Scala analysis: young
Thomas Young well temperament (1807), also Luigi Malerbi nr.2 (1794)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 196.090 cents 196.090000 3: 32/27 294.134997 Pythagorean minor third 4: 392.180 cents 392.180000 5: 4/3 498.044999 perfect fourth 6: 1024/729 588.269995 Pythagorean diminished fifth 7: 698.045 cents 698.045000 8: 128/81 792.179997 Pythagorean minor sixth 9: 894.135 cents 894.135000 10: 16/9 996.089998 Pythagorean minor seventh 11: 1090.225 cents 1090.225000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 109.7750 cents 109.7750 1: 256/243 90.2250 limma, Pythagorean minor second 2: 105.8650 cents 105.8650 3: 98.0450 cents 98.0450 4: 98.0450 cents 98.0450 5: 105.8650 cents 105.8650 6: 256/243 90.2250 limma, Pythagorean minor second 7: 109.7750 cents 109.7750 8: 94.1350 cents 94.1350 9: 101.9550 cents 101.9550 10: 101.9550 cents 101.9550 11: 94.1350 cents 94.1350 12: 109.7750 cents 109.7750
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 2 94.13500 cents 1: 2 98.04500 cents 1: 2 101.95500 cents 1: 2 105.86500 cents 1: 2 109.77501 cents 2: 5 196.09000 cents 2: 2 200.00000 cents 2: 5 9/8 203.910 cents major whole tone 3: 4 32/27 294.135 cents Pythagorean minor third 3: 2 298.04500 cents 3: 2 301.95500 cents 3: 4 305.86500 cents 4: 3 392.18000 cents 4: 2 396.09000 cents 4: 2 400.00000 cents 4: 2 403.91000 cents 4: 3 81/64 407.820 cents Pythagorean major third 5: 6 4/3 498.045 cents perfect fourth 5: 6 501.95500 cents 6: 1 1024/729 588.270 cents Pythagorean diminished fifth 6: 2 592.18000 cents 6: 2 596.09000 cents 6: 2 600.00000 cents 6: 2 603.91000 cents 6: 2 607.82000 cents 6: 1 729/512 611.730 cents Pythagorean tritone 7: 6 698.04500 cents 7: 6 3/2 701.955 cents perfect fifth 8: 3 128/81 792.180 cents Pythagorean minor sixth 8: 2 796.09000 cents 8: 2 800.00000 cents 8: 2 803.91000 cents 8: 3 807.82000 cents 9: 4 894.13500 cents 9: 2 898.04500 cents 9: 2 901.95500 cents 9: 4 27/16 905.865 cents Pythagorean major sixth 10: 5 16/9 996.090 cents Pythagorean minor seventh 10: 2 1000.00000 cents 10: 5 1003.91000 cents 11: 2 1090.22500 cents 11: 2 1094.13500 cents 11: 2 1098.04500 cents 11: 2 1101.95500 cents 11: 2 1105.86500 cents 11: 2 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 4.27273 = 47/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 90.2 196.1 294.1 392.2 498.0 588.3 698.0 792.2 894.1 996.1 1090.2 1200.0 90.2 : 105.9 203.9 302.0 407.8 498.0 607.8 702.0 803.9 905.9 1000.0 1109.8 1200.0 196.1 : 98.0 196.1 302.0 392.2 502.0 596.1 698.0 800.0 894.1 1003.9 1094.1 1200.0 294.1 : 98.0 203.9 294.1 403.9 498.0 600.0 702.0 796.1 905.9 996.1 1102.0 1200.0 392.2 : 105.9 196.1 305.9 400.0 502.0 603.9 698.0 807.8 898.0 1003.9 1102.0 1200.0 498.0 : 90.2 200.0 294.1 396.1 498.0 592.2 702.0 792.2 898.0 996.1 1094.1 1200.0 588.3 : 109.8 203.9 305.9 407.8 502.0 611.7 702.0 807.8 905.9 1003.9 1109.8 1200.0 698.0 : 94.1 196.1 298.0 392.2 502.0 592.2 698.0 796.1 894.1 1000.0 1090.2 1200.0 792.2 : 102.0 203.9 298.0 407.8 498.0 603.9 702.0 800.0 905.9 996.1 1105.9 1200.0 894.1 : 102.0 196.1 305.9 396.1 502.0 600.0 698.0 803.9 894.1 1003.9 1098.0 1200.0 996.1 : 94.1 203.9 294.1 400.0 498.0 596.1 702.0 792.2 902.0 996.1 1098.0 1200.0 1090.2: 109.8 200.0 305.9 403.9 502.0 607.8 698.0 807.8 902.0 1003.9 1105.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 109.7750 cents 19.55001 cents 256/243, 90.2250 cents 2: 196.0900 .. 203.9100 cents 7.82000 cents 86.31499 cents 3: 294.1350 .. 305.8650 cents 11.73000 cents 256/243, 90.2250 cents 4: 392.1800 .. 407.8200 cents 15.64000 cents 86.31500 cents 5: 498.0450 .. 501.9550 cents 3.91000 cents 256/243, 90.2250 cents 6: 588.2700 .. 611.7300 cents 531441/524288, 23.4600 cents 86.31499 cents 7: 698.0450 .. 701.9550 cents 3.91000 cents 86.31499 cents 8: 792.1800 .. 807.8200 cents 15.64000 cents 256/243, 90.2250 cents 9: 894.1350 .. 905.8650 cents 11.73000 cents 86.31500 cents 10: 996.0900 .. 1003.9100 cents 7.82000 cents 256/243, 90.2250 cents 11: 1090.2250 .. 1109.7750 cents 19.55000 cents 86.31500 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 109.77501 cents Average / Smallest step : 1.108340 Largest / Average step : 1.097750 Largest / Smallest step : 1.216681 Median interval of one step : 100.00000 cents, amount: 0 Least squares average step : 99.35034 cents, oct.: 1192.20406 cents Scale is strictly proper Step pattern alph. order: ABCCBADEFFED Step pattern size order : AECCEAFBDDBF Scale is a Constant Structure, by a margin of 86.31499 cents Scale diversity : 1.097864 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.882700 Rothenberg efficiency : 0.282558 redundancy: 0.717442 Efficiency x scale size : 3.390693 Number of different interval sizes : 47 = 4.27273 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 4.27273 = 47/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 3.91000 cents Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 2 different sizes of fifth Scale is a temperament ordinaire Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 23.4600 cents: 2 3 4 5 7 8 9 10 Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 9 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.8192 c. M:-11.7300 c. Twelve-tone Chromatic (1/11-comma) 41: 3 4 3 3 4 3 4 3 4 3 3 4 SP M ME SD: 6.3351 c. M:-13.1821 c. 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 5.9696 c. M:-12.8417 c. Meantone Chromatic (1/5-comma) 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 4.6770 c. M: 11.1161 c. Schismic-12 55: 4 5 4 5 5 4 5 4 5 5 4 5 SP M ME SD: 4.4446 c. M: 10.4986 c. 64: 5 5 6 5 6 4 6 5 6 5 5 6 SP D3 SD: 5.2228 c. M: 8.5900 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.6701 c. M: 7.9812 c. 67: 5 6 5 6 6 5 6 5 6 6 5 6 SP M ME SD: 3.5776 c. M: 7.5678 c. 76: 6 6 7 6 7 5 7 6 7 6 6 7 SP D3 SD: 4.3657 c. M:-7.2182 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.3306 c. M:-6.5074 c. 79: 6 7 6 7 7 6 7 6 7 7 6 7 SP M ME SD: 3.3141 c. M:-6.4416 c. 86: 6 8 7 7 8 6 8 7 7 7 7 8 SP D3 S SD: 3.0751 c. M: 6.5041 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 3.3335 c. M:-6.1572 c. 90: 7 8 7 7 8 7 8 7 8 8 7 8 SP D3 S SD: 3.6395 c. M: 5.5133 c. 91: 7 8 7 8 8 7 8 7 8 8 7 8 SP M ME SD: 3.3517 c. M:-6.1078 c. 94: 7 8 8 8 8 7 9 7 8 8 7 9 SP D3 S SD: 2.5775 c. M: 5.1186 c. 98: 7 9 8 8 9 7 9 8 8 8 8 9 SP D3 S SD: 2.3999 c. M: 4.5107 c. 102: 8 9 8 8 9 8 9 8 9 9 8 9 SP D3 S SD: 3.1996 c. M: 3.9447 c. 106: 8 9 9 9 9 8 10 8 9 9 8 10 SP D3 S SD: 2.1720 c. M:-4.0464 c. 110: 8 10 9 9 10 8 10 9 9 9 9 10 SP D3 S SD: 2.1141 c. M:-4.1836 c. 118: 9 10 10 10 10 9 11 9 10 10 9 11 SP D3 S SD: 2.0879 c. M:-4.4302 c. 122: 9 11 10 10 11 9 11 10 10 10 10 11 SP D3 S SD: 2.1096 c. M:-4.5413 c. 130: 10 11 11 11 11 10 12 10 11 11 10 12 SP D3 S SD: 2.1999 c. M:-4.7431 c. 132: 10 12 10 11 12 10 12 10 11 12 10 12 SP T3 SD: 2.4181 c. M:-3.9100 c. 134: 10 12 11 11 12 10 12 11 11 11 11 12 SP D3 S SD: 2.2610 c. M:-4.8349 c. 135: 10 12 11 11 12 10 13 10 12 11 11 12 SP SD: 2.0064 c. M:-4.1772 c. 139: 10 13 11 11 13 10 13 11 12 11 11 13 SP SD: 2.5860 c. M: 3.8941 c. 141: 11 12 12 11 13 10 13 11 12 12 11 13 SP SD: 1.9462 c. M:-4.0827 c. 143: 11 12 12 12 12 11 13 11 13 12 11 13 SP SD: 2.2922 c. M:-3.7671 c. 145: 11 13 12 11 13 11 13 12 12 12 12 13 SP SD: 2.2709 c. M:-3.7960 c. 146: 11 13 12 12 13 11 13 12 12 12 12 13 SP D3 S SD: 2.4766 c. M:-5.0803 c. 147: 11 13 12 12 13 11 14 11 13 12 12 13 SP SD: 1.9311 c. M:-3.9958 c. 153: 12 13 13 12 14 11 14 12 13 13 12 14 SP SD: 1.9522 c. M:-3.9158 c. 159: 12 14 13 13 14 12 14 13 13 14 12 15 SP SD: 1.7974 c. M: 3.7054 c. 161: 12 14 13 14 14 12 15 12 14 14 12 15 SP SD: 2.0505 c. M: 3.4518 c. 163: 12 15 13 13 15 12 15 13 13 14 13 15 SP SD: 2.0147 c. M: 3.3375 c. 164: 12 15 13 13 15 12 15 13 14 14 13 15 SP S SD: 2.1071 c. M: 4.3751 c. 165: 12 15 13 14 14 13 15 13 14 14 13 15 SP SD: 1.6695 c. M: 3.4995 c. 168: 13 14 14 14 15 12 16 13 14 14 14 15 SP SD: 2.1039 c. M: 3.2329 c. 171: 13 15 14 14 15 13 15 14 14 15 13 16 SP SD: 1.5848 c. M: 3.3082 c. 172: 13 15 14 14 15 13 16 13 15 15 13 16 SP S SD: 1.7850 c. M: 3.8079 c. 173: 13 15 14 15 15 13 16 13 15 15 13 16 SP SD: 1.8968 c. M:-3.1957 c. 175: 13 16 14 14 16 13 16 14 14 15 14 16 SP SD: 1.8846 c. M:-3.2486 c. 176: 13 16 14 14 16 13 16 14 15 15 14 16 SP S SD: 1.6460 c. M: 3.5436 c. 177: 13 16 14 15 15 14 16 14 15 15 14 16 SP SD: 1.5405 c. M: 3.1297 c. 183: 14 16 15 15 16 14 16 15 15 16 14 17 SP SD: 1.5321 c. M: 2.9630 c. 184: 14 16 15 15 16 14 17 14 16 16 14 17 SP S SD: 1.4141 c. M: 3.0496 c. 186: 14 16 16 15 16 14 17 15 16 15 15 17 SP SD: 1.7132 c. M:-2.6392 c. 188: 14 17 15 15 17 14 17 15 16 16 15 17 SP S SD: 1.3226 c. M: 2.8183 c. 196: 15 17 16 16 17 15 18 15 17 17 15 18 SP S SD: 1.1914 c. M: 2.3841 c. 200: 15 18 16 16 18 15 18 16 17 17 16 18 SP S SD: 1.1524 c. M: 2.1800 c. 204: 15 18 17 17 18 15 19 16 17 17 16 19 SP S SD: 1.6035 c. M: 1.9897 c. 208: 16 18 17 17 18 16 19 16 18 18 16 19 SP S SD: 1.1250 c. M:-2.0827 c. 212: 16 19 17 17 19 16 19 17 18 18 17 19 SP S SD: 1.1341 c. M:-2.2278 c. 220: 17 19 18 18 19 17 20 17 19 19 17 20 SP S SD: 1.1885 c. M:-2.5023 c. 227: 17 20 18 19 20 17 21 18 19 19 18 21 SP SD: 1.4183 c. M: 3.3861 c. 229: 17 20 19 19 20 17 21 18 19 20 18 21 SP SD: 1.3696 c. M: 3.3053 c. 232: 17 21 19 19 20 18 21 18 20 20 18 21 SP SD: 1.2329 c. M: 2.2940 c. 239: 18 21 19 20 21 18 22 19 20 20 19 22 SP SD: 1.1646 c. M: 2.9216 c. 241: 18 21 20 20 21 18 22 19 20 21 19 22 SP SD: 1.1319 c. M: 2.8487 c. 251: 19 22 21 20 22 19 23 20 21 21 20 23 SP SD: 0.9687 c. M:-2.2793 c. 270: 20 24 22 22 24 20 25 21 23 23 21 25 SP S SD: 0.9321 c. M: 1.6033 c. 282: 21 25 23 23 25 21 26 22 24 24 22 26 SP S SD: 0.6022 c. M: 1.0360 c. 294: 22 26 24 24 26 22 27 23 25 25 23 27 SP S SD: 0.2993 c. M: 0.5149 c. 306: 23 27 25 25 27 23 28 24 26 26 24 28 SP S SD: 0.0202 c. M: 0.0347 c. 2154: 162 190 176 176 190 162 197 169 183 183 169 197 SP S SD: 0.0179 c. M:-0.0308 c.
FIT/HARMONIC
1 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 4 S SD: 1.9550 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.2588 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.0402 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.5385 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.3731 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.9571 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.4419 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.2292 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3239 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.0734 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.7424 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.4182 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.9915 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.2786 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.0793 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.8099 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 3.9656 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4819 cents 27:28:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4295 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.2097 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.4922 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.4594 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.2337 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.9788 cents 42:44:47:50:53:56:59:63:66:70:75:79:84 SD: 1.9419 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.6349 cents 55:58:62:65:69:73:77:82:87:92:98:103:110 SD: 1.5401 cents 58:61:65:69:73:77:81:87:92:97:103:109:116 SD: 1.5026 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.0633 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 0.9876 cents 90:95:101:107:113:120:126:135:142:151:160:169:180 SD: 0.8957 cents 91:96:102:108:114:121:128:136:144:153:162:171:182 SD: 0.8149 cents 99:104:111:117:124:132:139:148:156:166:176:186:198 SD: 0.7882 cents 107:113:120:127:134:143:150:160:169:179:190:201:214 SD: 0.7683 cents 109:115:122:129:137:145:153:163:172:183:194:205:218 SD: 0.7249 cents 114:120:128:135:143:152:160:171:180:191:203:214:228 SD: 0.5995 cents 141:149:158:167:177:188:198:211:223:236:251:265:282 SD: 0.5941 cents 145:153:162:172:182:193:204:217:229:243:258:272:290 SD: 0.5888 cents 150:158:168:178:188:200:211:224:237:251:267:282:300 SD: 0.5706 cents 153:161:171:181:192:204:215:229:242:256:272:287:306 SD: 0.5329 cents 166:175:186:197:208:221:233:248:262:278:295:312:332 SD: 0.5267 cents 169:178:189:200:212:225:237:253:267:283:300:317:338 SD: 0.5176 cents 173:182:194:205:217:231:243:259:273:290:308:325:346 SD: 0.4693 cents 183:193:205:217:230:244:257:274:289:307:325:344:366 SD: 0.4619 cents 185:195:207:219:232:247:260:277:292:310:329:347:370 SD: 0.3816 cents 210:221:235:249:263:280:295:314:332:352:373:394:420 SD: 0.3607 cents 225:237:252:267:282:300:316:337:356:377:400:422:450 SD: 0.3260 cents 243:256:272:288:305:324:341:364:384:407:432:456:486 SD: 0.2559 cents 260:274:291:308:326:347:365:389:411:436:462:488:520 SD: 0.2405 cents 302:318:338:358:379:403:424:452:477:506:537:567:604 SD: 0.2244 cents 318:335:356:377:399:424:447:476:503:533:565:597:636 SD: 0.2135 cents 324:341:363:384:406:432:455:485:512:543:576:608:648 SD: 0.2123 cents 334:352:374:396:419:445:469:500:528:560:594:627:668 SD: 0.1751 cents 393:414:440:466:493:524:552:588:621:659:699:738:786 SD: 0.1456 cents 507:534:568:601:636:676:712:759:801:850:901:952:1014 SD: 0.1223 cents