Relationship Between key Signature and key
A key signature is not the same as a key; key signatures are merely notational devices. They are convenient principally for diatonic or tonal music. Some pieces that change key (modulate) insert a new key signature on the staff partway, while others use accidentals: natural signs to neutralize the key signature and other sharps or flats for the new key.
For a given musical mode the key signature defines the diatonic scale that a piece of music uses. Most scales require that some notes be consistently sharped or flatted. For example, the only sharp in the G major scale is F sharp, so the key signature associated with the G major key is the one-sharp key signature. However, the connection is not absolute; a piece with a one-sharp key signature is not necessarily in the key of G major, and likewise, a piece in G major may not always be written with a one-sharp key signature. This is particularly true of minor keys. Keys which are associated with the same key signature are called relative keys.
The Dorian Toccata and Fugue in D minor, BWV 538 by Bach has no key signature, which accords with its Dorian mode status (empty signature on D) in preference to its minor key status (which would have a single B♭ signature). The B♭s that occur in the piece are written with accidentals.
When musical modes, such as Lydian or Dorian, are written using key signatures, they are called transposed modes.
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