716:
395:
1948:
28:
239:
208:
177:
146:
463:
441:
833:
815:
803:
780:
862:
723:
496:
402:
761:
746:
556:
matches both intervals closely and is also the smallest widely used equal temperament that uniquely matches both intervals. Tuning systems that temper out the
1669:
536:
Approximations to the 12:11 and 11:10 neutral seconds can be found in a number of equally tempered tuning systems. 11:10 is very closely matched by
508:
between the two tones, a hair smaller than a ratio of frequencies between the two tones of 12:11, and exactly half of an equal-tempered minor third.
845:
of the two tones, or about 1061 cents. This is the largest neutral seventh, and occurs infrequently in music, as little music utilizes the 13th
874:
between the two tones, a hair larger than the 11:6 ratio, and exactly half of an equal-tempered major thirteenth (octave plus major sixth).
471:, has a ratio of 11:10 between the two tones and is about 165.00 cents wide. The lesser undecimal neutral second may be derived from the
1012:
981:
948:
520:). Because the equal tempered neutral second is essentially a semitone (minor second) plus a quarter-tone, they may be considered
78:
sharp from minor intervals and a quarter tone flat from major intervals. In just intonation, as well as in tunings such as
1461:
1441:
902:
1567:
1970:
1573:
1356:
878:
These intervals are all within about 12 cents of each other and are difficult for most people to distinguish.
1951:
1689:
1628:
1005:
912:
907:
480:
472:
1975:
1749:
1744:
1555:
1931:
1684:
1591:
1585:
1171:
583:
561:
553:
549:
545:
537:
270:
87:
83:
79:
68:
1714:
1579:
1561:
1827:
1264:
998:
525:
521:
453:
tone to the lower-frequency tone of 12:11 and is about 150.64 cents wide, while the larger one,
1769:
1709:
1270:
1246:
1234:
1215:
1029:
977:
944:
854:
684:
488:
476:
363:
52:
1839:
1664:
1609:
1603:
1597:
1281:
1258:
1240:
1185:
1179:
1021:
917:
889:. Based on its positioning in the harmonic series, the undecimal neutral seventh implies a
517:
44:
1807:
1531:
1319:
1209:
1203:
1191:
1134:
1097:
704:
667:
564:
has a neutral second between 12:11 and 13:12, and a neutral third between 16:13 and 11:9.
383:
346:
275:
238:
207:
176:
145:
48:
1787:
1781:
1775:
1547:
1074:
644:
588:
323:
71:
to a neutral interval. For example, the inverse of a neutral third is a neutral sixth.
1964:
1911:
1760:
1679:
1674:
1620:
1481:
1421:
1307:
1295:
1160:
1123:
1080:
886:
882:
755:
740:
557:
104:
99:
90:, which more closely approximate just intonation, the intervals are closer together.
715:
479:
and twelfth harmonics. The greater undecimal neutral second may be derived from the
1926:
1883:
1878:
1739:
1385:
1142:
1105:
890:
871:
694:
677:
541:
513:
505:
427:
423:
394:
373:
356:
75:
60:
36:
1888:
1719:
1154:
1148:
1117:
1111:
842:
796:
64:
56:
27:
17:
1921:
1815:
1313:
1226:
951:. 3/4-tone, undecimal neutral second and 21/4-tone, undecimal neutral seventh.
1821:
1325:
450:
1853:
1301:
1049:
846:
621:
300:
1859:
1847:
1833:
1252:
1197:
1916:
1893:
1801:
1795:
1086:
1068:
67:
is 300 cents, and a neutral third is 350 cents. A neutral interval
1289:
714:
393:
26:
994:
990:
769:. Four distinct intervals may be termed neutral sevenths:
430:. Three distinct intervals may be termed neutral seconds:
560:
of 121:120 do not distinguish between the two intervals.
483:
as the interval between the tenth and eleventh harmonics.
512:
The equal-tempered neutral is found in some traditional
893:
one perfect fifth below the lower of the two notes.
1902:
1869:
1758:
1728:
1698:
1655:
1646:
1619:
1546:
1529:
1371:
1354:
1343:
1280:
1225:
1170:
1133:
1096:
1061:
1043:
1028:
703:
693:
683:
676:
666:
643:
620:
615:
607:
599:
594:
582:
382:
372:
362:
355:
345:
322:
299:
294:
286:
281:
269:
974:Cooking with Csound: Woodwind and Brass Recipes
960:Haluska (2003), p.?. Septimal neutral seventh.
881:A neutral seventh can be formed by stacking a
1006:
8:
577:
434:The intermediate neutral second, called the
264:
1947:
1652:
1543:
1368:
1351:
1058:
1040:
1013:
999:
991:
811:. Alternately, 13:7 or about 1071.7 cents
51:, but instead in between. For example, in
968:
966:
935:
933:
870:is characterized by a difference in 1050
788:has a ratio of 64:35 or about 1045 cents.
504:is characterized by a difference in 150
114:
941:The Mathematical Theory of Tone Systems
929:
799:of the two tones, or about 1049 cents
576:
263:
7:
109:
972:Andrew Horner, Lydia Ayres (2002).
739:is a musical interval wider than a
94:
25:
841:has a ratio of 24:13 between the
449:, has a ratio between the higher-
74:Roughly, neutral intervals are a
1946:
795:has a ratio of 11:6 between the
458:greater undecimal neutral second
237:
206:
175:
144:
436:lesser undecimal neutral second
540:, whereas 12:11 is matched by
1:
903:Major fourth and minor fifth
475:as the interval between the
422:is an interval wider than a
1568:septimal chromatic semitone
1992:
1574:septimal diatonic semitone
1362:(Numbers in brackets refer
828:tridecimal neutral seventh
1944:
1364:to fractional semitones.)
1357:24-tone equal temperament
793:undecimal neutral seventh
695:24-Tone equal temperament
685:12-Tone equal temperament
374:24-Tone equal temperament
364:12-Tone equal temperament
775:septimal neutral seventh
1952:List of pitch intervals
1690:Subminor and supermajor
1629:minor diatonic semitone
1539:refer to pitch ratios.)
913:List of pitch intervals
908:Subminor and supermajor
1750:Undecimal quarter tone
732:
411:
32:
1745:Septimal quarter tone
1556:septimal quarter tone
939:Haluska, Jan (2003).
719:Neutral seventh on C
718:
672:11:6, 64:35, or 24:13
397:
30:
1932:Incomposite interval
1685:Pythagorean interval
1537:(Numbers in brackets
1045:(Numbers in brackets
754:but narrower than a
532:In equal temperament
426:and narrower than a
398:Neutral second on C
1715:Pythagorean apotome
1562:septimal third tone
709:1049, 1045, or 1061
579:
522:three-quarter tones
266:
1828:Septimal semicomma
733:
526:quarter tone scale
412:
47:that is neither a
33:
1971:Neutral intervals
1958:
1957:
1940:
1939:
1770:Pythagorean comma
1710:Pythagorean limma
1642:
1641:
1638:
1637:
1604:supermajor fourth
1580:supermajor second
1525:
1524:
1339:
1338:
1335:
1334:
1047:are the number of
713:
712:
392:
391:
254:
253:
53:equal temperament
16:(Redirected from
1983:
1950:
1949:
1840:Septimal kleisma
1653:
1610:subminor seventh
1592:supermajor third
1544:
1532:Just intonations
1517:
1516:
1512:
1509:
1497:
1496:
1492:
1489:
1477:
1476:
1472:
1469:
1457:
1456:
1452:
1449:
1437:
1436:
1432:
1429:
1417:
1416:
1412:
1409:
1397:
1396:
1392:
1369:
1352:
1059:
1041:
1015:
1008:
1001:
992:
985:
970:
961:
958:
952:
937:
918:Microtonal music
885:together with a
869:
868:
867:
865:
840:
839:
838:
836:
822:
821:
820:
818:
810:
809:
808:
806:
787:
786:
785:
783:
768:
767:
766:
764:
753:
752:
751:
749:
730:
729:
728:
726:
662:
661:
657:
654:
639:
638:
634:
631:
580:
574:Musical interval
518:Arab tone system
503:
502:
501:
499:
470:
469:
468:
466:
448:
447:
446:
444:
409:
408:
407:
405:
341:
340:
336:
333:
318:
317:
313:
310:
267:
261:Musical interval
250:
249:
242:
241:
232:
231:
219:
218:
211:
210:
201:
200:
188:
187:
180:
179:
170:
169:
157:
156:
149:
148:
139:
138:
115:
41:neutral interval
21:
1991:
1990:
1986:
1985:
1984:
1982:
1981:
1980:
1961:
1960:
1959:
1954:
1936:
1898:
1865:
1808:Septimal diesis
1754:
1724:
1694:
1648:
1634:
1615:
1538:
1535:
1521:
1514:
1510:
1507:
1505:
1494:
1490:
1487:
1485:
1474:
1470:
1467:
1465:
1454:
1450:
1447:
1445:
1434:
1430:
1427:
1425:
1414:
1410:
1407:
1405:
1394:
1390:
1389:
1379:
1378:
1377:
1373:
1363:
1360:
1347:
1345:
1331:
1276:
1221:
1166:
1129:
1092:
1053:
1048:
1046:
1036:
1034:
1031:
1024:
1019:
989:
988:
971:
964:
959:
955:
938:
931:
926:
899:
863:
861:
860:
859:
857:neutral seventh
834:
832:
831:
830:
816:
814:
813:
812:
804:
802:
801:
800:
781:
779:
778:
777:
762:
760:
759:
758:
747:
745:
744:
743:
737:neutral seventh
724:
722:
721:
720:
705:Just intonation
659:
655:
652:
650:
636:
632:
629:
627:
578:Neutral seventh
575:
570:
534:
497:
495:
494:
493:
481:harmonic series
473:harmonic series
464:
462:
461:
460:
442:
440:
439:
438:
403:
401:
400:
399:
384:Just intonation
338:
334:
331:
329:
315:
311:
308:
306:
276:neutral seventh
262:
259:
247:
246:
236:
229:
228:
216:
215:
205:
198:
197:
185:
184:
174:
167:
166:
154:
153:
143:
136:
135:
110:Neutral seventh
49:major nor minor
23:
22:
18:Neutral seventh
15:
12:
11:
5:
1989:
1987:
1979:
1978:
1973:
1963:
1962:
1956:
1955:
1945:
1942:
1941:
1938:
1937:
1935:
1934:
1929:
1924:
1919:
1914:
1908:
1906:
1900:
1899:
1897:
1896:
1891:
1886:
1881:
1875:
1873:
1867:
1866:
1864:
1863:
1857:
1851:
1844:
1843:
1837:
1831:
1825:
1819:
1812:
1811:
1805:
1802:Greater diesis
1799:
1792:
1791:
1788:Septimal comma
1785:
1782:Holdrian comma
1779:
1776:Syntonic comma
1773:
1766:
1764:
1756:
1755:
1753:
1752:
1747:
1742:
1736:
1734:
1726:
1725:
1723:
1722:
1717:
1712:
1706:
1704:
1696:
1695:
1693:
1692:
1687:
1682:
1677:
1672:
1667:
1661:
1659:
1650:
1644:
1643:
1640:
1639:
1636:
1635:
1633:
1632:
1625:
1623:
1617:
1616:
1614:
1613:
1607:
1601:
1598:subminor fifth
1595:
1589:
1586:subminor third
1583:
1577:
1571:
1565:
1559:
1552:
1550:
1541:
1527:
1526:
1523:
1522:
1520:
1519:
1499:
1479:
1459:
1439:
1419:
1399:
1382:
1380:
1372:
1366:
1349:
1341:
1340:
1337:
1336:
1333:
1332:
1330:
1329:
1323:
1317:
1311:
1305:
1299:
1293:
1286:
1284:
1278:
1277:
1275:
1274:
1268:
1262:
1256:
1250:
1244:
1238:
1231:
1229:
1223:
1222:
1220:
1219:
1213:
1207:
1201:
1195:
1189:
1183:
1176:
1174:
1168:
1167:
1165:
1164:
1158:
1152:
1146:
1139:
1137:
1131:
1130:
1128:
1127:
1121:
1115:
1109:
1102:
1100:
1094:
1093:
1091:
1090:
1084:
1078:
1072:
1065:
1063:
1056:
1038:
1026:
1025:
1020:
1018:
1017:
1010:
1003:
995:
987:
986:
962:
953:
928:
927:
925:
922:
921:
920:
915:
910:
905:
898:
895:
876:
875:
855:equal-tempered
850:
824:
789:
711:
710:
707:
701:
700:
697:
691:
690:
687:
681:
680:
674:
673:
670:
664:
663:
647:
645:Interval class
641:
640:
624:
618:
617:
613:
612:
609:
605:
604:
601:
597:
596:
592:
591:
589:neutral second
586:
573:
569:
566:
533:
530:
510:
509:
491:neutral second
489:equal-tempered
484:
454:
416:neutral second
390:
389:
386:
380:
379:
376:
370:
369:
366:
360:
359:
353:
352:
351:11:10 or 12:11
349:
343:
342:
326:
324:Interval class
320:
319:
303:
297:
296:
292:
291:
288:
284:
283:
279:
278:
273:
265:Neutral second
260:
258:
255:
252:
251:
243:
233:
225:
221:
220:
212:
202:
194:
190:
189:
181:
171:
163:
159:
158:
150:
140:
132:
128:
127:
124:
121:
118:
113:
112:
107:
102:
97:
95:Neutral second
24:
14:
13:
10:
9:
6:
4:
3:
2:
1988:
1977:
1976:Quarter tones
1974:
1972:
1969:
1968:
1966:
1953:
1943:
1933:
1930:
1928:
1925:
1923:
1920:
1918:
1915:
1913:
1910:
1909:
1907:
1905:
1901:
1895:
1892:
1890:
1887:
1885:
1882:
1880:
1877:
1876:
1874:
1872:
1868:
1861:
1858:
1855:
1852:
1849:
1846:
1845:
1841:
1838:
1835:
1832:
1829:
1826:
1823:
1820:
1817:
1814:
1813:
1809:
1806:
1803:
1800:
1797:
1796:Lesser diesis
1794:
1793:
1789:
1786:
1783:
1780:
1777:
1774:
1771:
1768:
1767:
1765:
1763:
1762:
1757:
1751:
1748:
1746:
1743:
1741:
1738:
1737:
1735:
1733:
1732:
1731:Quarter tones
1727:
1721:
1718:
1716:
1713:
1711:
1708:
1707:
1705:
1703:
1702:
1697:
1691:
1688:
1686:
1683:
1681:
1680:Pseudo-octave
1678:
1676:
1673:
1671:
1668:
1666:
1663:
1662:
1660:
1658:
1654:
1651:
1645:
1630:
1627:
1626:
1624:
1622:
1618:
1611:
1608:
1605:
1602:
1599:
1596:
1593:
1590:
1587:
1584:
1581:
1578:
1575:
1572:
1569:
1566:
1563:
1560:
1557:
1554:
1553:
1551:
1549:
1545:
1542:
1540:
1534:
1533:
1528:
1503:
1500:
1483:
1480:
1463:
1460:
1443:
1440:
1423:
1420:
1403:
1400:
1387:
1384:
1383:
1381:
1376:
1370:
1367:
1365:
1359:
1358:
1353:
1350:
1342:
1327:
1324:
1321:
1318:
1315:
1312:
1309:
1306:
1303:
1300:
1297:
1294:
1291:
1288:
1287:
1285:
1283:
1279:
1272:
1269:
1266:
1263:
1260:
1257:
1254:
1251:
1248:
1245:
1242:
1239:
1236:
1233:
1232:
1230:
1228:
1224:
1217:
1214:
1211:
1208:
1205:
1202:
1199:
1196:
1193:
1190:
1187:
1184:
1181:
1178:
1177:
1175:
1173:
1169:
1162:
1159:
1156:
1153:
1150:
1147:
1144:
1141:
1140:
1138:
1136:
1132:
1125:
1122:
1119:
1116:
1113:
1110:
1107:
1104:
1103:
1101:
1099:
1095:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1066:
1064:
1060:
1057:
1055:
1051:
1042:
1039:
1033:
1027:
1023:
1016:
1011:
1009:
1004:
1002:
997:
996:
993:
983:
982:0-89579-507-8
979:
975:
969:
967:
963:
957:
954:
950:
949:0-8247-4714-3
946:
942:
936:
934:
930:
923:
919:
916:
914:
911:
909:
906:
904:
901:
900:
896:
894:
892:
888:
887:perfect fifth
884:
883:neutral third
879:
873:
866:
858:
856:
851:
848:
844:
837:
829:
825:
819:
807:
798:
794:
790:
784:
776:
772:
771:
770:
765:
757:
756:major seventh
750:
742:
741:minor seventh
738:
727:
717:
708:
706:
702:
698:
696:
692:
688:
686:
682:
679:
675:
671:
669:
668:Just interval
665:
648:
646:
642:
625:
623:
619:
614:
610:
606:
602:
598:
593:
590:
587:
585:
581:
572:
567:
565:
563:
559:
555:
551:
547:
543:
539:
531:
529:
527:
523:
519:
515:
507:
500:
492:
490:
485:
482:
478:
474:
467:
459:
455:
452:
445:
437:
433:
432:
431:
429:
425:
421:
420:medium second
417:
406:
396:
387:
385:
381:
377:
375:
371:
367:
365:
361:
358:
354:
350:
348:
347:Just interval
344:
327:
325:
321:
304:
302:
298:
293:
289:
285:
280:
277:
274:
272:
268:
256:
244:
240:
234:
226:
223:
222:
213:
209:
203:
195:
192:
191:
182:
178:
172:
164:
161:
160:
151:
147:
141:
133:
130:
129:
125:
122:
119:
117:
116:
111:
108:
106:
105:Neutral sixth
103:
101:
100:Neutral third
98:
96:
93:
92:
91:
89:
85:
81:
77:
72:
70:
66:
62:
58:
54:
50:
46:
42:
38:
31:Neutral third
29:
19:
1903:
1870:
1856:(0.72 cents)
1850:(1.95 cents)
1830:(13.8 cents)
1824:(10.1 cents)
1818:(19.5 cents)
1810:(35.7 cents)
1804:(62.6 cents)
1798:(41.1 cents)
1790:(27.3 cents)
1784:(22.6 cents)
1778:(21.5 cents)
1772:(23.5 cents)
1759:
1740:Quarter tone
1730:
1729:
1700:
1699:
1656:
1621:Higher-limit
1536:
1530:
1501:
1442:major fourth
1401:
1386:quarter tone
1374:
1361:
1355:
1044:
973:
956:
940:
880:
877:
853:
827:
792:
774:
736:
734:
689:1000 or 1100
608:Abbreviation
571:
535:
514:Arabic music
511:
487:
457:
435:
428:major second
424:minor second
419:
415:
413:
287:Abbreviation
76:quarter tone
73:
40:
37:music theory
34:
1889:Millioctave
1871:Measurement
1862:(0.4 cents)
1842:(7.7 cents)
1836:(8.1 cents)
1720:Major limma
1462:minor fifth
943:, p.xxiii.
843:frequencies
797:frequencies
600:Other names
65:minor third
57:major third
1965:Categories
1922:Semiditone
1816:Diaschisma
1631:(17-limit)
1322:(22 or 23)
1320:fourteenth
1316:(20 or 21)
1314:thirteenth
1310:(18 or 19)
1304:(17 or 18)
1298:(15 or 16)
1292:(13 or 14)
1227:Diminished
1054:interval.)
1035:(post-Bach
924:References
516:(see also
388:165 or 151
368:100 or 200
1884:Centitone
1822:Semicomma
1701:Semitones
1665:Microtone
1649:intervals
1326:fifteenth
1172:Augmented
1050:semitones
1022:Intervals
976:, p.131.
791:The just
622:Semitones
451:frequency
301:Semitones
224:sevenths
1854:Breedsma
1302:eleventh
1282:Compound
1037:Western)
1032:semitone
897:See also
847:harmonic
477:eleventh
248:♮
230:♭
217:♮
199:♭
186:♮
168:♭
155:♮
137:♭
131:seconds
123:neutral
45:interval
1860:Ragisma
1848:Schisma
1834:Kleisma
1670:5-limit
1576:(15:14)
1570:(21:20)
1564:(28:27)
1558:(36:35)
1548:7-limit
1513:⁄
1502:seventh
1493:⁄
1473:⁄
1453:⁄
1433:⁄
1413:⁄
1393:⁄
1375:Neutral
1348:systems
1308:twelfth
1265:seventh
1216:seventh
1161:seventh
1124:seventh
1062:Perfect
1030:Twelve-
658:⁄
635:⁄
584:Inverse
568:Seventh
524:in the
337:⁄
314:⁄
271:Inverse
257:Second
193:sixths
162:thirds
69:inverts
59:is 400
1917:Ditone
1904:Others
1894:Savart
1761:Commas
1657:Groups
1606:(10:7)
1402:second
1346:tuning
1271:octave
1247:fourth
1235:second
1198:fourth
1186:second
1180:unison
1143:second
1106:second
1087:octave
1075:fourth
1069:unison
1052:in the
980:
947:
126:major
120:minor
43:is an
1927:Secor
1675:Comma
1647:Other
1612:(7:4)
1600:(7:5)
1594:(9:7)
1588:(7:6)
1582:(8:7)
1482:sixth
1422:third
1344:Other
1296:tenth
1290:ninth
1259:sixth
1253:fifth
1241:third
1210:sixth
1204:fifth
1192:third
1155:sixth
1149:third
1135:Minor
1118:sixth
1112:third
1098:Major
1081:fifth
872:cents
678:Cents
562:17-ET
558:comma
554:72-ET
550:41-ET
546:31-ET
542:24-ET
538:22-ET
506:cents
357:Cents
88:72-ET
86:, or
84:41-ET
80:31-ET
61:cents
1912:Wolf
1879:Cent
1328:(24)
1273:(11)
1218:(12)
1212:(10)
1163:(10)
1126:(11)
1089:(12)
978:ISBN
945:ISBN
891:root
864:play
835:play
817:play
805:play
782:play
763:play
748:play
725:Play
699:1050
616:Size
595:Name
548:and
498:play
465:play
456:the
443:play
404:Play
295:Size
282:Name
63:, a
55:, a
39:, a
1267:(9)
1261:(7)
1255:(6)
1249:(4)
1243:(2)
1237:(0)
1206:(8)
1200:(6)
1194:(5)
1188:(3)
1182:(1)
1157:(8)
1151:(3)
1145:(1)
1120:(9)
1114:(4)
1108:(2)
1083:(7)
1077:(5)
1071:(0)
852:An
552:.
486:An
418:or
378:150
235:≊ B
204:≊ A
173:≊ E
142:≊ D
35:In
1967::
1506:10
965:^
932:^
826:A
773:A
735:A
628:10
611:n7
544:,
528:.
414:A
290:n2
82:,
1518:)
1515:2
1511:1
1508:+
1504:(
1498:)
1495:2
1491:1
1488:+
1486:8
1484:(
1478:)
1475:2
1471:1
1468:+
1466:6
1464:(
1458:)
1455:2
1451:1
1448:+
1446:5
1444:(
1438:)
1435:2
1431:1
1428:+
1426:3
1424:(
1418:)
1415:2
1411:1
1408:+
1406:1
1404:(
1398:)
1395:2
1391:1
1388:(
1014:e
1007:t
1000:v
984:.
849:.
823:.
731:.
660:2
656:1
653:+
651:1
649:~
637:2
633:1
630:+
626:~
603:-
410:.
339:2
335:1
332:+
330:1
328:~
316:2
312:1
309:+
307:1
305:~
245:B
227:B
214:A
196:A
183:E
165:E
152:D
134:D
20:)
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