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Simply a minor scale
The difference between a melodic minor scale and a harmonic minor scale is that in a melodic minor scale, the sixth and seventh scale degrees are raised on the way up, and on the way down they are the same as they would be in natural minor. In a harmonic minor scale, only the seventh scale degree is raised and stays the same on the way down.
B flat is in the d minor scale.
C is the third note of an A minor scale.
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A melodic minor scale is a minor scale where the sixth and seventh are raised by a half step as the scale ascends; however, the melodic minor scale is played exactly the same as a natural minor scale as it descends.
Simply a minor scale
The difference between a melodic minor scale and a harmonic minor scale is that in a melodic minor scale, the sixth and seventh scale degrees are raised on the way up, and on the way down they are the same as they would be in natural minor. In a harmonic minor scale, only the seventh scale degree is raised and stays the same on the way down.
B flat is in the d minor scale.
C is the third note of an A minor scale.
A major scale and its relative minor scale share the same key signature.
F Major has a relative minor scale of D Minor.
(X) Minor Scale = 3 semitones below (Y) Major Scale E.G. C Minor = E♭ Major
Because it has a minor third (eg in C minor scale, C-E flat is a minor third interval), and a minor 6th (again in c minor, C -A flat is a minor 6th). This creates the correct pattern for TSTTST1/2S
To turn a major scale to natural minor, lower the third, sixth, and seventh scale tones a half step. To create a natural minor scale from scratch, it is: whole step, half step, whole step, whole step, half step, whole step, whole step. A harmonic minor scale has a seventh raised by a half step above a natural minor scale. A melodic minor scale has a sixth and a seventh raised by a half step above a natural minor scale.
"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.