What are they.. and what's the formulae?? o_O
Note: Sorry if my grammar and/or vocabulary isn't very good, English is my 2nd language!

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Alt chords are altered dominant chords. The formula for a fully altered dominant chord would be 1 - 3 - b5 - #5 - b7 - b9 - #9, so C7alt, Calt or C7(b5, #5, b9, #9) would be C - E - Gb - G# - Bb - Db - D#. But of course, alt chords don't have to contain all the possible alterations to a dominant chord, C7(b5, #9) or C7(#5, b9) can still both be labelled as Calt, built from the seventh mode of melodic minor.

The fact the alt chord is built from the seventh mode of melodic minor is why they're labelled Calt, Dalt.. etc - because they are built from the altered mode, so the tag Xalt is only used when referring to an altered dominant chord built from this mode, so if you had a C7(#5, #11) chord built from the whole tone scale, while it is an altered dominant chord, you cannot call it Calt because it isn't derived from the altered mode.
Last edited by Johnljones7443 at Feb 23, 2007,
^You can use an altered dominant chord wherever you would use straight up unaltered dominant chord, _7 is often substituted by _7#9 in blues tunes for example, but the most common place is in a iiø - V7alt - i-Δ progression. In C, that would be Dø - G7alt - C-Δ, where Dø is built from F melodic minor, G7alt from Ab melodic minor and C-Δ from C melodic minor.

Another place they're used it to add spice to reharmonizations of basic ii - V and iii - vi - ii - V progressions. If you raise the minor third of the ii chord (D-7 in C), we get a D7 chord - which is the V chord of the V chord in the key of C, so now what you have is D7 - G7, a V/V - V progression - you can make both of those chords altered chords and play D7alt - G7alt. The same applies to the iii - vi - ii - V progression, the iii chord, vi and ii chord can all be made dominant by raising the minor third, so in C - instead of E-7 - A-7 - D-7 - G7, we get E7 - A7 - D7 - G7. All dominant chords descending in perfect fifths, a V/vi - V/ii - V/V - V progression. You can then add tension to each chord and be left with E7alt - A7alt - D7alt - G7alt.

The alt chord, built from the altered mode does tend to resolve in different ways than other alterations (b9, #11, susb9 etc).. the strongest resolutions for an alt chord are down a perfect fifth, up a half step or down a major third. So, if you came across a progression that was G7 - CΔ , G7 - G#Δ or G7 - EbΔ, turning them into G7alt - CΔ, G7alt - G#Δ and G7alt - EbΔ, you would get a stronger resolution.