Scala analysis: 501_M9
Miscellaneous tetrachord 90/89 * 89/88 * 176/135
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 90/89 19.343598 2: 45/44 38.905773 1/5-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 176/135 459.1392 1: 90/89 19.3436 2: 89/88 19.5622 3: 176/135 459.1392
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 90/89 19.344 cents 1: 1 89/88 19.562 cents 1: 1 176/135 459.139 cents 2: 1 45/44 38.906 cents 1/5-tone 2: 1 352/267 478.483 cents 2: 1 178/135 478.701 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 : 19.3 38.9 498.0 19.3 : 19.6 478.7 498.0 38.9 : 459.1 478.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.3436 .. 459.1392 cents 7832/6075, 439.7956 cents 90/89, 19.3436 cents 2: 38.9058 .. 478.7014 cents 7832/6075, 439.7956 cents 6075/7744,-420.2335 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 90/89, 19.3436 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 176/135, 459.1392 cents Average / Smallest step : 8.582426 Largest / Average step : 2.765649 Largest / Smallest step : 23.735978 Median interval of one step : 89/88, 19.5622 cents, amount: 1 Least squares average step : 113.66358 cents, oct.: 340.99074 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2189-tone equal temperament with octave 4/3 degrees: 85 171 2189 Least number of segments generator : 1095 of 249.136 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1631 of 371.088 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 19.34360 cents Scale diversity :-0.013299 Lumma stability : 0.077678 Lumma impropriety factor : 0.843766 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 : 7921/7920, 0.2186 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 439.5771 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 89 Odd number limit : 267 (O: 89 U: 267) Highest odd numerator or denominator: 89 Scale harmonicity : 0.027336 Fundamental : 1/11748, -13.5201 octaves, 0.0223 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 2.114640E+06, 21.01198 octaves Euler's gradus suavitatis : 113 Sum of Mann's harmonic distance : 137.5, average 45.83333 Mersenne's string divisions : 111517 Sum of van Prooijen's expressibility: 4.07972, average 1.35991 Sum of Tenney's harmonic distance : 8.27948, average 2.75983 Vogel's harmonic complexity : 78.33333 Wille's k value : 6007 Wilson's harmonic complexity : 114 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 19.52289, average 3.25382 Lattice compactness (without 2's) : 13.16446, average 2.19408 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 2 1.00000 5 1 5: 0 .. 1 0.66667 2 11: -1 .. 0 -0.33333 1 1 89: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 18 23 46| Scale is weakly epimorphic with val: <6 10 19 24 47| Scale is weakly epimorphic with val: <6 11 16 23 48| Scale is weakly epimorphic with val: <6 11 17 24 46| Scale is weakly epimorphic with val: <6 11 18 25 47| Scale is weakly epimorphic with val: <6 11 19 26 48| Scale is weakly epimorphic with val: <7 11 15 24 46| Scale is weakly epimorphic with val: <7 11 15 25 48| Scale is weakly epimorphic with val: <7 11 15 27 46| Scale is weakly epimorphic with val: <7 11 16 23 46| Scale is weakly epimorphic with val: <7 11 16 25 47| Scale is weakly epimorphic with val: <7 11 16 26 46| Scale is weakly epimorphic with val: <7 11 17 23 48| Scale is weakly epimorphic with val: <7 11 17 24 47| Scale is weakly epimorphic with val: <7 11 17 26 48| Scale is weakly epimorphic with val: <7 11 17 27 47| Scale is JI-epimorphic with val: <7 11 18 24 46| Scale is weakly epimorphic with val: <7 11 18 25 48| Scale is weakly epimorphic with val: <7 11 18 27 46| Scale is weakly epimorphic with val: <7 11 19 23 46| Scale is JI-epimorphic with val: <7 11 19 25 47| Scale is weakly epimorphic with val: <7 11 19 26 46| Scale is weakly epimorphic with val: <7 12 16 23 46| Scale is weakly epimorphic with val: <7 12 17 24 47| Scale is weakly epimorphic with val: <7 12 18 24 46| Scale is weakly epimorphic with val: <7 12 18 25 48| Scale is weakly epimorphic with val: <7 12 18 27 46| Scale is weakly epimorphic with val: <7 12 19 25 47| Scale is weakly epimorphic with val: <7 12 19 26 46| Scale is weakly epimorphic with val: <8 11 19 24 46| Scale is weakly epimorphic with val: <8 11 19 27 46| Scale is weakly epimorphic with val: <8 12 17 23 46| Scale is weakly epimorphic with val: <8 12 17 26 46| Scale is weakly epimorphic with val: <8 12 18 23 48| Scale is weakly epimorphic with val: <8 12 18 24 47| Scale is weakly epimorphic with val: <8 12 18 27 47| Scale is weakly epimorphic with val: <8 12 19 24 46| Scale is weakly epimorphic with val: <8 12 19 25 48|
FIT/MODE
3: 0 0 3 N M DE S SD: 25.0854 c. M: 38.9058 c. 9: 0 1 8 N G T3 SD: 14.6538 c. M: 19.3436 c. 10: 0 1 9 N G T3 SD: 12.8187 c. M: 19.3436 c. 11: 0 1 10 N G T3 SD: 11.7582 c. M: 19.3436 c. 12: 0 1 11 N G T3 SD: 11.2683 c. M: 19.3436 c. 13: 0 1 12 N G T3 SD: 11.1733 c. M: 19.3436 c. 14: 0 1 13 N G T3 SD: 11.3324 c. M: 19.3436 c. 15: 0 1 14 N G T3 SD: 11.6433 c. M: 19.3436 c. 16: 0 1 15 N G T3 SD: 12.0370 c. M: 19.3436 c. 17: 0 1 16 N G T3 SD: 12.4701 c. M: 19.3436 c. 18: 1 0 17 N G T3 SD: 8.0742 c. M: 11.2366 c. 19: 1 1 17 N M DE S SD: 8.7555 c. M:-13.5200 c. 20: 1 1 18 N M DE S SD: 7.0635 c. M:-10.8987 c. 21: 1 1 19 N M DE S SD: 5.5327 c. M:-8.5271 c. 22: 1 1 20 N M DE S SD: 4.1411 c. M:-6.3710 c. 23: 1 1 21 N M DE S SD: 2.8706 c. M:-4.4025 c. 24: 1 1 22 N M DE S SD: 1.7061 c. M:-2.5980 c. 25: 1 1 23 N M DE S SD: 0.6361 c. M:-0.9378 c. 26: 1 1 24 N M DE S SD: 0.3601 c. M: 0.5946 c. 51: 2 2 47 N M DE S SD: 0.1411 c. M:-0.1876 c. 77: 3 3 71 N M DE S SD: 0.0661 c. M: 0.0971 c. 128: 5 5 118 N M DE S SD: 0.0643 c. M:-0.1113 c. 205: 8 8 189 N M DE S SD: 0.0568 c. M:-0.0923 c. 282: 11 11 260 N M DE S SD: 0.0566 c. M:-0.0837 c. 359: 14 14 331 N M DE S SD: 0.0575 c. M:-0.0788 c. 436: 17 17 402 N M DE S SD: 0.0585 c. M:-0.0756 c. 487: 19 19 449 N M DE S SD: 0.0564 c. M:-0.0873 c. 513: 20 20 473 N M DE S SD: 0.0593 c. M:-0.0734 c. 538: 21 21 496 N M DE S SD: 0.0577 c. M:-0.0968 c. 641: 25 25 591 N M DE S SD: 0.0571 c. M:-0.0809 c. 692: 27 27 638 N M DE S SD: 0.0565 c. M:-0.0888 c. 1101: 43 43 1015 N M DE S SD: 0.0622 c. M:-0.1078 c. 1102: 43 43 1016 N M DE S SD: 0.0565 c. M:-0.0901 c. 1163: 45 46 1072 N T3 SD: 0.0560 c. M: 0.0727 c. 1164: 45 46 1073 N T3 SD: 0.0545 c. M: 0.0893 c. 1165: 45 46 1074 N T3 SD: 0.0611 c. M: 0.1058 c. 1179: 46 46 1087 N M DE S SD: 0.0564 c. M:-0.0882 c. 1189: 46 47 1096 N T3 SD: 0.0521 c. M: 0.0752 c. 1190: 46 47 1097 N T3 SD: 0.0537 c. M: 0.0914 c. 1191: 46 47 1098 N T3 SD: 0.0628 c. M: 0.1076 c. 1204: 47 47 1110 N M DE S SD: 0.0582 c. M:-0.0984 c. 1205: 47 47 1111 N M DE S SD: 0.0568 c. M:-0.0822 c. 1214: 47 48 1119 N T3 SD: 0.0531 c. M:-0.0681 c. 1215: 47 48 1120 N T3 SD: 0.0494 c. M: 0.0777 c. 1216: 47 48 1121 N T3 SD: 0.0540 c. M: 0.0935 c. 1240: 48 49 1143 N T3 SD: 0.0486 c. M: 0.0644 c. 1241: 48 49 1144 N T3 SD: 0.0480 c. M: 0.0800 c. 1242: 48 49 1145 N T3 SD: 0.0553 c. M: 0.0955 c. 1265: 49 50 1166 N T3 SD: 0.0510 c. M:-0.0717 c. 1266: 49 50 1167 N T3 SD: 0.0453 c. M: 0.0670 c. 1267: 49 50 1168 N T3 SD: 0.0478 c. M: 0.0822 c. 1291: 50 51 1190 N T3 SD: 0.0460 c. M:-0.0582 c. 1292: 50 51 1191 N T3 SD: 0.0432 c. M: 0.0694 c. 1293: 50 51 1192 N T3 SD: 0.0487 c. M: 0.0843 c. 1317: 51 52 1214 N T3 SD: 0.0421 c. M: 0.0571 c. 1318: 51 52 1215 N T3 SD: 0.0424 c. M: 0.0718 c. 1319: 51 52 1216 N T3 SD: 0.0505 c. M: 0.0864 c. 1342: 52 53 1237 N T3 SD: 0.0443 c. M:-0.0620 c. 1343: 52 53 1238 N T3 SD: 0.0393 c. M: 0.0597 c. 1344: 52 53 1239 N T3 SD: 0.0428 c. M: 0.0740 c. 1368: 53 54 1261 N T3 SD: 0.0398 c. M:-0.0495 c. 1369: 53 54 1262 N T3 SD: 0.0379 c. M: 0.0621 c. 1370: 53 54 1263 N T3 SD: 0.0442 c. M: 0.0762 c. 1393: 54 55 1284 N T3 SD: 0.0433 c. M:-0.0654 c. 1394: 54 55 1285 N T3 SD: 0.0364 c. M: 0.0506 c. 1395: 54 55 1286 N T3 SD: 0.0376 c. M: 0.0644 c. 1420: 55 56 1309 N T3 SD: 0.0341 c. M: 0.0531 c. 1421: 55 56 1310 N T3 SD: 0.0385 c. M: 0.0667 c. 1445: 56 57 1332 N T3 SD: 0.0342 c. M: 0.0422 c. 1446: 56 57 1333 N T3 SD: 0.0332 c. M: 0.0555 c. 1471: 57 58 1356 N T3 SD: 0.0313 c. M: 0.0448 c. 1472: 57 58 1357 N T3 SD: 0.0335 c. M: 0.0579 c. 1496: 58 59 1379 N T3 SD: 0.0330 c. M:-0.0456 c. 1497: 58 59 1380 N T3 SD: 0.0295 c. M: 0.0473 c. 1498: 58 59 1381 N T3 SD: 0.0349 c. M: 0.0601 c. 1522: 59 60 1403 N T3 SD: 0.0293 c. M: 0.0370 c. 1523: 59 60 1404 N T3 SD: 0.0292 c. M: 0.0497 c. 1548: 60 61 1427 N T3 SD: 0.0267 c. M: 0.0395 c. 1549: 60 61 1428 N T3 SD: 0.0300 c. M: 0.0520 c. 1573: 61 62 1450 N T3 SD: 0.0281 c. M:-0.0386 c. 1574: 61 62 1451 N T3 SD: 0.0255 c. M: 0.0420 c. 1599: 62 63 1474 N T3 SD: 0.0248 c. M: 0.0323 c. 1600: 62 63 1475 N T3 SD: 0.0257 c. M: 0.0444 c. 1625: 63 64 1498 N T3 SD: 0.0227 c. M: 0.0348 c. 1626: 63 64 1499 N T3 SD: 0.0271 c. M: 0.0467 c. 1650: 64 65 1521 N T3 SD: 0.0238 c. M:-0.0323 c. 1651: 64 65 1522 N T3 SD: 0.0221 c. M: 0.0372 c. 1676: 65 66 1545 N T3 SD: 0.0208 c. M: 0.0280 c. 1677: 65 66 1546 N T3 SD: 0.0228 c. M: 0.0395 c. 1702: 66 67 1569 N T3 SD: 0.0191 c. M: 0.0305 c. 1727: 67 68 1592 N T3 SD: 0.0198 c. M:-0.0265 c. 1728: 67 68 1593 N T3 SD: 0.0191 c. M: 0.0328 c. 1753: 68 69 1616 N T3 SD: 0.0171 c. M: 0.0241 c. 1754: 68 69 1617 N T3 SD: 0.0205 c. M: 0.0351 c. 1778: 69 70 1639 N T3 SD: 0.0197 c. M:-0.0303 c. 1779: 69 70 1640 N T3 SD: 0.0160 c. M: 0.0265 c. 1804: 70 71 1663 N T3 SD: 0.0161 c. M:-0.0212 c. 1805: 70 71 1664 N T3 SD: 0.0166 c. M: 0.0288 c. 1830: 71 72 1687 N T3 SD: 0.0139 c. M: 0.0205 c. 1856: 72 73 1711 N T3 SD: 0.0134 c. M: 0.0229 c. 1881: 73 74 1734 N T3 SD: 0.0128 c. M:-0.0164 c. 1882: 73 74 1735 N T3 SD: 0.0147 c. M: 0.0252 c. 1907: 74 75 1758 N T3 SD: 0.0110 c. M: 0.0173 c. 1933: 75 76 1782 N T3 SD: 0.0113 c. M: 0.0196 c. 1958: 76 77 1805 N T3 SD: 0.0097 c. M:-0.0119 c. 1984: 77 78 1829 N T3 SD: 0.0085 c. M: 0.0142 c. 2010: 78 79 1853 N T3 SD: 0.0098 c. M: 0.0165 c. 2035: 79 80 1876 N T3 SD: 0.0070 c. M: 0.0092 c. 2061: 80 81 1900 N T3 SD: 0.0066 c. M: 0.0114 c. 2112: 82 83 1947 N T3 SD: 0.0045 c. M: 0.0066 c. 2189: 85 86 2018 N T3 SD: 0.0025 c. M: 0.0043 c. 2240: 87 88 2065 N T3 SD: 0.0023 c. M:-0.0040 c. 2266: 88 89 2089 N T3 SD: 0.0020 c. M: 0.0029 c. 2317: 90 91 2136 N T3 SD: 0.0013 c. M:-0.0021 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: 113.9826 cents 7 x 8:9 S SD: 101.1573 cents 8 x 9:11 SD: 86.6954 cents 9 x 10:12 S SD: 71.7490 cents 10 x 11:13 SD: 66.7495 cents 11 x 12:15 S SD: 59.1556 cents 12 x 13:16 SD: 49.8334 cents 13 x 14:17 SD: 47.7523 cents 14 x 15:19 SD: 43.0847 cents 15 x 16:20 S SD: 36.4128 cents 16 x 17:21 SD: 35.7277 cents 17 x 18:23 SD: 32.5754 cents 18 x 19:24 SD: 27.3486 cents 19 x 20:25 S SD: 27.4559 cents 20 x 21:27 SD: 25.1911 cents 21 x 22:28 SD: 20.8156 cents 22 x 23:29 SD: 21.4437 cents 23 x 24:31 SD: 19.7458 cents 24 x 25:32 SD: 15.8833 cents 25 x 26:33 SD: 16.9073 cents 26 x 27:35 SD: 15.5972 cents 27 x 28:36 SD: 12.0276 cents 28 x 29:37 SD: 13.4007 cents 29 x 30:39 SD: 12.3724 cents 30 x 31:40 SD: 8.9305 cents 31 x 32:41 SD: 10.6582 cents 32 x 33:43 SD: 9.8480 cents 33 x 34:44 SD: 6.3883 cents 34 x 35:45 SD: 8.5213 cents 35 x 36:47 SD: 7.8921 cents 36 x 37:48 SD: 4.2641 cents 37 x 38:49 SD: 6.9014 cents 38 x 39:51 SD: 6.4352 cents 39 x 40:52 SD: 2.4626 cents 40 x 41:53 SD: 5.7572 cents 41 x 42:55 SD: 5.4468 cents 42 x 43:56 SD: 0.9155 cents 43 x 44:57 SD: 5.0671 cents 44 x 45:59 SD: 4.9044 cents 45 x 46:60 SD: 0.4276 cents 46 x 47:61 SD: 4.7909 cents 47 x 48:63 SD: 4.7537 cents 48 x 49:64 SD: 1.6045 cents 49 x 50:65 SD: 4.8442 cents 50 x 51:67 SD: 4.8971 cents 51 x 52:68 SD: 2.6443 cents 52 x 53:69 SD: 5.1177 cents 53 x 54:71 SD: 5.2253 cents 54 x 55:72 SD: 3.5696 cents 55 x 56:73 SD: 5.5153 cents 56 x 57:75 SD: 5.6515 cents 57 x 58:76 SD: 4.3983 cents 58 x 59:77 SD: 5.9713 cents 59:60 x 79 SD: 6.0975 cents 60:61 x 80 SD: 4.6362 cents 61:62 x 81 SD: 5.6594 cents 62:63 x 83 SD: 5.4399 cents 63:64 x 84 SD: 3.9602 cents 64:65 x 85 SD: 5.0529 cents 65:66 x 87 SD: 4.8581 cents 66:67:68:88 SD: 4.8075 cents 68:69:70:91 SD: 4.7462 cents 69:70:71:92 SD: 3.9796 cents 72:73:74:96 SD: 3.2198 cents 75:76:77:100 SD: 2.5202 cents 78:79:80:104 SD: 1.8740 cents 81:82:83:108 SD: 1.2753 cents 84:85:86:112 SD: 0.7198 cents 87:88:89:116 SD: 0.2084 cents 177:179:181:236 SD: 0.0810 cents 264:267:270:352 SD: 0.0729 cents 441:446:451:588 SD: 0.0650 cents