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As an example in caveman speak, the melody goes ONE-2-3-4-ONE-2-3-4, and the harmony goes 1-2-THREE-4,1-2-THREE-4.

I'm not sure this is actually an example of what I'm talking about, but in the intro of

(Zaveid's battle theme, 12 seconds in), there's a melody going, and when the bass kick harmony is added on, it seems a half-measure out-of-sync with what the melody is doing. It's an interesting effect, and I was wondering what it's called. That being said, I'm sure if, for the example I gave, I listened to it/analyzed it more closely, there isn't a desync between the harmony and melody. Still, I'd like an answer to the question, as well as a prototypical example.

P.S.: I guess a similar way to refer to the phenomenon is that the melody goes 1-2-THREE-4-1-2-THREE-4 (the emphasis seems to happen midway through the measure)

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I think what's going on here is a pet peeve of mine as a listener. Once the kick comes in, it's very clear where the beats are. In the preceding measures, the melodic material is just the same, but it's harder to tell where the beats are. The riff plays on beats one and four, but on beats two and three it has a rest on the exact moment of the beat, instead playing a moment later. In rhythmic syllables, if you count "1 e & a," you might say that it plays on the "e" of beats two and three: "ONE E (and a two) E (and a three) E (and a) FOUR E AND A." Or, notated, this:

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With no other instruments providing a strong sense of the beat, it's very disorienting on first listen. After all, we don't know that it's notated like this; all we get is bits of sound on a timeline. We wonder whether those isolated C and B are in fact beats, and then are thrown off by the final full set of 16ths. Once the kick comes in, it's not quite where we expect it and it takes a few seconds to calibrate.

There isn't a term, per se, for the cognitive dissonance we feel between the unclear (misperceived?) meter of the intro and the clarity of a few bars later, and I can't think of a good term for a contrast between a voice with simple rhythm and one with a more complex one. But there might be good terms to describe the guitar part. One might use "syncopated," but that could be confusing. Syncopation is often about emphasizing weak beats, or "stretching" simple notes so that they begin early or end late; think ragtime. I think "displacement" might be the most useful word. Google "beat displacement" or "rhythmic displacement" and you find a lot of videos and blogs, like this one, talking about the idea of shifting notes to be ahead of or behind the beat.

So it's not a single handy phrase, but maybe the best way to describe this is "The guitar part displaces the notes on the second and third beat, delaying them by a sixteenth note. This creates some metric ambiguity until the kick drum enters, marking each beat directly."

You mention a "prototypical example": perhaps the simplest and best example of the potential confusion between offbeat and onbeat was mentioned in a comment thread linked above, "She's a Woman" by the Beatles:

The only sonic information we get at the outset is the regularly-spaced guitar chords. Given no other information, we are forced to perceive them as beats. But once the drums enter they're revealed to be offbeats.

Similarly, my nemesis for decades has been this track by AfroCelt Sound System:

Around the 4:00 mark most instruments drop out and there's no strong sense of the beat. Then the vocalist comes back with a repeated "Cha! Cha!," and the guitar has a choppy strum at the same time. It's near impossible not to hear these strums and chants as being on the beat. But when everybody drops back in at 4:23 they're revealed to be offbeats and we feel like we stepped off a moving sidewalk on the wrong foot.

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    I always thought this one was easy, but once when I was depping on drums with a function band it turned out none of them had ever figured out the entire track starts on the 2, so they were all counting a 3/4 bar as the main song comes in, thinking the claps & kick were on the 1. It took me a while to get it through their heads... Rose Royce, Car Wash
    – Tetsujin
    Jun 21, 2023 at 16:57
  • And this one - all the clues are there (the bass starts right on the one, so you've no real excuse;) but then the crash on 4 and throws you every time, especially as the snare is on-beat, not off like you might expect. Takes a while to get the hang of it. Kings of Leon, Charmer I do like this band for their intentional 'mis-cues' every so often.
    – Tetsujin
    Jun 21, 2023 at 17:55
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    I don't see why syncopation isn't the description of the anime tune. The down beat seemed clear to me even before the kick bass was in. The Beatles example does seem to present something else, both because the guitar strokes are evenly spaced and isolated for the very beginning. At the very beginning there really isn't context to hear weak/strong beat. But it's also a sort of arranging trick of removing the other instruments to create the ambiguity. Once all the parts are going the guitar is just syncopated backbeat placement. Jun 21, 2023 at 19:14
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    @Tetsujin, Kings of Leon, Charmer, is really interesting. It's so hard to not hear the snare as backbeat in rock. The song's rhythm is really disorienting. Jun 21, 2023 at 19:40
  • @MichaelCurtis - just for fun, try this one. There's no timing difficulty in this one, instead they throw you with the key. It's all a really simple 3-chord turnaround in E, pedal E all the way… but it's not. Melody comes in on C, with bass on A. Messes with your head a bit on first listen. youtube.com/watch?v=GOAu1HzChlY Much softer song than the other one, too.
    – Tetsujin
    Jun 22, 2023 at 10:37

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