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For example, in the Phantasy Star Online Intro song, the main melody starts to play in 3/4 time, whereas the overall song (and the harmony) remains playing in 4/4 time. (starts after 10 seconds, at the 0:50 mark). Technically, you can probably say it's 4/4 time, or 12/12 time if you want to be silly, but it's clear that the melody and harmony here are seemingly playing with different time signatures, only syncing up every few measures (4 in this case).

Does this have a name or any way it's referred to commonly? I can't really think of any other songs that do it off the top of my head, so perhaps it's not notable enough....

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When two parts are playing in different time signatures, it's called polymeter.

However, that isn't what's happening in this piece.

Both parts are in 4/4 time, but at the 0:50 mark, the accompaniment part speeds up, and the two parts play at different tempos. This is called polytempo.

From about 0:30 to 0:50, the tempo clocks in at 84 BPM. At 0:52, the singer sustains her note on "world", which allows the accompaniment to begin speeding up. Thereafter, the melodic parts stay at 84 BPM, but the accompaniment gradually speeds up from 84 BPM to about 90 BPM before rejoining the melody at the original tempo.

This particular effect is a cousin of phasing, a technique credited to the composer Steven Reich, in which two or more instruments begin in rhythmic unison, but gradually move out of phase with each other until eventually syncing up at the end of the piece.

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    I can hear the string melody get wayyyy ahead of the beat at 0:54, and I can hear everything come back together leading up to 1:14. BUT. if you follow it closely, you will see that the melody does not gain or lose any beats in that time, relative to the percussion. The part was just way ahead and finally settled back to being in time. It's a lot more like an ensemble tear than anything else, and I think describing what's happening in terms of "phase" and "phase locking" will be more useful than describing in terms of "tempo"
    – Edward
    Nov 26, 2022 at 23:30
  • ("Phase" is a term I have heard used, but I'm not sure if it is the accepted term- basically, where you are in the beat. Ahead? Behind? Right on it?)
    – Edward
    Nov 26, 2022 at 23:31
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    And this effect is completely seperate from what OP is describing- there is indeed a 6-note ostinato in 4/4.
    – Edward
    Nov 26, 2022 at 23:36
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    The strings get a bit ahead of the the beat, but calling that 'polytempo' is a bit far-fetched. I agree with @Edward that OP is hearing the eighth-note strings ostinato with the accents 12345678 which could cause a naive listener to think the strings are playing in 3/8..
    – PiedPiper
    Nov 27, 2022 at 9:31
  • @PiedPiper or even a sophisticated listener who is prone to confusion. But reading this answer, I wonder to what extent Reich and his contemporaries were inspired by mensural canons, for example by Johannes Ockeghem.
    – phoog
    Nov 28, 2022 at 9:51
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I don't think there's anything terribly complicated going on here. The tempo and beat don't change. There's a whole-note thing going on, and an 8th-note one, grouped in threes. We could call it 'cross-rhythm.

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One term is "polyrhythm." It also applies when several parts move in different rhythms.

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