Scala analysis: 9tonegoldsilvercombined
9 note gold silver combined may 8th 2009
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 118.863 cents 118.863320 2: 235.777 cents 235.777380 3: 366.913 cents 366.912540 4: 510.732 cents 510.731630 5: 599.996 cents 599.995640 6: 718.861 cents 718.861360 7: 13/8 840.527662 tridecimal neutral sixth 8: 1076.298 cents 1076.298070 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 123.7019 cents 123.7019 1: 118.8633 cents 118.8633 2: 116.9141 cents 116.9141 3: 131.1352 cents 131.1352 4: 143.8191 cents 143.8191 5: 89.2640 cents 89.2640 6: 118.8657 cents 118.8657 7: 121.6663 cents 121.6663 8: 235.7704 cents 235.7704 9: 123.7019 cents 123.7019
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 89.26401 cents 1: 1 116.91406 cents 1: 1 118.86332 cents 1: 1 118.86572 cents 1: 1 121.66630 cents 1: 1 123.70193 cents 1: 1 131.13516 cents 1: 1 143.81909 cents 1: 1 235.77041 cents 2: 1 208.12973 cents 2: 1 233.08310 cents 2: 1 235.77738 cents 2: 1 240.53202 cents 2: 1 242.56525 cents 2: 1 248.04922 cents 2: 1 274.95425 cents 2: 1 357.43671 cents 2: 1 16/13 359.472 cents tridecimal neutral third 3: 1 329.79603 cents 3: 1 351.94882 cents 3: 1 359.47931 cents 3: 1 364.21826 cents 3: 1 366.91254 cents 3: 1 391.86831 cents 3: 1 476.30243 cents 3: 1 478.33566 cents 3: 1 481.13864 cents 4: 1 473.61512 cents 4: 1 481.13232 cents 4: 1 483.08398 cents 4: 1 490.61447 cents 4: 1 510.73163 cents 4: 1 565.56644 cents 4: 1 595.24972 cents 4: 1 600.00196 cents 4: 1 600.00436 cents 5: 1 599.99564 cents 5: 1 599.99804 cents 5: 1 604.75028 cents 5: 1 634.43356 cents 5: 1 689.26837 cents 5: 1 709.38553 cents 5: 1 716.91602 cents 5: 1 718.86768 cents 5: 1 726.38488 cents 6: 1 718.86136 cents 6: 1 721.66434 cents 6: 1 723.69757 cents 6: 1 808.13169 cents 6: 1 833.08746 cents 6: 1 835.78174 cents 6: 1 840.52069 cents 6: 1 848.05118 cents 6: 1 870.20397 cents 7: 1 13/8 840.528 cents tridecimal neutral sixth 7: 1 842.56329 cents 7: 1 925.04575 cents 7: 1 951.95078 cents 7: 1 957.43475 cents 7: 1 959.46798 cents 7: 1 964.22262 cents 7: 1 966.91690 cents 7: 1 991.87027 cents 8: 1 964.22959 cents 8: 1 1056.18091 cents 8: 1 1068.86484 cents 8: 1 1076.29807 cents 8: 1 1078.33370 cents 8: 1 1081.13428 cents 8: 1 1081.13668 cents 8: 1 1083.08594 cents 8: 1 1110.73599 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 9.00000 = 9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 118.9 235.8 366.9 510.7 600.0 718.9 840.5 1076.3 1200.0 118.9 : 116.9 248.0 391.9 481.1 600.0 721.7 957.4 1081.1 1200.0 235.8 : 131.1 275.0 364.2 483.1 604.8 840.5 964.2 1083.1 1200.0 366.9 : 143.8 233.1 351.9 473.6 709.4 833.1 952.0 1068.9 1200.0 510.7 : 89.3 208.1 329.8 565.6 689.3 808.1 925.0 1056.2 1200.0 600.0 : 118.9 240.5 476.3 600.0 718.9 835.8 966.9 1110.7 1200.0 718.9 : 121.7 357.4 481.1 600.0 716.9 848.1 991.9 1081.1 1200.0 840.5 : 235.8 359.5 478.3 595.2 726.4 870.2 959.5 1078.3 1200.0 1076.3: 123.7 242.6 359.5 490.6 634.4 723.7 842.6 964.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.2640 .. 235.7704 cents 146.50640 cents 89.26401 cents 2: 208.1297 .. 359.4723 cents 151.34261 cents -27.64068 cents 3: 329.7960 .. 481.1386 cents 151.34261 cents -29.67631 cents 4: 473.6151 .. 600.0044 cents 126.38924 cents -7.52352 cents 5: 599.9956 .. 726.3849 cents 126.38924 cents -0.00872 cents 6: 718.8614 .. 870.2040 cents 151.34261 cents -7.52352 cents 7: 840.5277 .. 991.8703 cents 151.34261 cents -29.67631 cents 8: 964.2296 .. 1110.7360 cents 146.50640 cents -27.64068 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 89.26401 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 235.77041 cents Average / Smallest step : 1.493696 Largest / Average step : 1.768278 Largest / Smallest step : 2.641271 Median interval of one step : 121.66630 cents, amount: 1 Least squares average step : 127.51336 cents, oct.: 1147.62021 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : CBGHADEIF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.00392 cents Scale diversity : 1.449844 Lumma stability : 0.148773 Lumma impropriety factor : 0.108075 Rothenberg efficiency : 0.222222 redundancy: 0.777778 Efficiency x scale size : 2.000000 Number of different interval sizes : 72 = 9.00000 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 9.00000 = 9 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 0.00240 cents Number of recognisable fifths : 5, average 710.6598 cents Number of appreciable fifths : 2, average 699.3270 cents Formal octave complements present : 1 = 11.1111% -- Rational properties -- Prime limit : 13 (not all pitches rational)
FIT/MODE
9: 1 1 1 1 0 1 1 2 1 N T3 SD: 36.0132 c. M: 66.6623 c. 10: 1 1 1 1 1 1 1 2 1 P M ME S SD: 10.6803 c. M: 30.7316 c. 20: 2 2 2 3 1 2 2 4 2 N SD: 10.2134 c. M:-29.2684 c. 21: 2 2 2 3 2 2 2 4 2 P T3 SD: 16.4022 c. M:-28.5758 c. 22: 2 2 3 2 2 2 2 5 2 N T3 SD: 14.2536 c. M: 22.3458 c. 26: 3 2 3 3 2 3 2 5 3 N SD: 11.1606 c. M:-19.6002 c. 28: 3 3 3 3 2 3 3 5 3 P SD: 12.0689 c. M:-21.3655 c. 30: 3 3 3 4 2 3 3 6 3 N SD: 4.3216 c. M:-9.2684 c. 40: 4 4 4 5 3 4 4 8 4 N SD: 3.0317 c. M: 6.9125 c. 68: 7 6 8 8 5 7 7 13 7 N SD: 3.9630 c. M:-6.5312 c. 70: 7 7 7 9 5 7 7 14 7 N SD: 3.2458 c. M: 6.9125 c. 78: 8 7 9 9 6 8 8 15 8 N SD: 3.4523 c. M:-5.6262 c. 82: 8 8 9 10 6 8 8 16 9 N SD: 3.6076 c. M: 8.0054 c. 87: 9 8 10 10 7 8 9 17 9 N SD: 3.5130 c. M:-6.9009 c. 88: 9 8 10 10 7 9 9 17 9 N SD: 3.5064 c. M: 6.1862 c. 90: 9 9 10 10 7 9 9 18 9 N SD: 3.1999 c. M:-6.4208 c. 92: 9 9 10 11 7 9 9 18 10 N SD: 3.1741 c. M: 6.7329 c. 98: 10 9 11 12 7 10 10 19 10 N SD: 2.7685 c. M:-4.3703 c. 100: 10 10 11 12 7 10 10 20 10 N SD: 3.1277 c. M:-5.2684 c. 102: 10 10 11 12 8 10 10 20 11 N SD: 3.1896 c. M: 5.7098 c. 104: 10 10 12 12 8 10 11 20 11 N SD: 2.9331 c. M: 5.0081 c. 108: 11 10 12 13 8 11 11 21 11 N SD: 2.2678 c. M:-3.9168 c. 110: 11 11 12 13 8 11 11 22 11 N SD: 2.4576 c. M:-4.2226 c. 118: 12 11 13 14 9 12 12 23 12 N SD: 2.2290 c. M:-3.5401 c. 120: 12 12 13 14 9 12 12 24 12 N SD: 2.2228 c. M:-4.2226 c. 124: 12 12 14 15 9 12 13 24 13 N SD: 2.0855 c. M: 3.5193 c. 132: 13 13 14 16 10 13 13 26 14 N SD: 2.2307 c. M: 4.1640 c. 134: 13 13 15 16 10 13 14 26 14 N SD: 1.6712 c. M: 2.9416 c. 144: 14 14 16 17 11 14 15 28 15 N SD: 1.6469 c. M: 2.4440 c. 164: 16 16 18 20 12 16 17 32 17 N SD: 1.2327 c. M: 1.7901 c. 174: 17 17 19 21 13 17 18 34 18 N SD: 1.0511 c. M: 1.6219 c. 204: 20 20 22 25 15 20 21 40 21 N SD: 1.0314 c. M: 2.2067 c. 214: 21 21 23 26 16 21 22 42 22 N SD: 1.0039 c. M: 2.4266 c. 244: 24 24 27 29 18 24 25 48 25 N SD: 0.8530 c. M:-1.9399 c. 254: 25 25 28 30 19 25 26 50 26 N SD: 0.7477 c. M:-1.5914 c. 284: 28 28 31 34 21 28 29 56 29 N SD: 0.6280 c. M:-1.1667 c. 294: 29 29 32 35 22 29 30 58 30 N SD: 0.6260 c. M:-1.2530 c. 310: 31 30 34 37 23 31 31 61 32 N SD: 0.6466 c. M:-1.1386 c. 350: 35 34 38 42 26 35 35 69 36 N SD: 0.6317 c. M:-1.1386 c. 376: 37 37 41 45 28 37 38 74 39 N SD: 0.6082 c. M: 1.1660 c. 392: 39 38 43 47 29 39 40 77 40 N SD: 0.6889 c. M:-1.3091 c. 402: 40 39 44 48 30 40 41 79 41 N SD: 0.6711 c. M:-1.3139 c. 406: 40 40 44 49 30 40 41 80 42 N SD: 0.5994 c. M: 1.1188 c. 416: 41 41 45 50 31 41 42 82 43 N SD: 0.5736 c. M: 1.1046 c. 426: 42 42 46 51 32 42 43 84 44 N SD: 0.6533 c. M: 1.0910 c. 428: 42 42 47 51 32 42 44 84 44 N SD: 0.6078 c. M: 1.1063 c. 434: 43 42 48 52 32 43 44 85 45 N SD: 0.5168 c. M:-0.8294 c. 444: 44 43 49 53 33 44 45 87 46 N SD: 0.3714 c. M:-0.6550 c. 454: 45 44 50 54 34 45 46 89 47 N SD: 0.3613 c. M: 0.5995 c. 474: 47 46 52 57 35 47 48 93 49 N SD: 0.2853 c. M:-0.6608 c. 484: 48 47 53 58 36 48 49 95 50 N SD: 0.1385 c. M: 0.2650 c. 1008: 100 98 110 121 75 100 102 198 104 N SD: 0.1281 c. M: 0.2459 c. 1252: 124 122 137 150 93 124 127 246 129 N SD: 0.0787 c. M:-0.1801 c. 1262: 125 123 138 151 94 125 128 248 130 N SD: 0.0662 c. M:-0.1239 c. 1736: 172 169 190 208 129 172 176 341 179 N SD: 0.0635 c. M:-0.1382 c. 1746: 173 170 191 209 130 173 177 343 180 N SD: 0.0480 c. M:-0.0978 c. 1776: 176 173 194 213 132 176 180 349 183 N SD: 0.0438 c. M:-0.0792 c. 2260: 224 220 247 271 168 224 229 444 233 N SD: 0.0430 c. M:-0.0767 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x 4 S SD: 8.4532 cents 3 x x x 4 x x 5 x 6 S SD: 15.2101 cents 4 x x 5 x x 6 x 7:8 S SD: 27.6275 cents 5 x x 6 x 7 x 8:9:10 S SD: 16.8532 cents 6 x 7 x 8 x 9:10:11:12 S SD: 10.6200 cents 7 x 8:9 x 10 x 11:13:14 SD: 15.2423 cents 8 x 9:10:11 x 12:13:15:16 SD: 8.4132 cents 9 x 10:11:12:13:14:15:17:18 SD: 12.1101 cents 10:11 x 12:13:14:15:16:19:20 SD: 12.7977 cents 11:12:13:14:15:16:17:18:20:22 S SD: 12.4440 cents 12:13:14:15:16:17:18:20:22:24 S SD: 7.7253 cents 13:14:15:16:17:18:20:21:24:26 S SD: 7.7170 cents 14:15:16:17:19:20:21:23:26:28 SD: 5.2850 cents 21:22:24:26:28:30:32:34:39:42 SD: 5.1326 cents 25:27:29:31:34:35:38:41:47:50 SD: 4.9956 cents 26:28:30:32:35:37:39:42:48:52 SD: 3.5697 cents 27:29:31:33:36:38:41:44:50:54 SD: 3.1033 cents 29:31:33:36:39:41:44:47:54:58 SD: 1.7464 cents 43:46:49:53:58:61:65:70:80:86 SD: 1.6799 cents 55:59:63:68:74:78:83:89:102:110 SD: 1.5074 cents 56:60:64:69:75:79:85:91:104:112 SD: 1.2617 cents 82:88:94:101:110:116:124:133:153:164 SD: 1.0278 cents 96:103:110:119:129:136:145:156:179:192 SD: 0.9452 cents 97:104:111:120:130:137:147:158:181:194 SD: 0.8683 cents 101:108:116:125:136:143:153:164:188:202 SD: 0.8142 cents 111:119:127:137:149:157:168:180:207:222 SD: 0.6938 cents 123:132:141:152:165:174:186:200:229:246 SD: 0.5737 cents 152:163:174:188:204:215:230:247:283:304 SD: 0.4125 cents 157:168:180:194:211:222:238:255:292:314 SD: 0.3809 cents 198:212:227:245:266:280:300:322:369:396 SD: 0.3277 cents 225:241:258:278:302:318:341:366:419:450 SD: 0.3239 cents 253:271:290:313:340:358:383:411:471:506 SD: 0.2704 cents 254:272:291:314:341:359:385:413:473:508 SD: 0.2337 cents 280:300:321:346:376:396:424:455:521:560 SD: 0.1995 cents 309:331:354:382:415:437:468:502:575:618 SD: 0.1503 cents 437:468:501:540:587:618:662:710:814:874 SD: 0.1357 cents 466:499:534:576:626:659:706:757:868:932 SD: 0.1102 cents 507:543:581:627:681:717:768:824:944:1014 SD: 0.1032 cents 589:631:675:728:791:833:892:957:1097:1178 SD: 0.0820 cents