The notes to E harmonic minor are E F# G A B C D# E. You can write it out on your own staff paper.
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a harmonic minor
"That would be A minor. Go a minor third below the tonic of the major scale to find the relative minor." Technically, there is no relative harmonic major to the key of C Major. The relative minor scale of C Major would the natural minor scale of A. A harmonic minor scale raises the 7th note of the scale a half step, giving us G#, which is not in the key of C Major.
To determine what the seventh note (leading note) is in a minor scale, you need to determine which minor scale you are playing. The seventh note of a natural minor scale, you take the note which is a whole tone (2 notes) below your tonic (the note which is the name of your scale). Example: In A natural minor scale the leading note is G. The seventh note of a harmonic minor scale is a semitone (1 note) below your tonic note. Ex: In E harmonic minor scale, the leading note is D sharp. The seventh note of a melodic minor scale (ascending) will be a semitone below your tonic note, like your harmonic minor scale. Descending the melodic minor scale reverts to its natural state, therefore your seventh note will be a whole tone below your tonic.
The 7th note (leading note) is raised by a semitone in a harmonic minor scale.
Natural minor, harmonic minor, and melodic minor