Modulation across the circle of fifths

Question

After studying some of the theory surrounding performing smooth-sounding modulations between keys in an effort to make more interesting compositions, I have come to understand that the circle of fifths can be employed to find "neighbor" keys who share several notes and therefore are good candidates to modulate to.

What I'm having trouble with is how one would modulate to the more extreme distances in the circle, say the direct opposite (read as a clock face). Take for example this song:

What I'm hearing here (corrections welcome!):

• The initial riff is in B minor, with some notes borrowed from Dorian B at the end ("This is how a legend is born" until "a beauty I'll guard until the end of time.") 0:09
• Modulates to the relative major, Dmaj, ("Rain melts down from the stars...") 0:31
• The big key change, G#maj ("At a glance we both were falling...") 0:56
• Bridge back into B, this time borrowing Phyrgian? 1:25
• Dm later on after second chorus ("Cantisti sonta dia...") 2:45

What are the techniques employed here in order to make this sound coherent? A few things I can try to pick out:

• The limited usage of the tonic in the melody in the second section
• The open break (direct modulation?) before G#maj section
• I am guessing some of the borrowed modal notes help but can't understand why.

Are there names for what's being employed here? Usage of a specific bridge note? Is there some theory that could explain how this sounds so seamless?

Answer 1

There are several methods. One main idea is to rather quickly play the dominant of the target key. This makes for several really easy modulations (but not necessarily dramatic ones). Using a C-major to F-major modulation for example ("one-flat down the cycle of fifths"). You could play the home key tonic (C), make it a dominant (C7) then play the new home key (F). This is called the "pivot chord" strategy; one plays a chord that has different meanings in each key and pivots across keys. Going more steps may take more steps. Using C-major to Bb-major could be effected by playing a C-minor chord (not diatonic in C but still close); treating this as a iim in Bb so follow with F7 (V7 in the new key) then Bb (I); a bit abrupt but serviceable.

Using the I7 chord (as V7 of the original IV) allows easy movement in the flat direction. One can use the i-minor chord as ii of the new key also. Chromatic chords like the Augmented Sixth chords is another easy shortcut but mostly down (or up in this case) 6 fifths. From C (I) one goes to cm or fm (i or iv) then Ab7 (any of the augmented chords) then to Db7 (treating the Ab7 as the new dominant).

Various theory books usually discuss these possibilities and others.

Answer 2

I think it sounds seamless, because within the different sections the harmonies are fairly straight forward and when it makes the dramatic key change the vocal part smooths it out by moving by single steps.

The part around 0:31 sounds to me like D major to A major to f# minor - root moves up a fifth then to a relative minor. The part around 0:56 sounds like f minor, Ab major, Db major, Eb major, Ab major, f minor - a bit of IV V I and then a relative minor. That seems conventional to me.

When around 0:56 it moves from D major to Ab major it sounds like the harmony moves from f# minor to f (natural) minor. At this point I think the voices are singing A over F# moving down half-steps to A flat over F natural. It's a big tonality change, but the voices move by smooth half-steps.

It's not using methods like pivot chords, or enharmonic modulation. I think you would call this a direct modulation, because it just goes straight into the other key.