When a song has a key change, often towards the end, it goes up, rather than down. There is probably a reason for this.
Not asking about modulations, but actual key changes (tonicization), as in the last chorus moves up to another key.
Often that new key is one semitone, or one tone higher than the original. What's the reason for those particular changes, above any others?
Key changes upwards combine several emotional effects:
Before language existed, the ancestors of humans evolved communication via emotional expressions such as changes of the average pitch of grunts and shrieks and emotional reactions to them. Pitch changes remained a useful "paralanguage" also after language emerged. Music key changes upwards may partially activate brain pathways associated with this instinctive emotional response (alertness, excitement, ...) to raised pitch.
With more music-listening experience, emotional responses become more nuanced due to learned associations between music patterns and emotional context (such as correlating music patterns, lyrics, movie scenes).
Things are most interesting when they are neither too predictable nor completely chaotic, that's a variant of the Goldilocks principle. A key change may feel unusual because it deviates from the pattern of the music. It doesn't deviate too much if it maintains a similar pitch and song structure.
This video about unprepared key changes upwards states that such key changes feel "clichéd" (see #2 above) but also feel like "injecting new energy" (see #1 and #2) and "jarring" (see #1 and #3). Key changes by a semitone up, due to not sharing many notes between keys, are described as "noticeable" and particularly jarring, probably because the brain wasn't necessarily expecting so many new pitch classes at that moment. (Even if the listener already knows the song, the way it breaks the musical pattern may still evoke emotions.)
These key changes achieve certain effects, other key changes achieve a different effect, see videos about other kinds of key changes.
Changing key up a perfect fifth (e.g. from C major to G major) mostly keeps the familiar set of tones. Just one note in the set is sharpened (F to F#). The difference is that this new note has a pitch/frequency 106% higher/greater; it has a little bit more energy.
If we go up a major second instead (C major to D major), there are two notes with more energy than before. But more importantly, our old familiar tonic isn’t even in this new set of tones, it’s become sharper (C to C#). And this note isn’t particularly stable in the new key either, it wants to move us up another half-step up to the new tonic.
When the whole key moves up a semitone (C major to C# major) every note in the scale becomes more energised — I’m using the term energy in both a physics sense, but also in the sense that a DJ might. This key change isn’t subtle.
Similarly, a key change: down perfect fifth (C major to F major), down a major second (C major to Bb major), or down a semitone (C major to Cb major) flattens notes in the set, and thus reduces one form of energy in the music.
Other key changes have more complicated things going on, and can be analysed/utilised in different ways.
I think @root's answer addresses the question of "why?" High pitch is psychologically associated with excitement. Modulating/transposing up is a fundamental of building excitement or tension which exploits that psychology. If you are looking for music theory to corroborate that, some things to consider:
You might say that begs the question of why those upward movements are used to build tension and excitement. We then just get into a circular discussion going back to the point about pitch and psychological excitement. Perhaps you might ask why high pitch is associated with psychological excitement. And you could try shifting to physics and answer that higher pitch/fast frequencies have more energy, and the natural world tends to not expend energy unless compelled to. Think survival scenarios where things speed up, like running speed, heart rate, etc. and that's excitement. At a certain point I like to direct people to this interview with Richard Feynman. You should make the connection around :54 into the video, but watch from the beginning to understand what triggered Feynman.
When a song has a key change, often towards the end, it goes up, rather than down. There is probably a reason for this.
If yet another repeat of pop song chorus risks monotony, transposing up is a simple way to inject some excitement into the music. I supposed a shift downward could work too, but it makes sense to shift in a direction that fits the original mood of the song. An upbeat rock song would probably want to maintain not lessen the energy level. On the other hand, if the song were mellow, a shift down might be an effective way to extend an ending, a way to effect a denouement.
Often that new key is one semitone, or one tone higher than the original. What's the reason for those particular changes, above any others?
Vocal range must be a practical consideration when the shift is a literal transposition up.
You could make some comparisons between the common tones of the keys, but I think that doesn't matter. That is normally an aspect of "smooth" modulation where the supposed concern is to not notice the change. But in the case of adding excitement to a repetitious chorus the whole point is to notice the change, and hopefully react with excitement. Any more specific emotional reaction beyond a "refresh" or "excitement" probably will depend more upon the main content of the song that the size of the upward transposition.
In my opinion, and by my observation, a number of popular songs regularly heard on the radio employ a half-step up modulation as a clever songwriting device designed to either create a tension in the mind of the listener, or to offer an uplifting, gratifying ambience or mood.
George Benson's song, On Broadway, for instance. Part of the way through the song, the key climbs from G# major to A major. Smooth and interesting.
Michael Jackson, Man In The Mirror. G major to A flat major Right on the lyric, "CHANGE". Brilliant.
Ain't No Mountain High Enough by Marvin Gaye. Why does this work? It just does.
From a psychological perspective, perhaps radio listeners find the modulation to be interesting. More interesting that formulamatic songs that offer nothing that turns their head.
Taking the examples in OP's last paragraph, I think the 'smoothness' (as opposed to the already mentioned truck driver's gear change) is related to pivot notes.
Let's take key C> key C♯. Tonic chord in C is, well, C:CEG. To get to key C♯, often the V of that new key is used - G♯7. Comprising G♯B♯D♯ and F♯. The common note ( pivot note) here is the C/B♯. Not only is it the tonic pitch of the old key, but the leading note of the new.So the transition is smooth.
Let's look at key C to key D. CEG goes to the V of key D, which comprises A C♯ E G. Thus two pivot notes, from the old key to the V of D. Again quite smooth.
There's the obvious changes key C>F and key C>G, with many common notes, but as far as songs are concerned, singing half an octave up or down from what happened in the previous chorus is often a bridge too far.
Yes, a 'truck driver's' key change, shifting wholesale into a final chorus, is typically up a semitone or up a tone. A slightly more sophisticated 'up a minor 3rd' is also reasonably common.
Why? Well, you do it to give the song a boost, an 'upper'. And going up is an upper!
Just now and again a song with a 'big ending' will actually be taken DOWN a key. Usually, I think, to accommodate a particular singer who finds a song lies well for their voice in one particular key but wants to go for a higher 'money note' at the end. Rather than lowering the whole song, they'll get the arranger to concoct a key shift DOWN for the last chorus, putting the high note into their vocal range, but to do it in a way that doesn't SOUND like a 'downer'. A rising melody can disguise a downward modulation! Clever.
