I was reading older posts in this forum about this and because there are so many complaints about dredging up old threads, I decided to post this as a new topic. I did not see any posts that gave a rational explaination (I may have missed it though) for their use so here's my take.

I think they are mostly used to make it easier to recognize dim or aug triads. By using them it protects the alphabetical sequence of triads. ie: ceg, fac, gbd, etc. And again to make recognition of + or º triads. Make sense?

Every scale, major or minor, must use every letter of the musical alphabet.

Take G# major.
- Start with G#.
- The second is A#.
- Next is B#. You might think "that's a C". But you have to use the next letter after A, so it's B#.
- Now up a half-step to C#.
- Whole step to D#.
- Whole step to E#. Yes, that's the same as F, but we need the letter E after the D#.
- Whole step to Fx (F double-sharp). Yes, that's a G, but we have to use the next letter in sequence ... an F.
- Half step to G#, the tonic.

So we have G#, A#, B#, C#, D#, E#, Fx, and back to G#. All the letters are there, in sequence.

Yes. They have nothing to do with aug and dim chords. I think that in classical music double sharps are used mostly in plain dominant chords, for example chord sequence G#min, D#(7), G#min etc., you need ##f for this scenario.

Ragdoll, I suggest you buy a music theory text book. All of your questions will be answered.

Theory is to music as grammar is to language.

They [x & bb] have nothing to do with aug and dim chords

Maybe so, per se, but augs and diminished chords would likely to be some of the first examples of their use that you'd come across because they are often 'altered' or non-diatonic chords.
(B augmented in the relatively common and 'simple' key of E major, for example - B, D#, Fx)

And Ragdoll is right - you need to use them to keep the correct letter names of the notes so that triads (and other chords) are still recognisable & logical, despite the fact they would appear to complicate rather than simplify when you first come across them.

Yes, that's true. What about 7th chords, for example C-Eb-Gb-A is pretty common, shouldn't it be double-flat B instead of A? Sometimes it's even spelled C-Eb-F#-A.
(I know very little of harmony, maybe I mix apples and oranges)

What if you have something in the key of B# major? Would it go B#, C##, D##, E#, F##, G##, A##, B#? Interesting...

It would do (in theory), but there isn't a key signature with double sharps in it, so C# Major (with 7 sharps) is the limit.

yes, that chord is a diminished 7th and, as such, I suppose the last note - the 'A' - should be called B double flat. Remember that chords are built in thirds or alternate letters, so it's c-e-g-b plus the alterations. B natural gives a major 7th, B flat gives a minor 7th, so Bbb would be a diminished 7th....which is after all, the interval that names this particular chord.

PS; the 'F#' would read 'G flat', of course: C, Eb, Gb, Bbb = C diminished.

As toddy notes, the strict spelling of Cdim7 is C-Eb-Gb-Bbb, and in classical harmony you would expect it to go to Dbm soon. The spelling C-Eb-F#-A can be rearranged into a pile of thirds as F#-A-C-Eb, so C-Eb-F#-A is an orthodox spelling of a dim7 chord, and in classical harmony you would expect it to go to Gm soon. Exceptions abound, sometimes they go to the major chord (Db and G) instead, sometimes other chords intervene, but in analysing classical music I have so far found these relations to occur far more often than not.

[ETA: You can also rearrange C-Eb-Gb-A into a pile of thirds as A-C-Eb-Gb, so C-Eb-Gb-A is also an orthodox spelling (of what I would obstinately call Adim7/C rather than Cdim7, though gather leadsheet conventions are different). In classical harmony the chord spelled this way could be expected to go to Bbm soon.]

...yes of course you're right Piano Student 88 - dim7 chords can be seen as inversions deriving from other keys, as in your example. That's one reason dim chords are so useful - they can resolve in various ways (sometimes being a bridge to a completely new key, for example) and so they are quite ambiguous and potentially very expressive.

I dunno why . . . But Shubert had no consideration for DP players when he wrote his impromptu . . .

Thank you. Do I understand it correctly than dim7 chords are basically 9th chords minus root? That way, F#-A-C-Eb would be "D7 plus flattened 9th, minus D", thus resolving to G or Gm, like you said. Similarly for other examples. If this point of view is correct, when do you use diminished 9th (D-F#-A-Eb) and when do you use normal 9th (D-F#-A-E)? I know that I frequently see both but can't quite get the hang of the difference, function-wise.

BTW, it just occured to me that in many ragtimes F#-A-C-Eb resolves to plain C or C/G, what is the explanation here?

Yes! I see what you mean about the ragtimes - but afaics, that's a kind of half-hearted resolution - it's not like a full dominant-tonic cadence.

And you can, just for a start use the dim7: F#, A, C, Eb with:

D in the bass, in which case it resolves most easily to G
F in the bass, in which case it resolves most easily to Bb
Ab in the bass, in which case it resolves most easily to Db or
B in the bass, in which case it resolves most easily to E

But I wouldn't worry about the theory (and names of extended triads) too much. Compose what you hear in your head first and delight yourself with the technical details later, if you've nothing better to do....it can be fun.

Thanks Toddy, and yes my first experience with this concept was when I started to study dim and aug triads in my second theory book