The Vertical Dimension

1
The Vertical Dimension

• Chords and Simultaneities

2
Harmony

• With the exception of a few voice-leading chords,
  harmony from the Common Practice period consists
  of thirds.
• This was a result of the classifications of
  consonance and dissonance and the development of
  voice-leading procedures over the centuries.
• The music of the twentieth century also uses
  tertian harmonies, but there is a lot of music
  using chords built with 2nds, 4ths, 5ths, etc.
• Some chords are the result of somewhat accidental
  combinations of independent lines.

3
Conventional Tertian Sonorities

• Some composers make more use of triads and
  seventh chords than others.
• 9th, 11th, and 13th chords are beginning to be
  used by the end of the nineteenth and start of
  the twentieth centuries.
• These extensions are most commonly applied to
  dominant and secondary dominant chords, and
  sometimes to the supertonic and submediant
  chords.
• Chromatic alteration, especially to dominant
  functioning chords is common.
• Often the sonorities are incomplete.
• These chords can be inverted, however these
  inversions can be ambiguous.

4
Chords of Addition

• Chords with added notes became accepted in the
  twentieth century.
• 2nds, 6ths, and sometimes 4ths.
• The musical context is what decides the analysis
  of the chord -- an added sixth could be an
  inverted seventh chord.
• 2nds and 4ths are considered the same as 9ths and
  11ths -- it all depends on where the added note
  is in relation to the root.

5
Split Chord Members

• Split chord members are a special kind of added
  note.
• They have an added note that is a minor second
  away from another chord member.
• Commonly a triad or seventh chord with a split
  third.
• Split roots, fifths, and sevenths do occur.

6
Chord of Omission

• The open-fifth chord is the only important chord
  of omission.
• Leaving out any other chord member only results
  in another traditional harmony.
• The sound of this sonority quickly becomes
  tiresome, therefore extended passages using the
  open-fifth chord are rare.

7
Quartal and Quintal Chords

• Quartal and Quintal chords can have as few as
  three pitches to many more.
• The voicings, octave duplications, and
  orchestration determine the chord.
• 3 x 4 on E means a quartal chord with 3 members
  built on E. 7 x 5 on D means a quintal chord
  with 7 members built on D.
• The use of augmented fifths and diminished
  fourths can be confusing because they sound like
  thirds and sixths.

8
Other Chords

• Secundal chords can be voiced as sevenths, but
  the notes are most commonly voiced adjacent to
  each other.
• Often referred to as a tone cluster.
• Mixed-interval chords combine two or more
  interval types.
• Since they can often be arranged in various
  manners -- as quintal, quartal, or tertian chords
  -- the chord should be analyzed within the
  context of the music.
• Polychords are formed by combining two or more
  chords into a sonority.
• They must be heard as two chords played
  simultaneously -- separated by register or timbre
  -- or they are probably 11th or 13th chords.