Scala analysis: 500_M8
Miscellaneous tetrachord 92/91 * 91/90 * 30/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92/91 18.920779 2: 46/45 38.050632 23rd-partial chroma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 30/23 459.9944 1: 92/91 18.9208 2: 91/90 19.1299 medium tridecimal comma, superleap 3: 30/23 459.9944
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 92/91 18.921 cents 1: 1 91/90 19.130 cents medium tridecimal comma, superleap 1: 1 30/23 459.994 cents 2: 1 46/45 38.051 cents 23rd-partial chroma 2: 1 120/91 478.915 cents 2: 1 91/69 479.124 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 18.9 38.1 498.0 18.9 : 19.1 479.1 498.0 38.1 : 460.0 478.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.9208 .. 459.9944 cents 1365/1058, 441.0736 cents 92/91, 18.9208 cents 2: 38.0506 .. 479.1242 cents 1365/1058, 441.0736 cents 529/675,-421.9437 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 92/91, 18.9208 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 30/23, 459.9944 cents Average / Smallest step : 8.774216 Largest / Average step : 2.770800 Largest / Smallest step : 24.311598 Median interval of one step : 91/90, 19.1299 cents, amount: 1 Least squares average step : 113.51122 cents, oct.: 340.53365 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2238-tone equal temperament with octave 4/3 degrees: 85 171 2238 Least number of segments generator : 1121 of 249.468 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2033 of 452.424 cents and inv. generated superset size: 77 = 74 more = 2566.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 18.92078 cents Scale diversity :-0.019146 Lumma stability : 0.075980 Lumma impropriety factor : 0.847200 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 8281/8280, 0.2091 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 440.8645 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 23 Odd number limit : 91 (O: 91 U: 91) Highest odd numerator or denominator: 91 Scale harmonicity : 0.011330 Average absolute harmonicity : 0.081864 Specific harmonicity : 0.051524 Fundamental : 1/4095, -11.9996 octaves, 0.0639 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 3.767400E+05, 18.52321 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 140.5, average 46.83333 Mersenne's string divisions : 16653 Sum of van Prooijen's expressibility: 4.08938, average 1.36313 Sum of Tenney's harmonic distance : 8.31798, average 2.77266 Vogel's harmonic complexity : 36.66667 Wille's k value : 1046 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.35600, average 2.39267 Lattice compactness (without 2's) : 11.55934, average 1.92656 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 .. 0 -1.00000 3 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 16 19 27 33| Scale is weakly epimorphic with val: <7 11 16 19 28 32| Scale is weakly epimorphic with val: <7 11 16 19 28 35| Scale is JI-epimorphic with val: <7 11 16 20 26 33| Scale is weakly epimorphic with val: <7 11 16 20 27 32| Scale is weakly epimorphic with val: <7 11 16 20 27 35| Scale is weakly epimorphic with val: <7 11 16 21 26 32| Scale is weakly epimorphic with val: <7 11 16 21 26 35| Scale is weakly epimorphic with val: <7 11 16 21 28 33| Scale is weakly epimorphic with val: <7 11 17 19 26 33| Scale is JI-epimorphic with val: <7 11 17 19 28 34| Scale is JI-epimorphic with val: <7 11 17 20 27 34| Scale is weakly epimorphic with val: <7 11 17 20 28 33| Scale is JI-epimorphic with val: <7 11 17 21 26 34| Scale is weakly epimorphic with val: <7 11 17 21 27 33| Scale is weakly epimorphic with val: <7 11 18 19 26 32| Scale is weakly epimorphic with val: <7 11 18 19 26 35| Scale is weakly epimorphic with val: <7 11 18 19 27 34| Scale is weakly epimorphic with val: <7 11 18 20 26 34| Scale is weakly epimorphic with val: <7 11 18 20 28 32| Scale is JI-epimorphic with val: <7 11 18 20 28 35| Scale is weakly epimorphic with val: <7 11 18 21 27 32| Scale is JI-epimorphic with val: <7 11 18 21 27 35| Scale is weakly epimorphic with val: <7 11 18 21 28 34| Scale is weakly epimorphic with val: <7 12 16 19 26 34| Scale is weakly epimorphic with val: <7 12 17 19 27 35| Scale is weakly epimorphic with val: <7 12 17 20 26 35|
FIT/MODE
3: 0 0 3 N M DE S SD: 24.5346 c. M: 38.0506 c. 9: 0 1 8 N G T3 SD: 14.7971 c. M: 18.9208 c. 10: 0 1 9 N G T3 SD: 12.8601 c. M: 18.9208 c. 11: 0 1 10 N G T3 SD: 11.6935 c. M: 18.9208 c. 12: 0 1 11 N G T3 SD: 11.1044 c. M: 18.9208 c. 13: 0 1 12 N G T3 SD: 10.9250 c. M: 18.9208 c. 14: 0 1 13 N G T3 SD: 11.0171 c. M: 18.9208 c. 15: 0 1 14 N G T3 SD: 11.2768 c. M: 18.9208 c. 16: 0 1 15 N G T3 SD: 11.6322 c. M: 18.9208 c. 17: 0 1 16 N G T3 SD: 12.0364 c. M: 18.9208 c. 19: 1 0 18 N G T3 SD: 8.0272 c. M: 11.8377 c. 20: 1 1 18 N M DE S SD: 7.6143 c. M:-11.7539 c. 21: 1 1 19 N M DE S SD: 6.0834 c. M:-9.3822 c. 22: 1 1 20 N M DE S SD: 4.6918 c. M:-7.2262 c. 23: 1 1 21 N M DE S SD: 3.4212 c. M:-5.2576 c. 24: 1 1 22 N M DE S SD: 2.2566 c. M:-3.4531 c. 25: 1 1 23 N M DE S SD: 1.1856 c. M:-1.7930 c. 26: 1 1 24 N M DE S SD: 0.2025 c. M:-0.2605 c. 79: 3 3 73 N M DE S SD: 0.1297 c. M: 0.2244 c. 105: 4 4 97 N M DE S SD: 0.0674 c. M: 0.1043 c. 131: 5 5 121 N M DE S SD: 0.0544 c. M:-0.0886 c. 236: 9 9 218 N M DE S SD: 0.0559 c. M:-0.0725 c. 288: 11 11 266 N M DE S SD: 0.0588 c. M:-0.1018 c. 341: 13 13 315 N M DE S SD: 0.0584 c. M: 0.0765 c. 367: 14 14 339 N M DE S SD: 0.0544 c. M:-0.0782 c. 445: 17 17 411 N M DE S SD: 0.0610 c. M:-0.1057 c. 446: 17 17 412 N M DE S SD: 0.0602 c. M: 0.0831 c. 498: 19 19 460 N M DE S SD: 0.0541 c. M:-0.0809 c. 577: 22 22 533 N M DE S SD: 0.0573 c. M: 0.0715 c. 603: 23 23 557 N M DE S SD: 0.0549 c. M:-0.0760 c. 629: 24 24 581 N M DE S SD: 0.0540 c. M:-0.0825 c. 733: 28 28 677 N M DE S SD: 0.0601 c. M:-0.1041 c. 760: 29 29 702 N M DE S SD: 0.0540 c. M:-0.0836 c. 813: 31 31 751 N M DE S SD: 0.0568 c. M:-0.0699 c. 839: 32 32 775 N M DE S SD: 0.0551 c. M:-0.0750 c. 865: 33 33 799 N M DE S SD: 0.0542 c. M:-0.0798 c. 891: 34 34 823 N M DE S SD: 0.0540 c. M:-0.0843 c. 1178: 45 45 1088 N M DE S SD: 0.0605 c. M:-0.1047 c. 1189: 45 46 1098 N T3 SD: 0.0566 c. M: 0.0713 c. 1190: 45 46 1099 N T3 SD: 0.0543 c. M: 0.0871 c. 1216: 46 47 1123 N T3 SD: 0.0518 c. M: 0.0803 c. 1217: 46 47 1124 N T3 SD: 0.0555 c. M: 0.0957 c. 1232: 47 47 1138 N M DE S SD: 0.0543 c. M:-0.0793 c. 1242: 47 48 1147 N T3 SD: 0.0497 c. M: 0.0737 c. 1243: 47 48 1148 N T3 SD: 0.0519 c. M: 0.0888 c. 1268: 48 49 1171 N T3 SD: 0.0481 c. M: 0.0673 c. 1269: 48 49 1172 N T3 SD: 0.0487 c. M: 0.0822 c. 1270: 48 49 1173 N T3 SD: 0.0564 c. M: 0.0970 c. 1284: 49 49 1186 N M DE S SD: 0.0540 c. M:-0.0856 c. 1294: 49 50 1195 N T3 SD: 0.0469 c. M: 0.0613 c. 1295: 49 50 1196 N T3 SD: 0.0459 c. M: 0.0758 c. 1296: 49 50 1197 N T3 SD: 0.0523 c. M: 0.0904 c. 1320: 50 51 1219 N T3 SD: 0.0461 c. M:-0.0574 c. 1321: 50 51 1220 N T3 SD: 0.0435 c. M: 0.0697 c. 1322: 50 51 1221 N T3 SD: 0.0485 c. M: 0.0840 c. 1346: 51 52 1243 N T3 SD: 0.0456 c. M:-0.0613 c. 1347: 51 52 1244 N T3 SD: 0.0415 c. M: 0.0638 c. 1348: 51 52 1245 N T3 SD: 0.0450 c. M: 0.0778 c. 1373: 52 53 1268 N T3 SD: 0.0399 c. M: 0.0582 c. 1374: 52 53 1269 N T3 SD: 0.0419 c. M: 0.0719 c. 1399: 53 54 1292 N T3 SD: 0.0387 c. M: 0.0527 c. 1400: 53 54 1293 N T3 SD: 0.0391 c. M: 0.0662 c. 1401: 53 54 1294 N T3 SD: 0.0466 c. M: 0.0797 c. 1424: 54 55 1315 N T3 SD: 0.0461 c. M:-0.0722 c. 1425: 54 55 1316 N T3 SD: 0.0380 c. M: 0.0475 c. 1426: 54 55 1317 N T3 SD: 0.0367 c. M: 0.0607 c. 1427: 54 55 1318 N T3 SD: 0.0429 c. M: 0.0739 c. 1451: 55 56 1340 N T3 SD: 0.0376 c. M:-0.0493 c. 1452: 55 56 1341 N T3 SD: 0.0347 c. M: 0.0554 c. 1453: 55 56 1342 N T3 SD: 0.0395 c. M: 0.0684 c. 1477: 56 57 1364 N T3 SD: 0.0375 c. M:-0.0530 c. 1478: 56 57 1365 N T3 SD: 0.0330 c. M: 0.0503 c. 1479: 56 57 1366 N T3 SD: 0.0364 c. M: 0.0631 c. 1504: 57 58 1389 N T3 SD: 0.0318 c. M: 0.0454 c. 1505: 57 58 1390 N T3 SD: 0.0336 c. M: 0.0579 c. 1530: 58 59 1413 N T3 SD: 0.0310 c. M: 0.0406 c. 1531: 58 59 1414 N T3 SD: 0.0312 c. M: 0.0530 c. 1556: 59 60 1437 N T3 SD: 0.0306 c. M:-0.0389 c. 1557: 59 60 1438 N T3 SD: 0.0290 c. M: 0.0482 c. 1583: 60 61 1462 N T3 SD: 0.0273 c. M: 0.0435 c. 1584: 60 61 1463 N T3 SD: 0.0322 c. M: 0.0554 c. 1608: 61 62 1485 N T3 SD: 0.0309 c. M:-0.0461 c. 1609: 61 62 1486 N T3 SD: 0.0260 c. M: 0.0390 c. 1610: 61 62 1487 N T3 SD: 0.0293 c. M: 0.0508 c. 1635: 62 63 1510 N T3 SD: 0.0251 c. M: 0.0347 c. 1636: 62 63 1511 N T3 SD: 0.0267 c. M: 0.0462 c. 1661: 63 64 1534 N T3 SD: 0.0246 c. M: 0.0305 c. 1662: 63 64 1535 N T3 SD: 0.0245 c. M: 0.0418 c. 1688: 64 65 1559 N T3 SD: 0.0226 c. M: 0.0376 c. 1714: 65 66 1583 N T3 SD: 0.0211 c. M: 0.0334 c. 1740: 66 67 1607 N T3 SD: 0.0200 c. M: 0.0294 c. 1741: 66 67 1608 N T3 SD: 0.0233 c. M: 0.0403 c. 1766: 67 68 1631 N T3 SD: 0.0194 c. M: 0.0255 c. 1767: 67 68 1632 N T3 SD: 0.0209 c. M: 0.0362 c. 1792: 68 69 1655 N T3 SD: 0.0193 c. M:-0.0254 c. 1793: 68 69 1656 N T3 SD: 0.0188 c. M: 0.0323 c. 1819: 69 70 1680 N T3 SD: 0.0170 c. M: 0.0285 c. 1845: 70 71 1704 N T3 SD: 0.0157 c. M: 0.0248 c. 1871: 71 72 1728 N T3 SD: 0.0149 c. M: 0.0212 c. 1897: 72 73 1752 N T3 SD: 0.0146 c. M:-0.0182 c. 1898: 72 73 1753 N T3 SD: 0.0160 c. M: 0.0276 c. 1923: 73 74 1776 N T3 SD: 0.0149 c. M:-0.0215 c. 1924: 73 74 1777 N T3 SD: 0.0139 c. M: 0.0241 c. 1950: 74 75 1801 N T3 SD: 0.0123 c. M: 0.0206 c. 1976: 75 76 1825 N T3 SD: 0.0111 c. M: 0.0172 c. 2002: 76 77 1849 N T3 SD: 0.0105 c. M: 0.0140 c. 2029: 77 78 1874 N T3 SD: 0.0118 c. M: 0.0201 c. 2054: 78 79 1897 N T3 SD: 0.0113 c. M:-0.0180 c. 2055: 78 79 1898 N T3 SD: 0.0098 c. M: 0.0169 c. 2081: 79 80 1922 N T3 SD: 0.0081 c. M: 0.0137 c. 2107: 80 81 1946 N T3 SD: 0.0071 c. M: 0.0107 c. 2133: 81 82 1970 N T3 SD: 0.0069 c. M:-0.0091 c. 2186: 83 84 2019 N T3 SD: 0.0062 c. M: 0.0106 c. 2212: 84 85 2043 N T3 SD: 0.0045 c. M: 0.0077 c. 2238: 85 86 2067 N T3 SD: 0.0035 c. M: 0.0049 c. 2317: 88 89 2140 N T3 SD: 0.0037 c. M: 0.0050 c. 2343: 89 90 2164 N T3 SD: 0.0015 c. M: 0.0023 c. 2369: 90 91 2188 N T3 SD: 0.0010 c. M:-0.0018 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 114.4101 cents 7 x 8:9 S SD: 101.5637 cents 8 x 9:11 SD: 87.1024 cents 9 x 10:12 S SD: 72.1765 cents 10 x 11:13 SD: 67.1535 cents 11 x 12:15 S SD: 59.5596 cents 12 x 13:16 SD: 50.2610 cents 13 x 14:17 SD: 48.1528 cents 14 x 15:19 SD: 43.4846 cents 15 x 16:20 S SD: 36.8403 cents 16 x 17:21 SD: 36.1233 cents 17 x 18:23 SD: 32.9699 cents 18 x 19:24 SD: 27.7762 cents 19 x 20:25 S SD: 27.8450 cents 20 x 21:27 SD: 25.5784 cents 21 x 22:28 SD: 21.2432 cents 22 x 23:29 SD: 21.8239 cents 23 x 24:31 SD: 20.1233 cents 24 x 25:32 SD: 16.3109 cents 25 x 26:33 SD: 17.2753 cents 26 x 27:35 SD: 15.9611 cents 27 x 28:36 SD: 12.4551 cents 28 x 29:37 SD: 13.7514 cents 29 x 30:39 SD: 12.7169 cents 30 x 31:40 SD: 9.3581 cents 31 x 32:41 SD: 10.9839 cents 32 x 33:43 SD: 10.1641 cents 33 x 34:44 SD: 6.8159 cents 34 x 35:45 SD: 8.8100 cents 35 x 36:47 SD: 8.1662 cents 36 x 37:48 SD: 4.6917 cents 37 x 38:49 SD: 7.1356 cents 38 x 39:51 SD: 6.6474 cents 39 x 40:52 SD: 2.8902 cents 40 x 41:53 SD: 5.9136 cents 41 x 42:55 SD: 5.5725 cents 42 x 43:56 SD: 1.3431 cents 43 x 44:57 SD: 5.1226 cents 44 x 45:59 SD: 4.9230 cents 45 x 46:60 SD: 0.0000 cents 46 x 47:61 SD: 4.7350 cents 47 x 48:63 SD: 4.6615 cents 48 x 49:64 SD: 1.1769 cents 49 x 50:65 SD: 4.6871 cents 50 x 51:67 SD: 4.7104 cents 51 x 52:68 SD: 2.2167 cents 52 x 53:69 SD: 4.8825 cents 53 x 54:71 SD: 4.9687 cents 54 x 55:72 SD: 3.1420 cents 55 x 56:73 SD: 5.2254 cents 56 x 57:75 SD: 5.3468 cents 57 x 58:76 SD: 3.9707 cents 58 x 59:77 SD: 5.6443 cents 59 x 60:79 SD: 5.7826 cents 60 x 61:80 SD: 4.7173 cents 61:62 x 81 SD: 5.8254 cents 62:63 x 83 SD: 5.6039 cents 63:64 x 84 SD: 4.1717 cents 64:65 x 85 SD: 5.2117 cents 65:66 x 87 SD: 5.0145 cents 66:67 x 88 SD: 3.5567 cents 67:68 x 89 SD: 4.6676 cents 69:70:71:92 SD: 4.2974 cents 71:72:73:95 SD: 4.2933 cents 72:73:74:96 SD: 3.5377 cents 75:76:77:100 SD: 2.8380 cents 78:79:80:104 SD: 2.1917 cents 81:82:83:108 SD: 1.5929 cents 84:85:86:112 SD: 1.0367 cents 87:88:89:116 SD: 0.5197 cents 90:91:92:120 SD: 0.0697 cents