Scala analysis: bad
badscale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 1067/1000 112.272211 2: 117/100 271.810236 3: 59/40 672.857945 4: 823/500 862.757203 5: 347/200 953.922795 6: 909/500 1034.822639 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 1000/909 165.1774 1: 1067/1000 112.2722 2: 1170/1067 159.5380 3: 295/234 401.0477 4: 1646/1475 189.8993 5: 1735/1646 91.1656 6: 1818/1735 80.8998 7: 1000/909 165.1774
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1818/1735 80.900 cents 1: 1 1735/1646 91.166 cents 1: 1 1067/1000 112.272 cents 1: 1 1170/1067 159.538 cents 1: 1 1000/909 165.177 cents 1: 1 1646/1475 189.899 cents 1: 1 295/234 401.048 cents 2: 1 909/823 172.065 cents 2: 1 400/347 246.077 cents 2: 1 117/100 271.810 cents 2: 1 1067/909 277.450 cents 2: 1 347/295 281.065 cents 2: 1 1475/1067 560.586 cents 2: 1 823/585 590.947 cents 3: 1 1000/823 337.243 cents 3: 1 2134/1735 358.349 cents 3: 1 1818/1475 361.965 cents 3: 1 130/101 436.988 cents 3: 1 59/40 672.858 cents 3: 1 347/234 682.113 cents 3: 1 1646/1067 750.485 cents 4: 1 1067/823 449.515 cents 4: 1 468/347 517.887 cents 4: 1 80/59 527.142 cents 4: 1 101/65 763.012 cents 4: 1 1475/909 838.035 cents 4: 1 1735/1067 841.651 cents 4: 1 823/500 862.757 cents 5: 1 1170/823 609.053 cents 5: 1 2134/1475 639.414 cents 5: 1 590/347 918.935 cents 5: 1 1818/1067 922.550 cents 5: 1 200/117 928.190 cents 5: 1 347/200 953.923 cents 5: 1 1646/909 1027.935 cents 6: 1 468/295 798.952 cents 6: 1 1475/823 1010.101 cents 6: 1 909/500 1034.823 cents 6: 1 1067/585 1040.462 cents 6: 1 2000/1067 1087.728 cents 6: 1 3292/1735 1108.834 cents 6: 1 1735/909 1119.100 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 112.3 271.8 672.9 862.8 953.9 1034.8 1200.0 112.3 : 159.5 560.6 750.5 841.7 922.6 1087.7 1200.0 271.8 : 401.0 590.9 682.1 763.0 928.2 1040.5 1200.0 672.9 : 189.9 281.1 362.0 527.1 639.4 799.0 1200.0 862.8 : 91.2 172.1 337.2 449.5 609.1 1010.1 1200.0 953.9 : 80.9 246.1 358.3 517.9 918.9 1108.8 1200.0 1034.8: 165.2 277.4 437.0 838.0 1027.9 1119.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.8998 .. 401.0477 cents 511825/425412, 320.1479 cents 1818/1735, 80.8998 cents 2: 172.0654 .. 590.9470 cents 677329/531765, 418.8815 cents 212706/242785,-228.9823 cents 3: 337.2428 .. 750.4850 cents 677329/533500, 413.2422 cents 585000/677329,-253.7042 cents 4: 449.5150 .. 862.7572 cents 677329/533500, 413.2422 cents 1138489/1354658,-300.9700 cents 5: 609.0530 .. 1027.9346 cents 677329/531765, 418.8815 cents 585000/677329,-253.7042 cents 6: 798.9523 .. 1119.1002 cents 511825/425412, 320.1479 cents 212706/242785,-228.9823 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1818/1735, 80.8998 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 295/234, 401.0477 cents Average / Smallest step : 2.119022 Largest / Average step : 2.339445 Largest / Smallest step : 4.957336 Median interval of one step : 1170/1067, 159.5380 cents, amount: 1 Least squares average step : 182.17175 cents, oct.: 1275.20226 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : CDGFBAE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 6.88808 cents Scale diversity : 1.684583 Lumma stability : 0.134833 Lumma impropriety factor : 0.713224 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 315423/314765, 3.6153 cents Number of recognisable fifths : 0 Formal octave complements present : 1 = 14.2857% -- Rational properties -- Prime limit : 823 Odd number limit : 1735 (O: 1735 U: 1735) Highest odd numerator or denominator: 1067 Scale harmonicity : 0.014520 Fundamental : 1/1000, -9.9658 octaves, 0.2616 Hz. Guide tone : too high to compute Exponens Consonantiae : 4.248963E+17, 58.55989 octaves Euler's gradus suavitatis : 1465 Sum of Mann's harmonic distance : 2832.5, average 404.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.28150, average 2.18307 Sum of Tenney's harmonic distance : 29.88356, average 4.26908 Vogel's harmonic complexity : 215.00000 Wille's k value : 867 Wilson's harmonic complexity : 1472 Rectangular lattice diameter : 12 Triangular lattice diameter : 4 Lattice compactness : 81.73202, average 2.91900 Lattice compactness (without 2's) : 60.68151, average 2.16720 Number of different primes : 10 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -2.00000 16 1 3: 0 .. 2 0.57143 4 5: -3 .. 0 -2.00000 14 11: 0 .. 1 0.14286 1 13: 0 .. 1 0.14286 1 1 59: 0 .. 1 0.14286 1 1 97: 0 .. 1 0.14286 1 1 101: 0 .. 1 0.14286 1 1 347: 0 .. 1 0.14286 1 1 823: 0 .. 1 0.14286 1 1 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 25 / 7 = 3.57143 Scale is weakly epimorphic with val: <7 11 16 24 27 41 47 48 58 68| Scale is weakly epimorphic with val: <7 11 16 24 27 41 47 48 59 67| Scale is weakly epimorphic with val: <7 11 16 25 26 41 47 48 58 68| Scale is weakly epimorphic with val: <7 11 16 25 26 41 47 48 59 67| Scale is weakly epimorphic with val: <7 11 16 25 27 41 46 48 58 68| Scale is weakly epimorphic with val: <7 11 16 25 27 41 46 48 59 67|
FIT/MODE
7: 1 1 2 1 1 0 1 N T3 SD: 45.2855 c. M:-74.6486 c. 8: 1 1 3 1 0 1 1 N SD: 42.5844 c. M:-77.1421 c. 9: 1 1 3 1 1 1 1 N M DE S SD: 28.9946 c. M: 62.7572 c. 10: 1 1 4 1 1 1 1 N M DE S SD: 29.0069 c. M:-47.1421 c. 13: 1 2 4 2 1 1 2 N SD: 22.3299 c. M: 31.9880 c. 14: 1 2 5 2 1 1 2 N SD: 13.5161 c. M: 26.5579 c. 19: 2 2 7 3 1 1 3 N SD: 17.4734 c. M: 24.2963 c. 20: 2 2 7 3 2 1 3 N SD: 16.9515 c. M: 31.8102 c. 21: 2 3 7 3 2 1 3 N SD: 10.2798 c. M:-17.5058 c. 28: 3 3 10 4 2 2 4 N SD: 10.9488 c. M:-16.2992 c. 29: 3 4 9 5 2 2 4 N SD: 9.4046 c. M:-17.8449 c. 30: 3 4 10 5 2 2 4 N SD: 8.7738 c. M:-17.2428 c. 31: 3 4 10 5 3 2 4 N SD: 9.6842 c. M: 14.7934 c. 32: 3 4 11 5 2 3 4 N SD: 9.1920 c. M: 16.4228 c. 34: 3 5 11 5 3 2 5 N SD: 8.7184 c. M: 15.6984 c. 35: 3 5 12 5 3 2 5 N SD: 7.2466 c. M:-12.8563 c. 36: 3 5 12 6 3 2 5 N SD: 7.5148 c. M:-12.7439 c. 39: 4 5 13 6 3 3 5 N SD: 6.4287 c. M:-11.3312 c. 43: 4 6 14 7 3 3 6 N SD: 3.7649 c. M:-7.2595 c. 53: 5 7 18 8 4 4 7 N SD: 3.7974 c. M:-6.6868 c. 57: 5 8 19 9 4 4 8 N SD: 3.9090 c. M: 7.0091 c. 63: 6 8 21 10 5 4 9 N SD: 4.5011 c. M: 6.2512 c. 64: 6 8 22 10 5 4 9 N SD: 3.9563 c. M: 9.3102 c. 72: 7 9 24 12 5 5 10 N SD: 4.0881 c. M: 6.1913 c. 74: 7 10 25 11 6 5 10 N SD: 4.0018 c. M:-8.2231 c. 75: 7 10 25 12 6 5 10 N SD: 3.0736 c. M:-6.0772 c. 78: 7 11 26 12 6 5 11 N SD: 3.4135 c. M:-5.1128 c. 79: 7 11 26 13 6 5 11 N SD: 3.3906 c. M: 5.9431 c. 87: 8 12 29 14 6 6 12 N SD: 3.2216 c. M:-6.2083 c. 88: 8 12 29 14 7 6 12 N SD: 2.6466 c. M: 4.6761 c. 89: 8 12 30 14 7 6 12 N SD: 2.6349 c. M: 4.4070 c. 93: 9 12 31 15 7 6 13 N SD: 2.0587 c. M:-3.8568 c. 107: 10 14 36 17 8 7 15 N SD: 1.5760 c. M: 3.0469 c. 118: 11 16 39 19 9 8 16 N SD: 1.8302 c. M:-2.7660 c. 128: 12 17 43 20 10 8 18 N SD: 1.8083 c. M: 3.5726 c. 132: 12 18 44 21 10 9 18 N SD: 1.4399 c. M: 3.1813 c. 136: 13 18 45 22 10 9 19 N SD: 1.8857 c. M: 2.4697 c. 146: 14 19 49 23 11 10 20 N SD: 1.2153 c. M:-2.7963 c. 160: 15 21 54 25 12 11 22 N SD: 1.1976 c. M:-2.1421 c. 182: 17 24 61 29 14 12 25 N SD: 1.0630 c. M:-2.1212 c. 189: 18 25 63 30 14 13 26 N SD: 1.0993 c. M:-2.0135 c. 195: 18 26 65 31 15 13 27 N SD: 1.2042 c. M: 2.0887 c. 203: 19 27 68 32 15 14 28 N SD: 0.9351 c. M: 2.1987 c. 211: 20 28 70 34 16 14 29 N SD: 1.3066 c. M: 1.7679 c. 216: 20 29 72 34 17 14 30 N SD: 1.1659 c. M: 1.6461 c. 224: 21 30 75 35 17 15 31 N SD: 1.0420 c. M:-2.1421 c. 225: 21 30 75 36 17 15 31 N SD: 0.6512 c. M:-1.2428 c. 234: 22 31 78 37 18 16 32 N SD: 0.7632 c. M: 1.2187 c. 278: 26 37 93 44 21 19 38 N SD: 0.5235 c. M:-1.1486 c. 321: 30 43 107 51 24 22 44 N SD: 0.6247 c. M:-1.0870 c. 341: 32 45 114 54 26 23 47 N SD: 0.5066 c. M: 0.8425 c. 371: 35 49 124 59 28 25 51 N SD: 0.4981 c. M:-0.9353 c. 385: 36 51 129 61 29 26 53 N SD: 0.3733 c. M: 0.6414 c. 473: 44 63 158 75 36 32 65 N SD: 0.3686 c. M: 0.6443 c. 565: 53 75 189 89 43 38 78 N SD: 0.3367 c. M: 0.4864 c. 619: 58 82 207 98 47 42 85 N SD: 0.2377 c. M: 0.4047 c. 640: 60 85 214 101 49 43 88 N SD: 0.2477 c. M:-0.4522 c. 662: 62 88 221 105 50 45 91 N SD: 0.2397 c. M: 0.4485 c. 683: 64 91 228 108 52 46 94 N SD: 0.2141 c. M:-0.5177 c. 697: 65 93 233 110 53 47 96 N SD: 0.2211 c. M: 0.3640 c. 747: 70 99 250 118 57 50 103 N SD: 0.2300 c. M: 0.3243 c. 790: 74 105 264 125 60 53 109 N SD: 0.1617 c. M: 0.3923 c. 1024: 96 136 342 162 78 69 141 N SD: 0.1542 c. M: 0.2572 c. 1038: 97 138 347 164 79 70 143 N SD: 0.1657 c. M: 0.3295 c. 1068: 100 142 357 169 81 72 147 N SD: 0.1039 c. M:-0.1758 c. 1263: 118 168 422 200 96 85 174 N SD: 0.1096 c. M: 0.1739 c. 1316: 123 175 440 208 100 89 181 N SD: 0.1071 c. M: 0.1432 c. 1409: 132 187 471 223 107 95 194 N SD: 0.0805 c. M:-0.1479 c. 1541: 144 205 515 244 117 104 212 N SD: 0.0699 c. M: 0.1372 c. 1946: 182 259 650 308 148 131 268 N SD: 0.0760 c. M:-0.1322 c. 1999: 187 266 668 316 152 135 275 N SD: 0.0838 c. M: 0.1259 c. 2092: 196 278 699 331 159 141 288 N SD: 0.0693 c. M:-0.1561 c. 2106: 197 280 704 333 160 142 290 N SD: 0.0572 c. M: 0.0791 c. 2331: 218 310 779 369 177 157 321 N SD: 0.0379 c. M: 0.0736 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 14.5485 cents 3 x x 4:5 x x 6 S SD: 58.7142 cents 4 x 5:6 x 7 x 8 S SD: 29.7697 cents 5 x 6:7:8 x 9:10 S SD: 22.6170 cents 6 x 7:9:10 x 11:12 SD: 7.8717 cents 7 x 8:10 x 12:13:14 S SD: 16.1364 cents 8 x 9:12:13:14:15:16 S SD: 15.8376 cents 9:10:11:13:15 x 16:18 SD: 19.6593 cents 10:11:12:15:16:17:18:20 S SD: 13.9225 cents 11:12:13:16:18:19:20:22 SD: 7.1744 cents 12:13:14:18:20:21:22:24 SD: 7.0897 cents 16:17:19:24:26:28:29:32 SD: 6.8580 cents 17:18:20:25:28:29:31:34 SD: 4.9132 cents 27:29:32:40:44:47:49:54 SD: 4.5809 cents 28:30:33:41:46:49:51:56 SD: 3.5401 cents 29:31:34:43:48:50:53:58 SD: 2.8537 cents 34:36:40:50:56:59:62:68 SD: 2.5730 cents 42:45:49:62:69:73:76:84 SD: 1.8277 cents 48:51:56:71:79:83:87:96 SD: 1.8257 cents 57:61:67:84:94:99:104:114 SD: 1.7283 cents 59:63:69:87:97:102:107:118 SD: 1.1320 cents 76:81:89:112:125:132:138:152 SD: 0.6103 cents 105:112:123:155:173:182:191:210 SD: 0.5223 cents 147:157:172:217:242:255:267:294 SD: 0.3898 cents 181:193:212:267:298:314:329:362 SD: 0.3248 cents 223:238:261:329:367:387:405:446 SD: 0.2886 cents 282:301:330:416:464:489:513:564 SD: 0.2489 cents 313:334:366:462:515:543:569:626 SD: 0.2465 cents 328:350:384:484:540:569:596:656 SD: 0.2332 cents 341:364:399:503:561:592:620:682 SD: 0.2260 cents 347:370:406:512:571:602:631:694 SD: 0.2092 cents 358:382:419:528:589:621:651:716 SD: 0.1622 cents 446:476:522:658:734:774:811:892 SD: 0.1489 cents 494:527:578:729:813:857:898:988 SD: 0.1380 cents 506:540:592:746:833:878:920:1012 SD: 0.1347 cents 554:591:648:817:912:961:1007:1108 SD: 0.1199 cents