I still need to make time to watch the videos (I'm posting this mostly to remind myself!)
But I wanted to say something about this:
"For example, if I practice a piece for 10 hours but spread it over a month, I will make much more progress than practicing 10 hours in a single week."
This is super, super interesting! In my day job, I'm a linguist and I teach a foreign language to uni students. I always tell my students that they will have better results if they study 10 minutes every day than if they study for 70 minutes once a week. It's the same principle you're describing.
But! At the same time, there's something that happens we do an activity very intensely for a set amount of time. For example, language learners often report significant gains from short intensive programs where they have class every day for four hours, for eight weeks. This kind of mimics the level of input you might get from going abroad and immersing yourself.
And I have always told my students that they may see the true fruits of such intense study not immediately, at the end of the program, but a few weeks afterward, after some resting. And I always tell my students that sleep is the single most important thing they can do to progress, whether they're doing an intensive program, or they're studying abroad.
One of the things that happens with these kinds of intensive language programs is the development of fluency -- students become better able to convey their ideas through spoken language, they often report their first experience of dreaming in the language etc.
So I have always felt that there is something qualitatively different that happens, in other words, that you can't experience the same kind of learning over the same amount of time, that something different happens in those condensed periods.
So what is the corollary with piano? I'm not sure, because I've never experienced an intensive piano study that mimics these language intensive programs...
Still I can't help but wonder whether there's something similar with music learning. So first, as has been discussed here, consistent (daily) practice, not super long, with lots of good quality sleep, is going to be essential.
But what about the bust of intensity? What would the learning gains be from a week of being totally piano-focused and spending more time then you normally do, both at the keyboard and also mentally, studying the score or some similar non-keyboard musical study. And not really doing anything else.
I would imagine that alternating between intense study and more "spread out" study would be beneficial, but in what ways. I'd love to know.
I wonder if Noa Kageyama has ever written about this...
