> [...] beat #3 is an echo of beat #2 [...]

This doesn't match the hierarchy of beats present in most music written in 4/4, where beats #1 and #3 are strong beats-- with beat #1 getting a greater emphasis than beat #3-- and beats #2 and #4 being weak beats. Much of the music of the classical period supports this fundamental pattern-- in 4/4 cadential formulae are generally articulated on beat #1 or beat #3, and rarely on beat #2 or #4.

One could make the argument that beat #3 is an echo of #1. But then beat #2 couldn't also be an echo of beat #1. (And there isn't a similar hierarchy of weak beats with #2 and #4.)

Furthermore, this hierarchy usually extends out exponentially in larger durations. So in a Mozart string quartet you'll hear how rhythmic material of measures 1 and 2 is often repeated (or slightly varied) in measures 3 and 4, with measures 2 and 4 being the "weak" measures. A lot of repertoire from the classical period extends at least two levels further so that the first four measures are a group balanced by another group of four. That 8 measure phrase then has a matching 8 measure phrase, although once we get that far out the rhythms aren't usually strictly symmetrical or imitative anymore.

I haven't read the literature but I'd imagine music cognitive research can shed light on just how far out humans can track those rhythmic groups. On the one hand, I know it has to be smaller than, say, an entire section of a sonata (I've never perceived a development section as the "weak" rhythmic group, for example). But techno music makes me speculate that at least in simplistic musical structures these groups can extend quite far.

There's so much in your comment that I could respond to. I probably won't get to everything.

But here is a "proof" that beats are perceived as if they were echos, using a rock beat. A (natural) echo is softer than the original, because the sound is traveling a greater distance to get to your ear. So, an artificial echo should also be softer. I used to play drums and I remember instinctively hitting the hi hat like (on quarter notes):

  (DAH-Dah)-(Dah-dah)

where the hardness was like 3-2-2-1 or 3-1-2-1. If I'm using terminology correctly: I hit it hardest on the down beat and second hardest on up beats. It just sounded right.

So the echo pattern would be like

  #1 Downbeat
  #2  (echo of #1)
  #3   (echo of #2)
  #4    (echo of #3)

(On the high hat)

OR

  #1 Downbeat
  #2    (Small echo of #1)
  #3  (Big echo of #1)
  #4    (Small echo of #3)

(On the high hat)

The way to test a theory of causation is to remove beats and see if it sounds right to your ear. Pay attention to how the transition sounds. Does the transition sound natural? This is kind of hard to do with rock rhythms. The theory becomes more interesting as the rhythms get more complex. When I was thinking about this, I was imagining house music or other electronic dance music.

I don't know much classical music, so I haven't really even thought about it.

I don't know anything about music, but it sounds like you said "Here's proof that beats are perceived as echoes: I play them like echoes."

>>One could make the argument that beat #3 is an echo of #1. But then beat #2 couldn't also be an echo of beat #1.

That isn't true! Beat #1 can have an infinite number of echos.

N.B.: When I was initially thinking about this I was thinking of subsequent beats as "echos," and I mentioned the echo concept here in the hope that it would be something concrete and instantly relatable. But the echo concept only goes so far, because the "echos" don't have to sound like the original (orig: crash! echo: whistle), and the echos can be removed and replaced over time (say, a change every 4 bars).

The concept of an "echo" is that

  1. It comes after the "cause"
  2. It's less accentuated

The theory is supposed to describe how rhythms sound to the ear. The concept is that the listener builds a theory of "what goes with what", i.e. they break the rhythm down into groups of sounds and form a tree of causation. Presumably, this is how we are able to perceive very complex rhythms: we unconsciously form a tree where earlier sounds "cause" later sounds, and this breaks the rhythm down and makes it easier to build a mental model of how the rhythm works. Your mind internalizes the rhythm and anticipates what's coming next. Rather than treat each sound as independent, we just remember transitions from one sound to the next.

For example, when listening to a rhythm, you construct rules like:

  "Boom" comes before "whoosh"

So you hear "boom" and you start expecting "whoosh". It will sound awkward if "boom" goes away and "whoosh" remains in place, because you thought "whoosh" was caused by "boom". It will sound slightly less awkward if "whoosh" goes away but "boom" stays.

I had another brainstorm. With respect to rhythms where #3 is relatively loud, which describes most rock:

I think it's actually a bit of a trick. It causes the song to sound faster. The reason is because the snare or whatever on #3 is perceived as being incongruously loud, too loud to be an echo. Which gives the impression that it's a second main beat, splitting the measure into two halves and making it sound like 2/4.

Having said that, it might also make sense to consider it an echo of the bass drum. You could remove the snare and leave the bass drum and it would sound ok. If you tried to remove the bass drum and leave snare on #3, it really wouldn't sound right.

I like your idea that it feels like sounds cause each other. But I disagree that beat 1 is always the cause. The pattern of dah-DUM is pretty common, and the dah would typically be a quarter or eight note before the DUM on the 1.

>>But I disagree that beat 1 is always the cause

I agree that that's a weak part of the theory and it could use more thought.

>>The pattern of dah-DUM is pretty common, and the dah would typically be a quarter or eight note before the DUM on the 1.

I thought about that case, and I considered whether to create the concept of a pre-echo.

Another edge case is when beat #3 is accentuated, like in almost any rock song:

BASS-tick-SNARE-tick

The echo pattern is what the listener expects to hear. When a beat is louder than it's "supposed" to be, it makes that beat sound louder and brings it out. I think the snare sounds more powerful as a consequence of being unexpectedly loud.

Wrt pre-echos, I think you could consider them a deliberate deviation from the echo pattern to achieve a particular sound. The difference between theory and actual rhythms is what we call music, right?

ive tried reading this a couple times now. im not sure what you are trying to explain. it almost reads like a markov chain.

It's not really a Markov chain, because Markov chains are random. It could be a degenerate Markov chain where probabilities are either 1 or 0, so that the same pattern repeats over and over.

The pattern can change, say, every 4 bars. Then you are manipulating the chain.

I believe the parent was comparing your post to the output of a Markov chain, not rhythms themselves. Though I didn’t have any problem making sense of it…

Oh! Gotcha. Thanks for the vote of confidence.

no i mean you are not making sense to me, mostly because i dont know what it is about rhythm you are explaining.

I wrote the comment with the expectation that the reader would have enough musical background to understand it. I can easily picture a rhythm as it would appear in sheet music (well, maybe not easily), because I used to play drums and I had to be able to read music.

Playing drums is probably the ideal background to be able to follow along with what I wrote.

The idea is kind of hard to explain to begin with.

well i play music professionally, and went to a conservatory of music, so i definitely have the background

Sorry to imply that you don't know music. When someone just says "i don't understand that" it's impossible to know what's​ preventing them from understanding.

thats ok, you dont have any way of knowing. your post does kind of make me think you are someone who doesn't know what you dont know, but thats ok since im that person often too. i dont understand what about rhythm you are trying to explain. like, what is the question you are answering. that the moeller stroke / hard soft eighth notes (or swung, the two seem to kind of do the same thing in alot of cases) is imitating an echo? i guess it can sound a bit similar? i think it has more to do with establishing a hierarchy of beats, or creating a kind of forward motion. if you dont create a hierachy of beats, just like you do with bars, sections etc, you can lose some form, which gives you less shape to the piece. its also a product of the way some instruments are played, like guitar, where upstrokes are naturally weaker than downstrokes. i do not understand what you mean about causality. i dont hear it that way. i guess in most cases, to keep it simple, i hear it as tension and release, same as harmony or melody.