Music Theory II

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Music Theory II

• New York University

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Agenda

• The Six-Four Chord
• The Pre-Dominant Function

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The Six-Four Chord Reconsidered

• Although both first and second inversion triads
  are created through bass arpeggiation, second
  inversion triads are not used as substitutes for
  the root position. This is due to the fact that
  the second inversion triad is considered to be a
  much less stable sonority than either the first
  inversion or root position.
• Why?

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Six-Four (contd)

• For centuries, the P4 was considered to be
  dissonant if the lowest voice in the texture was
  sounding the bottom pitch of the P4 (see rules of
  counterpoint)

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Six-Four (contd)

• Because the composers of the tonal era recognized
  the instability of the six-four chord (the only
  position in which there is a 4th above the bass),
  the chord is not used as a substitute for the
  more stable root position or 1st inversion
  sonorities.
• It is used in bass arpeggiations

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BASS ARPEGGIATION AND THE MELODIC BASS

• May come about through a bass arpeggiation
  involving a root position triad, a first
  inversion triad, or both (see example 9.2)
• Analysis of the real bass note will be
  dependent on the context.
• Another incidental way in which six-four chords
  can be formed is through a melodic bass. If the
  bass part has an important melodic line, any
  number of inverted chords may result. (see
  example 9.3)

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Ex. 9.3 - Beethoven, String Quartet Op. 59, No.
1, I
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THE CADENTIAL SIX-FOUR

• Besides Bass Arpeggiation, the six-four tends to
  be used in three stereotyped contexts. Compare
  the two halves of Ex. 9.4 and see that they have
  much in common. Both begin on a tonic triad and
  end with a V-I progression. However, in example
  9-4(b), the movement from ii6 to V is delayed by
  a tonic six-four in a metrically stronger
  position. This is a very typical illustration of
  a cadential six-four, the most familiar of all
  six-four uses. Notice that the tonic six-four
  resolves to a root position V chord.

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THE CADENTIAL SIX-FOUR (contd)

• There are contrary views as to how to analyze the
  cadential six-four
• a) a harmonic progression (tonic six-four to
  V), or
• b) a V, treating (1) and (3) as non-chord
  tones.
• Although all the notes of the tonic triad are
  present, the function of the cadential six-four
  is purely decorative. It does not substitute for
  the root position tonic.
• The symbols used in Ex. 9.4 and elsewhere are a
  compromise and reflect the validity of both
  schools of thought.

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THE CADENTIAL SIX-FOUR (contd)

• Voice leading into and away from the cadential
  six-four is usually smooth (see example 9-4) and
  the resolution of the tonic six-four to V usually
  sees scale degrees (1) and (3) moving down to (7)
  and (2) respectively.

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THE CADENTIAL SIX-FOUR (contd)

• The cadential tonic six-four occurs either on a
  stronger beat than the V (ex. 9-4), or on a
  stronger portion of the beat (ex. 9-5).
  Exception In triple meter, if the V chord occurs
  on the third beat of the measure, the tonic
  six-four will frequently appear on the normally
  weaker 2nd beat (ex. 9-6)
• Used for dramatic effect at the cadenza of many
  solo concertos (ex. 9-7)

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Example 9.7
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THE CADENTIAL SIX-FOUR (contd)

• Note the similarity in function between the
  cadential tonic six-four, and the special use of
  the III6 in minor (see ex. 9-8)
• Compare the progressions in 9.8.
• It is clear that the same principle - the
  momentary delay of the dominant - is operating in
  each case.
• The cadential III6 is clearly a linear event and
  is not part of III - V progression.

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THE PASSING SIX-FOUR

• Frequently encountered harmonizing the middle
  note of a three note scalar figure in the bass.
  (this usage is called a passing six-four).
  Although any triad may be used as a passing
  six-four chord, those in Example 9-9 are the most
  common and are found in both major and minor.

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THE PASSING SIX-FOUR (contd)

• As with the cadential six-four, some theorists
  prefer not to assign a roman numeral to passing
  six-fours because of their weak harmonic
  function.
• Ex. 9-10 contains both a passing tonic six-four
  (m. 25) and a cadential tonic six-four (m.27) in
  a three-part texture.

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THE PASSING SIX-FOUR (contd)

• Longer stepwise motion in the bass often use
  passing six-four chords, as in example 9-11. The
  textural reduction shows that the melody is
  essentially stepwise and moves for several
  measures in parallel motion with the bass (p.151)

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Ex. 9.11 (textural reduction)
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THE PEDAL SIX-FOUR

• A way of elaborating a static root position triad
  by moving the 3rd and 5th of the triad up by step
  then back down by step to their original
  positions. The resulting sonority is a six-four
  chord. (ex. 9-12). Because this elaboration is
  similar to a pedal point (chapter 12), it is
  called a pedal six-four. The roman numeral
  beneath a pedal six-four is put in parentheses to
  indicate its weak harmonic function.

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THE PEDAL SIX-FOUR

• The bass may move after the six-four chord and
  before the return of the root position triad as
  in Ex. 9-13.

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THE PEDAL SIX-FOUR

• See Ex. 9-14 for an example of the pedal six-four
  in a popular musical context.

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PART WRITING FOR SECOND INVERSION TRIADS

• In a four-part texture, the bass (5th of the
  chord) should be doubled.
• The other voices generally move as smoothly as
  possibleoften by stepboth into and out of the
  six-four chord.
• In a three-part texture, it is generally best to
  have all members of the triad present (ex.
  9-15a), but sometimes the root or 3rd is omitted,
  in which case the 5th is doubled (Exx. 9-15b and
  9-15c).

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Six-Four Summary

• SIX-FOUR CHORDS MAY COME ABOUT
• Incidentally through bass arpeggiations, or
• They may occur if the melody is in the bass.
• In other contexts, they are treated carefully
  because in tonal music, the six-four is
  considered dissonant.
• CADENTIAL SIX-FOUR
• A tonic (second inversion) triad that delays the
  arrival of the dominant. It is dependent on V and
  should not be thought of as a substitute for a
  tonic triad in root position.

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Six-Four Summary (contd)

• Passing six-four
• Harmonizes the middle note of a three note scalar
  figure in the bass. Most common forms
  V(six-four) and I (six-four)
• Pedal six-four
• Elaborates the root position chord that precedes
  it and usually follows it as well. Usually I
  (six-four) or IV (six-four).
• Voice leading into and out of the six-four chord
  is usually as smooth as possible.

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Ch. 13 The Pre-Dominant Function and the Phrase
Model

• Up to now, our studies have focused primarily on
  the tonic and dominant functions.
• At this point, we shall add a 3rd harmonic
  function that adds a new dimension to the
  relationship between tension and resolution that
  characterizes the musical language.
• In 13.1, listen for chords or chord successions
  we have not seen before

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The Pre-Dominant Function

• Each of these examples contain a chord that falls
  between the tonic and dominant not yet
  encountered.
• These chords are distinct from the contrapuntal
  chords we studies in chapter 2 and do not serve
  to expand the tonic or dominant.
• They are independent sonorities that provide a
  connective link between tonic and dominant.
• We shall refer to them as pre-dominants.
• The most important are IV and ii.
• First level of analysis Roman numeral fig.
  bass.
• Second level of analysis PD

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The Subdominant (IV)

• A frequent choice since I-IV proceeds by
  descending 5th.
• Also, the ascent from 4 to 5 in the bass makes
  for a smooth motion to the dominant. As the bass
  ascends by step, the upper voices usually descend
  by step.
• In Ex. 13.2, IV is used in major and minor. In
  13.2A, the 4 in the soprano prepares the 7th of
  the upcoming dominant

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The Subdominant (IV) contd

• In 13.2B, the dissonant 6th of the cadential
  six-four becomes a passing tone between 4 and 2.

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The Subdominant (IV) contd

• When we first used the V7, we could harmonize
  stepwise descents and ascents in the soprano
  from 5 to 1 or 1 to 5 using either IV6 or V43 to
  harmonize 4.
• Now using pre-dominants, we can write a stepwise
  line in the bass that ascends from 1 to 5.
• First, expand the tonic with scale degrees 1 to 3
  in the bass then, use the pre-dominant to link 3
  with 5.

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The Subdominant (IV) contd

• IV often approaches the dominant from above by
  melodically descending from its 1st inversion
  (IV6-V).
• This occurs much more frequently in minor than
  major as a result of the powerful half-step
  motion between b6 and 5.

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The Subdominant (IV) contd

• The sound of the b6 to 5 is striking enough to
  stop harmonic motion on the dominant creating a
  Phrygian cadence (PHRY).
• In 13.4B and C, note the b6-5 motion in the bass
  and listen to the upper melodic voice which often
  approaches 5 in contrary motion

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The Supertonic (ii)

• The supertonic (ii in major and iiº in minor) is
  a striking sonority. It is the most common
  pre-dominant because it leads to the dominant
  just as the dominant leads to the tonic, by
  descending 5th motion, the strongest motion in
  tonal music. There are at least 2 reasons why
  composers favor the supertonic as an effective
  pre-dominant
• It provides modal contrast
• It is often set to 2-7-1 in the soprano, versus
  the less dynamic 1-7-1 which is common when the
  IV functions as a pre-dominant.
• In 13.5, note the double-neighbor melodic motion
  that encircles the upcoming 1

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The Supertonic (ii) contd

• While root position IV occurs freely in major and
  minor, root position ii usually occurs in major.
  This is due to the fact that iiº in minor is a
  dissonant diminished triad, and any root position
  diminished triad has an unsettling effect given
  its exposed tritone between the bass and an upper
  voice. This effect is softened by the use of the
  first inversion (iiº6). See 13.6A B

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The Supertonic (ii) contd

• Following the model of iiº6 composers often use
  ii6 in major as well. The 1st inversion
  supertonic embodies the best attributes of ii and
  IV. From ii we get the color contrast of a minor
  predominant in major, and from IV we get the
  smooth voice leading of 4-5.
• Composers often precede IV or ii with a I6, and
  especially powerful effect in the major mode. In
  13.7, Chopin writes a stepwise 5th ascent in the
  bass from 1 to 5 by first expanding the tonic
  with a passing V4-3 that leads to I6 and then the
  pre-dominant IV that leads to V7

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Assignment

• Analysis 13.2A, B C