 7 8 8 7 8 7 9 7 7 8 7 9 SP SD: 3.6508 c. M:-6.0580 c. 93: 7 8 8 7 9 7 8 7 8 8 7 9 SP SD: 2.9737 c. M:-5.2784 c. 94: 7 8 8 7 9 7 9 7 8 8 7 9 SP D3 SD: 2.2453 c. M: 5.0464 c. 98: 7 9 8 8 9 7 9 8 8 8 8 9 SP D3 S SD: 2.9223 c. M: 4.5107 c. 105: 8 9 9 8 10 7 10 8 9 9 8 10 SP SD: 2.6068 c. M: 5.4129 c. 106: 8 9 9 8 10 8 10 8 9 9 8 10 SP D3 SD: 1.7683 c. M:-3.5969 c. 118: 9 10 10 9 11 9 11 9 10 10 9 11 SP D3 SD: 1.7870 c. M:-3.4685 c. 130: 10 11 11 10 12 10 12 10 11 11 10 12 SP D3 SD: 2.0718 c. M:-3.9379 c. 135: 10 12 11 11 12 10 12 11 11 12 10 13 SP SD: 2.0636 c. M: 4.9565 c. 136: 10 12 11 11 12 11 12 11 11 12 10 13 SP SD: 1.9260 c. M: 3.9274 c. 147: 11 13 12 12 13 11 14 11 12 13 11 14 SP SD: 1.6698 c. M:-3.8116 c. 158: 12 14 13 12 15 11 15 12 13 14 12 15 SP SD: 2.0340 c. M: 3.4599 c. 159: 12 14 13 12 15 12 15 12 13 14 12 15 SP SD: 1.4703 c. M:-3.5969 c. 160: 12 14 13 13 14 12 15 13 13 14 12 15 SP SD: 1.8185 c. M: 3.2700 c. 167: 13 14 14 13 15 13 15 13 14 15 12 16 SP SD: 1.6066 c. M:-3.1882 c. 170: 13 15 14 13 16 12 16 13 14 15 13 16 SP SD: 1.8084 c. M:-3.1315 c. 171: 13 15 14 13 16 13 16 13 14 15 13 16 SP SD: 1.4307 c. M:-3.4645 c. 179: 13 16 15 14 16 14 16 14 15 16 13 17 SP SD: 1.5265 c. M: 3.0742 c. 182: 14 16 15 14 17 13 17 14 15 16 14 17 SP SD: 1.7761 c. M:-3.0539 c. 183: 14 16 15 14 17 14 17 14 15 16 14 17 SP SD: 1.5819 c. M:-3.3495 c. 188: 14 16 16 15 17 14 17 15 16 16 14 18 SP SD: 1.5429 c. M: 3.3789 c. 189: 14 17 15 15 17 15 17 15 15 17 14 18 SP SD: 1.6532 c. M: 2.8069 c. 190: 14 17 16 14 18 14 18 14 16 17 14 18 SP SD: 1.8200 c. M:-2.7628 c. 191: 14 17 16 15 17 15 17 15 16 17 14 18 SP SD: 1.5043 c. M:-2.8629 c. 192: 14 17 16 15 18 14 18 15 16 16 15 18 SP SD: 1.6096 c. M: 2.7250 c. 195: 15 17 16 15 18 15 18 15 16 17 15 18 SP SD: 1.8239 c. M:-3.2486 c. 196: 15 17 16 15 18 15 18 15 17 17 14 19 SP SD: 1.7337 c. M: 2.6415 c. 198: 15 17 16 16 18 15 18 16 16 17 15 19 SP SD: 1.4425 c. M: 3.2259 c. 200: 15 17 17 16 18 15 18 16 17 17 15 19 SP SD: 1.4193 c. M: 2.8683 c. 210: 16 18 17 17 19 16 19 17 17 18 16 20 SP SD: 1.2807 c. M: 2.7064 c. 211: 16 18 18 16 20 15 20 16 18 18 16 20 SP SD: 1.4786 c. M: 2.4880 c. 213: 16 19 17 17 19 16 20 17 17 19 16 20 SP SD: 1.4927 c. M: 2.3545 c. 217: 16 19 18 17 20 16 20 17 18 19 16 21 SP SD: 1.3914 c. M: 2.4440 c. 222: 17 19 18 18 20 17 20 18 18 19 17 21 SP SD: 1.2885 c. M:-2.4146 c. 224: 17 19 19 17 21 17 20 18 18 20 17 21 SP S SD: 1.3395 c. M: 2.3109 c. 229: 17 20 19 18 21 17 21 18 19 20 17 22 SP SD: 0.9365 c. M: 1.5988 c. 241: 18 21 20 19 22 18 22 19 20 21 18 23 SP SD: 0.5805 c. M: 1.1944 c. 253: 19 22 21 20 23 19 23 20 21 22 19 24 SP SD: 0.4310 c. M: 1.0566 c. 359: 27 31 30 28 33 27 33 28 30 31 27 34 SP SD: 0.4323 c. M:-1.0324 c. 400: 30 35 33 31 37 30 37 31 33 35 30 38 SP SD: 0.4139 c. M: 1.0251 c. 412: 31 36 34 32 38 31 38 32 34 36 31 39 SP SD: 0.3028 c. M:-0.7393 c. 424: 32 37 35 33 39 32 39 33 35 37 32 40 SP SD: 0.3534 c. M:-0.7668 c. 559: 42 49 46 44 51 42 51 44 46 49 42 53 SP SD: 0.3207 c. M: 0.6154 c. 612: 46 53 51 48 56 46 56 48 51 53 46 58 SP SD: 0.3135 c. M: 0.7506 c. 641: 48 56 53 50 59 48 59 50 53 56 48 61 SP SD: 0.3093 c. M: 0.5116 c. 653: 49 57 54 51 60 49 60 51 54 57 49 62 SP SD: 0.1563 c. M: 0.2763 c. 665: 50 58 55 52 61 50 61 52 55 58 50 63 SP SD: 0.0239 c. M:-0.0560 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: 1.8326 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.3627 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.8906 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.5385 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.7683 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.4564 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.4301 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.9762 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4873 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.1500 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.7326 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.2645 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.0565 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.3585 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.1185 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.9062 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.1751 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4235 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.3050 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.5711 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.4857 cents 36:38:40:43:45:48:51:54:57:60:64:67:72 SD: 2.3011 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.2517 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.9582 cents 49:52:55:58:61:65:69:73:77:82:87:92:98 SD: 1.9527 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.9236 cents 52:55:58:62:65:69:73:78:82:87:92:97:104 SD: 1.6814 cents 55:58:62:65:69:73:77:82:87:92:98:103:110 SD: 1.5959 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.2989 cents 60:63:67:71:75:80:84:90:95:100:107:112:120 SD: 1.2601 cents 72:76:81:85:90:96:101:108:114:120:128:135:144 SD: 1.2537 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.2410 cents 75:79:84:89:94:100:105:112:119:126:133:140:150 SD: 1.2094 cents 76:80:85:90:95:101:107:114:120:127:135:142:152 SD: 0.8232 cents 107:113:120:127:134:143:150:160:169:179:190:200:214 SD: 0.7827 cents 108:114:121:128:135:144:152:162:171:181:192:202:216 SD: 0.6765 cents 119:125:133:141:149:159:167:178:188:199:212:223:238 SD: 0.6762 cents 126:133:141:149:158:168:177:189:199:211:224:236:252 SD: 0.6255 cents 131:138:147:155:164:175:184:196:207:219:233:245:262 SD: 0.6018 cents 135:142:151:160:169:180:190:202:213:226:240:253:270 SD: 0.4538 cents 167:176:187:198:209:223:235:250:264:279:297:313:334 SD: 0.4518 cents 171:180:191:203:214:228:240:256:270:286:304:320:342 SD: 0.4475 cents 183:193:205:217:229:244:257:274:289:306:325:343:366 SD: 0.3301 cents 227:239:254:269:284:303:319:340:359:380:404:425:454 SD: 0.2990 cents 243:256:272:288:304:324:341:364:384:407:432:455:486 SD: 0.2198 cents 334:352:374:396:418:445:469:500:528:559:594:626:668 SD: 0.2110 cents 336:354:376:398:420:448:472:503:531:562:597:629:672 SD: 0.2106 cents 378:398:423:448:473:504:531:566:597:633:672:708:756 SD: 0.1580 cents 410:432:459:486:513:547:576:614:648:686:729:768:820 SD: 0.1370 cents 546:575:611:647:683:728:767:817:863:914:971:1023:1092 SD: 0.1252 cents 561:591:628:665:702:748:788:840:887:939:997:1051:1122 SD: 0.1239 cents 598:630:669:709:748:797:840:895:945:1001:1063:1120:1196 SD: 0.1145 cents