MUS 111 Study Guide I (Chapter 9)

The Triad in Inversion

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  1. Inverting a chord simply means placing a chord member other than the root as the lowest sounding voice.  The exclusive use of root position chords is not common.  Use of inversion has two advantages–one harmonic and the other melodic.

  1. The triad in first inversion:

Harmonic advantage:  A triad and its inversions provide three different sonorities while using the same letter names–four for seventh chords.  Inversions provide an interesting harmonic change.  The easiest way to introduce an inversion is by arpeggiating the bass line.

Melodic advantage:  Without inversions, the lowest voice lacks any sense of being a melodic line.  With inversions, scale steps can be introduced and the bass can truly become melodic.  In a series of first inversions in which the bass moves stepwise, any chord progression may appear, even those that are uncommon.  The use of the progression V-IV is limited, but in a succession of first inversions its use is common.

Inversions can create musical interest by:  (a) arpeggiating a triad, (b) progressing by leap from triad root to inversion, or from inversion to inversion, (c) using a scale line in the bass, where the inversion is found intermittently, or when inversions are in succession, (d) moving the bass line in thirds or sixths with an upper voice.

  1. The triad in second inversion:

In contrast to the liberal use of first inversions, the second inversion is restricted to a limited number of specific devices.  (This is due to the fact that second inversion creates a P4 between the bass and one of the upper voices, which was considered a dissonance in the early days, and requires a specific resolution.  In essence, it is an unstable chord.)

  1. The Cadential Six-Four Chord:  so-named because of its frequency of use at a cadence point, though it appears in other locations.  Harmonic movement culminating in a I 6/4-V-I cadence is so common that the progression is virtually a "trademark" of tonal harmony.  In essence, the I 6/4 chord functions as a V chord with two nonharmonic tones above the "root."  The "root," of course, is the dominant scale degree.  It is still analyzed as a I 6/4 chord.  The chord "resolves" to the V chord at the cadence.  Used in this manner, the 6/4 chord is a decoration of the V chord–with the "6" and "4" of the I 6/4 resolving to "5" and "3" of the V chord.  The bass note is doubled. (See later example.)  [Note:  "6/4" is the easiest way to indicate a second inversion symbol here on the web ...  See actual music example, later, too see how it "really" looks.  ;-)]

  1. The Passing Six-Four Chord:  The bass note (5th factor) of the 6/4 acts as a passing tone.  The passing bass may be found as a tonic 6/4 between the IV and IV6 chords, or as a dominant 6/4 between the I and I6 chords.  The bass note is doubled. (See later example.)

  1. The Arpeggiated Bass Six-Four Chord:  The bass note (5th factor) participates in an arpeggiation of the same chord.  The usage of 6/4 chords occurs occasionally with triads other than the tonic.  The bass note is doubled.  (See later example.)

  1. The Pedal Bass Six-Four Chord:  Also known as static bass or neighboring tone chords, the bass note (5th factor) is preceded and followed by the same tone and is interspersed between two root positions of the same triad.  This type also occurs occasionally with the IV 6/4 as well as the tonic.  The bass note is doubled.  (See later example.)

  1. Note:  The bass note is doubled in all 6-4 types. Also, a general rule is the bass of a 6-4 chord must be prepared either by step or repetition and must resolve by step or repetition.  The exception is the arpeggiated bass.

  1. Writing a Triad in First Inversion:  With major triads the soprano note is usually doubled.  Although, any chord factor which facilitates smooth voice-leading is acceptable.  With minor triads the same guideline applies, however, doubling the third is also common.

  1. Writing to or from a Triad in First Inversion:  It is easiest to first write the two voices that lead to and from the doubled note.  These two voices can move in three different ways in relation to each other:

Contrary motion:  the two voices move in opposite directions.

Oblique motion:  one voice remains stationary while the other moves.

Similar motion:  the two voices move in the same direction.

It is always best to use contrary or oblique motion in approaching and leaving the doubled note.  Similar motion is usually only necessary in cases when one voice must be brought into a better range or to effect a change in position.

  1. The most efficient procedure for part-writing to or from a triad in first inversion is as follows:

Complete the first of the two triads.

Approach or resolve the doubled note by contrary or oblique motion if possible.

Fill in the remaining voice with the note necessary to produce normal doubling.  When the doubled note moves by contrary or oblique motion, the remaining voice usually moves by step or remains stationary, rarely moving by leap.

  1. Writing Successive Triads in First Inversion:  When triads in first inversion are used in succession, it is impossible for each of these triads to be found with the usual doubling in the same pair of voices, since parallel octaves and fifths will result.  To avoid these, use a different doubling for each triad, if necessary.  When selecting doublings, be sure not to double the leading tone or any altered tone.
  1. Writing a Triad in Second Inversion:  The fifth (bass note) is ordinarily doubled.  Approach and resolution:

Cadential:  The bass note is not approached from the same tone or from the leading tone.  As stated earlier, scale degree 6 moves to 5 above the bass, and 4 moves to 3.

Pedal:  Motion above the bass is usually stepwise.

Passing:  The "dissonant" fourth remains stationary.

  1. Other Part-Writing Considerations:

    The Melodic Augmented Fourth:  should be avoided.  Both tones of the interval have strong resolution tendencies–the upper resolving up and the lower resolving down.  In a melodic leap, both resolutions cannot be accommodated, and the undesirable large leap must continue in the same direction.  The problem is easily resolved by using the A4's inversion, the diminished fifth (d5), thus allowing melodic change of direction.

Overlapping Voices:  occurs between two chords when one voice moves above or below the previous pitch of an adjacent voice.  Overlap should be avoided; however, if necessary, do not overlap two adjacent voices more than a whole step.  Correction is sometimes as simple as changing the direction of one voice.  Otherwise, change the triad position at some point before the overlapping pair.

Hidden Octaves and Hidden Fifths:  (also called Direct Octaves and Direct Fifths)  A hidden octave occurs when two voices progress in similar motion to a perfect octave ... ditto for the hidden fifth.  Although not parallel, they often produce the aural effect of parallel movement.  These two motions are a problem only when they occur between the two outside voices (soprano and bass).  They are acceptable under the following two circumstances:  (1) when the soprano moves by step, as in the P.A. cadence, soprano scale steps 2-1 with bass descending, and, (2) when the bass moves by the interval of an octave–considered the same as a repeated tone.  In other circumstances, a hidden fifth or octave between outside voices is not necessarily unusable, but should be a last resort.

  1. Melody Harmonization:  When harmonizing a melody using inversions, you must decide which triads will be in inversion and which will be in root position.  That said, you should write the complete bass line first.  When the bass moves with the soprano, their related movements can be in any one of four directions:

Contrary motion to each other.

Oblique motion–soprano stays on the same tone while the bass moves, or vice versa.

Similar motion to each other.

Stationary motion–both soprano and bass repeat their tones.

Again, contrary and oblique motion are used most often.  Similar motion is effective for intervals of thirds or sixths between soprano and bass, but otherwise should be used with care, avoiding parallel or hidden octaves and fifths.

As a final test of the chosen bass line, play it with the soprano.  The two lines alone should be musically effective, even without the inner voices.

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