Diminished and augmented key signature?
Now I know that augmented chords and diminished chords are dissonant normally. Arpeggiate it and it is much more consonant. 3rd octave and it is much more consonant. But can you actually have something in the key of C augmented? If so would it be based on this scale: C C# D# E F G G# B C which is an octotonic scale similar to the diminished scale except it is based off of augmented chords instead of diminished? This would have all of the first four sharps except for F#. Likewise can you have something in the key of C diminished? If so would it be based off of the diminished scale?