If I go from F# to D# down (F#-D#) is that a diminished third or augmented second interval?
I am composing in minor mode and want to know because augmented intervals are forbidden in part writing.
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In equal temperament it can be either, depending on the context. If you're writing a descending D#-minor triad it's a minor third. If you're writing a descending harmonic G-minor scale it's an augmented second. You should actually write it as F#-Eb then although it will sound just the same on a piano, for example. But even pianists may play the interval differently depending on what you write, and might get a little confused if what you've written is not what it should be. If you don't have the theoretical knowledge to decide which one it is, try listening to it. If it sounds tense, it's probably a second. If it's relaxed, it's probably a third.
You always count from the lowest not up when trying to get an interval. It would in this case D# to F#. If the accidentals are bothering you try and lower each not by a semitone. That should help you get this pesky interval.
D - F is a minor third. D major does not have a F but rather an F# but d minor has an natural F. Hence the title of fitting into the interval of minor. D# to F# will have the same interval as D to F.
F# down to D# is a minor 3rd. It is equivalent to an augmented 2nd in distance, but because it is an F down to a D it has to be a third. The equivalent interval as an augmented 2nd would be an F# down to Eb which does exist in the G harmonic minor (pointed out by nonpop) so if you are using that scale it is an augmented second.
The intervals can also be looked at in as inverted where an F# up to a D# would be a Major 6th and an F# up to a Eb would be a diminished 7th.
This distance from one letter name to another determines what the name of an interval is so the key you are in is must know knowledge for analysing intervals.