Your question about enharmonic accidentals in a scale does not directly correlate to your question about major, minor, and perfect intervals. In an octave, the perfect intervals are the Unison, the Fourth, the Fifth, and the Octave. The second, third, sixth, and seventh can be major or minor. In addition to those you can have augmented and diminished intervals.

You got one answer about selecting which note to apply the accidental to, which relied on writing chords, but there are better reasons to use a specific accidental than simply "I can't draw a note and the same note (but altered)in a chord." The things you would generally rely on for selecting the proper note to apply an accidental to are: functional harmony, and voice leading.

For one typical functional harmony example: in functional harmony, you might have a pile of notes in a chord that functions harmonically as a dominant seventh chord. That will have a root, a major third, a perfect fifth, and a minor seventh. Say you're in a piece in C major, and your dominant seventh chord is a secondary dominant of IV, that is V of IV, often written V/IV. That would be a dominant seventh chord with a root of C, so you'd have a C, E, G, and a B-flat. You wouldn't choose A-sharp here, because the pile of notes is functioning as a dominant seventh chord, and the seventh degree of C is B, and as a minor seventh, it's B-flat, not A-sharp.

Likewise, for a typical voice-leading example, consider a piece written for solo flute or voice, something with just a single note at a time melody. There's no chords, so chords can't be the answer to how you select the note to apply the accidental to. In voice-leading, you'll find that the melody may modulate temporarily to another key. If the melody modulates to another key, the accidentals of the new key signature would come into play. If your melody were in C major for example, and it modulated to G major, you'd get an F-sharp, not a G-flat. Likewise if the melody modulated to F major, you'd get a B-flat, not an A-sharp. So you'd consider the key signature of the temporary-tonic for picking your accidentals. Also, any temporary tonicizations in some other key will typically get a half-step leading tone. If you're in a minor key, you'll often find the raised-seventh scale degree, so in C-minor for example, you can expect to find melody in voice-leading that will include a B-natural moving to C. The B-flat in the key signature will acquire the natural accidental, you wouldn't make a C-flat moving to C. Also, as a general guide, flattened notes tend to resolve down a half step, and sharpened notes tend to resolve up a half step. Consider a natural accidental when applied to a note that is flattened in the key signature to be functionally the same as making it sharp, and likewise consider a natural accidental when applied to a note that is sharpened in the key signature to be functionally the same as making it flat.
Source(s):
Masters Degree in Music Theory from the Cincinnati Conservatory of Music.

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