see bach and his http://en.wikipedia.org/wiki/Well_temperament system for why the intervals are the way the are. and you should also try looking at the Circle of 5th's. It'll help you learn the order of the scales, and their key signatures really quickly.

http://www.mariadewi.com/wordpress/w...-of-fifths.jpg

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Can anyone tell me what kind of chords these are? If they even have a 'name' or function.

f - a flat - d flat

b - e flat (or d sharp?) - g sharp (or a flat?)

b- e flat (or d sharp?) - f sharp (or g flat?)

first is Db major

e flat - g sharp - b would be an Eb augmented
Alternatively spelling the chord as b - d sharp - a flat would change it to a B major 7th without the 5th.

e flat - g flat - b = eb augmented
b - d sharp - fsharp = B major

Im afraid that function depends entirely upon the context in which the chords are found.

Eb, G#, B is not augmented. I'm not sure where you're getting that from. Eb augmented would be Eb, G, B (and thus be G augmented and B augmented as well).

Also, B, D#, Ab is not a B major 7 but rather a B diminshed seventh with a major third.

From what it looks like to me, it's just a misspelled Ab minor (or G# minor) chord.
G# B D# - or Ab - Cb - Eb

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B.M. Music Theory (in progress)
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That first chord could also be considered a neapolitan sixth chord which is normally used to substitute the subdominant chord before an authentic cadence of V-I.

thank you for the corrections

Trivia questions!

1) Can you move from a V to a IV chord in traditional music?
2) What can't be doubled in a V first inversion chord?
3) Why is the cadential I 6/4 chord annotated as (I 6/4) (with parenthesis)?

I'll have a go.

1) Yes. Often in deceptive cadences.
2) Any tone can be doubled. What the textbooks say shouldn't be doubled is another matter.
3) The I six-four chord is very often used as a preparation to the V chord in cadences. The parentheses just show the chord is more or less an appogiature into the V.

Here's my questions.

What non-diatonic chords are available through use of the church modes?

In a dimished seventh (or as I prefer incomplete dominiant ninth) chord what reason is there for flattening the seventh (ninth)? e.g the Bb in (A) C#, E, G, Bb.

If you're in the key of Bb and there are the tones E, Gb, Bb and Db it is a (German) augmented sixth chord yet is enharmonically equivalent to an F# dom7 chord (F#, A#, C#, E) or Gb dom7. So is the chord in question better described as an augmented sixth chord or the V of the Neapolitan? And is there any difference other than spelling?

But if we're talking strict voice leading, then the 3rd of the V chord can't be doubled because it is the leading tone of the tonic and you never double the leading tone. Never! And it doesn't matter what inversion the V chord is in.

Yes.

And as for the thing about Deceptive Cadences, that is the only time you can more from V to IV (it would be a IV6) in traditional music.

Flattening the B would make it a fully diminished as opposed to half diminished (which would require a B natural). Is that what you're looking for?

No. I understand that but meant what is the threoretical reasoning behind the creation of the diminished seventh interval. Why is this aspect of chromatic change permissable in tonal harmony?

I understand how it is formed in minor where the dimished seventh is diatonic (in d minor, C#, E, G, Bb are all in the scale with raised seventh tone C# and unraised sixth tone Bb) but in major the Bb is foreign. Is it a case of using tones from the parallel minor temporarily to artificially create the dim7 or is the Bb a kind of reverse leading tone downward into the A (the V root or the I fifth). Then there will be both leading tones into the D upward (C#) and the A downward (Bb).