#1
1) ... "Name the interval from supertonic up to submediant in the harmonic minor scale."

am i doing this right

-C D Eb F G Ab B
-take D (because its the supertonic) and make it the new tonic
-D E F# G A B C#
-then take Ab(because it is the submediant of the first scale) and see how it relates in the D scale
-so the interval would be a dim 5

2)Why are naturals used when their are no #'s or b's befor it?
wouldn't it be considered natural already

3)I read that dissonance intervals can be used for sense of movement and rythme.. how would that work?
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#2
1. I would just check the interval between the two notes, but yes, it is a b5.

2. If there is a # or b in the key signature?

3. Dissonance creates tension, which can be resolved by consonance. So when you play a dissonant chord, it feels that it should resolve to another chord ~ movement.