Scala analysis: unimajorpenta
Pentacircle (896/891) tempered unimajor, 259et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78.764 cents 78.764480 2: 208.494 cents 208.494210 3: 287.259 cents 287.258690 4: 416.988 cents 416.988420 5: 495.753 cents 495.752900 6: 625.483 cents 625.482630 7: 704.247 cents 704.247100 8: 783.012 cents 783.011580 9: 912.741 cents 912.741310 10: 991.506 cents 991.505790 11: 1121.236 cents 1121.235520 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 78.7645 cents 78.7645 1: 78.7645 cents 78.7645 2: 129.7297 cents 129.7297 3: 78.7645 cents 78.7645 4: 129.7297 cents 129.7297 5: 78.7645 cents 78.7645 6: 129.7297 cents 129.7297 7: 78.7645 cents 78.7645 8: 78.7645 cents 78.7645 9: 129.7297 cents 129.7297 10: 78.7645 cents 78.7645 11: 129.7297 cents 129.7297 12: 78.7645 cents 78.7645
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 78.76448 cents 1: 5 129.72973 cents 2: 2 157.52895 cents 2: 10 208.49421 cents 3: 9 287.25869 cents 3: 3 338.22394 cents 4: 4 366.02316 cents 4: 8 416.98842 cents 5: 11 495.75290 cents 5: 1 546.71815 cents 6: 6 574.51737 cents 6: 6 625.48263 cents 7: 1 653.28185 cents 7: 11 704.24710 cents 8: 8 783.01158 cents 8: 4 833.97683 cents 9: 3 861.77606 cents 9: 9 912.74131 cents 10: 10 991.50579 cents 10: 2 1042.47104 cents 11: 5 1070.27027 cents 11: 7 1121.23552 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 : 78.8 208.5 287.3 417.0 495.8 625.5 704.2 783.0 912.7 991.5 1121.2 1200.0 78.8 : 129.7 208.5 338.2 417.0 546.7 625.5 704.2 834.0 912.7 1042.5 1121.2 1200.0 208.5 : 78.8 208.5 287.3 417.0 495.8 574.5 704.2 783.0 912.7 991.5 1070.3 1200.0 287.3 : 129.7 208.5 338.2 417.0 495.8 625.5 704.2 834.0 912.7 991.5 1121.2 1200.0 417.0 : 78.8 208.5 287.3 366.0 495.8 574.5 704.2 783.0 861.8 991.5 1070.3 1200.0 495.8 : 129.7 208.5 287.3 417.0 495.8 625.5 704.2 783.0 912.7 991.5 1121.2 1200.0 625.5 : 78.8 157.5 287.3 366.0 495.8 574.5 653.3 783.0 861.8 991.5 1070.3 1200.0 704.2 : 78.8 208.5 287.3 417.0 495.8 574.5 704.2 783.0 912.7 991.5 1121.2 1200.0 783.0 : 129.7 208.5 338.2 417.0 495.8 625.5 704.2 834.0 912.7 1042.5 1121.2 1200.0 912.7 : 78.8 208.5 287.3 366.0 495.8 574.5 704.2 783.0 912.7 991.5 1070.3 1200.0 991.5 : 129.7 208.5 287.3 417.0 495.8 625.5 704.2 834.0 912.7 991.5 1121.2 1200.0 1121.2: 78.8 157.5 287.3 366.0 495.8 574.5 704.2 783.0 861.8 991.5 1070.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.7645 .. 129.7297 cents 50.96525 cents 78.76448 cents 2: 157.5290 .. 208.4942 cents 50.96526 cents 27.79922 cents 3: 287.2587 .. 338.2239 cents 50.96525 cents 78.76448 cents 4: 366.0232 .. 416.9884 cents 50.96526 cents 27.79922 cents 5: 495.7529 .. 546.7181 cents 50.96525 cents 78.76448 cents 6: 574.5174 .. 625.4826 cents 50.96526 cents 27.79922 cents 7: 653.2819 .. 704.2471 cents 50.96525 cents 27.79922 cents 8: 783.0116 .. 833.9768 cents 50.96525 cents 78.76448 cents 9: 861.7761 .. 912.7413 cents 50.96525 cents 27.79923 cents 10: 991.5058 .. 1042.4710 cents 50.96525 cents 78.76448 cents 11: 1070.2703 .. 1121.2355 cents 50.96525 cents 27.79923 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 78.76447 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 129.72973 cents Average / Smallest step : 1.269608 Largest / Average step : 1.297297 Largest / Smallest step : 1.647059 Median interval of one step : 78.76448 cents, amount: 7 Most common interval of one step : 78.76448 cents, amount: 7 Least squares average step : 100.48352 cents, oct.: 1205.80220 cents Scale is strictly proper Scale has Myhill's property chromas: 50.96525 cents and 27.79923 cents, ratio: 1.833333 generators: 5 of 495.75290 cents and 7 of 704.24710 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 259-tone equal temperament with octave 1200.000 cents degrees: 17 45 62 90 107 135 152 169 197 214 242 259 generators: 107 and 152 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABAABABA Step pattern size order : SLSLSLSSLSLS Scale is a Constant Structure, by a margin of 27.79922 cents Ratio Whole / Half tone : 2.647058 Scale diversity : 1.214433 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.532819 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 : 27.79922 cents Most common intervals : 495.75290 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 78.764 704.247 cents Most common triad is 0.0 495.753 704.247 cents, amount: 10 Number of recognisable fifths : 11, average 704.2471 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.8142 c. M: 25.4826 c. Twelve-tone Chromatic (1/11-comma) 17: 1 2 1 2 1 2 1 1 2 1 2 1 P M ME SD: 5.7039 c. M:-9.8115 c. 29: 2 3 2 3 2 3 2 2 3 2 3 2 SP M ME SD: 2.7864 c. M: 4.7930 c. 46: 3 5 3 5 3 5 3 3 5 3 5 3 SP M DE SD: 0.3513 c. M:-0.6043 c. 167: 11 18 11 18 11 18 11 11 18 11 18 11 SP M DE SD: 0.1935 c. M: 0.3329 c. 213: 14 23 14 23 14 23 14 14 23 14 23 14 SP M DE SD: 0.0759 c. M: 0.1305 c. 259: 17 28 17 28 17 28 17 17 28 17 28 17 SP M DE SD: 0.0000 c. M: 0.0000 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: 1.1460 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.4917 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.5543 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.0747 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.2783 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.7776 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 11.8348 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.5991 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 8.7702 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 9.7281 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.5803 cents 13:14:15 x x 17:19 x 20:22:23:25:26 SD: 9.6156 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.8999 cents 16:17:18:19:20:21:23:24:25:27:28:31:32 SD: 5.0178 cents 18:19:20:21:23:24:26:27:28:30:32:34:36 SD: 4.6151 cents 21:22:24:25:27:28:30:32:33:36:37:40:42 SD: 4.0128 cents 22:23:25:26:28:29:32:33:35:37:39:42:44 SD: 3.3531 cents 23:24:26:27:29:31:33:35:36:39:41:44:46 SD: 3.2044 cents 30:31:34:35:38:40:43:45:47:51:53:57:60 SD: 2.9467 cents 37:39:42:44:47:49:53:56:58:63:66:71:74 SD: 2.6019 cents 39:41:44:46:50:52:56:59:61:66:69:75:78 SD: 2.0537 cents 40:42:45:47:51:53:57:60:63:68:71:76:80 SD: 1.8872 cents 44:46:50:52:56:59:63:66:69:75:78:84:88 SD: 1.8078 cents 48:50:54:57:61:64:69:72:75:81:85:92:96 SD: 1.6666 cents 60:63:68:71:76:80:86:90:94:102:106:115:120 SD: 1.5041 cents 62:65:70:73:79:83:89:93:97:105:110:118:124 SD: 1.3125 cents 66:69:74:78:84:88:95:99:104:112:117:126:132 SD: 1.1223 cents 78:82:88:92:99:104:112:117:123:132:138:149:156 SD: 0.9915 cents 84:88:95:99:107:112:121:126:132:142:149:161:168 SD: 0.9432 cents 88:92:99:104:112:117:126:132:138:149:156:168:176 SD: 0.7372 cents 110:115:124:130:140:146:158:165:173:186:195:210:220 SD: 0.6596 cents 124:130:140:146:158:165:178:186:195:210:220:237:248 SD: 0.5746 cents 133:139:150:157:169:177:191:200:209:225:236:254:266 SD: 0.4329 cents 154:161:174:182:196:205:221:231:242:261:273:294:308 SD: 0.4180 cents 172:180:194:203:219:229:247:258:270:291:305:329:344 SD: 0.3902 cents 212:222:239:250:270:282:304:318:333:359:376:405:424 SD: 0.3882 cents 217:227:245:256:276:289:311:326:341:368:385:415:434 SD: 0.3410 cents 235:246:265:277:299:313:337:353:369:398:417:449:470 SD: 0.3235 cents 239:250:270:282:304:318:343:359:376:405:424:457:478 SD: 0.3187 cents 257:269:290:303:327:342:369:386:404:435:456:491:514 SD: 0.2821 cents 283:296:319:334:360:377:406:425:445:479:502:541:566 SD: 0.2335 cents 304:318:343:359:387:405:436:457:478:515:539:581:608 SD: 0.2179 cents 305:319:344:360:388:406:438:458:479:517:541:583:610 SD: 0.2158 cents 327:342:369:386:416:435:469:491:514:554:580:625:654 SD: 0.2144 cents 344:360:388:406:438:458:494:517:541:583:610:657:688 SD: 0.2063 cents 360:377:406:425:458:479:517:541:566:610:638:688:720 SD: 0.2055 cents 367:384:414:433:467:489:527:551:577:622:651:701:734 SD: 0.1967 cents 383:401:432:452:487:510:550:575:602:649:679:732:766 SD: 0.1633 cents 470:492:530:555:598:626:675:706:739:796:833:898:940 SD: 0.1587 cents 476:498:537:562:606:634:683:715:748:806:844:910:952 SD: 0.1561 cents 492:515:555:581:626:655:706:739:773:834:872:940:984 SD: 0.1423 cents 510:534:575:602:649:679:732:766:802:864:904:975:1020 SD: 0.1388 cents 554:580:625:654:705:738:795:832:871:939:982:1059:1108 SD: 0.1266 cents