152:
1673:
133:
159:
310:
285:
140:
376:
Any note will only appear in major scales from any of its minor sixth major scale notes (for example, C is the minor sixth note from E and E will only appear in C, D, E, F, G, A and B major scales).
203:, the major sixth nine. For example, the interval from A to F is a minor sixth, as the note F lies eight semitones above A, and there are six staff positions from A to F.
625:. "The proportion 11:7, obtained by isolating one 35° angle from its complement within the 90° quadrant, similarly corresponds to an undecimal minor sixth (782.5 cents)."
1394:
355:. In the common practice period, sixths were considered interesting and dynamic consonances along with their inverses the thirds, but in
737:
706:
685:
664:
643:
622:
601:
580:
211:
sixths span the same number of staff positions, but consist of a different number of semitones (seven and ten respectively).
1186:
1166:
1292:
1298:
513:
1081:
224:
1695:
1700:
1676:
1414:
1353:
730:
359:
they were considered dissonances unusable in a stable final sonority. In that period they were tuned to the
172:
1474:
1469:
1280:
1656:
1409:
1316:
1310:
896:
393:
36:
1439:
1304:
1286:
1552:
989:
723:
571:
363:
265:
151:
1494:
1434:
995:
971:
959:
940:
754:
702:
681:
660:
639:
618:
597:
576:
496:
460:
232:
220:
111:
1564:
1389:
1334:
1328:
1322:
1226:
1126:
1099:
1006:
983:
965:
910:
904:
746:
398:
204:
188:
180:
1532:
1256:
1044:
934:
928:
916:
859:
822:
523:
499:
which includes ratios such as 14:9 and 63:40. of 764.9 cents or 786.4 cents respectively.
480:
443:
370:
332:
303:
257:
235:
major and dominant seventh chords and second inversion minor chords. It is equal to eight
228:
208:
121:
94:
613:
International
Institute for Advanced Studies in Systems Research and Cybernetics (2003).
191:
for more details), and is one of two commonly occurring sixths (the other one being the
1512:
1506:
1500:
1272:
799:
508:
433:
356:
352:
278:
184:
84:
1689:
1636:
1485:
1404:
1399:
1345:
1206:
1146:
1032:
1020:
885:
848:
805:
367:
344:
17:
1651:
1608:
1603:
1464:
1110:
867:
830:
527:
470:
453:
240:
104:
272:
than the 12-ET-minor sixth. This is denoted with a "-" (minus) sign (see figure).
1613:
1444:
873:
842:
836:
518:
348:
192:
41:
132:
1646:
1540:
1038:
951:
617:: Music, Environmental Design, and the Choreography of Space, Volume 5, p.18.
1546:
1050:
558:
On the
Sensations of Tone as a Physiological Basis for the Theory of Music
1578:
1026:
774:
423:
236:
200:
74:
268:, the minor sixth is the ratio 128:81, or 792.18 cents, i.e. 7.82 cents
1584:
1572:
1558:
977:
922:
1641:
1618:
1526:
1520:
811:
793:
340:
336:
1014:
199:
because it is the smaller of the two: the minor sixth spans eight
150:
131:
239:, i.e. a ratio of 2:1 or simplified to 2:1 (about 1.587), or 800
281:, a minor sixth most often corresponds to a pitch ratio of 8:5 (
719:
715:
56:
minor hexachord, hexachordon minus, lesser hexachord
556:
Hermann von
Helmholtz and Alexander John Ellis (1912).
373:, the minor sixth of 8:5 is classed as a consonance.
678:
Sound and Light: La Monte Young & Marian
Zazeela
1627:
1594:
1483:
1453:
1423:
1380:
1371:
1344:
1271:
1254:
1096:
1079:
1068:
1005:
950:
895:
858:
821:
786:
768:
753:
479:
469:
459:
452:
442:
432:
422:
417:
409:
404:
392:
120:
110:
103:
93:
83:
73:
68:
60:
52:
47:
35:
260:multiple definitions of a minor sixth can exist:
731:
8:
387:
30:
1672:
1377:
1268:
1093:
1076:
783:
765:
738:
724:
716:
331:The minor sixth is one of consonances of
657:The Mathematical Theory of Tone Systems
636:The Mathematical Theory of Tone Systems
540:
386:
29:
7:
167:, four Pythagorean perfect fifths.
25:
1671:
676:Duckworth & Fleming (1996).
293:) or 814 cents; i.e. 13.7 cents
594:Music: A Mathematical Offering
1:
155:Pythagorean minor sixth on C
615:Systems Research in the Arts
223:(12-ET), the minor sixth is
1293:septimal chromatic semitone
297:than the 12-ET-minor sixth.
1717:
1299:septimal diatonic semitone
1087:(Numbers in brackets refer
514:List of meantone intervals
366:minor sixth of 128:81. In
347:, major and minor thirds,
1669:
1089:to fractional semitones.)
1082:24-tone equal temperament
592:Benson, David J. (2006).
471:24-Tone equal temperament
461:12-Tone equal temperament
225:enharmonically equivalent
112:12-Tone equal temperament
697:Hewitt, Michael (2000).
264:In 3-limit tuning, i.e.
1677:List of pitch intervals
1415:Subminor and supermajor
1354:minor diatonic semitone
1264:refer to pitch ratios.)
646:. Septimal minor sixth.
173:Western classical music
1475:Undecimal quarter tone
569:Partch, Harry (1979).
335:music, along with the
195:). It is qualified as
168:
148:
1470:Septimal quarter tone
1281:septimal quarter tone
634:Haluska, Jan (2003).
547:Benson (2006), p.163.
320:undecimal minor sixth
231:. It occurs in first
154:
135:
18:Undecimal minor sixth
1657:Incomposite interval
1410:Pythagorean interval
1262:(Numbers in brackets
770:(Numbers in brackets
655:Jan Haluska (2003).
351:and (sometimes) the
1440:Pythagorean apotome
1287:septimal third tone
389:
32:
1553:Septimal semicomma
572:Genesis of a Music
266:Pythagorean tuning
169:
149:
1683:
1682:
1665:
1664:
1495:Pythagorean comma
1435:Pythagorean limma
1367:
1366:
1363:
1362:
1329:supermajor fourth
1305:supermajor second
1250:
1249:
1064:
1063:
1060:
1059:
772:are the number of
699:The Tonal Phoenix
497:subminor interval
491:In addition, the
489:
488:
221:equal temperament
215:Equal temperament
183:encompassing six
130:
129:
99:8:5, 128:81, 11:7
16:(Redirected from
1708:
1675:
1674:
1565:Septimal kleisma
1378:
1335:subminor seventh
1317:supermajor third
1269:
1257:Just intonations
1242:
1241:
1237:
1234:
1222:
1221:
1217:
1214:
1202:
1201:
1197:
1194:
1182:
1181:
1177:
1174:
1162:
1161:
1157:
1154:
1142:
1141:
1137:
1134:
1122:
1121:
1117:
1094:
1077:
784:
766:
740:
733:
726:
717:
710:
695:
689:
674:
668:
653:
647:
632:
626:
611:
605:
590:
584:
567:
561:
554:
548:
545:
399:supermajor third
390:
384:Musical interval
322:is 782.49 cents.
317:
316:
315:
313:
292:
291:
290:
288:
247:Just temperament
181:musical interval
166:
165:
164:
162:
147:
146:
145:
143:
33:
27:Musical interval
21:
1716:
1715:
1711:
1710:
1709:
1707:
1706:
1705:
1696:Minor intervals
1686:
1685:
1684:
1679:
1661:
1623:
1590:
1533:Septimal diesis
1479:
1449:
1419:
1373:
1359:
1340:
1263:
1260:
1246:
1239:
1235:
1232:
1230:
1219:
1215:
1212:
1210:
1199:
1195:
1192:
1190:
1179:
1175:
1172:
1170:
1159:
1155:
1152:
1150:
1139:
1135:
1132:
1130:
1119:
1115:
1114:
1104:
1103:
1102:
1098:
1088:
1085:
1072:
1070:
1056:
1001:
946:
891:
854:
817:
778:
773:
771:
761:
759:
756:
749:
744:
714:
713:
696:
692:
675:
671:
654:
650:
633:
629:
612:
608:
591:
587:
568:
564:
555:
551:
546:
542:
537:
530:= 833.09 cents)
524:833 cents scale
505:
481:Just intonation
385:
382:
371:just intonation
333:common practice
329:
311:
309:
308:
307:
304:11-limit tuning
286:
284:
283:
282:
258:just intonation
254:
249:
229:augmented fifth
217:
189:Interval number
185:staff positions
160:
158:
157:
156:
141:
139:
138:
137:
122:Just intonation
28:
23:
22:
15:
12:
11:
5:
1714:
1712:
1704:
1703:
1701:Sixths (music)
1698:
1688:
1687:
1681:
1680:
1670:
1667:
1666:
1663:
1662:
1660:
1659:
1654:
1649:
1644:
1639:
1633:
1631:
1625:
1624:
1622:
1621:
1616:
1611:
1606:
1600:
1598:
1592:
1591:
1589:
1588:
1582:
1576:
1569:
1568:
1562:
1556:
1550:
1544:
1537:
1536:
1530:
1527:Greater diesis
1524:
1517:
1516:
1513:Septimal comma
1510:
1507:Holdrian comma
1504:
1501:Syntonic comma
1498:
1491:
1489:
1481:
1480:
1478:
1477:
1472:
1467:
1461:
1459:
1451:
1450:
1448:
1447:
1442:
1437:
1431:
1429:
1421:
1420:
1418:
1417:
1412:
1407:
1402:
1397:
1392:
1386:
1384:
1375:
1369:
1368:
1365:
1364:
1361:
1360:
1358:
1357:
1350:
1348:
1342:
1341:
1339:
1338:
1332:
1326:
1323:subminor fifth
1320:
1314:
1311:subminor third
1308:
1302:
1296:
1290:
1284:
1277:
1275:
1266:
1252:
1251:
1248:
1247:
1245:
1244:
1224:
1204:
1184:
1164:
1144:
1124:
1107:
1105:
1097:
1091:
1074:
1066:
1065:
1062:
1061:
1058:
1057:
1055:
1054:
1048:
1042:
1036:
1030:
1024:
1018:
1011:
1009:
1003:
1002:
1000:
999:
993:
987:
981:
975:
969:
963:
956:
954:
948:
947:
945:
944:
938:
932:
926:
920:
914:
908:
901:
899:
893:
892:
890:
889:
883:
877:
871:
864:
862:
856:
855:
853:
852:
846:
840:
834:
827:
825:
819:
818:
816:
815:
809:
803:
797:
790:
788:
781:
763:
751:
750:
745:
743:
742:
735:
728:
720:
712:
711:
690:
669:
648:
627:
606:
585:
562:
549:
539:
538:
536:
533:
532:
531:
521:
516:
511:
509:Musical tuning
504:
501:
493:subminor sixth
487:
486:
483:
477:
476:
473:
467:
466:
463:
457:
456:
450:
449:
446:
440:
439:
436:
434:Interval class
430:
429:
426:
420:
419:
415:
414:
411:
407:
406:
402:
401:
396:
388:subminor sixth
383:
381:
380:Subminor sixth
378:
357:medieval times
353:perfect fourth
328:
325:
324:
323:
299:
298:
279:5-limit tuning
274:
273:
253:
250:
248:
245:
216:
213:
128:
127:
124:
118:
117:
114:
108:
107:
101:
100:
97:
91:
90:
87:
85:Interval class
81:
80:
77:
71:
70:
66:
65:
62:
58:
57:
54:
50:
49:
45:
44:
39:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1713:
1702:
1699:
1697:
1694:
1693:
1691:
1678:
1668:
1658:
1655:
1653:
1650:
1648:
1645:
1643:
1640:
1638:
1635:
1634:
1632:
1630:
1626:
1620:
1617:
1615:
1612:
1610:
1607:
1605:
1602:
1601:
1599:
1597:
1593:
1586:
1583:
1580:
1577:
1574:
1571:
1570:
1566:
1563:
1560:
1557:
1554:
1551:
1548:
1545:
1542:
1539:
1538:
1534:
1531:
1528:
1525:
1522:
1521:Lesser diesis
1519:
1518:
1514:
1511:
1508:
1505:
1502:
1499:
1496:
1493:
1492:
1490:
1488:
1487:
1482:
1476:
1473:
1471:
1468:
1466:
1463:
1462:
1460:
1458:
1457:
1456:Quarter tones
1452:
1446:
1443:
1441:
1438:
1436:
1433:
1432:
1430:
1428:
1427:
1422:
1416:
1413:
1411:
1408:
1406:
1405:Pseudo-octave
1403:
1401:
1398:
1396:
1393:
1391:
1388:
1387:
1385:
1383:
1379:
1376:
1370:
1355:
1352:
1351:
1349:
1347:
1343:
1336:
1333:
1330:
1327:
1324:
1321:
1318:
1315:
1312:
1309:
1306:
1303:
1300:
1297:
1294:
1291:
1288:
1285:
1282:
1279:
1278:
1276:
1274:
1270:
1267:
1265:
1259:
1258:
1253:
1228:
1225:
1208:
1205:
1188:
1185:
1168:
1165:
1148:
1145:
1128:
1125:
1112:
1109:
1108:
1106:
1101:
1095:
1092:
1090:
1084:
1083:
1078:
1075:
1067:
1052:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
1013:
1012:
1010:
1008:
1004:
997:
994:
991:
988:
985:
982:
979:
976:
973:
970:
967:
964:
961:
958:
957:
955:
953:
949:
942:
939:
936:
933:
930:
927:
924:
921:
918:
915:
912:
909:
906:
903:
902:
900:
898:
894:
887:
884:
881:
878:
875:
872:
869:
866:
865:
863:
861:
857:
850:
847:
844:
841:
838:
835:
832:
829:
828:
826:
824:
820:
813:
810:
807:
804:
801:
798:
795:
792:
791:
789:
785:
782:
780:
776:
767:
764:
758:
752:
748:
741:
736:
734:
729:
727:
722:
721:
718:
708:
707:3-922626-96-3
704:
700:
694:
691:
687:
686:0-8387-5346-9
683:
679:
673:
670:
666:
665:0-8247-4714-3
662:
658:
652:
649:
645:
644:0-8247-4714-3
641:
637:
631:
628:
624:
623:1-894613-32-5
620:
616:
610:
607:
603:
602:0-521-85387-7
599:
595:
589:
586:
582:
581:0-306-80106-X
578:
574:
573:
566:
563:
559:
553:
550:
544:
541:
534:
529:
525:
522:
520:
517:
515:
512:
510:
507:
506:
502:
500:
498:
494:
484:
482:
478:
474:
472:
468:
464:
462:
458:
455:
451:
448:14:9 or 63:40
447:
445:
444:Just interval
441:
437:
435:
431:
427:
425:
421:
416:
412:
408:
403:
400:
397:
395:
391:
379:
377:
374:
372:
369:
365:
362:
358:
354:
350:
346:
345:perfect fifth
342:
338:
334:
326:
321:
314:
305:
301:
300:
296:
289:
280:
276:
275:
271:
267:
263:
262:
261:
259:
251:
246:
244:
242:
238:
234:
230:
226:
222:
214:
212:
210:
206:
202:
198:
194:
190:
186:
182:
178:
174:
163:
153:
144:
134:
126:814, 792, 782
125:
123:
119:
115:
113:
109:
106:
102:
98:
96:
95:Just interval
92:
88:
86:
82:
78:
76:
72:
67:
63:
59:
55:
51:
46:
43:
40:
38:
34:
19:
1628:
1595:
1581:(0.72 cents)
1575:(1.95 cents)
1555:(13.8 cents)
1549:(10.1 cents)
1543:(19.5 cents)
1535:(35.7 cents)
1529:(62.6 cents)
1523:(41.1 cents)
1515:(27.3 cents)
1509:(22.6 cents)
1503:(21.5 cents)
1497:(23.5 cents)
1484:
1465:Quarter tone
1455:
1454:
1425:
1424:
1381:
1346:Higher-limit
1261:
1255:
1167:major fourth
1111:quarter tone
1086:
1080:
879:
769:
698:
693:
677:
672:
656:
651:
635:
630:
614:
609:
593:
588:
570:
565:
557:
552:
543:
528:golden ratio
492:
490:
410:Abbreviation
375:
360:
330:
319:
306:, the 11:7 (
294:
269:
255:
218:
196:
176:
170:
136:Minor sixth
61:Abbreviation
1614:Millioctave
1596:Measurement
1587:(0.4 cents)
1567:(7.7 cents)
1561:(8.1 cents)
1445:Major limma
1187:minor fifth
659:, p.xxiii.
638:, p.xxiii.
519:Sixth chord
364:Pythagorean
349:major sixth
219:In 12-tone
193:major sixth
177:minor sixth
53:Other names
42:major third
31:minor sixth
1690:Categories
1647:Semiditone
1541:Diaschisma
1356:(17-limit)
1047:(22 or 23)
1045:fourteenth
1041:(20 or 21)
1039:thirteenth
1035:(18 or 19)
1029:(17 or 18)
1023:(15 or 16)
1017:(13 or 14)
952:Diminished
779:interval.)
760:(post-Bach
535:References
485:765 or 786
327:Consonance
252:Definition
205:Diminished
1609:Centitone
1547:Semicomma
1426:Semitones
1390:Microtone
1374:intervals
1051:fifteenth
897:Augmented
775:semitones
747:Intervals
701:, p.137.
680:, p.167.
596:, p.370.
424:Semitones
237:semitones
233:inversion
209:augmented
201:semitones
75:Semitones
1579:Breedsma
1027:eleventh
1007:Compound
762:Western)
757:semitone
575:, p.68.
560:, p.456.
503:See also
1585:Ragisma
1573:Schisma
1559:Kleisma
1395:5-limit
1301:(15:14)
1295:(21:20)
1289:(28:27)
1283:(36:35)
1273:7-limit
1238:⁄
1227:seventh
1218:⁄
1198:⁄
1178:⁄
1158:⁄
1138:⁄
1118:⁄
1100:Neutral
1073:systems
1033:twelfth
990:seventh
941:seventh
886:seventh
849:seventh
787:Perfect
755:Twelve-
495:, is a
394:Inverse
368:5-limit
361:flatter
295:sharper
270:flatter
227:to the
37:Inverse
1642:Ditone
1629:Others
1619:Savart
1486:Commas
1382:Groups
1331:(10:7)
1127:second
1071:tuning
996:octave
972:fourth
960:second
923:fourth
911:second
905:unison
868:second
831:second
812:octave
800:fourth
794:unison
777:in the
705:
684:
663:
642:
621:
600:
579:
341:octave
337:unison
1652:Secor
1400:Comma
1372:Other
1337:(7:4)
1325:(7:5)
1319:(9:7)
1313:(7:6)
1307:(8:7)
1207:sixth
1147:third
1069:Other
1021:tenth
1015:ninth
984:sixth
978:fifth
966:third
935:sixth
929:fifth
917:third
880:sixth
874:third
860:Minor
843:sixth
837:third
823:Major
806:fifth
454:Cents
241:cents
197:minor
187:(see
179:is a
105:Cents
1637:Wolf
1604:Cent
1053:(24)
998:(11)
943:(12)
937:(10)
888:(10)
851:(11)
814:(12)
703:ISBN
682:ISBN
661:ISBN
640:ISBN
619:ISBN
598:ISBN
577:ISBN
418:Size
405:Name
312:Play
287:play
207:and
175:, a
161:Play
142:Play
69:Size
48:Name
992:(9)
986:(7)
980:(6)
974:(4)
968:(2)
962:(0)
931:(8)
925:(6)
919:(5)
913:(3)
907:(1)
882:(8)
876:(3)
870:(1)
845:(9)
839:(4)
833:(2)
808:(7)
802:(5)
796:(0)
475:750
465:800
302:In
277:In
256:In
171:In
116:800
1692::
1231:10
413:m6
343:,
339:,
318:)
243:.
64:m6
1243:)
1240:2
1236:1
1233:+
1229:(
1223:)
1220:2
1216:1
1213:+
1211:8
1209:(
1203:)
1200:2
1196:1
1193:+
1191:6
1189:(
1183:)
1180:2
1176:1
1173:+
1171:5
1169:(
1163:)
1160:2
1156:1
1153:+
1151:3
1149:(
1143:)
1140:2
1136:1
1133:+
1131:1
1129:(
1123:)
1120:2
1116:1
1113:(
739:e
732:t
725:v
709:.
688:.
667:.
604:.
583:.
526:(
438:4
428:8
89:4
79:8
20:)
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