Table of Contents

Section 3: 

Set theory
Rhythm/ form 
12- tone 
Polyrhythm
Metric modulation
Meter

Section 4: 

Basic Assumptions 
Motive, Phrase and Period
Cadence
Binary form
Ternary form
Rounded binary form
Sonata form
Rondo form
Theme and variation
Dance forms

Section 5: 

Basic assumptions 
and procedures
Harmony
Form and rhythm
Melody
Timbre

Section 6: Bibliography

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modulation

Basic Concepts:

1.  Modulation means a change of tonic.

2.  Usually, the new tonic will be confirmed with a dominant sonority.

3.  Opinions regarding modulation vary widely. Therefore, this chapter will deal in basic principles, not steadfast rules.

4.  Some modulations use a pivot chord.  The pivot chord, also known as the common chord, is the chord that is diatonic to both the old key and the new key, and it usually sounds before the modulating chord (if there is one).  Do not confuse the pivot chord with the modulating chord.  Remember, this chord is common to both keys.  

5.  The modulating chord is often a secondary dominant.  This chord establishes the new tonic in a variety of ways. (Elaboration on the modulating chord will be a topic in the instructional paper for this chapter.)

6.  Since opinion regarding modulation varies so widely, it is best for the student to decide whether a passage modulates, then offer proof for the opinion.

Conditions for modulation: In tonal music, there is a tonal center, the tonic, that lends roles to the other pitches of the key.  The usual confirmation of this tonic includes phrases or periods ending with a cadence such as V-I.  

Secondary dominants tonicize other notes and sometime effect modulation, but often, the new tonic is merely temporary say, for one beat.  In this case, the original tonic really is not weakened, it is merely adorned. 

Modulation occurs when the tonic is cancelled. Sometimes, the new tonic is not established right away, and there may be a modulatory passage.  Other times, the new tonic may be established right away. In either case, once the first tonic has been cancelled, it is useful to begin tracking the harmony according to the eventual tonic. 

Types of modulation: many types or formulas of modulation have been defined such as the static modulation or the pivot chord modulation, but these labels do not seem useful. Better to let the music tell you how the modulation is effected, and then to describe it appropriately.  This usually will mean showing in the Roman numeral analysis where the modulation occurs and what the harmony did to make it convincing.

Since typical theory courses require you to learn the general types, some common types are defined here.

1.  Phrase modulation/static modulation.  Phrase modulation is a change of tonic (key) at the juncture of two phrases. The first phrase will end in one key, and the next phrase will begin in another. Static modulation is similar to phrase modulation, except that it can change the key anywhere, not just between phrases.  Both types are generally unprepared modulations, and sound surprising.

2.  Pivot Chord Modulation. This is a harmonic construction that usually features the pivot chord, or chord diatonic to both keys, followed by a secondary dominant or other modulating chord, then the new key.

3.  Sequential Modulation.  Sometimes a modulation will take place through a sequence during which several keys may be visited for one or two beats at a time.  In the example below, the overall key changes from C major to G major, but between these two keys, both A and D are tonicized before the arrival at G.

Notice in this example that the harmony was tracked in C throughout the sequence.  This will not always be the case.  Had the first D triad been major, this might have worked better tracking G as tonic beginning with the E7 chord.  With the D minor triad, C still has a lingering presence as tonic.  Were the D triad major, the pull of G as tonic may be strong enough that the analysis would track the sequence in G.  

Notice also, that G is well established as tonic through a typical cadential figure.  This is the hallmark of tonal modulation: the new tonic is set up convincingly.  

Finally, notice in this example how the Roman numerals are handled.  It is common to show the new key on a second level under the system, with the name of the new key clearly marked.  Also, on the next system, if the new key remains in effect, it will be clearly marked there as well.

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