Monthly Archives: August 2010

If you play a bass instrument, you are more aware of the bass in music than someone who does not play the bass. More often than not, the bass is the second most important part of a musical texture, second only to the melody. Some would even argue that the bass is the most important part because it outlines the harmonic framework. In either case, a good bass line goes a long way in making a passage of music more interesting. Here’s a demonstration:

Chord Inversions

The first passage below is taken from a Beethoven piano sonata; the rhythm of the bass has been simplified for clarity. Also different from the original is that every chord is in root position, meaning the bass plays only the roots of the chords:

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Now listen to the excerpt again, this time as Beethoven harmonized it: using chord inversions:

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Do you notice how much more melodic and elegant the bass is in the second example? Instead of leaping from one chord root to another, it moves primarily by step through the use of chord inversions.

In the original, Beethoven uses broken octaves to provide rhythmic movement to the music. Here’s how Beethoven actually wrote the passage:

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I-V⁶-I Chord Progression

Just as secondary triads can substitute for primary triads, so can chord inversions. The I-V6-I progression is the I-V-I progression with the V6 chord acting as a chord substitution for the V chord in root position. In four voices, the doubling of the V6 chord will always adhere to the standard doubling procedures: double the root or fifth, not the third, to avoid a doubled leading tone. Due to the leading tone’s strong tendency to resolve to , it should never be doubled:

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I-I⁶-V-V⁶-I Chord Progression

In this progression, we extend or prolong the I-V-I progression by moving from the root of each chord to its first inversion. The bass of the final V6 chord leaps down a sixth giving the melody a nice balance in musical space. Take note of how the upper voice that has the third of the chord when it is in root position, moves away from the third (to the root or fifth of the chord) when the bass moves to the third, thus  avoiding doubling the third of the first inversion triad.

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Since the bass is moving by thirds, we can smooth out the bass melody by adding passing tones between each chord tone. Passing tones are one of many non-chord tones that most often fill in the space between two chord tones. In this case, the passing tones fill in the space between the root and the third, and the third and the fifth. Here, the bass moves up the entire scale. Remember, in the minor scale, we use the melodic minor form of the scale when ascending:

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You can download the progressions used for this lesson, written out in every major and minor key in pdf format on the Harmonic Progressions Page.

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Download a terrific performance of the Beethoven Piano Sonata No. 15, Op. 28, Second Movement,  used for this lesson:

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In the last music theory lesson we learned about chord substitution and chord classes. Here’s a quick review:

Chord Substitution

There are three primary triads: Tonic (I), Subdominant (IV), and Dominant (V).

You can use the rest of the chords of a key (ii, iii, vi, vii) instead of one of the primary triads:

• vi is a good substitute for I
• ii is a good substitute for IV
• iii and vii° are good substitutes for V, but you have to be careful with those or your progression won’t sound right.

Chord Class Review

• Because vi can be used instead of I, we say both chords (I and vi) belong to the Tonic Chord Class.
• Because ii can be used instead of IV, we say both chords (IV and ii) belong to the Subdominant Chord Class.
• Because iii and vii° can be used instead of V, we say all three chords (V, vii, iii) belong to the Dominant Chord Class.

• Remember that the primary triads and their secondary counterparts are a third apart and have two notes in common.
• We’ll use the abbreviations T, S and D to refer to the chord classes.
• See the previous music theory lesson for progression examples using substitutions.

Making Chord Progressions Longer (Chord Prolongation)

Tonic Prolongation

A good way to make a chord progression longer, and to ensure that it sounds good, is to use both chords from the tonic and subdominant chord class, one after the other. For the best progression always start with the primary triad, then move to the secondary triad. In other words, descending thirds (e.g., I-vi) usually sound better than ascending thirds (e.g., vi-I):

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The chord progression above is the basic I-IV-V-I progression, but the first tonic chord moves to the vi before going to the IV, thus prolonging the tonic chord class. We call this tonic prolongation. This progression is very common in classical and popular music, especially popular music from the 1950s. A classic example is Those Magic Changes from the musical Grease.

Subdominant Prolongation

We can make the I-IV-V-I progression even longer by moving to the ii chord after the IV chord:

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You can download a pdf version of this progression written out in every major and minor key on the Harmonic Progressions page.

Harmonic Rhythm

Of course any chord progression can be made longer by holding the chord for a longer period of time. Harmonic Rhythm refers to how fast the harmony changes. For example, if chords change every quarter note, we say the harmonic rhythm is the quarter note.

As you learn to play and write chord progressions, it is important to be aware of the rhythmic tendencies of certain chords. In reality, it is impossible to separate rhythm and harmony. You may have noticed that the last progression above changes the rhythm of the last two chords (V – I).

• The resolution to the tonic chord at the end of a progression usually sounds best if it ends on a strong beat.

If the V chord of the progression above were a quarter note, the tonic chord would fall on beat two, a weak beat. Again, don’t think of this as a rule, as much as a tendency. If your progression doesn’t sound right, and you’re not sure why, it may be a rhythm problem.

The TSDT Principle

The TSDT principle is a way of understanding harmonic tendencies. This principle, in one form or another, usually is introduced in formal harmony lessons as rules. From one music theory textbook to the next, the terminology and teaching methods vary, but the essential principle is the same:

• Tonic Class Chords (I, vi) are free to move anywhere, that is, they may move to a subdominant class chord or a dominant class chord.

• Subdominant Class Chords (IV, ii)
  • A IV chord is free to move to a dominant class chord, or back to a tonic class chord.
  • A ii chord tends to sound best when it moves to a dominant class chord, but not a tonic class chord.
• Dominant Class Chords (V, vii°, iii) usually sound best when moving to a tonic class chord, not a subdominant class chord.

The following diagram summarizes the TSDT principle:

When we follow the TSDT principle all chord progressions (other than harmonic sequences) will follow one of these three patterns:

1. T-D-T
2. T-S-T (I-IV-I only)
3. T-S-D-T

Retrogressions

We’ve already discussed the dominant chord’s strong tendency to move to the tonic. That’s why we call a V-IV a retrogression. It’s not wrong to have a retrogression. Music is art, not science. You can find retrogressions all over the place, whether it be Bach, Mozart, or the 12-bar blues! But it is important for you, as a music student, to understand harmonic tendencies, as stated in the TSDT principle.

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