Apart how, like separate from a single human nervous system? Serious question.
I don't see the value of that distinction. All that coordination/independence is is notes in unison and notes in sequence, both of which are forms of working together.
Well, I thought the neurological example was more or less perfect in showing there are two different phenomena at play. So, I'm not totally sure why you want to disregard that and have me produce a different argument. But, I'll try anyway.
To start, I think you're being a bit reductionistic. Two things are not the same because they share things in common, or even because at some level they are composed of the same stuff. Categories are defined by differences.
This is just the first example that comes to mind, but a float is not an int is not a string. What you're arguing sounds a lot like someone saying: "All that ints/floats/strings are is sequences of bits, so they're actually all the same." Well, no. You can't perform arithmetic on strings.
In terms of drumming, coordination and independence
feel different and have different failure modes. Take a single stroke roll and keep speeding it up; eventually it just loses coherence when you reach the point that you lack sufficient control to place notes where you want them to go. What you don't feel is one limb tugging at the other to conform with it, to rebel against the motion it is being asked to perform. Well, a beginner might, but for you or I, I suspect that simple "one hand then the other" independence has been solved a long time ago.
And I don't think your "if you just slow it down to a crawl and look where the notes land, you can play anything" example totally holds up either (and because I'm addressing this, which I think is your strongest argument, I'd appreciate it if you addressed my neurological point if/when you reply in the future).
Slowing things down lowers the bar for coordination
and independence. And, starting very slow and gradually speeding up can help with both too.
But they're still different things.
So, while I don't think the "reduction" is valid, I also don't think it works all the time either. Isaac Jamba playing an ostinato at a constant tempo with his right hand while the left hand plays singles, smoothly transitioning from slow to fast, back and forth again, in a continuous rather than a discrete fashion... I don't think you can reduce that to "just play it slow." There isn't even a coordination element. It's 100% independence and 0% coordination. Jamba has developed this context to such a point that the left and right hand have next to no pull on one another. Two human beings can do the same thing effortlessly, with zero coordination between them. They don't even need to be in the same room, the fundamental for reason is that, absent some kind of telepathy, is that the motions my limbs make do not tug on the motions yours make. But if we divide the left and right side of paradiddles between us, that's a different matter.
Going back to the neurological thing, coordination is
making connections between limbs, independence is
breaking them.
I also think "slow it down enough and you can see they are the same" fails when you think of limb motions and not just note placement. A two-stroke push-pull motion against a three-stroke Moeller motion becomes easier when you slow things down, but that's because the motions become more discrete and less continuous. You can feel one limb "pulling" the other into its motion and overcome it at a slow enough tempo not because you can "coordinate" the motions perfectly, but because you can disrupt the motions to some extent and still hit the notes. Critically, if you just take some polyrhythm and slow it down to the point that the notes are light-years apart, and you
don't care about the motions of the limbs, then you don't feel your limbs "pulling" at one another at all.
They're different things.
