Scala analysis: xen18-erlich-superpyth-05
2L 3s MOS for Superpyth, L=270.69, s=218.74
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 218.740 cents 218.740000 2: 489.430 cents 489.430000 3: 708.170 cents 708.170000 4: 978.860 cents 978.860000 5: 1197.600 cents 1197.600000
SHOW/INTERVAL
0: 218.7400 cents 218.7400 1: 218.7400 cents 218.7400 2: 270.6900 cents 270.6900 3: 218.7400 cents 218.7400 4: 270.6900 cents 270.6900 5: 218.7400 cents 218.7400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 218.74000 cents 1: 2 270.69000 cents 2: 1 437.48000 cents 2: 4 489.43000 cents 3: 4 708.17000 cents 3: 1 760.12000 cents 4: 2 926.91000 cents 4: 3 978.86000 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 0.0 : 218.7 489.4 708.2 978.9 1197.6 218.7 : 270.7 489.4 760.1 978.9 1197.6 489.4 : 218.7 489.4 708.2 926.9 1197.6 708.2 : 270.7 489.4 708.2 978.9 1197.6 978.9 : 218.7 437.5 708.2 926.9 1197.6 1197.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 218.7400 .. 270.6900 cents 51.95000 cents 218.74000 cents 2: 437.4800 .. 489.4300 cents 51.95000 cents 166.79000 cents 3: 708.1700 .. 760.1200 cents 51.95000 cents 218.74000 cents 4: 926.9100 .. 978.8600 cents 51.95000 cents 166.79000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 218.74000 cents, class 1 Average step (divided formal octave): 239.5200 cents Largest one step interval : 270.69000 cents Average / Smallest step : 1.094999 Largest / Average step : 1.130135 Largest / Smallest step : 1.237497 Median interval of one step : 218.74000 cents, amount: 3 Most common interval of one step : 218.74000 cents, amount: 3 Least squares average step : 240.46455 cents, oct.: 1202.32273 cents Scale is strictly proper Scale has Myhill's property chromas: 51.95000 cents and 166.79000 cents, ratio: 3.210587 generators: 2 of 489.43000 cents and 3 of 708.17000 cents ET pair of linear temperament : 22&93 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 438-tone equal temperament with octave 1197.600 cents degrees: 80 179 259 358 438 generators: 179 and 259 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABA Step pattern size order : SLSLS Scale is a Constant Structure, by a margin of 166.79000 cents Scale diversity : 1.196929 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.826486 Rothenberg efficiency : 0.800000 redundancy: 0.200000 Efficiency x scale size : 4.000000 Number of different interval sizes : 8 = 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 : 51.95000 cents Most common intervals : 489.43000 cents & inv., amount: 4 Scale is a chain of 2 triads 0.0 489.430 978.860 cents Most common triad is 0.0 489.430 708.170 cents, amount: 3 Number of recognisable fifths : 4, average 708.1700 cents Number of recognisable fourths : 4, average 489.4300 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 5 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 14.6937 c. M:-20.7800 c. 12: 2 3 2 3 2 SP M ME I SD: 13.5340 c. M:-19.1400 c. Suspended Pentatonic, Raga Madhyamavati, Madhmat Sarang, Megh, Egyptian, Shang, Rui Bin, Jin Yu, Qing Yu: China, Yo: Japan, Ngu Cung Dao: Vietnam, Yematebela wofe: Ethiopia 17: 3 4 3 4 3 SP M ME I SD: 5.2318 c. M:-7.3988 c. Seventeen-tone Suspended Pentatonic 22: 4 5 4 5 4 SP M ME I SD: 0.7032 c. M:-0.9945 c. 71: 13 16 13 16 13 SP M DE I SD: 0.3810 c. M:-0.5389 c. 93: 17 21 17 21 17 SP M DE I SD: 0.1245 c. M: 0.1761 c. 115: 21 26 21 26 21 SP M DE I SD: 0.0338 c. M:-0.0478 c. 323: 59 73 59 73 59 SP M DE I SD: 0.0118 c. M:-0.0167 c. 438: 80 99 80 99 80 SP M DE I SD: 0.0002 c. M:-0.0003 c.
FIT/HARMONIC
1 x x x x 2 S SD: 2.4000 cents 2 x x 3 x 4 S SD: 3.3311 cents 3 x 4 x 5:6 S SD: 31.6412 cents 4 x 5:6:7:8 S SD: 25.9543 cents 6:7:8:9:11:12 SD: 17.2115 cents 8:9:11:12:14:16 SD: 12.9539 cents 12:14:16:18:21:24 S SD: 10.0715 cents 14:16:19:21:25:28 SD: 9.7205 cents 15:17:20:23:26:30 SD: 8.4978 cents 16:18:21:24:28:32 S SD: 5.3396 cents 21:24:28:32:37:42 SD: 5.2175 cents 22:25:29:33:39:44 SD: 3.6176 cents 30:34:40:45:53:60 SD: 2.5571 cents 37:42:49:56:65:74 SD: 2.1355 cents 46:52:61:69:81:92 SD: 1.8720 cents 58:66:77:87:102:116 SD: 1.7037 cents 59:67:78:89:104:118 SD: 1.5987 cents 67:76:89:101:118:134 SD: 0.8318 cents 125:142:166:188:220:250 SD: 0.7806 cents 141:160:187:212:248:282 SD: 0.7024 cents 150:170:199:226:264:300 SD: 0.6971 cents 162:184:215:244:285:324 SD: 0.6525 cents 178:202:236:268:313:356 SD: 0.6364 cents 184:209:244:277:324:367 SD: 0.6256 cents 192:218:255:289:338:383 SD: 0.6074 cents 208:236:276:313:366:415 SD: 0.3980 cents 245:278:325:369:431:489 SD: 0.3462 cents 267:303:354:402:470:533 SD: 0.2930 cents 275:312:365:414:484:549 SD: 0.2161 cents 297:337:394:447:523:593 SD: 0.2020 cents 334:379:443:503:588:667 SD: 0.1823 cents 364:413:483:548:641:727 SD: 0.1722 cents 459:521:609:691:808:917 SD: 0.1646 cents 475:539:630:715:836:949 SD: 0.1629 cents 572:649:759:861:1007:1142 SD: 0.1557 cents