4ths and 5ths don’t really denote the tonality of the chord – they’re “open” intervals. In addition to perfect 4ths/5ths there are augmented 4ths and diminished 5ths (which are the same interval). But the major and minor qualities of a chord come primarily from the 3rd and 7th – which is why in voicing chords the 5th is usually the first chord member which is dropped.
The fifth is very strongly suggested by the root of the chord because it is prominent in the overtone series – which might be the reason for its “perfect” moniker (third strongest harmonic with a ratio is 2:3 where the fundamental is 1:1 and the octave is 2:1). Also a perfect fifth inverted is a perfect fourth, where a major third inverted is a minor sixth, major seventh inverted is a minor second, etc. So the “open”, consonant quality is pretty stable in that interval.
Once upon a time, perfect fourths and fifths were the only intervals considered consonant, and thirds (which to us define the major/minor quality) and sixths (which to us “sweeten” the chord) were considered horrid dissonant noise.
As Wombat said, there are a lot of chords where the 5th isn’t “perfect”. Diminished would be a good example. I believe all the intervals are minor 3rds.
In a diminished chord, yes, though the dim 5th or “tritone” contained within was known as the Devil’s interval because of its dissonant quality.
The second is the real puzzler. Essentially the transition I explained is as Henke said. Using the new key as the root insert the subdominant followed by the dominant.
This is basically what we were talking about not that long ago, transitioning to a new key imposing a IV/V/I cadence in that key. The B chord in D major is a minor chord, by altering the third of the chord (raising the D to D#) you set up the cadence to the new key, in this case E. It worked nicely because the A major chord is already there in the key of D as the dominant, so you used that as a sort of pivot toward the dominant in the new key. It wouldn’t have worked so well to go from C major to E major, for example.
I figure there are other types of transition. I’ll have to experiment or wait for rh to post.
Hahaha … well, thanks for waiting but i don’t have too much new to add to the discussion here. A lot of modulation is based on the circle of fifths and the IV/V7/I or ii/V7/I formulas, or extending the chord structure to include 9ths, 11ths, etc, to give you more possibilities but those are not real trad sounding.