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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special uses of diminished sevenths

Basic Concepts:

1.  Fully diminished seventh chords consist of three minor thirds stacked, as shown below.  There are only three of these chords, if one dismisses the spelling: the vii°7 chord built on C#, the one built on D, and the one built on D sharp.  The one built on E has the same pitches as the one built on C sharp. Identifying an inversion of a fully diminished seventh chord by ear, out of the context of its key, is impossible, since any of the sounding pitches can function as its root.

2.  Because of this special property of the vii°7, it serves as a great chord for modulating.  For example, in the key of C minor, the vii°7 chord (B-D-F-A flat) can tonicize C, E flat, G flat, or A.

3.  Another special property of the diminished seventh chord is its ability to prolong the tonic or dominant triads in a major key. In the example below, the G major chord is followed by a diminished seventh chord that includes two lower neighbors to G major chord tones, A sharp and C sharp.  When the G major chord returns, its presence seems an apt resolution, even though it is not the ordinary resolution of a diminished seventh chord.  Here, there is no leading tone function to the root of the G chord, there is only the neighboring figure of the A sharp and C sharp.

Some theorists call these types of chords #ii°7 or #vi°7 chords.  The reason for this is that, spelled correctly, the the root and third of the chord serve as neighbors to the prolonged chord, and the root of the prolonged chord is included in the diminished chord.  Consider the example above.  If this figure happened in the key of G major, the chord would be considered a #ii°7, and the tonic triad would be prolonged.  If it were in C major, the chord would be considered a #vi°7, and the dominant triad would be prolonged.  The root of this chord, when stacked in thirds, is A sharp.  

It is important to understand that in common practice, diminished sevenths chords are often not spelled according to their function in harmony.  Often the spelling relates more to voice leading.  So be careful when analyzing diminished seventh chords; the spelling will not always suggest the operating inversion.  When the root is misspelled, just label the chord vii°7; trying to characterize the inversion may cause confusion.   

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