Scala analysis: SilverRatio
Silver Ratio scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150.000 cents 150.000000 2: 212.132 cents 212.132000 3: 300.000 cents 300.000000 4: 424.264 cents 424.264000 5: 548.528 cents 548.528000 6: 600.000 cents 600.000000 7: 724.264 cents 724.264000 8: 775.736 cents 775.736000 9: 848.528 cents 848.528000 10: 972.792 cents 972.792000 11: 1024.264 cents 1024.264000 12: 1097.056 cents 1097.056000 13: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 102.9440 cents 102.9440 1: 150.0000 cents 150.0000 2: 62.1320 cents 62.1320 3: 87.8680 cents 87.8680 4: 124.2640 cents 124.2640 5: 124.2640 cents 124.2640 6: 51.4720 cents 51.4720 7: 124.2640 cents 124.2640 8: 51.4720 cents 51.4720 9: 72.7920 cents 72.7920 10: 124.2640 cents 124.2640 11: 51.4720 cents 51.4720 12: 72.7920 cents 72.7920 13: 102.9440 cents 102.9440
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 51.47200 cents 1: 1 62.13200 cents 1: 2 72.79200 cents 1: 1 87.86800 cents 1: 1 102.94400 cents 1: 4 124.26400 cents 1: 1 150.00000 cents 2: 2 124.26400 cents 2: 1 150.00000 cents 2: 5 175.73600 cents 2: 1 197.05600 cents 2: 2 212.13200 cents 2: 1 248.52800 cents 2: 1 252.94400 cents 3: 2 227.20800 cents 3: 4 248.52800 cents 3: 1 274.26400 cents 3: 3 300.00000 cents 3: 1 315.07600 cents 3: 1 325.73600 cents 3: 1 336.39600 cents 4: 2 300.00000 cents 4: 1 321.32000 cents 4: 2 351.47200 cents 4: 1 372.79200 cents 4: 1 377.20800 cents 4: 2 387.86800 cents 4: 1 398.52800 cents 4: 1 402.94400 cents 4: 2 424.26400 cents 5: 1 372.79200 cents 5: 4 424.26400 cents 5: 1 439.34000 cents 5: 1 450.00000 cents 5: 2 475.73600 cents 5: 1 501.47200 cents 5: 1 512.13200 cents 5: 1 527.20800 cents 5: 1 548.52800 cents 6: 2 475.73600 cents 6: 1 497.05600 cents 6: 1 527.20800 cents 6: 2 548.52800 cents 6: 2 563.60400 cents 6: 2 574.26400 cents 6: 2 600.00000 cents 6: 1 651.47200 cents 7: 1 548.52800 cents 7: 2 600.00000 cents 7: 2 625.73600 cents 7: 2 636.39600 cents 7: 2 651.47200 cents 7: 1 672.79200 cents 7: 1 702.94400 cents 7: 2 724.26400 cents 8: 1 651.47200 cents 8: 1 672.79200 cents 8: 1 687.86800 cents 8: 1 698.52800 cents 8: 2 724.26400 cents 8: 1 750.00000 cents 8: 1 760.66000 cents 8: 4 775.73600 cents 8: 1 827.20800 cents 9: 2 775.73600 cents 9: 1 797.05600 cents 9: 1 801.47200 cents 9: 2 812.13200 cents 9: 1 822.79200 cents 9: 1 827.20800 cents 9: 2 848.52800 cents 9: 1 878.68000 cents 9: 2 900.00000 cents 10: 1 863.60400 cents 10: 1 874.26400 cents 10: 1 884.92400 cents 10: 3 900.00000 cents 10: 1 925.73600 cents 10: 4 951.47200 cents 10: 2 972.79200 cents 11: 1 947.05600 cents 11: 1 951.47200 cents 11: 2 987.86800 cents 11: 1 1002.94400 cents 11: 5 1024.26400 cents 11: 1 1050.00000 cents 11: 2 1075.73600 cents 12: 1 1050.00000 cents 12: 4 1075.73600 cents 12: 1 1097.05600 cents 12: 1 1112.13200 cents 12: 2 1127.20800 cents 12: 1 1137.86800 cents 12: 3 1148.52800 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 7.83333 = 47/6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 150.0 212.1 300.0 424.3 548.5 600.0 724.3 775.7 848.5 972.8 1024.3 1097.1 1200.0 150.0 : 62.1 150.0 274.3 398.5 450.0 574.3 625.7 698.5 822.8 874.3 947.1 1050.0 1200.0 212.1 : 87.9 212.1 336.4 387.9 512.1 563.6 636.4 760.7 812.1 884.9 987.9 1137.9 1200.0 300.0 : 124.3 248.5 300.0 424.3 475.7 548.5 672.8 724.3 797.1 900.0 1050.0 1112.1 1200.0 424.3 : 124.3 175.7 300.0 351.5 424.3 548.5 600.0 672.8 775.7 925.7 987.9 1075.7 1200.0 548.5 : 51.5 175.7 227.2 300.0 424.3 475.7 548.5 651.5 801.5 863.6 951.5 1075.7 1200.0 600.0 : 124.3 175.7 248.5 372.8 424.3 497.1 600.0 750.0 812.1 900.0 1024.3 1148.5 1200.0 724.3 : 51.5 124.3 248.5 300.0 372.8 475.7 625.7 687.9 775.7 900.0 1024.3 1075.7 1200.0 775.7 : 72.8 197.1 248.5 321.3 424.3 574.3 636.4 724.3 848.5 972.8 1024.3 1148.5 1200.0 848.5 : 124.3 175.7 248.5 351.5 501.5 563.6 651.5 775.7 900.0 951.5 1075.7 1127.2 1200.0 972.8 : 51.5 124.3 227.2 377.2 439.3 527.2 651.5 775.7 827.2 951.5 1002.9 1075.7 1200.0 1024.3: 72.8 175.7 325.7 387.9 475.7 600.0 724.3 775.7 900.0 951.5 1024.3 1148.5 1200.0 1097.1: 102.9 252.9 315.1 402.9 527.2 651.5 702.9 827.2 878.7 951.5 1075.7 1127.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.4720 .. 150.0000 cents 98.52800 cents 51.47200 cents 2: 124.2640 .. 252.9440 cents 128.68000 cents -25.73600 cents 3: 227.2080 .. 336.3960 cents 109.18800 cents -25.73600 cents 4: 300.0000 .. 424.2640 cents 124.26400 cents -36.39600 cents 5: 372.7920 .. 548.5280 cents 175.73600 cents -51.47200 cents 6: 475.7360 .. 651.4720 cents 175.73600 cents -72.79200 cents 7: 548.5280 .. 724.2640 cents 175.73600 cents -102.94400 cents 8: 651.4720 .. 827.2080 cents 175.73600 cents -72.79200 cents 9: 775.7360 .. 900.0000 cents 124.26400 cents -51.47200 cents 10: 863.6040 .. 972.7920 cents 109.18800 cents -36.39600 cents 11: 947.0560 .. 1075.7360 cents 128.68000 cents -25.73600 cents 12: 1050.0000 .. 1148.5280 cents 98.52800 cents -25.73600 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 51.47200 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 150.00000 cents Average / Smallest step : 1.793357 Largest / Average step : 1.625000 Largest / Smallest step : 2.914206 Median interval of one step : 87.86800 cents, amount: 1 Most common interval of one step : 124.26400 cents, amount: 4 Least squares average step : 95.46513 cents, oct.: 1241.04673 cents Scale is not proper Step pattern alph. order: ABCDDEDEFDEFG Step pattern size order : GBDFFAFACFACE Scale is not a Constant Structure Scale diversity : 1.574515 Lumma stability : 0.085787 Lumma impropriety factor : 0.439340 Number of different interval sizes : 73 = 6.08333 / class Number of one step interval sizes : 7 Highest interval variety : 9 Mean interval variety : 7.83333 = 47/6 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 4.41600 cents Most common triad is 0.0 124.264 775.736 cents, amount: 4 Number of recognisable fifths : 3, average 696.4467 cents Number of appreciable fifths : 2, average 700.7360 cents Formal octave complements present : 4 = 30.7692% -- Rational properties --
FIT/MODE
13: 1 1 1 1 2 0 2 0 1 1 1 1 1 N T3 SD: 33.2532 c. M: 57.6923 c. 14: 2 0 1 2 1 1 1 1 1 1 1 1 1 N D3 SD: 24.7046 c. M: 42.8571 c. 15: 2 1 1 1 2 1 1 1 1 1 1 1 1 N D3 S SD: 21.7186 c. M:-40.0000 c. 16: 2 1 1 2 1 1 2 0 1 2 1 1 1 N D3 SD: 19.0300 c. M:-27.9440 c. 20: 2 1 2 2 2 1 2 1 1 2 1 1 2 N SD: 14.1562 c. M: 32.1320 c. 22: 3 1 2 2 2 1 2 1 2 2 1 1 2 N SD: 13.4453 c. M:-27.2727 c. 23: 3 1 2 2 3 1 2 1 1 3 1 1 2 N SD: 14.1006 c. M:-26.0870 c. 24: 3 1 2 2 3 1 2 1 2 2 1 2 2 N SD: 15.4627 c. M: 25.7360 c. 26: 3 2 1 3 3 1 3 1 1 3 1 2 2 N SD: 12.1548 c. M: 23.0769 c. 28: 4 1 2 3 3 1 3 1 2 3 1 2 2 N SD: 9.4067 c. M:-21.4286 c. 30: 4 1 2 4 3 1 3 1 2 3 2 1 3 N SD: 12.6099 c. M: 20.0000 c. 31: 4 1 3 3 3 1 4 1 2 3 1 2 3 N SD: 10.8744 c. M: 19.3548 c. 32: 4 2 2 3 4 1 3 2 2 3 1 2 3 N SD: 9.6308 c. M:-13.9720 c. 33: 4 2 2 4 3 1 4 1 2 4 1 2 3 N SD: 9.1400 c. M: 18.1818 c. 37: 5 2 2 4 4 2 3 2 2 4 2 2 3 N SD: 9.1150 c. M:-16.2162 c. 40: 5 2 3 4 4 2 4 2 2 4 2 2 4 N SD: 7.2179 c. M: 17.0560 c. 43: 5 3 3 4 5 2 4 2 2 5 2 2 4 N SD: 8.4250 c. M:-13.9535 c. 46: 6 2 3 5 5 2 5 2 2 5 2 3 4 N SD: 7.0875 c. M: 13.7454 c. 48: 6 2 4 5 5 2 5 2 3 5 2 3 4 N SD: 3.5866 c. M: 12.1320 c. 54: 7 3 4 5 6 2 6 2 3 6 2 3 5 N SD: 6.2543 c. M:-11.1111 c. 56: 7 3 4 6 6 2 6 2 4 5 3 3 5 N SD: 4.9402 c. M:-8.6149 c. 62: 8 3 4 7 6 3 6 3 4 6 3 4 5 N SD: 4.8637 c. M: 9.6774 c. 68: 8 4 5 7 7 3 7 3 4 7 3 4 6 N SD: 2.7450 c. M: 8.8235 c. 70: 9 3 5 8 7 3 7 3 4 8 3 4 6 N SD: 4.7921 c. M: 8.5714 c. 74: 9 4 5 8 8 3 8 3 4 8 3 5 6 N SD: 3.9474 c. M: 8.1081 c. 79: 10 4 6 8 8 3 9 3 5 8 3 5 7 N SD: 3.5485 c. M: 7.5949 c. 80: 10 4 6 8 9 3 8 4 5 8 3 5 7 N SD: 3.6178 c. M:-6.4720 c. 88: 11 4 7 9 9 4 9 4 5 9 4 5 8 N SD: 3.3390 c. M: 7.5865 c. 90: 11 5 6 10 9 4 9 4 6 9 4 5 8 N SD: 3.2010 c. M: 6.6667 c. 94: 12 5 6 10 10 4 10 4 5 10 4 6 8 N SD: 3.4677 c. M: 6.3830 c. 96: 12 5 7 10 10 4 10 4 6 10 4 6 8 N SD: 1.2459 c. M:-2.9440 c. 136: 17 7 10 14 14 6 14 6 8 14 6 8 12 N SD: 1.2435 c. M: 2.9384 c. 164: 21 8 12 17 17 7 17 7 10 17 7 10 14 N SD: 1.0370 c. M:-3.6585 c. 184: 23 9 14 19 19 8 19 8 11 19 8 11 16 N SD: 1.1220 c. M: 3.4363 c. 200: 25 10 15 21 20 9 21 8 12 21 9 12 17 N SD: 1.5417 c. M: 2.5280 c. 204: 25 11 15 21 21 9 21 9 12 21 9 12 18 N SD: 1.4872 c. M: 2.9412 c. 210: 26 11 15 22 22 9 22 9 12 22 9 13 18 N SD: 1.4813 c. M: 2.8571 c. 212: 27 11 15 22 22 9 22 9 13 22 9 13 18 N SD: 1.2207 c. M:-2.9623 c. 224: 28 12 16 23 23 10 23 10 13 24 9 14 19 N SD: 1.3609 c. M:-2.2080 c. 232: 29 12 17 24 24 10 24 10 14 24 10 14 20 N SD: 0.2134 c. M: 0.5043 c. 560: 70 29 41 58 58 24 58 24 34 58 24 34 48 N SD: 0.0368 c. M:-0.0869 c. 792: 99 41 58 82 82 34 82 34 48 82 34 48 68 N SD: 0.0365 c. M: 0.0863 c. 1352: 169 70 99 140 140 58 140 58 82 140 58 82 116 N SD: 0.0062 c. M: 0.0146 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x x 4 S SD: 11.1545 cents 3 x x x x 4 x x x 5 x x x 6 S SD: 20.6354 cents 4 x x x 5 x x 6 x x 7 x x 8 S SD: 11.0500 cents 5 x x 6 x x 7 x x 8 x 9 x 10 S SD: 8.5062 cents 6 x x 7 x 8 x 9 x 10 x 11 x 12 S SD: 12.9717 cents 7 x 8 x 9 x 10 x 11 x 12 x 13:14 S SD: 7.8858 cents 8 x 9 x 10:11 x 12 x 13:14 x 15:16 S SD: 5.8232 cents 9 x 10:11 x 12:13 x 14:15:16 x 17:18 S SD: 10.5294 cents 10:11 x 12:13 x 14:15 x 16 x 18:19:20 S SD: 6.6932 cents 11:12 x 13:14:15:16 x 17:18:19:20:21:22 S SD: 6.0956 cents 12:13 x 14:15:16:17:18:19:20:21:22:23:24 S SD: 7.8627 cents 13:14:15 x 17:18 x 20 x 21:23 x 25:26 SD: 8.4777 cents 14:15:16:17:18:19:20:21:22:23 x 25:26:28 SD: 5.9759 cents 15:16:17:18:19 x 21:23 x 24:26:27:28:30 SD: 6.0721 cents 16:17:18:19:20:22:23:24:25:26:28:29:30:32 S SD: 5.4625 cents 17 x 19:20:22:23:24:26:27:28:30:31:32:34 SD: 4.7327 cents 18 x 20:21:23:25 x 27:28:29:32:33:34:36 SD: 6.2423 cents 19:21 x 23:24:26:27:29:30:31:33:34:36:38 SD: 4.5096 cents 21:23:24:25:27:29:30:32:33:34:37:38:40:42 SD: 3.1100 cents 25:27:28:30:32:34:35:38:39:41:44:45:47:50 SD: 3.0300 cents 32:35:36:38:41:44:45:49:50:52:56:58:60:64 SD: 1.8853 cents 43:47:49:51:55:59:61:65:67:70:75:78:81:86 SD: 1.8420 cents 46:50:52:55:59:63:65:70:72:75:81:83:87:92 SD: 1.2964 cents 62:68:70:74:79:85:88:94:97:101:109:112:117:124 SD: 1.2411 cents 68:74:77:81:87:93:96:103:106:111:119:123:128:136 SD: 1.0635 cents 69:75:78:82:88:95:98:105:108:113:121:125:130:138 SD: 1.0344 cents 78:85:88:93:100:107:110:119:122:127:137:141:147:156 SD: 1.0052 cents 85:93:96:101:109:117:120:129:133:139:149:154:160:170 SD: 0.9314 cents 89:97:101:106:114:122:126:135:139:145:156:161:168:178 SD: 0.8864 cents 90:98:102:107:115:124:127:137:141:147:158:163:170:180 SD: 0.8722 cents 100:109:113:119:128:137:141:152:157:163:175:181:188:200 SD: 0.8674 cents 101:110:114:120:129:139:143:153:158:165:177:183:190:202 SD: 0.7743 cents 115:125:130:137:147:158:163:175:180:188:202:208:217:230 SD: 0.7102 cents 121:132:137:144:155:166:171:184:189:198:212:219:228:242 SD: 0.6732 cents 123:134:139:146:157:169:174:187:193:201:216:222:232:246 SD: 0.5495 cents 131:143:148:156:167:180:185:199:205:214:230:237:247:262 SD: 0.5055 cents 147:160:166:175:188:202:208:223:230:240:258:266:277:294 SD: 0.4819 cents 154:168:174:183:197:211:218:234:241:251:270:278:290:308 SD: 0.4496 cents 166:181:188:197:212:228:235:252:260:271:291:300:313:332 SD: 0.4490 cents 179:195:202:213:229:246:253:272:280:292:314:323:337:358 SD: 0.4464 cents 190:207:215:226:243:261:269:289:297:310:333:343:358:380 SD: 0.4123 cents 191:208:216:227:244:262:270:290:299:312:335:345:360:382 SD: 0.2787 cents 223:243:252:265:285:306:315:339:349:364:391:403:420:446 SD: 0.2525 cents 244:266:276:290:312:335:345:371:382:398:428:441:460:488 SD: 0.2297 cents 285:311:322:339:364:391:403:433:446:465:500:515:537:570 SD: 0.1767 cents 354:386:400:421:452:486:501:538:554:578:621:640:667:708 SD: 0.1686 cents 408:445:461:485:521:560:577:620:639:666:716:737:769:816 SD: 0.1590 cents 451:492:510:536:576:619:638:685:706:736:791:815:850:902 SD: 0.1528 cents 454:495:513:540:580:623:642:690:711:741:796:820:856:908 SD: 0.1526 cents 476:519:538:566:608:653:673:723:745:777:835:860:897:952 SD: 0.1228 cents 529:577:598:629:676:726:748:804:828:864:928:956:997:1058 SD: 0.0954 cents