I have music theory homework due tomorrow and have absolutely no clue how to do it. I am given directions that say things like "Write the parallel melodic minor of D" or "Write the Parallel harmonic minor of A flat." Any ideas on what to do??
A scale can have a Parallel and a Relative scale.
Relative scales are those that share the same key signature, like C Major having A minor as its relative scale.
Meanwhile Parallel scales are those that begin in the same pitch, ignoring the key signatures, like A Major and A minor as its parallel scale.
As for the minor scales, each one can be natural, harmonic, or melodic.
A natural minor is just as seen in their key signatures, like A minor.
A harmonic minor raises the seventh to create a leading tone into the Tonic. In A minor, it would raise G to G#.
A melodic minor raises the sixth and seventh when going up, to create a leading tone with the seven and to close the 3 half steps gap between the six and seventh that would otherwise occur (like in the harmonic). When going down, it lowers both pitches again, to lead into the Dominant. When this happens, it ends up with the same accidentals as a natural minor. In A minor, it would raise F and G, to F# and G#, then lower them on the way back down.
Source: Some of what I remember about it in The Complete Musician, 3rd edition. You can probably easily find it in Wikipedia too.
Parallel in this context simply means that you write the scale requested with that note as the root. The context parallel is being used is odd as just telling you to write a scale starting on the given note.
Typically, you would only refer to it when the context the scale is in question. For example the parallel minor of D major is obviously D minor, but the relative minor is B minor. Both are extremely important to know especially in the context of analysis where a song may jump between all three.