Thirteenth

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|caption=Dominant thirteenth chord in four-part writing{{sfn|Benward|Saker|2009|p=179}}}}

Most commonly, 13th chords serve a dominant function (V¹³),{{sfn|Benward|Saker|2009|p=180}} whether they have the exact intervals of a dominant thirteenth or not. Typically, a dominant chord anticipating a major resolution will feature a natural 13, while a dominant chord anticipating a minor resolution will feature a flat 13.{{sfn|Benward|Saker|2009|p=179}} Since thirteenth chords contain more than four notes, in four-voice writing the root, third, seventh, and thirteenth are most often included,{{sfn|Benward|Saker|2009|p=179}} excluding the fifth, ninth, and eleventh {{Audio|Dominant thirteenth chord on C four voices.mid|Play}}. The third indicates the quality of the chord as major or minor, the seventh is important for the quality as a dominant chord, while the thirteenth is necessary in a thirteenth chord.

File:Prelude to the Afternoon of a Faun dominant thirteenth chord.png's Prélude à l'après-midi d'un faune (1894)Cope, David (2000). New Directions in Music, p.6. {{ISBN|1-57766-108-7}}. {{Audio|Prelude to the Afternoon of a Faun dominant thirteenth chord.mid|Play}}]]

In modern pop and jazz harmony, after the dominant thirteenth, a thirteenth chord (usually notated as X¹³, e.g. C¹³) contains an implied flatted seventh interval. Thus, a C¹³ consists of C, E, G, B{{music|flat}}, and A. The underlying harmony during a thirteenth chord is usually Mixolydian or Lydian dominant (see chord-scale system). A thirteenth chord does not imply the quality of the ninth or eleventh scale degrees. In general, what gives a thirteenth chord its characteristic sound is the dissonance between the flat seventh and the thirteenth, an interval of a major seventh.

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<< { e'\glissando c' e'\glissando d' } \\ { f e f e } >>

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\new Staff { \clef bass << { b g b g } \\ { g, c g, c } >> }

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\markup { V \super 13 } I \bar "||"

\markup { V \super 13 } \markup { I \super 9 } \bar "||"

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|width=300|caption=Voice leading for dominant thirteenth chords in the common practice period.{{sfn|Benward|Saker|2009|pp=183–84}}}}

In the common practice period the "most common" pitches present in V¹³ chord are the root, 3rd, 7th, and 13th; with the 5th, 9th, and 11th "typically omitted".{{sfn|Benward|Saker|2009|pp=183-84}} The 13th is most often in the soprano, or highest voice, and usually resolves down by a 3rd to the tonic I or i. If the V¹³ is followed by a I⁹ the 13th may resolve to the 9th.{{sfn|Benward|Saker|2009|pp=183–84}}

File:13chords.png

These voice leading guidelines may not be followed after the common practice period in techniques such as parallel harmony and in the following example:

File:All Points West 'Railroad sonority'.png (1937) by Rodgers & Hart.{{cite journal |last1=Cox |first1=Felix |title='A Faltering Step in a Basically Right Direction': Richard Rodgers and All Points West |journal=American Music |date=Autumn 2005 |volume=23 |issue=3 |page=360 |doi=10.2307/4153058|jstor=4153058 }} {{Audio|All Points West 'Railroad sonority'.mid|Play}}]]

13th chords may less often be built on degrees other than the dominant, such as the tonic or subdominant.{{sfn|Benward|Saker|2009|p=180}}

File:I Found a New Baby 13th chord.png's ending to "I Found a New Baby" (recorded 1946) is a "tonic thirteenth chord"{{cite journal |last1=Everett |first1=Walter |title=A Royal Scam: The Abstruse and Ironic Bop-Rock Harmony of Steely Dan |journal=Music Theory Spectrum |date=October 2004 |volume=26 |issue=2 |page=205 |doi=10.1525/mts.2004.26.2.201}} in lydian. {{Audio|I Found a New Baby 13th chord.mid|Play}}]]

While the dominant thirteenth is the most common thirteenth chord, the major thirteenth is also fairly common.Hal Leonard Corp. (2003). Picture Chord Encyclopedia: Photos, Diagrams and Music Notation for Over 1,600 Keyboard Chords, p.10. {{ISBN|0-634-05828-2}}. A major thirteenth chord (containing a major seventh) will nearly always feature a chromatically raised eleventh (C E G B D F{{music|sharp}} A) (see Lydian mode), except for cases when the eleventh is omitted altogether. "It is customary to omit the eleventh on dominant or major thirteenth chords because the eleventh conflicts with the third," in these chords by a semitone.

File:Noreen's Nocturne.png in measures 5–8 of "Noreen's Nocturne" by Oscar Peterson (transcribed by Brent Edstrom) features 13th chords and also reveals the distinction between the compound and simple intervals of a 13th and an added 6th, respectively.{{sfn|Benward|Saker|2009|pp=183–84}} {{Audio|Noreen's Nocturne.mid|Play}}]]

File:Thirteenth chord inversions.png.]]

Generally found in root position,{{sfn|Benward|Saker|2009|p=179}} the inversion of a complete thirteenth chord including all seven notes, itself, "a rare phenomenon", is a theoretical impossibility since a new thirteenth chord with a different root is produced, for example Cmaj¹³ (C-E-G-B-D-F-A) becomes {{Disputed inline|Talk page section|date=June 2020}} Em^{13{{music|b}}9} (E-G-B-D-F-A-C) then G¹³ (G-B-D-F-A-C-E), and so on, when inverted.{{sfn|Cooper|1981|p=372}}

Given the number of notes that may be included, there are a great variety of thirteenth chords. The following chords are notated below lead sheet symbols:

Image:Thirteenth chord Cm13.png|Thirteenth chord based on minor triadKostka & Payne (1995). Tonal Harmony, p.493. Third Edition. {{ISBN|0-07-300056-6}}. {{Audio|Thirteenth chord Cm13.mid|Play}}

Image:Thirteenth chord C13+11b9.png|Thirteenth chord with flat ninth {{Audio|Thirteenth chord C13+11b9.mid|Play}}

Image:Thirteenth chord CMA7(add13).png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord CMA7(add13).mid|Play}}

File:Thirteenth chord CMA13.png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord CMA13.mid|Play}}

File:Thirteenth chord C13.png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord C13.mid|Play}}

File:Thirteenth chord CMI7(add13).png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord CMI7(add13).mid|Play}}

File:Thirteenth chord C13sus.png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord C13sus.mid|Play}}

File:Thirteenth chord CMA13(sharp11).png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord CMA13(sharp11).mid|Play}}

File:Thirteenth chord C13(b5).png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord C13(b5).mid|Play}}

File:Thirteenth chord C13(b9).png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord C13(b9).mid|Play}}

File:Thirteenth chord C13(sharp11).png|{{sfn|Benward|Saker|2009|p=185}} {{Audio|Thirteenth chord C13(sharp11).mid|Play}}

Image:Thirteenth chord C13b9.png|Bass note: C or alternatively G.Manus, M. (1978). Piano Chord Dictionary, p.21. {{ISBN|0-88284-154-8}}. {{Audio|Thirteenth chord C13b9.mid|Play}}

Image:Thirteenth chord C13 guitar.png|"Thirteenth chord inversion with no fifth or ninth and the flatted seventh in the bass."{{sfn|Capone|2006|pp=84–85}}Hal Leonard Corp. (2004). Guitar Chords Deluxe: Full-Color Photos and Diagrams for Over 1,600 Chords, p.12. {{ISBN|0-634-07389-3}}. {{Audio|Thirteenth chord C13 guitar.mid|Play}}

Image:Thirteenth chord C13 guitar b.png|Different voicing for guitar.{{sfn|Capone|2006|p=79}} {{Audio|Thirteenth chord C13 guitar b.mid|Play}}

Image:Dominant thirteenth chord on C 4 voice 2.png|Dominant thirteenth: four-voice version. "This disposition is typical."{{sfn|Cooper|1981|pp=371–372}} {{Audio|Dominant thirteenth chord on C 4 voice 2.mid|Play}}

Image:Thirteenth chord collapsed.png|A thirteenth chord "collapsed" into one octave results in a dissonant, seemingly secundal tone cluster. {{Audio|Thirteenth chord collapsed.mid|Play}}

Image:Dominant thirteenth chord on C m13.png|A dominant thirteenth in F minor. {{Audio|Dominant thirteenth chord on C m13.mid|Play}}

File:Thirteenth chord Pelléas et Mélisande motif.png motif, at Mélisande's entrance and later when Golaud asks if she ever loved Pelléas, features, in addition to the already usual ninth, a thirteenth is added and the chords are inverted so as to be founded on a "warm" close-position fourth.Nichols, Roger (1989). Claude Debussy: Pelléas et Mélisande, p.105. {{ISBN|0-521-31446-1}}. {{Audio|Thirteenth chord Pelléas et Mélisande motif.mid|Play}}]]

File:Music in Twelve Parts transitional thirteenth chord.png by Philip GlassPotter, Keith (2002). Four musical minimalists, p.319. {{ISBN|0-521-01501-4}}. {{Audio|Music in Twelve Parts transitional thirteenth chord.mid|Play}}]]

• Jazz chord
• Harmonic planing
• Ladder of thirds
• Mystic chord

{{reflist}}

{{refbegin}}

• {{cite book

|last1=Benward |first1=Bruce

|last2=Saker |first2=Marilyn

|year=2009

|title=Music in Theory and Practice

|volume=II

|edition=Eight

|location=New York

|publisher=McGraw-Hill

|isbn=978-0-07-310188-0

}}

• {{cite book

|last=Capone |first=Phil

|year=2006

|title=Guitar Chord Bible: Over 500 Illustrated Chords for Rock, Blues, Soul, Country, Jazz, and Classical

|isbn=0-7858-2083-3

}}

• {{cite book

|last=Cooper |first=Paul |author-link=Paul Cooper (composer)

|year=1981

|title=Perspectives in Music Theory: An Historical-Analytical Approach

|edition=Second

|location=New York

|publisher=Harper & Row

|isbn=0-06-041373-5

|url=https://archive.org/details/perspectivesinmu0000coop

|url-access=registration

}}

{{refend}}

{{Chords}}

{{Chord factors}}

{{Intervals}}

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Category:Extended chords

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Category:Compound intervals