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40:
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1345:, but this symphonic finale trumps even that piece in its scale and ambition. If the story of that operatic tune first movement is to turn instinctive emotion into contrapuntal experience, the finale does exactly the reverse, transmuting the most complex arts of compositional craft into pure, exhilarating feeling. Its models in
930:. For example, a C-major chord in first inversion (i.e., with E in the bass) would be notated as "C/E". This notation works even when a note not present in a triad is the bass; for example, F/G is a way of notating a particular approach to voicing an Fadd chord (G–F–A–C). This is quite different from analytical notations of
1311:
140:
so that the higher note becomes the lower note and vice versa. For example, the inversion of an interval consisting of a C with an E above it (the third measure below) is an E with a C above it – to work this out, the C may be moved up, the E may be lowered, or both may be moved.
1853:
Sets are said to be inversionally symmetrical if they map onto themselves under inversion. The pitch that the sets must be inverted around is said to be the axis of symmetry (or center). An axis may either be at a specific pitch or halfway between two pitches (assuming that
1312:
1127:
A in the high voice moves down a sixth, and motif B in the low voice moves up a fifth, in such a way as to result in A and B having exchanged registers, then the two are in double counterpoint at the tenth (6 + 5 – 1 = 10).
281:
under inversion. Thus, perfect intervals remain perfect, major intervals become minor and vice versa, and augmented intervals become diminished and vice versa. (Doubly diminished intervals become doubly augmented intervals, and vice versa.).
285:
Traditional interval numbers add up to nine: seconds become sevenths and vice versa, thirds become sixths and vice versa, and so on. Thus, a perfect fourth becomes a perfect fifth, an augmented fourth becomes a diminished fifth, and a
892:
pairs of upper voices themselves – for example, in a C–E–G triad, the figured bass does not signify the interval relationship between E–G, and they do not express notes in upper voices that double, or are unison with, the bass note.
1271:
1231:
1196:
1978:
transposition. Thus, if D-A-G (P5 up, M2 down) is inverted to D-G-A (P5 down, M2 up) the "pitch axis" is D. However, if it is inverted to C-F-G the pitch axis is G while if the pitch axis is A, the melody inverts to E-A-B.
1265:
involves exploring the combination of three themes. Two of these are announced in the opening two bars. A third idea joins them in bars 3–4. When this passage is repeated a few bars later in bars 7–9, the three parts are
1076:, having previously accompanied each other once, accompany each other again but with the melody that had been in the high voice now in the low, and vice versa. The action of changing the voices is called
1272:
1232:
1197:
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equivalent and he has been credited as being the first person to recognise their underlying similarity. Earlier theorists spoke of different intervals using alternative descriptions, such as the
416:
in root position, since the lowest note is the root. The rearrangement of the notes above the bass into different octaves (here, the note E) and the doubling of notes (here, G), is known as
1145:
is at the octave, the second canon at the tenth, the third canon at the twelfth, and the fourth canon in augmentation and contrary motion. Other exemplars can be found in the fugues in
1850:
theory, though it is assumed that sets that can be inverted into each other are remotely in common. However, they are only assumed identical or nearly identical in musical set theory.
74:, Book 1. Though they start on different pitches (A and E), the second highlighted melody is the upside-down version of the first highlighted melody. That is, when the first goes
1982:
The notation of octave position may determine how many lines and spaces appear to share the axis. The pitch axis of D-A-G and its inversion A-D-E either appear to be between C/B
1310:
952:
Lower-case letters may be placed after a chord symbol to indicate root position or inversion. Hence, in the key of C major, a C-major chord in first inversion may be notated as
896:
However, the figures are often used on their own (without the bass) in music theory simply to specify a chord's inversion. This is the basis for the terms given above such as "
1803:
1313:
1758:
1569:
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of the triad – with the root and the third above it (both again shifted an octave higher), forming a fourth and a sixth above the (inverted) bass of G, respectively.
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1699:
1616:
1719:
1664:
1636:
1589:
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Figured-bass numerals express distinct intervals in a chord only as they relate to the bass note. They make no reference to the key of the progression (unlike
2705:
1321:
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often categorically refers to the different possibilities, though it may also be restricted to only those chords where the lowest note is not also the
2736:
1270:
1230:
1195:
118:
lines of music. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in
401:
of its inversions. For example, the root of a C-major triad is C, so a C-major triad will be in root position if C is the lowest note and its
2118:
1526:
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the lowest note. The inversions are numbered in the order their lowest notes appear in a close root-position chord (from bottom to top).
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1924:
This article is about the central pitch of an inverted melody. For the most important pitch of certain types of chord progressions, see
1273:
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2157:
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Certain conventional abbreviations exist in the use of figured bass. For instance, root-position triads appear without symbols (the
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are unquestionable, but Mozart simultaneously pays homage to them – and transcends them. Now that's what I call real originality.
486:
of the triad – with the fifth and the root stacked above it (the root now shifted an octave higher), forming the intervals of a
1449:, "The intervals between successive pitches may remain exact or, more often in tonal music, they may be the equivalents in the
1445:
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1060:
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on music history as well as his own. As a musical achievement, its most obvious predecessor is really the fugal finale of his
310:
2557:
2405:
2305:
2272:
1342:
1123:. To calculate the interval of inversion, add the intervals by which each voice has moved and subtract one. For example: If
2729:
1951:
1157:
1149:
842:). For example, in root-position triad C–E–G, the intervals above bass note C are a third and a fifth, giving the figures
1385:
1370:
1042:
524:
461:
437:
43:
2801:
2629:
2498:
2341:
1453:. Hence c'–d–e' may become c'–b–a (where the first descent is by a semitone rather than by a whole tone) instead of c'–b
1843:
1469:
start on the same pitch as the original melody, but it does not have to, as illustrated by the example to the right.
344:'s inversion describes the relationship of its lowest notes to the other notes in the chord. For instance, a C major
1247:
1212:
31:
513:) work in a similar way, except that they have three inversions, instead of just two. The three inversions of a G
2843:
2654:
1408:
1168:
924:
is to write the name of a chord followed by a forward slash and then the name of the bass note. This is called a
290:(that is, one that is narrower than an octave) and its inversion, when added together, equal an octave. See also
70:
2853:
2722:
1329:
The whole passage brings the symphony to a conclusion in a blaze of brilliant orchestral writing. According to
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1975:
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contains the tones C, E and G; its inversion is determined by which of these tones is the lowest note (or
2527:
2471:
2428:
1967:
1674:, from 12 (by convention, inversion is around pitch class 0). Then we apply the transposition operation
1643:
1478:
995:
313:
2577:
2542:
2007:
1498:
977:
2771:
2659:
2519:
1486:
982:
1760:, first subtract 3 from 12 (giving 9) and then add 5 (giving 14, which is equivalent to 2). Thus,
114:
is a rearrangement of the top-to-bottom elements in an interval, a chord, a melody, or a group of
2679:
2532:
2451:
2263:(fourth ed.). Cambridge, Massachusetts: Belknap Press of Harvard University Press. pp.
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2206:
1966:
The "pitch axis" works in the context of the compound operation transpositional inversion, where
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838:. Each numeral expresses the interval that results from the voices above it (usually assuming
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is understood), and first-inversion triads are customarily abbreviated as just , rather than
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2793:
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when three are involved. The inversion in two-part invertible counterpoint is also known as
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is carried out after inversion. However, unlike in set theory, the transposition may be a
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would apply, due to the intervals of a third and a sixth appearing above the bass note E.
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154:
1412:, Book 1. The lowest voice in mm. 28–30 is an inversion of the opening melody in mm. 1–3.
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Book 2, both of which contain invertible counterpoint at the octave, tenth, and twelfth.
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One of the most spectacular examples of invertible counterpoint occurs in the finale of
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1191:, Book 1, the following passage, from bars 9–18, involves two lines, one in each hand:
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As shown above, a C-major triad (or any chord with three notes) has two inversions:
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1901:
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1029:
960:. (Less commonly, the root of the chord is named, followed by a lower-case letter:
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360:
328:
115:
107:
86:
2026:
The root-position triad at the end has no fifth above the root. This is common at
964:). If no letter is added, the chord is assumed to be in root inversion, as though
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has an axis at F, and an axis, a tritone away, at B if the set is listed as F
409:(E and G, respectively) are above it – or, on occasion, do not sound at all.
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1831:
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90:
1805:. To invert a set of pitches, simply invert each pitch in the set in turn.
2510:
2193:. Vol. 1 (7th ed.). London: Oxford University Press. p. 95.
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2493:
2488:
1847:
1639:
1482:
1430:
897:
83:
1429:, then the inverted melody has a falling major third (or, especially in
1277:
Bach's three-part
Invention (Sinfonia) in F minor BWV 795, bars 1–9
2027:
1115:. Invertible counterpoint can occur at various intervals, usually the
136:
is inverted by raising or lowering either of the notes by one or more
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1418:
1116:
1073:
137:
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1320:
1308:
1280:
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1226:
When this passage returns in bars 25–35 these lines are exchanged:
1211:
1193:
851:. If this triad were in first inversion (e.g., E–G–C), the figure
363:
of the chord. Texts that follow this restriction may use the term
61:
1642:. Thus, inversion is a combination of an inversion followed by a
1421:
is inverted by flipping it "upside-down", reversing the melody's
1963:, a pitch axis is the center around which a melody is inverted.
1337:
Mozart's composition of the finale of the
Jupiter Symphony is a
2718:
2401:
2300:. Englewood Cliffs, New Jersey: Prentice Hall. pp. 34–35.
2220:
The inversion of the parts in two-part
Invertible counterpoint.
1002:
ones and would not propose, for example, a resemblance between
994:("rule of sixths and thirds"). This required the resolution of
2087:
Adapted from
Measures 14–16, Parry H (1897) "Rustington". In:
331:(1897), showing all three positions of the C major chord. See
1285:
Bach's three-part
Invention (Sinfonia) BWV 795, bars 1–9
367:
instead, to refer to all of the possibilities as a category.
2107:
Harmony and Theory: A Comprehensive Source for All
Musicians
2065:"Inversion | Jazz, Improvisation & Harmony | Britannica"
1293:
of how these three lines can be combined in counterpoint.
1387:
Audio playback is not supported in your browser. You can
1372:
Audio playback is not supported in your browser. You can
1044:
Audio playback is not supported in your browser. You can
822:
is a notation in which chord inversions are indicated by
526:
Audio playback is not supported in your browser. You can
463:
Audio playback is not supported in your browser. You can
439:
Audio playback is not supported in your browser. You can
312:
Audio playback is not supported in your browser. You can
45:
Audio playback is not supported in your browser. You can
1107:
be developed in this way without violating the rules of
1055:
An example of contrapuntal inversion in one measure of
912:
the term I refers to a tonic triad in first inversion.
1289:
The piece goes on to explore four of the six possible
986:(1722), chords in different inversions are considered
1766:
1727:
1707:
1680:
1652:
1624:
1597:
1577:
1547:
1306:. Here, no less than five themes are heard together:
881:. The table to the right displays these conventions.
1425:. For instance, if the original melody has a rising
2622:
2556:
2518:
2439:
1541:, the inverse operation is sometimes designated as
397:is the lowest note. This is sometimes known as the
1797:
1752:
1713:
1693:
1658:
1630:
1610:
1583:
1563:
335:below for a description of the numerical symbols.
2174:Rameau and musical thought in the Enlightenment,
1325:Mozart Symphony No. 41 Finale, bars 389–396
1317:Mozart Symphony No. 41 Finale, bars 389–396
1335:
2393:Chord Inversions and Exercises for Jazz Guitar
908:" for a second inversion triad. Similarly, in
2730:
2413:
1834:are the same when inverted. It is similar to
1263:Three-Part Invention in F minor, BWV 795
920:A notation for chord inversion often used in
548:Common Conventional Symbols for Figured Bass
8:
2706:List of dodecaphonic and serial compositions
1846:. Inversional equivalency is used little in
273:The tables to the right show the changes in
936:; e.g., the notation "IV/V" represents the
494:above the inverted bass of E, respectively.
2737:
2723:
2715:
2701:
2420:
2406:
2398:
2095:'s "See, the Conqueror Mounts in Triumph".
546:
2348:, Yale University Press, pp. 10–11,
2234:. (2014) "Symphony Guide: Mozart's 41st (
2089:The Australian hymn book: harmony edition
1771:
1765:
1732:
1726:
1706:
1685:
1679:
1651:
1623:
1602:
1596:
1576:
1552:
1546:
1181:For example, in the keyboard prelude in A
689:
589:
215:
150:
2216:10.1093/gmo/9781561592630.article.23544
2047:
2019:
1910:and an axis at B/C if it is listed as F
1894:–E. As another example, the set C–E–F–F
1858:are not used). For example, the set C–E
323:The closing phrase of the hymn-setting
2328:
2152:, London: Bell & Hyman, p. ,
2105:Wyatt, Keith; Schroeder, Carl (1998).
2369:Jazz Composition: Theory and Practice
538:Notating root position and inversions
93:alteration); and when the first goes
7:
1809:Inversional equivalency and symmetry
1501:). These four permutations (labeled
1061:Invention No. 13 in A minor, BWV 784
1646:. To apply the inversion operation
1521:nversion) for the tone row used in
393:A chord is in root position if its
1618:means "transpose by some interval
450:In an inverted chord, the root is
25:
2298:Introduction to Post-Tonal Theory
1084:when two voices are involved and
888:), they do not express intervals
412:The following C-major triads are
371:Root position and inverted chords
332:
2700:
2509:
1527:Variations for Orchestra, Op. 31
509:Chords with four notes (such as
2260:The Harvard Dictionary of Music
2191:The Listener's History of Music
1485:is one of its four traditional
1446:The Harvard Dictionary of Music
886:Roman-numeral harmonic analysis
1786:
1780:
1747:
1741:
1:
2134:F/G chord chart - Chordsology
1952:Twinkle, Twinkle, Little Star
1343:G major String Quartet K. 387
1119:, less often at the tenth or
501:, the lowest note is G – the
482:, the lowest note is E – the
426:voicing, while the second is
57:
2630:All-interval twelve-tone row
1721:. For example, to calculate
1384:
1369:
1041:
830:) either above or below the
802:
779:
762:
739:
722:
699:
687:
664:
656:
653:
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645:
626:
616:
609:
599:
586:
576:
568:
565:
560:
557:
523:
460:
436:
309:
42:
2172:Christensen, Thomas. 1994.
1844:transpositional equivalency
1798:{\displaystyle T_{5}I(3)=2}
1465:." Moreover, the inversion
2870:
2296:Straus, Joseph N. (1990).
1950:Pitch axis inversions of "
1923:
1027:
992:regola delle terze e seste
374:
32:Inversion (disambiguation)
29:
2752:
2698:
2507:
1753:{\displaystyle T_{5}I(3)}
1433:music, perhaps a falling
1409:The Well-Tempered Clavier
1189:The Well-Tempered Clavier
1169:The Well-Tempered Clavier
640:
552:
218:
153:
101:the same number of steps.
71:The Well-Tempered Clavier
2346:The Music of Béla Bartók
2030:as a consequence of the
1900:–G–B has an axis at the
1638:" measured in number of
958:chord I, first inversion
327:by the English composer
2111:Hal Leonard Corporation
2054:Schuijer (2008), p. 66.
1988:or the single pitch F.
1820:inversional equivalency
1389:download the audio file
1374:download the audio file
1187:major from J.S. Bach's
1113:invertible counterpoint
1096:Invertible counterpoint
1046:download the audio file
528:download the audio file
465:download the audio file
441:download the audio file
422:– the first voicing is
314:download the audio file
47:download the audio file
2767:Close and open harmony
2635:All-trichord hexachord
2583:Second Viennese School
2204:"Rivolgimento (It.)".
2150:The Rudiments of Music
2093:Christopher Wordsworth
1836:enharmonic equivalency
1799:
1754:
1715:
1695:
1660:
1632:
1612:
1585:
1565:
1564:{\displaystyle T_{n}I}
1489:(the others being the
1355:
1326:
1318:
1286:
1278:
1258:
1244:
1223:
1209:
916:Popular-music notation
515:dominant seventh chord
2429:Twelve-tone technique
1800:
1755:
1716:
1696:
1694:{\displaystyle T_{n}}
1661:
1633:
1613:
1611:{\displaystyle T_{n}}
1586:
1566:
1481:, the inversion of a
1479:twelve-tone technique
1324:
1316:
1284:
1276:
1250:
1236:
1215:
1201:
996:imperfect consonances
2578:Josef Matthias Hauer
2543:Retrograde inversion
2176:pp. 51–61. Cambridge
2008:Retrograde inversion
1822:is the concept that
1764:
1725:
1705:
1678:
1650:
1622:
1595:
1575:
1545:
1499:retrograde inversion
1257:from WTC1 bars 25–35
1243:from WTC1 bars 25–36
978:Jean-Philippe Rameau
836:harmonic progression
30:For other uses, see
2660:Formula composition
2367:Pease, Ted (2003).
2255:Randel, Don Michael
1666:, you subtract the
1591:means "invert" and
1398:Two lines from the
1251:Bach's Prelude in A
1237:Bach's Prelude in A
1222:from WTC1 bars 9–18
1216:Bach's Prelude in A
1208:from WTC1 bars 9–18
1202:Bach's prelude in A
1086:triple counterpoint
1082:double counterpoint
983:Treatise on Harmony
968:had been inserted.
549:
82:the same number of
2207:Grove Music Online
2069:www.britannica.com
1840:octave equivalency
1795:
1750:
1711:
1691:
1656:
1628:
1608:
1581:
1561:
1327:
1319:
1287:
1279:
1259:
1245:
1224:
1210:
1152:2010-03-27 at the
1111:are said to be in
1078:textural inversion
948:Lower-case letters
840:octave equivalence
547:
292:complement (music)
120:musical set theory
97:, the second goes
78:, the second goes
2826:
2825:
2712:
2711:
2665:Modernism (music)
2593:Arnold Schoenberg
2187:Scholes, Percy A.
2146:Lovelock, William
2120:978-0-7935-7991-4
2003:Pitch axis theory
1926:pitch axis theory
1714:{\displaystyle n}
1659:{\displaystyle I}
1631:{\displaystyle n}
1584:{\displaystyle I}
1529:are shown below.
1523:Arnold Schoenberg
1473:Twelve-tone music
1393:
1378:
1314:
1274:
1234:
1199:
1166:from J.S. Bach's
1080:. This is called
1050:
910:harmonic analysis
817:
816:
532:
469:
445:
318:
271:
270:
214:
213:
206:
205:
58:melodic inversion
51:
16:(Redirected from
2861:
2844:Musical symmetry
2746:Voicing in music
2739:
2732:
2725:
2716:
2704:
2703:
2623:Related articles
2605:Charles Wuorinen
2513:
2447:Combinatoriality
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2415:
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2091:, 1977, p. 492.
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1987:
1986:
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1672:integer notation
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1657:
1637:
1635:
1634:
1629:
1617:
1615:
1614:
1609:
1607:
1606:
1590:
1588:
1587:
1582:
1570:
1568:
1567:
1562:
1557:
1556:
1464:
1463:
1458:
1457:
1402:in G major from
1315:
1303:Jupiter Symphony
1275:
1256:
1255:
1242:
1241:
1235:
1221:
1220:
1207:
1206:
1200:
1186:
1185:
1163:
1162:
1138:The Art of Fugue
1019:
1018:
1010:
1009:
905:
904:
880:
879:
871:
870:
859:
858:
850:
849:
812:
811:
810:
800:
799:
798:
797:
796:
795:
792:
784:
772:
771:
770:
760:
759:
758:
757:
756:
755:
752:
744:
732:
731:
730:
720:
719:
718:
717:
716:
715:
712:
704:
685:
684:
683:
682:
681:
680:
677:
669:
636:
635:
634:
624:
623:
607:
606:
584:
583:
550:
499:second inversion
352:) in the chord.
275:interval quality
223:under inversion
220:Interval quality
216:
208:
207:
158:under inversion
151:
64:in D minor from
21:
2869:
2868:
2864:
2863:
2862:
2860:
2859:
2858:
2854:Voicing (music)
2829:
2828:
2827:
2822:
2748:
2743:
2713:
2708:
2694:
2650:Duration series
2645:Chromatic scale
2618:
2559:
2552:
2514:
2505:
2482:Cross partition
2452:Complementation
2435:
2426:
2389:
2384:
2383:
2366:
2362:
2356:
2340:
2339:
2335:
2327:
2323:
2308:
2295:
2294:
2290:
2275:
2253:
2252:
2248:
2230:
2226:
2203:
2202:
2198:
2185:
2184:
2180:
2171:
2167:
2160:
2144:
2143:
2139:
2132:
2128:
2121:
2104:
2103:
2099:
2086:
2082:
2073:
2071:
2063:
2062:
2058:
2053:
2049:
2044:
2039:
2038:
2025:
2021:
2016:
1998:Voicing (music)
1994:
1984:
1983:
1957:
1956:
1955:
1954:" about C and A
1948:
1947:
1944:
1941:
1938:
1935:
1929:
1922:
1912:
1911:
1906:
1905:
1896:
1895:
1890:
1889:
1884:
1883:
1878:
1877:
1872:
1871:
1866:
1865:
1860:
1859:
1832:sets of pitches
1818:In set theory,
1816:
1811:
1767:
1762:
1761:
1728:
1723:
1722:
1703:
1702:
1681:
1676:
1675:
1648:
1647:
1620:
1619:
1598:
1593:
1592:
1573:
1572:
1548:
1543:
1542:
1535:
1534:
1475:
1461:
1460:
1455:
1454:
1415:
1414:
1413:
1396:
1395:
1394:
1392:
1380:
1379:
1377:
1360:
1309:
1269:
1253:
1252:
1239:
1238:
1229:
1218:
1217:
1204:
1203:
1194:
1183:
1182:
1179:
1160:
1159:
1154:Wayback Machine
1098:
1072:inversion, two
1066:
1065:
1064:
1053:
1052:
1051:
1049:
1032:
1026:
1017:
1014:
1013:
1012:
1008:
1005:
1004:
1003:
974:
950:
918:
903:
900:
899:
898:
878:
875:
874:
873:
869:
866:
865:
864:
857:
854:
853:
852:
848:
845:
844:
843:
834:, indicating a
824:Arabic numerals
809:
806:
805:
804:
803:
793:
790:
788:
787:
786:
785:
782:
781:
780:
769:
766:
765:
764:
763:
753:
750:
748:
747:
746:
745:
742:
741:
740:
729:
726:
725:
724:
723:
713:
710:
708:
707:
706:
705:
702:
701:
700:
692:
678:
675:
673:
672:
671:
670:
667:
666:
665:
650:
641:Seventh chords
633:
630:
629:
628:
627:
622:
619:
618:
617:
605:
602:
601:
600:
592:
582:
579:
578:
577:
562:
545:
540:
535:
534:
533:
531:
480:first inversion
472:
471:
470:
468:
448:
447:
446:
444:
391:
375:Main articles:
373:
338:
337:
336:
321:
320:
319:
317:
300:
288:simple interval
279:interval number
222:
157:
155:Interval number
147:
128:
104:
103:
102:
54:
53:
52:
50:
35:
28:
23:
22:
15:
12:
11:
5:
2867:
2865:
2857:
2856:
2851:
2846:
2841:
2831:
2830:
2824:
2823:
2821:
2820:
2815:
2810:
2805:
2779:
2774:
2769:
2764:
2759:
2753:
2750:
2749:
2744:
2742:
2741:
2734:
2727:
2719:
2710:
2709:
2699:
2696:
2695:
2693:
2692:
2687:
2682:
2677:
2672:
2667:
2662:
2657:
2652:
2647:
2642:
2637:
2632:
2626:
2624:
2620:
2619:
2617:
2616:
2607:
2602:
2601:
2600:
2595:
2590:
2580:
2575:
2570:
2568:Milton Babbitt
2564:
2562:
2554:
2553:
2551:
2550:
2548:Multiplication
2545:
2540:
2535:
2530:
2524:
2522:
2516:
2515:
2508:
2506:
2504:
2503:
2502:
2501:
2496:
2486:
2485:
2484:
2474:
2469:
2467:Interval class
2464:
2459:
2454:
2449:
2443:
2441:
2437:
2436:
2427:
2425:
2424:
2417:
2410:
2402:
2396:
2395:
2388:
2387:External links
2385:
2382:
2381:
2360:
2354:
2333:
2321:
2306:
2288:
2273:
2257:, ed. (2003).
2246:
2224:
2196:
2178:
2165:
2158:
2137:
2126:
2119:
2113:. p. 74.
2097:
2080:
2056:
2046:
2045:
2043:
2040:
2037:
2036:
2018:
2017:
2015:
2012:
2011:
2010:
2005:
2000:
1993:
1990:
1949:
1945:
1942:
1939:
1936:
1933:
1932:
1931:
1930:
1921:
1918:
1815:
1812:
1810:
1807:
1794:
1791:
1788:
1785:
1782:
1779:
1774:
1770:
1749:
1746:
1743:
1740:
1735:
1731:
1710:
1688:
1684:
1655:
1627:
1605:
1601:
1580:
1560:
1555:
1551:
1532:
1531:
1513:nversion, and
1474:
1471:
1468:
1451:diatonic scale
1437:
1397:
1386:
1383:
1381:
1371:
1368:
1366:
1365:
1364:
1363:
1359:
1356:
1178:
1175:
1106:
1097:
1094:
1054:
1043:
1040:
1038:
1037:
1036:
1035:
1028:Main article:
1025:
1022:
1015:
1006:
973:
970:
949:
946:
917:
914:
901:
891:
876:
867:
855:
846:
815:
814:
807:
801:
778:
777:3rd inversion
774:
773:
767:
761:
738:
737:2nd inversion
734:
733:
727:
721:
698:
697:1st inversion
694:
693:
690:
688:
686:
663:
662:Root position
659:
658:
655:
652:
647:
643:
642:
638:
637:
631:
625:
620:
615:
614:2nd inversion
611:
610:
608:
603:
598:
597:1st inversion
594:
593:
590:
588:
585:
580:
575:
574:Root position
571:
570:
567:
564:
559:
555:
554:
544:
541:
539:
536:
525:
522:
520:
519:
511:seventh chords
507:
506:
495:
462:
459:
457:
456:
453:
438:
435:
433:
432:
415:
389:3rd inversions
372:
369:
322:
311:
308:
306:
305:
304:
303:
299:
296:
269:
268:
265:
262:
258:
257:
254:
251:
247:
246:
243:
240:
236:
235:
232:
229:
225:
224:
212:
211:
204:
203:
200:
197:
193:
192:
189:
186:
182:
181:
178:
175:
171:
170:
167:
164:
160:
159:
149:
148:
145:
127:
124:
100:
96:
81:
77:
56:An example of
55:
44:
41:
39:
38:
37:
36:
26:
24:
18:Inverted chord
14:
13:
10:
9:
6:
4:
3:
2:
2866:
2855:
2852:
2850:
2847:
2845:
2842:
2840:
2837:
2836:
2834:
2819:
2818:Voice leading
2816:
2814:
2811:
2809:
2806:
2803:
2799:
2795:
2791:
2787:
2783:
2782:Root position
2780:
2778:
2775:
2773:
2770:
2768:
2765:
2763:
2760:
2758:
2755:
2754:
2751:
2747:
2740:
2735:
2733:
2728:
2726:
2721:
2720:
2717:
2707:
2697:
2691:
2688:
2686:
2683:
2681:
2678:
2676:
2673:
2671:
2668:
2666:
2663:
2661:
2658:
2656:
2653:
2651:
2648:
2646:
2643:
2641:
2638:
2636:
2633:
2631:
2628:
2627:
2625:
2621:
2614:
2613:
2608:
2606:
2603:
2599:
2596:
2594:
2591:
2589:
2586:
2585:
2584:
2581:
2579:
2576:
2574:
2573:Pierre Boulez
2571:
2569:
2566:
2565:
2563:
2561:
2555:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2525:
2523:
2521:
2517:
2512:
2500:
2497:
2495:
2492:
2491:
2490:
2487:
2483:
2480:
2479:
2478:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2453:
2450:
2448:
2445:
2444:
2442:
2438:
2434:
2430:
2423:
2418:
2416:
2411:
2409:
2404:
2403:
2400:
2394:
2391:
2390:
2386:
2378:
2377:0-87639-001-7
2374:
2370:
2364:
2361:
2357:
2355:0-300-05111-5
2351:
2347:
2343:
2337:
2334:
2331:, p. 36.
2330:
2325:
2322:
2317:
2313:
2309:
2303:
2299:
2292:
2289:
2284:
2280:
2276:
2270:
2266:
2262:
2261:
2256:
2250:
2247:
2243:
2242:
2237:
2233:
2228:
2225:
2221:
2217:
2213:
2209:
2208:
2200:
2197:
2192:
2188:
2182:
2179:
2175:
2169:
2166:
2161:
2159:0-7135-0744-6
2155:
2151:
2147:
2141:
2138:
2135:
2130:
2127:
2122:
2116:
2112:
2108:
2101:
2098:
2094:
2090:
2084:
2081:
2070:
2066:
2060:
2057:
2051:
2048:
2041:
2033:
2032:voice leading
2029:
2023:
2020:
2013:
2009:
2006:
2004:
2001:
1999:
1996:
1995:
1991:
1989:
1980:
1977:
1973:
1969:
1968:transposition
1964:
1962:
1953:
1927:
1919:
1917:
1903:
1857:
1851:
1849:
1845:
1841:
1837:
1833:
1829:
1825:
1821:
1813:
1808:
1806:
1792:
1789:
1783:
1777:
1772:
1768:
1744:
1738:
1733:
1729:
1708:
1686:
1682:
1673:
1669:
1653:
1645:
1644:transposition
1641:
1625:
1603:
1599:
1578:
1558:
1553:
1549:
1540:
1530:
1528:
1524:
1520:
1516:
1512:
1508:
1504:
1500:
1496:
1492:
1488:
1484:
1480:
1472:
1470:
1466:
1452:
1448:
1447:
1443:According to
1441:
1439:
1435:
1432:
1428:
1424:
1420:
1411:
1410:
1405:
1401:
1390:
1375:
1362:
1357:
1354:
1352:
1348:
1344:
1340:
1334:
1332:
1323:
1307:
1305:
1304:
1299:
1294:
1292:
1283:
1267:
1266:interchanged:
1264:
1249:
1227:
1214:
1192:
1190:
1176:
1174:
1172:
1170:
1165:
1155:
1151:
1148:
1144:
1140:
1139:
1134:
1129:
1126:
1122:
1118:
1114:
1110:
1104:
1102:
1095:
1093:
1091:
1087:
1083:
1079:
1075:
1071:
1062:
1058:
1047:
1034:
1031:
1023:
1021:
1001:
997:
993:
989:
985:
984:
979:
971:
969:
967:
963:
959:
956:, indicating
955:
947:
945:
943:
939:
935:
934:
929:
928:
923:
922:popular music
915:
913:
911:
907:
894:
889:
887:
882:
861:
841:
837:
833:
829:
825:
821:
776:
775:
736:
735:
696:
695:
661:
660:
644:
639:
613:
612:
596:
595:
573:
572:
556:
551:
542:
537:
529:
518:
516:
512:
504:
500:
496:
493:
489:
485:
481:
477:
476:
475:
466:
455:
451:
442:
431:
429:
425:
421:
420:
413:
410:
408:
404:
400:
396:
390:
386:
382:
378:
377:Root position
370:
368:
366:
362:
358:
353:
351:
347:
343:
334:
330:
326:
315:
302:
297:
295:
293:
289:
283:
280:
276:
266:
263:
260:
259:
255:
252:
249:
248:
244:
241:
238:
237:
233:
230:
227:
226:
221:
217:
210:
209:
201:
198:
195:
194:
190:
187:
184:
183:
179:
176:
173:
172:
168:
165:
162:
161:
156:
152:
144:
143:
142:
139:
135:
130:
125:
123:
121:
117:
113:
109:
98:
94:
92:
88:
85:
79:
75:
73:
72:
67:
63:
59:
48:
33:
19:
2757:Blind octave
2610:
2598:Anton Webern
2520:Permutations
2440:Fundamentals
2368:
2363:
2345:
2342:Wilson, Paul
2336:
2324:
2297:
2291:
2259:
2249:
2241:The Guardian
2239:
2235:
2232:Service, Tom
2227:
2219:
2205:
2199:
2190:
2181:
2173:
2168:
2149:
2140:
2129:
2106:
2100:
2088:
2083:
2072:. Retrieved
2068:
2059:
2050:
2022:
1981:
1965:
1958:
1916:–G–B–C–E–F.
1852:
1830:, and other
1819:
1817:
1536:
1518:
1514:
1510:
1506:
1502:
1487:permutations
1476:
1444:
1442:
1416:
1407:
1361:
1351:Joseph Haydn
1336:
1328:
1302:
1295:
1291:permutations
1288:
1261:J.S. Bach's
1260:
1225:
1188:
1180:
1167:
1141:, the first
1136:
1130:
1112:
1109:counterpoint
1099:
1090:rivolgimento
1089:
1085:
1081:
1077:
1070:contrapuntal
1067:
1033:
1030:Counterpoint
1024:Counterpoint
991:
988:functionally
981:
975:
965:
961:
957:
953:
951:
931:
925:
919:
895:
883:
862:
827:
820:Figured bass
818:
543:Figured bass
508:
473:
449:
418:
411:
399:parent chord
398:
392:
364:
356:
354:
339:
333:figured bass
329:Hubert Parry
324:
301:
284:
272:
131:
129:
116:contrapuntal
111:
108:music theory
105:
69:
27:Musical term
2804:inversions)
2772:Common tone
2762:Block chord
2670:Punctualism
2655:Equivalence
2329:Straus 1990
1961:jazz theory
1920:Jazz theory
1668:pitch class
1509:etrograde,
1427:major third
1331:Tom Service
938:subdominant
927:slash chord
651:above bass
563:above bass
492:minor sixth
488:minor third
256:Diminished
89:(with some
2833:Categories
2685:Time point
2680:Set theory
2588:Alban Berg
2533:Retrograde
2472:Invariance
2457:Derivation
2307:0136866921
2274:0674011635
2074:2024-01-26
2042:References
1856:microtones
1814:Set theory
1701:by adding
1539:set theory
1517:etrograde
1497:, and the
1495:retrograde
1491:prime form
1404:J. S. Bach
1339:palimpsest
832:bass notes
646:Inversion
558:Inversion
325:Rustington
250:Augmented
66:J. S. Bach
2786:Inversion
2640:Atonality
2560:composers
2538:Inversion
2528:Prime row
2494:Aggregate
2477:Partition
2462:Hexachord
2433:serialism
2371:, p.152.
2244:, 27 May.
1972:chromatic
1842:and even
1824:intervals
1640:semitones
1133:J.S. Bach
1057:J.S. Bach
649:Intervals
561:Intervals
357:inversion
355:The term
350:bass note
126:Intervals
112:inversion
91:chromatic
60:from the
2777:Doubling
2675:Semitone
2489:Tone row
2344:(1992),
2316:20012239
2283:52623743
2210:. 2001.
2189:(1954).
2148:(1981),
2028:cadences
1992:See also
1985:♮
1976:diatonic
1913:♯
1907:♯
1897:♯
1891:♭
1885:♭
1879:♯
1873:♭
1867:♯
1861:♭
1571:, where
1483:tone row
1462:♭
1456:♭
1358:Melodies
1254:♭
1240:♭
1219:♭
1205:♭
1184:♭
1177:Examples
1161:♭
1150:Archived
1074:melodies
1020:chords.
942:dominant
933:function
657:Example
569:Example
365:position
234:Perfect
228:Perfect
180:Seventh
134:interval
84:diatonic
2849:Harmony
2558:Notable
2236:Jupiter
1423:contour
1347:Michael
1147:G minor
1121:twelfth
1000:perfect
972:History
940:of the
890:between
828:figures
654:Symbol
566:Symbol
553:Triads
497:In the
478:In the
419:voicing
261:Accute
196:Fourth
174:Second
169:Octave
163:Unison
138:octaves
2839:Melody
2808:Octave
2802:higher
2800:, and
2375:
2352:
2314:
2304:
2281:
2271:
2156:
2117:
1828:chords
1505:rime,
1493:, the
1419:melody
1298:Mozart
1117:octave
1101:Themes
794:
754:
714:
679:
490:and a
387:, and
298:Chords
267:Grave
245:Minor
239:Major
202:Fifth
191:Sixth
185:Third
2813:Voice
2690:Trope
2014:Notes
1848:tonal
1670:, in
1438:third
1436:minor
1431:tonal
1400:fugue
1164:major
1143:canon
1125:motif
1103:that
906:chord
826:(the
587:None
517:are:
503:fifth
484:third
424:close
407:fifth
403:third
346:triad
342:chord
110:, an
87:steps
62:fugue
2784:and
2612:more
2499:List
2431:and
2373:ISBN
2350:ISBN
2312:OCLC
2302:ISBN
2279:OCLC
2269:ISBN
2238:)",
2154:ISBN
2115:ISBN
1902:dyad
1888:–C–E
1882:–G–B
1870:–G–B
1864:–E–F
1349:and
1156:and
1011:and
813:or
428:open
414:both
405:and
395:root
361:root
277:and
95:down
80:down
2798:3rd
2794:2nd
2790:1st
2615:...
2609:...
2265:418
2212:doi
1974:or
1959:In
1904:F/F
1537:In
1525:'s
1477:In
1467:may
1440:).
1406:'s
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1131:In
1105:can
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1059:'s
998:to
980:'s
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452:not
385:2nd
381:1st
132:An
106:In
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1826:,
1459:–a
1417:A
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1092:.
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954:Ib
944:.
430:.
383:,
379:,
340:A
294:.
264:↔
253:↔
242:↔
231:↔
199:↔
188:↔
177:↔
166:↔
122:.
99:up
76:up
2788:(
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2077:.
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1790:=
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1730:T
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1600:T
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1391:.
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1158:B
1063:.
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1016:3
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728:5
711:3
709:5
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676:3
674:5
668:7
632:4
621:4
604:3
581:3
530:.
467:.
443:.
316:.
49:.
34:.
20:)
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