Mark

Your understanding of theory is excellant and you should make no apologies.

I take issue with very little of what you say in the context in which you say it. A 7 above any chord does refer to a minor seventh.

A 7 above the dominant (or V) chord is referred to as a dominant seventh because it is the dominant chord in the key in which you are playing. The sound of the chord is relatively the same as adding a minor seventh over the tonic or the subdominant chord (I or IV).

By adding the 7 above a chord which is not dominant you are modulating temporarily. For example if you are in the key of C and you play the following chord progression:

C D7 G7 C

The D7 is not the dominant 7th. In theory notation it be II7 over V or the dominant of the dominant. It's like being inside a nested if in programming. These are distinctions that are important to the writer and reader of music, not especially the player. It is more important for a player to feel his way through a score than to think his way through.

That is the reason any inversion of a diminished seventh chord suffices as long as it has the root in it somewhere when you are playing. However, to a writer or reader it is very important how a chord is spelled.

If you are in the key of A, the leading tone (VII) is G#. It would not be correct to have a diminished seventh chord with an Ab in it because Ab does not "lead" to A.

There is no difference in pitch between Ab and G# but they are not interchangeable in the key of A just as cord and chord are not interchangeable in a sentence.

But also remember that when we "spell' chords, they must be spelled with the key in mind. In C Major, the fully diminished chord is only accomplished by a flatted A. Without the Ab you have a "half diminished" chord.

In c minor, the fully diminished chord occurs "naturally" because the A is flatted in the key signature.

I hope I haven't confused you or bored you. I also know that you are not disparaging pedants by your comments.

I have heard the statement, "I took some music lessons until it started to affect my playing" more than a few times and it rankles me every time I hear it. Everything has its importance including music theory for composers.