A Dorian key signature is an earlier style of key signature used on pieces in minor keys. A good example is J.S. Bach's Toccata and Fugue in D Minor, BWV 538, that was notated with a key signature of zero flats rather than the one flat of a contemporary key signature notation for D Minor. The Dorian mode is a mode of the major scale built off of the second scale degree of a major scale and, therefore, a Dorian key signature for D Minor would be the signature for the major scale a whole step below: C Major...therefore zero flats. The D Dorian scale is spelled D, E, F, G, A, B, C and therefore shares the same key signature as C Major in this older notational system. It is now customary within the western tonal system to relate minor keys to the key signature of the major key found a minor third above. D Minor is now written with one flat, the key signature of F Major. Today the "natural minor" scale or Aeolian mode (the mode built off the 6th scale degree of major) is the common reference point for a minor key's key signature.
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No. The mode of A Dorian uses the same key signature as G major, so the only sharp note is F.
The key signature indicates which notes are sharp, natural, or flat. Every key has a specific signature.
It comes before the time signature. The clef comes before the key signature.
D major has a key signature of F sharp and C sharp D minor has a key signature of B flat
There are no sharps or flats in the key signature of C Major.