MUS 212 Study Guide J (Chapter 10)

Chords of the 9th, 11th &13th

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  1. 9th chord:  Superposition of four 3rds--one 3rd above the 7th of a 7th chord.  Ex.: G B D F A = V9 in C major.
  1. 11th chord:  Superposition of five 3rds--one above the 9th of a 9th chord.  Ex.: G B D F A C = V11 in C major.
  1. 13th chord:  Superposition of six 3rds--one 3rd above the 11th of an 11th chord.  Ex.: G B D F A C E = V13 in C major.

Chords of the Ninth

  1. Ninth chords of dominant and secondary dominant function are those most frequently used, e.g.:  V9 and V9/V, etc.
  1. In major keys, the 9th may be lowered a half step:  Vb9 , Vb9/V, etc.
  1. In minor keys, the 9th is already b9 in some cases due to the key signature.  Ex.: In F minor (4 flats) V9 = C, E, G, Bb, Db (E natural due to leading tone).
  • One does not need to indicate "b"9 in such instances, as it will be assumed from the key signature.  (See No. 23.)
  1. The ninth chords ii9, iv9 and IV9 are occasionally seen, while others are quite uncommon, except in sequences.
  1. The 9th of the chord is most often found in the soprano voice.
  1. The 9th is found at the interval of at least a 9th (rather than a 2nd) above the root of the chord.
  1. When the 9th is not the highest note, the 3rd of the chord is almost invariably lower than the 9th.
  1. Examples of the chord with a note other than the root in the bass are uncommon, i.e., inversions are uncommon.

Ninth Chords in which the Ninth Resolves Before a Change of Root

  1. Often a chord contains the 7th and 9th with only the 9th resolving above the root.  The early resolution of the 9th can usually be considered simply a nonharmonic tone in the 7th chord.

Ninth Chords in which the 9th Resolves Simultaneously with the Chord Change

  1. Analysis of a sonority as a 9th chord is more secure when the 9th resolves together with a change of harmony.
  1. In minor keys, whether the chord is iv9 or IV9 is determined by the direction of the 6th scale step.  (The 6th scale step is the 3rd of the chord.  Melodic minor: #68, b69.)

Ninth Chords in which the 9th and 7th Are Arpeggiated

  1. The 9th may be resolved by leap to the 7th, or via a passing tone to the 7th.

Irregular Resolution of the Ninth

  1. Assuming the usual resolution of the 9th to be down by step, resolutions are occasionally found in which the 9th proceeds in some other way.

Ninth Chords in Sequence

  1. When found in sequence, 9th chords and7th chords are usually found alternately.
  • Use of sequence allows the presence of ninth chords not ordinarily encountered, such as the Vb9/ii and the Vb9/iii.

Eleventh and Thirteenth Chords

  1. It is common for these extended tertian structures to appear with tones omitted.  Following are the most common factors present in four-part writing:
Chord: Factors Present: Voice Leading Guidelines:
V9 R, 3, 7, 9 9th & 7th resolve down to 5th & 3rd of tonic triad.  
V11 R, 7, 9, 11 11th cannot resolve in V11-tonic because resolution is not present.  Retain the 11th as a common tone to both chords.
V13 R, 3, 7, 13 13th is most often in soprano; usually resolves down a 3rd to the tonic factor of I or i.
  1. In any chord that includes an 11th above the bass, the 3rd will be omitted, since the resolution of the 11th is to the third of the chord.
  1. In the 11th chord, the interval between the 9th and 11th may be either a 3rd or 10th.
  • When the interval is a 3rd, both the 11th and 9th resolve down by step to a 7th chord.
  • When the interval is a 10th, the 11th alone may resolve down by step, leaving a 9th chord.  See p. 301 for illustration.
  1. When the 7th, 9th, 11th & 13th all sound simultaneously: the 11th drops to the 10th, and the 9th drops out, leaving the simple V7 plus 13th.  See p. 301.


  1. Function Preference: Dominant (V) function is most often found--V9, V11, V13, although the chords may occur as other functions.
  1. Mode:  All three chords are found in both major and minor keys.
  • The 11th factor (4th scale degree) is not affected by the mode.
  • The 9th and 13th factors are affected by the mode.
    In major keys, these factors are major.
    In minor keys, these factors are minor.
  • The 9th and 13th factors of secondary dominant chords are also affected by the key signature.
  1. Position:  The above chords are usually found in root position, as they tend to lose their identity when inverted.
  1. Secondary Dominants: 9th, 11th & 13th chords may also be use as secondary dominants.  Ex.: V9/V, V11/V, V13/V, V9/ii, V11/ii, etc.
  1. Progression:  The addition of a 9th, 11th or 13th to 7th chords does not change their function.  E.g., V13 chords still tend to resolve to I or i; ii9 chords normally progress to V, etc.
  1. So that every little steenking passing tone eighth-note is not incorrectly analyzed as part of a 9th, 11th or 13th chord, the following guidelines may be helpful.  In order to qualify as a 9th, 11th or 13th chord, a particular vertical configuration must:
  • Contain a 9th, 11th or 13th factor that is at least the rhythmic value of the other chord factors.
  • Contain at least two dissonant factors:  that is, a 9th chord must also contain a 7th; an 11th chord must also contain either a 9th or a 7th; a 13th chord must also contain either a 7th, 9th or 11th.
  • Either not allow the dissonant factor to resolve until the entire chord changes, or occasionally (if the 9th, 11th or 13th chord is held longer than the surrounding chords) the highest factor may resolve before the chord changes.

The above limitations must be tempered by local circumstances surrounding such chords.

  1. Remember:  "9" indicates a note diatonic to the key, while "b9" indicates that the diatonic note is to be lowered one half-step.  Thus, "9" may indicate a M9 or m9 above the root, depending upon the key signature.
  • For example, in the key of C major, a iii9 chord (E, G, B, D, F) would actually be a "b9" chord because of the key signature.  The "b9" designation is not necessary in traditional music theory analysis.  With popular music chord symbols, however, the "b9" designation would be necessary, e.g.: Emi7(b9).  The popular chord symbol "Emi9" would indicate the chord:  E, G, B, D, F#.

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