Compound interval of a major thirteenth from F to D in the next octave up
Minor thirteenth: F to Db

In music or music theory, a thirteenth is the interval between the sixth and first scale degrees when the sixth is transposed up an octave, creating a compound sixth, or thirteenth. The thirteenth (an octave plus a sixth) is most commonly major About this sound Play or minor About this sound Play .

Dominant thirteenth extended chord: C E G B D F A About this sound play . The upper structure or extensions, i.e. notes beyond the seventh, in red.

A thirteenth chord is the stacking of six thirds, the last being above the 11th of an eleventh chord.[1] 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."[2] Since 13th chords tend to become unclear or confused with other chords when inverted they are generally found in root position.[3] For example, depending on voicing, a major triad with an added major sixth is usually called a sixth chord About this sound 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."[4] 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."[5]


Dominant thirteenth

Dominant thirteenth chord in four-part writing[3] About this sound Play .

Most commonly 13th chords serve a dominant function (V13),[6] 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.[3] Since thirteenth chords contain more than four notes, in four-voice writing the root, third, seventh, and thirteenth are most often included,[3] excluding the fifth, ninth, and eleventh About this sound 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.

Dominant thirteenth chord in Claude Debussy's Prelude to the Afternoon of a Faun. (1894)[7] About this sound Play

In modern pop/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♭ 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, a major seventh.

Voice leading for dominant thirteenth chords in the common practice period.[8] About this sound Play

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".[8] 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.[8]

Other thirteenth chords

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

Alternating ()13 and 13 chords in the "railroad sonority" from mm.1-4 of All Points West (1937) by Rodgers & Hart.[9] About this sound Play

13th chords may less often be built on degrees other than the dominant, such as the tonic or subdominant.[6]

Lennie Tristano's ending to "I Found a New Baby" (recorded 1946) is a "tonic thirteenth chord"[10] in lydian. About this sound Play

While the dominant thirteenth is the most common thirteenth chord, the major thirteenth is also fairly common.[11] A major thirteenth chord (containing a major seventh) will nearly always feature a chromatically raised eleventh (C E G B D F 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,"[11] in these chords by a semitone.

The cadence in measures 5-8 of "Noreen's Nocture" 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.[8] About this sound Play


CM13, first inversion = e13(9), 2nd inversion = G13... (About this sound Play ). Eventually seven chords along a ladder of thirds.

Generally found in root position,[3] the inversion of a complete thirteenth chord including all seven notes, itself, "a rare phenomenon",[4] is a theoretic impossible since a new thirteenth chord with a different root along the is produced, for example C major 13 (C-E-G-B-D-F-A) becomes e13 (E-G-B-D-F-A-C) then G13 (G-B-D-F-A-C-E), and so on, when inverted.[12]


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:

Debussy's 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 inverted to a "warm" close-position fourth.[21] About this sound Play
A non-functional example: transitional thirteenth chord from Music in Twelve Parts by Philip Glass[22] About this sound Play

See also


  1. ^ Benward & Saker (2009), p.360.
  2. ^ Capone, Phil (2006). Guitar Chord Bible: Over 500 Illustrated Chords for Rock, Blues, Soul, Country, Jazz, and Classical, p.48. ISBN 0785820833.
  3. ^ a b c d e Benward & Saker (2009). Music in Theory and Practice: Volume II, p.179. Eighth Edition. ISBN 978-0-07-310188-0.
  4. ^ a b Walter Piston (Jul., 1952). Untitled review of Harmonic practice by Roger Sessions, p.463, The Musical Quarterly, Vol. 38, No. 3, pp. 457-468.
  5. ^ Capone (2006), p.66.
  6. ^ a b Benward & Saker (2009), p.180.
  7. ^ a b Cope, David (2000). New Directions in Music, p.6. ISBN 1577661087.
  8. ^ a b c d Benward & Saker (2009), p.183-84.
  9. ^ Cox, Felix (Autumn, 2005). "'A Faltering Step in a Basically Right Direction': Richard Rodgers and All Points West", p.360, American Music, Vol. 23, No. 3, pp. 355-376.
  10. ^ Walter Everett (Autumn, 2004). "A Royal Scam: The Abstruse and Ironic Bop-Rock Harmony of Steely Dan", p.205, Music Theory Spectrum, Vol. 26, No. 2, pp. 201-235.
  11. ^ a b Hal Leonard Corp. (2003). Picture Chord Encyclopedia: Photos, Diagrams and Music Notation for Over 1,600 Keyboard Chords, p.10. ISBN 0634058282.
  12. ^ Cooper, Paul (1975). Perspectives in Music Theory, p.228. ISBN 0-396-06752-2.
  13. ^ a b Kostka & Payne (1995). Tonal Harmony, p.493. Third Edition. ISBN 0-07-300056-6.
  14. ^ a b c d e f g h i j Benward & Saker (2009), p.185.
  15. ^ Benjamin, et al. (2008). Techniques and Materials of Music, p.191. ISBN 0-495-50054-2.
  16. ^ Manus, M. (1978). Piano Chord Dictionary, p.21. ISBN 0882841548.
  17. ^ Capone (2006), p.84-85.
  18. ^ Hal Leonard Corp. (2004). Guitar Chords Deluxe: Full-Color Photos and Diagrams for Over 1,600 Chords, p.12. ISBN 0634073893.
  19. ^ Capone (2006), p.79.
  20. ^ Cooper (1975), p.227-28.
  21. ^ Nichols, Roger (1989). Claude Debussy: Pelléas et Mélisande, p.105. ISBN 0521314461.
  22. ^ Potter, Keith (2002). Four musical minimalists, p.319. ISBN 0521015014.

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  • Thirteenth — Thir teenth (th[ e]r t[=e]nth ), a. [From {Thirteen}: cf. AS. [thorn]re[ o]te[ o][eth]a.] 1. Next in order after the twelfth; the third after the tenth; the ordinal of thirteen; as, the thirteenth day of the month. [1913 Webster] 2. Constituting… …   The Collaborative International Dictionary of English

  • thirteenth — [thʉr′tēnth′] adj. [ME thirtenth: see THIRTEEN & TH2] 1. preceded by twelve others in a series; 13th 2. designating any of the thirteen equal parts of something n. 1. the one following the twelfth 2. any of …   English World dictionary

  • Thirteenth — Thir teenth , n. 1. The quotient of a unit divided by thirteen; one of thirteen equal parts into which anything is divided. [1913 Webster] 2. The next in order after the twelfth. [1913 Webster] 3. (Mus.) The interval comprising an octave and a… …   The Collaborative International Dictionary of English

  • thirteenth — /therr teenth /, adj. 1. next after the twelfth; being the ordinal number for 13. 2. being one of 13 equal parts. n. 3. a thirteenth part, esp. of one (1/13). 4. the thirteenth member of a series. [bef. 900; THIRTEEN + TH2; r. ME thrittenthe (see …   Universalium

  • thirteenth — /θɜˈtinθ/ (say ther teenth) adjective 1. next after the twelfth. 2. being one of thirteen equal parts. –noun 3. a thirteenth part, especially of one (¹⁄₁₃). 4. the thirteenth member of a series. {thirteen + th2} …   Australian-English dictionary

  • thirteenth — 1. adjective /ˌθɜːˈtiːnθ,ˌθɝˈtiːnθ/ The ordinal form of the number thirteen. 2. noun /ˌθɜːˈtiːnθ,ˌθɝˈtiːnθ/ a) The person or thing in the thirteenth position. b) One of thirteen equal parts of a whole …   Wiktionary

  • thirteenth — thir|teenth [ ,θɜr tinθ ] number 1. ) in the place or position counted as number 13: the thirteenth century 2. ) one of 13 equal parts of something …   Usage of the words and phrases in modern English

  • thirteenth — [[t]θɜ͟ː(r)ti͟ːnθ[/t]] ♦♦ ORD The thirteenth item in a series is the one that you count as number thirteen …   English dictionary

  • thirteenth — UK [ˌθɜː(r)ˈtiːnθ] / US [ˌθɜrˈtɪnθ] number 1) in the place or position counted as number 13 the thirteenth century 2) one of 13 equal parts of something …   English dictionary

  • thirteenth — thirteen ► CARDINAL NUMBER ▪ one more than twelve; 13. (Roman numeral: xiii or XIII.) DERIVATIVES thirteenth ordinal number. ORIGIN Old English …   English terms dictionary

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