Author: mrn
Date: 2008-08-12 00:41
A "diminished" chord is what you get when you stack minor 3rds on top of one another. If you stack two of them, you get a diminished triad. If you stack three (thus yielding 4 notes), you get a "diminshed 7th."
Since there are 12 semitones in the octave, if you keep stacking minor 3rds, you still have a diminshed 7th chord--the extra notes simply double the notes you already have. If you call each note name in the chromatic scale (C, C#, D, D#, etc.) a "pitch class," there are only three distinct set of pitch classes corresponding to diminished 7th chords. Yet there are 12 keys. Consequently, any time a dim7 chord is written down, you can't readily tell what the spelling is. C, Eb, F#, A might be Cdim7, or it might be Adim7 in first inversion, F#dim7 in second inversion, etc. The augmented 5th chord (C E G# in C major) is similarly ambiguous.
Because of this ambiguity, even music theorists don't agree on what the "root" of a dim7 chord is when played in a particular key. Some people say the root is the leading tone of the key. Others--including Walter Piston, who wrote my harmony textbook--analyze the diminished 7th as being an incomplete dominant 9th chord (a dominant 9th without the root).
The upshot of this is that in actual music you will see many different enharmonic spellings of the same set of pitch classes, regardless of key. The concept of key is thus less meaningful when applied to diminished chords. This is especially true of Klose's exercises, which are all written 20th-century style with no indication of key whatsoever.
Incidentally, Klose's scale pattern a few pages back is full of notational inconsistencies. Sometimes an accidental carries through from octave to octave and sometimes it doesn't--I don't know if this is intentional or not. I think what you have to keep in mind is that Klose was a performing clarinettist, not a composer or theorist, and his main concern was getting students to get the fingering patterns down, not theoretical purity. Note that in the instructions, he recommends that the scale pattern be memorized--so the sheet music is only intended to be a temporary crutch.
The trick in the dim7 exercise is learn to recognize the stacked minor 3rd pattern by sight and have it comfortably under your fingers. If you're trying to associate the notes on the page with particular keys, you're probably thinking too hard.
By the way, one thing that might be confusing you is that chords are named for their root notes, and NOT for the key they are in.
C7 (read C dominant 7) is C E G Bb and starts on C. C happens to be the dominant tone in the F major scale, but we don't care about that as far as chord naming goes. If you stack a major 3rd and two minor 3rds together, you get a dominant 7th chord. If the major 3rd starts on C (that is, the "root" is C), it's a C7 chord. If you have E G Bb C (same notes, but different order), it's still a C7 chord, but in first inversion. You can tell it's a C7, because you can figure out how to "un-invert" the chord to find the major 3rd interval there, which still starts on C. Notice that with a diminished 7th you can't do this, because no matter how you invert it, it's always a stack of three minor 3rds.
Post Edited (2008-08-12 14:36)
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