Music Theory - Arban's Diminished Seventh

[JayKosta]

I'd like to understand the music theory associated with Arban's Chord of the Diminished Seventh exercises.

SPECIFICALLY - in the top line of exercise #55 (no sharps or flats), the first and last measures appear to be standard A minor chords, and the 'inner measures' all appear to be variations on some sort of Bdim7 chords (the written G# is the dim7 interval from B, right?).
Starting from B, A# is a maj7, A is a min7, and G#(Ab) is a maj6/dim7).

So, what is the 'theory purpose' of the first and last measures being A minor chords? Other than to illustrate what minor chord is associated with the key signature.

And in the following lines of #55, what is the chord progression pattern going from the first measure to the second measure?

Yes, I can understand the 'playing technique skills' of these #55 exercises, it's just the 'theory' that has me confused.

Jay
_________________
Most Important Note ? - the next one !
KNOW (see) what the next note is BEFORE you have to play it.
PLAY the next note 'on time' and 'in rhythm'.
Oh ya, watch the conductor - they set what is 'on time'.

[mm55]

It puts the dim7 chord in a tonal context.

The diminished chord built on the major 7th scale degree, and its enharmonic equivalent built on the major 2nd scale degree, are commonly used in minor keys, but it's uncommon for a dim7 chord to be used as a tonal center, and was even more uncommon as a tonal center in Arban's time

Rather than simply arpeggiating the dim7 chord, this exercise frames it in a tonal context, allowing the student to hear how the chord might sound in a real performance composition, relative to a tonal center. This is how I interpret it, although I don't know Arban's thoughts on the matter
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[JayKosta]

[Turkle]

To back up what mm55 said...

Diminished chords are symmetrical (all minor thirds) so they don't have a key center. A Bo7 chord could conceivably resolve to A minor, C minor, Eb minor, or Gb minor. Arban likely just picked one so you don't sound like you're floating freely with no key center or resolution of the tension (diminished chords have two tritones so they demand to be resolved).

The theoretical reason for this is that the 7th chord that resolves to the minor chord is very commonly a 7b9. So you go E7b9 to A-. If you start a diminished 7th chord starting on the third of the E7b9, you get G#, B, D, F natural! That F natural is the b9, and it comfortably resolves to the E in the A- chord.

For this reason, diminished chords are often found in minor contexts.

Hope the above is helpful...
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[JayKosta]

mm55 and Turkle ,
Thanks for your very helpful (and understandable) explanations!

Jay
_________________
Most Important Note ? - the next one !
KNOW (see) what the next note is BEFORE you have to play it.
PLAY the next note 'on time' and 'in rhythm'.
Oh ya, watch the conductor - they set what is 'on time'.

[khedger]

[JayKosta]

Thanks for all the help about this.
It seems there is quite a bit of music theory involved with many of the simple looking exercises.
I never got to the stage of understanding the theory, or even the significance of the key signature progression of the exercises. My teachers never mentioned it, and there isn't much printed explanation in the method book that I've seen.

Jay
_________________
Most Important Note ? - the next one !
KNOW (see) what the next note is BEFORE you have to play it.
PLAY the next note 'on time' and 'in rhythm'.
Oh ya, watch the conductor - they set what is 'on time'.