2087:
1829:
50:
36:
1148:
1140:
179:
in the sixteenth and seventeenth centuries. It allows measurement and comparison of different intervals (frequency ratios) as consisting of different numbers of a single interval, the equal tempered semitone (for example, a minor third is 3 semitones, a major third is 4 semitones, and perfect fifth
1195:
typically have pitch adjustments of up to ±6%, generally used to match the playback or recording pitch to other music sources having slightly different tunings (or possibly recorded on equipment that was not running at quite the right speed). Modern recording studios utilize digital
163:
1189:
232:
1362:
93:
131:
1327:
1220:
may be the first
European to suggest twelve-tone equal temperament. The twelfth root of two was first calculated in 1584 by the Chinese mathematician and musician
1865:
1649:
1438:
1191:), increasing or decreasing the playback speed of a recording by 6% will shift the pitch up or down by about one semitone, or "half-step". Upscale
1134:
1492:
1618:
1594:
1517:
1415:
1192:
2086:
1204:
up to several half-steps. Reel-to-reel adjustments also affect the tempo of the recorded sound, while digital shifting does not.
1723:
1212:
Historically this number was proposed for the first time in relationship to musical tuning in 1580 (drafted, rewritten 1610) by
2129:
1858:
1642:
1508:
1992:
1547:
172:
369:(which has a ratio of 2:1) into twelve equal parts. Each note has a frequency that is 2 times that of the one below it.
2139:
1737:
2134:
1851:
1635:
2061:
1585:
1276:
1265:
1405:
1224:
using an abacus to reach twenty four decimal places accurately, calculated circa 1605 by
Flemish mathematician
1162:
1042:
2144:
1024:
187:
1922:
1947:
2103:
1684:
1580:
1270:
1260:
1255:
384:
1885:
1828:
2108:
2098:
1679:
1576:
1538:
1484:
1478:
1233:
1023:
perfect fifth is 3/2, and the difference between the equal tempered perfect fifth and the just is a
1932:
1915:
1332:
1833:
1699:
1609:
1564:
1020:
712:
69:
49:
2017:
1982:
1960:
1874:
1814:
1805:
1796:
1694:
1669:
1614:
1590:
1513:
1488:
1411:
1028:
362:
137:
101:
1299:
41:
Octaves (12 semitones) increase exponentially when measured on a linear frequency scale (Hz).
2054:
2049:
2027:
2012:
1977:
1895:
1791:
1786:
1781:
1776:
1771:
1704:
1689:
1658:
1556:
1217:
1152:
621:
358:
152:
134:
1742:
1674:
1250:
1016:
421:
35:
1910:
1900:
1229:
1147:
651:
176:
2123:
1965:
1927:
1747:
1728:
1718:
920:
870:
742:
391:
2032:
2002:
1757:
1752:
1709:
1604:
1453:
1225:
1213:
1201:
521:
482:
431:
181:
141:
372:
Applying this value successively to the tones of a chromatic scale, starting from
17:
1428:
1197:
1114:
1086:
1072:
831:
781:
610:
560:
1100:
1221:
1057:
145:
1139:
377:
243:
156:
96:
55:
Octaves are equally spaced when measured on a logarithmic scale (cents).
1568:
701:
390:) with a frequency of 440 Hz, produces the following sequence of
1843:
959:
441:
366:
1627:
1560:
140:, approximately equal to 1.0594631. It is most important in Western
1433:"Sequence A010774 (Decimal expansion of 12th root of 2)"
1146:
1138:
269:. Fraction approximations in increasing order of accuracy include
148:
175:. This number was proposed for the first time in relationship to
1245:
1847:
1631:
1296:"The smallest interval in an equal-tempered scale is the ratio
247:
1011:
Other tuning scales use slightly different interval ratios:
2071:
1432:
995:: 880 Hz) is exactly twice the frequency of the lower
1159:
Since the frequency ratio of a semitone is close to 106% (
1454:"Equal temperament | Definition & Facts | Britannica"
1541:(1933). "A Sixteenth Century Chinese Approximation for
180:
is 7 semitones). A semitone itself is divided into 100
1335:
1302:
1165:
190:
104:
72:
1155:
depicts equal distances between notes (logarithmic)
1061:(1954) makes use of the twenty-fifth root of five (
1045:
uses the interval of the thirteenth root of three (
1356:
1321:
1183:
226:
125:
87:
1068:), a compound major third divided into 5Ă5 parts.
1859:
1643:
1480:The Cambridge History of Western Music Theory
8:
1143:One octave of 12-tet on a monochord (linear)
1003:: 440 Hz), that is, one octave higher.
1866:
1852:
1844:
1650:
1636:
1628:
1522:New Remarks on the Study of Resonant Tubes
1439:On-Line Encyclopedia of Integer Sequences
1347:
1342:
1334:
1307:
1301:
1200:to achieve similar results, ranging from
1184:{\displaystyle 1.05946\times 100=105.946}
1164:
702:Augmented fourth/Diminished fifth/Tritone
214:
210:
196:
191:
189:
113:
109:
103:
78:
73:
71:
1251:Just intonation § Practical difficulties
396:
1399:
1397:
1395:
1393:
1389:
1289:
1135:Audio time stretching and pitch scaling
1228:, in 1636 by the French mathematician
1509:A Short History of the Chinese People
1410:, p.294-5. Third edition. Princeton.
227:{\displaystyle {\sqrt{2}}=2^{1/1200}}
7:
1193:reel-to-reel magnetic tape recorders
1408:: Non-European Roots of Mathematics
1403:Joseph, George Gheverghese (2010).
361:is a ratio of frequencies and the
353:The equal-tempered chromatic scale
25:
522:Major second/Full step/Whole tone
2085:
1827:
1506:Goodrich, L. Carrington (2013).
48:
34:
1232:and in 1691 by German musician
483:Minor second/Half step/Semitone
1:
1548:American Mathematical Monthly
1520:. Cites: Chu Tsai-yĂŒ (1584).
250:to 20 significant figures is
173:twelve-tone equal temperament
1477:Christensen, Thomas (2002),
1357:{\displaystyle r={\sqrt{p}}}
365:chromatic scale divides the
1738:Quadratic irrational number
1724:PisotâVijayaraghavan number
1216:. In 1581 Italian musician
27:Algebraic irrational number
2161:
1429:Sloane, N. J. A.
1372:(= 2/1 in an octave) into
1132:
1027:, the twelfth root of the
144:, where it represents the
88:{\displaystyle {\sqrt{2}}}
2094:
2083:
1881:
1823:
1665:
1586:On the Sensations of Tone
1277:The Well-Tempered Clavier
1266:Scientific pitch notation
403:Standard interval name(s)
1406:The Crest of the Peacock
418:(to six decimal places)
126:{\displaystyle 2^{1/12}}
1322:{\displaystyle r^{n}=p}
2130:Mathematical constants
1834:Mathematics portal
1589:. Dover Publications.
1358:
1323:
1185:
1156:
1144:
228:
127:
89:
1359:
1324:
1271:Twelve-tone technique
1261:Piano key frequencies
1256:Music and mathematics
1186:
1150:
1142:
229:
128:
90:
1680:Constructible number
1333:
1300:
1234:Andreas Werckmeister
1163:
188:
102:
70:
1806:Supersilver ratio (
1797:Supergolden ratio (
1043:BohlenâPierce scale
1041:The equal tempered
1007:Other tuning scales
64:twelfth root of two
2140:Irrational numbers
1875:Irrational numbers
1700:Eisenstein integer
1610:Genesis of a Music
1581:Helmholtz, Hermann
1458:www.britannica.com
1442:. OEIS Foundation.
1368:divides the ratio
1364:, where the ratio
1354:
1319:
1181:
1157:
1145:
405:relating to A 440
224:
123:
85:
2135:Algebraic numbers
2117:
2116:
2018:Supersilver ratio
1983:Supergolden ratio
1943:Twelfth root of 2
1841:
1840:
1815:Twelfth root of 2
1695:Doubling the cube
1685:Conway's constant
1670:Algebraic integer
1659:Algebraic numbers
1613:. Da Capo Press.
1352:
1029:Pythagorean comma
985:
984:
201:
138:irrational number
83:
18:Twelfth root of 2
16:(Redirected from
2152:
2089:
2077:
2067:
2055:Square root of 7
2050:Square root of 6
2045:
2028:Square root of 5
2023:
2013:Square root of 3
2008:
1998:
1988:
1978:Square root of 2
1971:
1956:
1938:
1906:
1891:
1868:
1861:
1854:
1845:
1832:
1831:
1809:
1800:
1792:Square root of 7
1787:Square root of 6
1782:Square root of 5
1777:Square root of 3
1772:Square root of 2
1765:
1761:
1732:
1713:
1705:Gaussian integer
1690:Cyclotomic field
1652:
1645:
1638:
1629:
1624:
1600:
1577:Ellis, Alexander
1572:
1544:
1525:
1504:
1498:
1497:
1474:
1468:
1467:
1465:
1464:
1450:
1444:
1443:
1425:
1419:
1401:
1377:
1363:
1361:
1360:
1355:
1353:
1351:
1343:
1328:
1326:
1325:
1320:
1312:
1311:
1294:
1218:Vincenzo Galilei
1190:
1188:
1187:
1182:
1153:chromatic circle
1129:Pitch adjustment
1123:
1122:
1109:
1108:
1095:
1094:
1081:
1080:
1067:
1066:
1051:
1050:
1037:
1036:
975:
974:
948:
947:
943:
936:
935:
917:
916:
911:
910:
898:
897:
893:
886:
885:
859:
858:
854:
847:
846:
828:
827:
822:
821:
809:
808:
804:
797:
796:
770:
769:
765:
758:
757:
731:
730:
726:
718:
717:
698:
697:
692:
691:
679:
678:
674:
667:
666:
640:
639:
635:
627:
626:
607:
606:
601:
600:
588:
587:
583:
576:
575:
549:
548:
544:
537:
536:
510:
509:
505:
498:
497:
479:
478:
473:
472:
457:
456:
397:
359:musical interval
348:
346:
345:
342:
339:
332:
330:
329:
326:
323:
316:
314:
313:
310:
307:
300:
298:
297:
294:
291:
284:
282:
281:
278:
275:
268:
267:
264:
261:
258:
255:
233:
231:
230:
225:
223:
222:
218:
202:
200:
192:
170:
169:
168:
166:
153:musical interval
132:
130:
129:
124:
122:
121:
117:
94:
92:
91:
86:
84:
82:
74:
52:
38:
21:
2160:
2159:
2155:
2154:
2153:
2151:
2150:
2149:
2120:
2119:
2118:
2113:
2090:
2081:
2075:
2065:
2044:
2036:
2021:
2006:
1996:
1986:
1969:
1951:
1936:
1904:
1889:
1877:
1872:
1842:
1837:
1826:
1819:
1807:
1798:
1766:
1763:
1759:
1743:Rational number
1730:
1729:Plastic ratio (
1711:
1675:Chebyshev nodes
1661:
1656:
1621:
1603:
1597:
1575:
1561:10.2307/2300937
1542:
1537:
1534:
1532:Further reading
1529:
1528:
1505:
1501:
1495:
1476:
1475:
1471:
1462:
1460:
1452:
1451:
1447:
1427:
1426:
1422:
1402:
1391:
1386:
1381:
1380:
1331:
1330:
1303:
1298:
1297:
1295:
1291:
1286:
1242:
1210:
1161:
1160:
1137:
1131:
1120:
1118:
1106:
1104:
1092:
1090:
1078:
1076:
1064:
1062:
1048:
1046:
1034:
1032:
1009:
1002:
994:
972:
970:
945:
941:
940:
933:
931:
914:
913:
908:
907:
895:
891:
890:
883:
881:
856:
852:
851:
844:
842:
825:
824:
819:
818:
806:
802:
801:
794:
792:
767:
763:
762:
755:
753:
728:
724:
723:
715:
713:
695:
694:
689:
688:
676:
672:
671:
664:
662:
637:
633:
632:
624:
622:
604:
603:
598:
597:
585:
581:
580:
573:
571:
546:
542:
541:
534:
532:
507:
503:
502:
495:
493:
476:
475:
470:
469:
454:
452:
429:
428:Just intonation
424:
422:Just intonation
417:
409:
404:
388:
355:
343:
340:
337:
336:
334:
327:
324:
321:
320:
318:
311:
308:
305:
304:
302:
295:
292:
289:
288:
286:
279:
276:
273:
272:
270:
265:
262:
259:
256:
253:
251:
240:
238:Numerical value
206:
186:
185:
164:
162:
161:
160:
105:
100:
99:
68:
67:
60:
59:
58:
57:
56:
53:
44:
43:
42:
39:
28:
23:
22:
15:
12:
11:
5:
2158:
2156:
2148:
2147:
2145:Musical tuning
2142:
2137:
2132:
2122:
2121:
2115:
2114:
2112:
2111:
2106:
2104:Transcendental
2101:
2095:
2092:
2091:
2084:
2082:
2080:
2079:
2069:
2058:
2057:
2052:
2047:
2040:
2030:
2025:
2015:
2010:
2000:
1990:
1980:
1974:
1973:
1963:
1961:Cube root of 2
1958:
1945:
1940:
1930:
1925:
1923:Logarithm of 2
1919:
1918:
1913:
1908:
1898:
1893:
1882:
1879:
1878:
1873:
1871:
1870:
1863:
1856:
1848:
1839:
1838:
1824:
1821:
1820:
1818:
1817:
1812:
1803:
1794:
1789:
1784:
1779:
1774:
1769:
1762:
1758:Silver ratio (
1755:
1750:
1745:
1740:
1735:
1726:
1721:
1716:
1710:Golden ratio (
1707:
1702:
1697:
1692:
1687:
1682:
1677:
1672:
1666:
1663:
1662:
1657:
1655:
1654:
1647:
1640:
1632:
1626:
1625:
1619:
1601:
1595:
1573:
1539:Barbour, J. M.
1533:
1530:
1527:
1526:
1499:
1494:978-0521686983
1493:
1469:
1445:
1420:
1388:
1387:
1385:
1382:
1379:
1378:
1350:
1346:
1341:
1338:
1318:
1315:
1310:
1306:
1288:
1287:
1285:
1282:
1281:
1280:
1273:
1268:
1263:
1258:
1253:
1248:
1241:
1238:
1230:Marin Mersenne
1209:
1206:
1198:pitch shifting
1180:
1177:
1174:
1171:
1168:
1130:
1127:
1126:
1125:
1111:
1097:
1083:
1069:
1055:Stockhausen's
1053:
1039:
1008:
1005:
1000:
992:
983:
982:
979:
976:
968:
965:
962:
957:
953:
952:
949:
937:
929:
926:
923:
918:
903:
902:
899:
887:
879:
876:
873:
868:
864:
863:
860:
848:
840:
837:
834:
829:
814:
813:
810:
798:
790:
787:
784:
779:
775:
774:
771:
759:
751:
748:
745:
740:
736:
735:
732:
720:
710:
707:
704:
699:
684:
683:
680:
668:
660:
657:
654:
652:Perfect fourth
649:
645:
644:
641:
629:
619:
616:
613:
608:
593:
592:
589:
577:
569:
566:
563:
558:
554:
553:
550:
538:
530:
527:
524:
519:
515:
514:
511:
499:
491:
488:
485:
480:
465:
464:
461:
458:
450:
447:
444:
439:
435:
434:
426:
419:
414:
411:
406:
401:
386:
363:equal-tempered
354:
351:
239:
236:
221:
217:
213:
209:
205:
199:
195:
177:musical tuning
120:
116:
112:
108:
81:
77:
54:
47:
46:
45:
40:
33:
32:
31:
30:
29:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2157:
2146:
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2127:
2125:
2110:
2109:Trigonometric
2107:
2105:
2102:
2100:
2099:Schizophrenic
2097:
2096:
2093:
2088:
2073:
2070:
2063:
2060:
2059:
2056:
2053:
2051:
2048:
2043:
2039:
2034:
2031:
2029:
2026:
2019:
2016:
2014:
2011:
2004:
2001:
1994:
1993:ErdĆsâBorwein
1991:
1984:
1981:
1979:
1976:
1975:
1967:
1966:Plastic ratio
1964:
1962:
1959:
1954:
1949:
1946:
1944:
1941:
1934:
1931:
1929:
1926:
1924:
1921:
1920:
1917:
1914:
1912:
1909:
1902:
1899:
1897:
1894:
1887:
1884:
1883:
1880:
1876:
1869:
1864:
1862:
1857:
1855:
1850:
1849:
1846:
1836:
1835:
1830:
1822:
1816:
1813:
1811:
1804:
1802:
1795:
1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1756:
1754:
1751:
1749:
1748:Root of unity
1746:
1744:
1741:
1739:
1736:
1734:
1727:
1725:
1722:
1720:
1719:Perron number
1717:
1715:
1708:
1706:
1703:
1701:
1698:
1696:
1693:
1691:
1688:
1686:
1683:
1681:
1678:
1676:
1673:
1671:
1668:
1667:
1664:
1660:
1653:
1648:
1646:
1641:
1639:
1634:
1633:
1630:
1622:
1620:0-306-80106-X
1616:
1612:
1611:
1606:
1605:Partch, Harry
1602:
1598:
1596:0-486-60753-4
1592:
1588:
1587:
1582:
1578:
1574:
1570:
1566:
1562:
1558:
1554:
1550:
1549:
1540:
1536:
1535:
1531:
1523:
1519:
1518:9780486169231
1515:
1512:, . Courier.
1511:
1510:
1503:
1500:
1496:
1490:
1486:
1482:
1481:
1473:
1470:
1459:
1455:
1449:
1446:
1441:
1440:
1434:
1430:
1424:
1421:
1417:
1416:9781400836369
1413:
1409:
1407:
1400:
1398:
1396:
1394:
1390:
1383:
1376:equal parts."
1375:
1371:
1367:
1348:
1344:
1339:
1336:
1316:
1313:
1308:
1304:
1293:
1290:
1283:
1279:
1278:
1274:
1272:
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1247:
1244:
1243:
1239:
1237:
1235:
1231:
1227:
1223:
1219:
1215:
1207:
1205:
1203:
1199:
1194:
1178:
1175:
1172:
1169:
1166:
1154:
1149:
1141:
1136:
1128:
1117:is based on â
1116:
1112:
1103:is based on â
1102:
1098:
1089:is based on â
1088:
1084:
1075:is based on â
1074:
1070:
1060:
1059:
1054:
1044:
1040:
1035:531441/524288
1030:
1026:
1022:
1018:
1014:
1013:
1012:
1006:
1004:
998:
990:
980:
977:
969:
966:
963:
961:
958:
955:
954:
950:
938:
930:
927:
924:
922:
921:Major seventh
919:
905:
904:
900:
888:
880:
877:
874:
872:
871:Minor seventh
869:
866:
865:
861:
849:
841:
838:
835:
833:
830:
816:
815:
811:
799:
791:
788:
785:
783:
780:
777:
776:
772:
760:
752:
749:
746:
744:
743:Perfect fifth
741:
738:
737:
733:
721:
719:
711:
708:
705:
703:
700:
686:
685:
681:
669:
661:
658:
655:
653:
650:
647:
646:
642:
630:
628:
620:
617:
614:
612:
609:
595:
594:
590:
578:
570:
567:
564:
562:
559:
556:
555:
551:
539:
531:
528:
525:
523:
520:
517:
516:
512:
500:
492:
489:
486:
484:
481:
467:
466:
462:
459:
451:
448:
445:
443:
440:
437:
436:
433:
427:
423:
420:
415:
412:
407:
402:
399:
398:
395:
393:
389:
382:
381:
375:
370:
368:
364:
360:
352:
350:
249:
245:
237:
235:
219:
215:
211:
207:
203:
197:
193:
183:
178:
174:
167:
158:
154:
150:
147:
143:
139:
136:
118:
114:
110:
106:
98:
79:
75:
65:
51:
37:
19:
2041:
2037:
2033:Silver ratio
2003:Golden ratio
1952:
1942:
1825:
1753:Salem number
1608:
1584:
1555:(2): 69â73.
1552:
1546:
1521:
1507:
1502:
1479:
1472:
1461:. Retrieved
1457:
1448:
1436:
1423:
1404:
1373:
1369:
1365:
1292:
1275:
1226:Simon Stevin
1214:Simon Stevin
1211:
1158:
1056:
1010:
996:
988:
986:
379:
373:
371:
356:
244:twelfth root
241:
142:music theory
97:equivalently
63:
61:
1115:alpha scale
1087:gamma scale
1073:delta scale
1021:Pythagorean
832:Major sixth
782:Minor sixth
611:Major third
561:Minor third
416:Coefficient
413:Multiplier
2124:Categories
1933:Lemniscate
1483:, p.
1463:2024-06-03
1384:References
1133:See also:
1101:beta scale
987:The final
383:(known as
184:(1 cent =
1896:Liouville
1886:Chaitin's
1222:Zhu Zaiyu
1170:×
1058:Studie II
408:Frequency
146:frequency
135:algebraic
1607:(1974).
1583:(1954).
1240:See also
915:♭
909:♯
826:♭
820:♯
696:♭
690:♯
605:♭
599:♯
477:♭
471:♯
157:semitone
133:) is an
2062:Euler's
1948:Apéry's
1569:2300937
1431:(ed.).
1208:History
1179:105.946
1167:1.05946
1119:√
1105:√
1091:√
1077:√
1063:√
1047:√
1033:√
951:-11.73
944:⁄
894:⁄
862:-15.64
855:⁄
812:+13.69
805:⁄
766:⁄
734:+17.49
727:⁄
675:⁄
643:-13.69
636:⁄
591:+15.64
584:⁄
545:⁄
513:+11.73
506:⁄
392:pitches
378:middle
347:
335:
331:
319:
315:
303:
299:
287:
283:
271:
155:) of a
1928:Dottie
1617:
1593:
1567:
1516:
1491:
1414:
964:880.00
960:Octave
925:830.61
901:+3.91
875:783.99
836:739.99
786:698.46
773:+1.96
747:659.26
706:622.25
682:-1.96
656:587.33
615:554.37
565:523.25
552:-3.91
526:493.88
487:466.16
446:440.00
442:Unison
425:ratio
376:above
367:octave
333:, and
1916:Cahen
1911:Omega
1901:Prime
1565:JSTOR
1329:, so
1284:Notes
1202:cents
971:2.000
932:1.887
882:1.781
843:1.681
793:1.587
754:1.498
714:1.414
663:1.334
623:1.259
572:1.189
533:1.122
494:1.059
453:1.000
432:cents
410:(Hz)
400:Note
344:17843
338:18904
252:1.059
182:cents
171:) in
149:ratio
1615:ISBN
1591:ISBN
1514:ISBN
1489:ISBN
1437:The
1412:ISBN
1246:Fret
1151:The
1113:The
1099:The
1085:The
1071:The
1025:grad
1017:just
1015:The
328:1564
322:1657
266:2646
242:The
220:1200
198:1200
165:Play
95:(or
62:The
1955:(3)
1557:doi
1545:".
1485:205
1173:100
1121:3/2
1107:3/2
1093:3/2
1079:3/2
1019:or
973:000
934:748
884:797
845:792
795:401
756:307
716:213
665:839
625:921
574:207
535:462
496:463
455:000
312:185
306:196
263:295
260:359
257:094
254:463
248:two
246:of
234:).
66:or
2126::
2072:Pi
1579:;
1563:.
1553:40
1551:.
1487:,
1456:.
1435:.
1392:^
1236:.
1052:).
1038:).
999:(A
991:(A
981:0
978:2
942:15
939:â
912:/A
892:16
889:â
850:â
823:/G
800:â
761:â
722:â
693:/E
670:â
631:â
602:/D
579:â
540:â
508:15
504:16
501:â
474:/B
463:0
460:1
430:±
394::
357:A
349:.
317:,
301:,
296:84
290:89
285:,
280:17
274:18
119:12
80:12
2078:)
2076:Ï
2074:(
2068:)
2066:e
2064:(
2046:)
2042:S
2038:ÎŽ
2035:(
2024:)
2022:Ï
2020:(
2009:)
2007:Ï
2005:(
1999:)
1997:E
1995:(
1989:)
1987:Ï
1985:(
1972:)
1970:Ï
1968:(
1957:)
1953:ζ
1950:(
1939:)
1937:Ï
1935:(
1907:)
1905:Ï
1903:(
1892:)
1890:Ω
1888:(
1867:e
1860:t
1853:v
1810:)
1808:Ï
1801:)
1799:Ï
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1764:S
1760:ÎŽ
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1623:.
1599:.
1571:.
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1543:Ï
1524:.
1466:.
1418:.
1374:n
1370:p
1366:r
1349:n
1345:p
1340:=
1337:r
1317:p
1314:=
1309:n
1305:r
1176:=
1124:.
1110:.
1096:.
1082:.
1065:5
1049:3
1031:(
1001:4
997:A
993:5
989:A
967:2
956:A
946:8
928:2
906:G
896:9
878:2
867:G
857:3
853:5
839:2
817:F
807:5
803:8
789:2
778:F
768:2
764:3
750:2
739:E
729:5
725:7
709:2
687:D
677:3
673:4
659:2
648:D
638:4
634:5
618:2
596:C
586:5
582:6
568:2
557:C
547:8
543:9
529:2
518:B
490:2
468:A
449:2
438:A
387:4
385:A
380:C
374:A
341:/
325:/
309:/
293:/
277:/
216:/
212:1
208:2
204:=
194:2
159:(
151:(
115:/
111:1
107:2
76:2
20:)
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