Scala analysis: leapday12
Leapday[12] in 46-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 130.435 cents 130.434783 2: 208.696 cents 208.695652 3: 286.957 cents 286.956522 4: 417.391 cents 417.391304 5: 495.652 cents 495.652174 6: 626.087 cents 626.086957 7: 704.348 cents 704.347826 8: 834.783 cents 834.782609 9: 913.043 cents 913.043478 10: 991.304 cents 991.304348 11: 1121.739 cents 1121.739130 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 78.2609 cents 78.2609 1: 130.4348 cents 130.4348 2: 78.2609 cents 78.2609 3: 78.2609 cents 78.2609 4: 130.4348 cents 130.4348 5: 78.2609 cents 78.2609 6: 130.4348 cents 130.4348 7: 78.2609 cents 78.2609 8: 130.4348 cents 130.4348 9: 78.2609 cents 78.2609 10: 78.2609 cents 78.2609 11: 130.4348 cents 130.4348 12: 78.2609 cents 78.2609
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 78.26087 cents 1: 5 130.43478 cents 2: 2 156.52174 cents 2: 10 208.69565 cents 3: 9 286.95652 cents 3: 3 339.13044 cents 4: 4 365.21739 cents 4: 8 417.39130 cents 5: 11 495.65217 cents 5: 1 547.82609 cents 6: 6 573.91304 cents 6: 6 626.08696 cents 7: 1 652.17391 cents 7: 11 704.34783 cents 8: 8 782.60870 cents 8: 4 834.78261 cents 9: 3 860.86957 cents 9: 9 913.04348 cents 10: 10 991.30435 cents 10: 2 1043.47826 cents 11: 5 1069.56522 cents 11: 7 1121.73913 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 : 130.4 208.7 287.0 417.4 495.7 626.1 704.3 834.8 913.0 991.3 1121.7 1200.0 130.4 : 78.3 156.5 287.0 365.2 495.7 573.9 704.3 782.6 860.9 991.3 1069.6 1200.0 208.7 : 78.3 208.7 287.0 417.4 495.7 626.1 704.3 782.6 913.0 991.3 1121.7 1200.0 287.0 : 130.4 208.7 339.1 417.4 547.8 626.1 704.3 834.8 913.0 1043.5 1121.7 1200.0 417.4 : 78.3 208.7 287.0 417.4 495.7 573.9 704.3 782.6 913.0 991.3 1069.6 1200.0 495.7 : 130.4 208.7 339.1 417.4 495.7 626.1 704.3 834.8 913.0 991.3 1121.7 1200.0 626.1 : 78.3 208.7 287.0 365.2 495.7 573.9 704.3 782.6 860.9 991.3 1069.6 1200.0 704.3 : 130.4 208.7 287.0 417.4 495.7 626.1 704.3 782.6 913.0 991.3 1121.7 1200.0 834.8 : 78.3 156.5 287.0 365.2 495.7 573.9 652.2 782.6 860.9 991.3 1069.6 1200.0 913.0 : 78.3 208.7 287.0 417.4 495.7 573.9 704.3 782.6 913.0 991.3 1121.7 1200.0 991.3 : 130.4 208.7 339.1 417.4 495.7 626.1 704.3 834.8 913.0 1043.5 1121.7 1200.0 1121.7: 78.3 208.7 287.0 365.2 495.7 573.9 704.3 782.6 913.0 991.3 1069.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.2609 .. 130.4348 cents 52.17391 cents 78.26087 cents 2: 156.5217 .. 208.6957 cents 52.17391 cents 26.08696 cents 3: 286.9565 .. 339.1304 cents 52.17391 cents 78.26087 cents 4: 365.2174 .. 417.3913 cents 52.17391 cents 26.08696 cents 5: 495.6522 .. 547.8261 cents 52.17391 cents 78.26087 cents 6: 573.9130 .. 626.0870 cents 52.17391 cents 26.08696 cents 7: 652.1739 .. 704.3478 cents 52.17391 cents 26.08696 cents 8: 782.6087 .. 834.7826 cents 52.17391 cents 78.26087 cents 9: 860.8696 .. 913.0435 cents 52.17391 cents 26.08696 cents 10: 991.3043 .. 1043.4783 cents 52.17391 cents 78.26087 cents 11: 1069.5652 .. 1121.7391 cents 52.17391 cents 26.08696 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 78.26087 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 130.43478 cents Average / Smallest step : 1.277778 Largest / Average step : 1.304348 Largest / Smallest step : 1.666667 Median interval of one step : 78.26087 cents, amount: 7 Most common interval of one step : 78.26087 cents, amount: 7 Least squares average step : 101.21739 cents, oct.: 1214.60870 cents Scale is strictly proper Scale has Myhill's property chromas: 52.17391 cents and 26.08696 cents, ratio: 2.000000 generators: 5 of 495.65217 cents and 7 of 704.34783 cents ET pair of linear temperament : 12&17 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 46-tone equal temperament with octave 1200.000 cents degrees: 5 8 11 16 19 24 27 32 35 38 43 46 generators: 19 and 27 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : LSSLSLSLSSLS Interval vector is [ 0 0 7 0 5 2 0 10 0 0 9 0 3 4 0 8 0 0 11 0 1 6 0 ] Scale is a Constant Structure, by a margin of 26.08696 cents Ratio Whole / Half tone : 2.666667 Scale diversity : 1.212477 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.521739 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 : 26.08696 cents Most common intervals : 495.65217 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 78.261 704.348 cents Most common triad is 0.0 495.652 704.348 cents, amount: 10 Number of recognisable fifths : 11, average 704.3478 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 --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.5315 c. M: 34.7826 c. Twelve-tone Chromatic (1/11-comma) 16: 2 1 1 2 1 1 1 2 1 1 2 1 P D3 SD: 20.0572 c. M:-32.6087 c. 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 6.5405 c. M:-12.2762 c. Twelve-tone Chromatic (2/11-comma positive) 29: 3 2 2 3 2 3 2 3 2 2 3 2 SP M ME SD: 3.8341 c. M: 7.1964 c. Twelve-tone Chromatic (1/14-comma positive) 46: 5 3 3 5 3 5 3 5 3 3 5 3 SP M DE SD: 0.0000 c. M: 0.0000 c. Twelve-tone Chromatic (1/9-comma positive)
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: 1.1964 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.5948 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.6074 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 12.4224 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.3143 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.5474 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.4800 cents 9 x 10:11 x 12:13:14 x 15:16:17:18 S SD: 10.7753 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.0975 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.3266 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3425 cents 13:14:15 x x 17:19:20:21:22:23:25:26 SD: 7.2949 cents 14:15:16:17:18:19:20:21:23:24:25:27:28 SD: 6.4173 cents 16:17:18:19:20:21:23:24:26:27:28:31:32 SD: 4.9378 cents 21:23:24:25:27:28:30:32:34:36:37:40:42 SD: 4.5857 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 3.6161 cents 23:25:26:27:29:31:33:35:37:39:41:44:46 SD: 3.4730 cents 26:28:29:31:33:35:37:39:42:44:46:50:52 SD: 3.1887 cents 30:32:34:35:38:40:43:45:49:51:53:57:60 SD: 2.9993 cents 34:37:38:40:43:45:49:51:55:58:60:65:68 SD: 2.6656 cents 37:40:42:44:47:49:53:56:60:63:66:71:74 SD: 2.3891 cents 39:42:44:46:50:52:56:59:63:66:69:75:78 SD: 1.8110 cents 48:52:54:57:61:64:69:72:78:81:85:92:96 SD: 1.5192 cents 55:59:62:65:70:73:79:83:89:93:98:105:110 SD: 1.3917 cents 62:67:70:73:79:83:89:93:100:105:110:119:124 SD: 1.2792 cents 66:71:74:78:84:88:95:99:107:112:117:126:132 SD: 1.1176 cents 76:82:86:90:97:101:109:114:123:129:135:145:152 SD: 0.9862 cents 78:84:88:92:99:104:112:117:126:132:138:149:156 SD: 0.7397 cents 115:124:130:136:146:153:165:173:186:195:204:220:230 SD: 0.6537 cents 124:134:140:146:158:165:178:186:201:210:220:237:248 SD: 0.5929 cents 140:151:158:165:178:186:201:210:227:237:248:268:280 SD: 0.5555 cents 150:162:169:177:191:200:215:225:243:254:266:287:300 SD: 0.5112 cents 154:166:174:182:196:205:221:231:249:261:273:294:308 SD: 0.4782 cents 166:179:187:196:211:221:238:249:269:281:294:317:332 SD: 0.4755 cents 177:191:200:209:225:236:254:266:287:300:314:338:354 SD: 0.4556 cents 179:193:202:211:228:238:257:269:290:303:317:342:358 SD: 0.3916 cents 193:208:218:228:246:257:277:290:313:327:342:369:386 SD: 0.3893 cents 205:221:231:242:261:273:294:308:332:347:363:392:410 SD: 0.3382 cents 227:245:256:268:289:302:326:341:368:385:402:434:454 SD: 0.3215 cents 239:258:270:282:304:318:343:359:387:405:424:457:478 SD: 0.3202 cents 257:277:290:303:327:342:369:386:416:435:456:491:514 SD: 0.3027 cents 271:292:306:320:345:361:389:407:439:459:480:518:542 SD: 0.2520 cents 305:329:344:360:388:406:438:458:494:517:541:583:610 SD: 0.1421 cents 422:455:476:498:537:562:606:634:683:715:748:807:844 SD: 0.1348 cents 498:537:562:588:634:663:715:748:807:844:883:952:996 SD: 0.1241 cents 510:550:575:602:649:679:732:766:826:864:904:975:1020 SD: 0.1089 cents 576:621:650:680:733:767:827:865:933:976:1021:1101:1152 SD: 0.0763 cents