Final answer:
The scales above A are A natural minor, A harmonic minor, and A melodic minor. Intervals above A include Major 6th, Perfect 5th, Diminished 4th, Minor 7th, Major 2nd, and Major 3rd. Their inversions would be formed by finding the intervals that, when added to the original intervals, equal an octave.
Step-by-step explanation:
To write the scales and intervals above A and then invert them, we need to understand the structure of the natural minor, harmonic minor, and melodic minor scales. Each minor scale has a distinct pattern of whole and half steps. Intervals are also an important part of music theory, referring to the distance between two notes.
For the natural minor scale above A, the notes would be A, B, C, D, E, F, and G. The inverted natural minor scale would start from the octave (A) and go down, resulting in A, G, F, E, D, C, B, and back to A. The harmonic minor scale is similar to the natural minor scale, but with a raised seventh degree. Thus, above A, it would be A, B, C, D, E, F, G#, A, and when inverted A, G#, F, E, D, C, B, A. The melodic minor scale is the same as the natural minor ascending but with a raised sixth and seventh degree, so A, B, C, D, E, F#, G#, A, which inverts to A, G#, F#, E, D, C, B, A when descending.
The intervals requested above A are: Major 6th (F#), Perfect 5th (E), Diminished 4th (D flat), Minor 7th (G), Major 2nd (B), and Major 3rd (C#). To invert these intervals, you would look for the complementary interval that adds up to 9 (since intervals sum to 9 when inverted).