View source for Thirteenth

{{about|the term's use in music theory}}
{{Use dmy dates|date=May 2015}}

{{Image frame|content=<score sound="1">
{ \omit Score.TimeSignature \key f \major \clef bass <f, d'>1 }
</score>|width=300|caption=Compound interval of a major thirteenth from F to D in the next octave up}}

{{Infobox musical interval
| main_interval_name = major thirteenth
| inverse = [[minor third]]
| other_names = compound sixth
| abbreviation = M13
| semitones = 21
| interval_class = 3
| just_interval = 
| cents_equal_temperament = 2100.0
| cents_24T_equal_temperament = 
| cents_just_intonation = 
}}

{{Image frame|content=<score sound="1">
{ \omit Score.TimeSignature \key f \minor \clef bass <f, des'>1 }
</score>|width=300|caption=Minor thirteenth: F to D{{music|b}}}}

{{Infobox musical interval
| main_interval_name = minor thirteenth
| inverse = [[major third]]
| other_names = 
| abbreviation = m13
| semitones = 20
| interval_class = 4
| just_interval = 
| cents_equal_temperament = 2000.0
| cents_24T_equal_temperament = 
| cents_just_intonation = 
}}

In [[music]] or [[music theory]], a '''thirteenth''' is the [[Musical note|note]] thirteen [[scale degree]]s from the [[root (chord)|root]] of a [[chord (music)|chord]] and also the [[interval (music)|interval]] between the root and the thirteenth. The thirteenth is most commonly major {{audio|Major thirteenth on F.mid|Play}} or minor {{audio|Minor thirteenth on F.mid|Play}}.

{{Image frame|content=<score sound="1">
\fixed c' {
  \omit Score.TimeSignature
  <c e g bes \tweak NoteHead.color #red d' \tweak NoteHead.color #red f' \tweak NoteHead.color #red a'>1
}
</score>|width=300|caption=Dominant thirteenth extended chord: C E G B{{music|flat}} D F A. The [[upper structure]] or extensions, i.e. notes beyond the seventh, in red.}}

A '''thirteenth chord''' is the stacking of six ([[major third|major]] or [[minor third|minor]]) thirds, the last being above the 11th of an [[eleventh chord]].{{sfn|Benward|Saker|2009|p=360}} Thus a thirteenth chord is a [[tertian]] (built from thirds) chord containing the interval of a thirteenth, and is an [[extended chord]] if it includes the [[ninth]] and/or the [[eleventh]]. "The jazzy thirteenth is a very versatile chord and is used in many genres."{{sfn|Capone|2006|p=48}} Since 13th chords tend to become unclear or confused with other chords when [[Inverted chord|inverted]], they are generally found in [[root position]].{{sfn|Benward|Saker|2009|p=179}} For example, depending on [[voicing (music)|voicing]], a major triad with an added major [[sixth (chord)|sixth]] is usually called a [[sixth chord]] {{Audio|Add6 chord on C.mid|Play}}, because the sixth serves as a substitution for the major seventh, thus considered a chord tone in such context. 

However, [[Walter Piston]], writing in 1952, considered that, "a true thirteenth chord, arrived at by superposition of thirds, is a rare phenomenon even in 20th-century music."<ref name="Piston">{{cite journal |last1=Piston |first1=Walter |title=''Harmonic Practice'' by Roger Sessions |journal=The Musical Quarterly |date=1952 |volume=38 |issue=3 |page=463 |doi=10.1093/mq/XXXVIII.3.457|department=Review}}</ref> This may be due to [[four-part writing]], instrument limitations, and [[voice leading]] and stylistic considerations. For example, "to make the chord more playable [on [[guitar]]], thirteenth chords often omit the fifth and the ninth."{{sfn|Capone|2006|p=66}}

==Dominant thirteenth==
{{Image frame|content=<score sound="1">
\new PianoStaff <<
  \new Staff { \key f \major a'1 }
  \new Staff { \key f \major \clef bass <c e bes> }
>>
</score>|caption=Dominant thirteenth chord in [[four-part writing]]{{sfn|Benward|Saker|2009|p=179}}}}

Most commonly, 13th chords serve a [[dominant (music)|dominant]] [[diatonic function|function]] (V<sup>13</sup>),{{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-part harmony|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|thumb|center|400px|Dominant thirteenth chord in [[Claude Debussy]]'s ''[[Prélude à l'après-midi d'un faune]]'' (1894)<ref name="Cope, David 2000 p.6">Cope, David (2000). ''New Directions in Music'', p.6. {{ISBN|1-57766-108-7}}.</ref> {{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 ''X<sup>13</sup>'', e.g. C<sup>13</sup>) contains an implied flatted seventh interval. Thus, a C<sup>13</sup> consists of C, E, G, B{{music|flat}}, and A. The underlying harmony during a thirteenth chord is usually [[Mixolydian mode|Mixolydian]] or [[Lydian dominant scale|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 (music)|interval]] of a [[major seventh]].

{{Image frame|content=<score sound="1">
\new PianoStaff <<
  \new Staff \fixed c' {
    \omit Score.TimeSignature \time 2/4
    << { e'\glissando c' e'\glissando d' } \\ { f e f e } >>
  }
  \new Staff { \clef bass << { b g b g } \\ { g, c g, c } >> }
  \new Lyrics \lyricmode {
    \markup { V \super 13 } I \bar "||"
    \markup { V \super 13 } \markup { I \super 9 } \bar "||"
  }
>>
</score>|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 V<sup>13</sup> 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 V<sup>13</sup> is followed by a I<sup>9</sup> the 13th may resolve to the 9th.{{sfn|Benward|Saker|2009|pp=183–84}}

==Other thirteenth chords==

[[File:13chords.png|thumb|Thirteenth chords and major thirteenth chords with sheet music.]]

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|thumb|center|400px|Alternating ({{music|natural}})13 and {{music|b}}13 chords in the "railroad sonority" from mm.1–4 of ''[[All Points West (monodrama)|All Points West]]'' (1937) by [[Rodgers & Hart]].<ref>{{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 }}</ref> {{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 (music)|tonic]] or [[subdominant]].{{sfn|Benward|Saker|2009|p=180}}

[[File:I Found a New Baby 13th chord.png|thumb|center|400px|[[Lennie Tristano]]'s ending to "[[I Found a New Baby]]" (recorded 1946) is a "tonic thirteenth chord"<ref>{{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}}</ref> 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.<ref name="Picture chord">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}}.</ref> 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,"<ref name="Picture chord"/> in these chords by a semitone.

[[File:Noreen's Nocturne.png|thumb|center|400px|The [[cadence (music)|cadence]] 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}}]]

==Inversions==
[[File:Thirteenth chord inversions.png|thumb|right|225px|CM<sup>13</sup>, first inversion = {{Disputed inline|date=June 2020}} Em<sup>13{{music|b}}9</sup>, 2nd inversion = G<sup>13</sup>... ({{audio|Thirteenth chord inversions.mid|Play}}). Eventually seven chords along a [[ladder of thirds]].]]

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

==Gallery==
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:

<gallery>
Image:Thirteenth chord Cm13.png|Thirteenth chord based on minor triad<ref name="K&P">Kostka & Payne (1995). ''Tonal Harmony'', p.493. Third Edition. {{ISBN|0-07-300056-6}}.</ref> {{Audio|Thirteenth chord Cm13.mid|Play}}
Image:Thirteenth chord C13+11b9.png|Thirteenth chord with flat ninth<ref name="K&P"/> {{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.<ref>Manus, M. (1978). ''Piano Chord Dictionary'', p.21. {{ISBN|0-88284-154-8}}.</ref> {{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}}<ref>Hal Leonard Corp. (2004). ''Guitar Chords Deluxe: Full-Color Photos and Diagrams for Over 1,600 Chords'', p.12. {{ISBN|0-634-07389-3}}.</ref> {{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 [[Consonance and dissonance|dissonant]], seemingly [[secundal]]<ref name="Cope, David 2000 p.6"/> [[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}}
</gallery>

[[File:Thirteenth chord Pelléas et Mélisande motif.png|thumb|center|400px|Debussy's ''[[Pelléas et Mélisande (opera)|Pelléas et Mélisande]]'' 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.<ref>Nichols, Roger (1989). ''Claude Debussy: Pelléas et Mélisande'', p.105. {{ISBN|0-521-31446-1}}.</ref> {{Audio|Thirteenth chord Pelléas et Mélisande motif.mid|Play}}]]

[[File:Music in Twelve Parts transitional thirteenth chord.png|thumb|center|400px|A non-functional example: transitional thirteenth chord from ''[[Music in Twelve Parts]]'' by [[Philip Glass]]<ref>Potter, Keith (2002). ''Four musical minimalists'', p.319. {{ISBN|0-521-01501-4}}.</ref> {{Audio|Music in Twelve Parts transitional thirteenth chord.mid|Play}}]]

==See also==
*[[Jazz chord]]
*[[Harmonic planing]]
*[[Ladder of thirds]]
*[[Mystic chord]]

==References==
{{reflist}}
==Bibliography==
{{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}}

[[Category:Chord factors]]
[[Category:Extended chords]]
[[Category:Sixths (music)]]
[[Category:Compound intervals]]