Parallel keys have the same tonic (root) note and octave but different key signatures. This applies when talking about the major and minor scales. If we take a minor the parallel key to that would be A major. Same root and octave notes but two different key signatures. The a minor has no sharps and no flats but the A Major has three sharps (F#,C#, & G#).
Why is this important?
Parallel keys are important to learn because when writing music they can be a great transition statement. For example, if you start off writing a song in c minor and want to transition to a more happier sound, you don’t have to change many notes to transition to the C major scale. You would just need to make the e, a, and b notes natural instead of flat.
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