A New Function

Whenever I'm attempting to master a new riff or passage, I find that my progress can typically be modeled by a logistic curve like the red one above. The variable t represents the amount of time that I have spent working on that particular riff, and y represents the maximum tempo at which I can comfortably play it. As t approaches infinity, y approaches the target tempo asymptotically. If the piece is too far beyond my ability level, then the graph of y(t) won't cross the asymptote until I climb around the mountain.

I have found that this model works even when the difficult aspect of a passage is coordination rather than speed or precision. Last semester I learned Pain of Salvation's "Fandango", in which the guitar parts are reasonably easy, the vocals are comfortably within my range, but many of the guitar and vocal rhythms simply don't match up at all. I had thought that if I wanted to perform both parts simultaneously, I would have to take a different approach to the challenge, but that wasn't necessary. I simply broke the song into chunks, started working on each chunk at a tempo that was much slower than the original song, and gradually built up speed as I normally do.

I had come to think that this was the only pattern that would be necessarily to reach all of my technical goals, but my efforts to master arbitrary subdivisions over the past few weeks has opened my eyes to a very different type of practicing. Playing 5 evenly-spaced notes in a given amount of time is not particularly difficult once you've already figured out the appropriate speed at which to play them, and the same is true of playing 7 evenly-spaced notes, or 10, or 11, or whatever. The difficulty comes from trying to seamlessly switch between these subdivisions.

Unlike the various other challenges I've attempted, this one simply does not get easier as one decreases the tempo. Switching between 5 and 7 subdivisions of a beat is just as hard to do at 40 beats per minute as it is at 80. So now what? After some pondering, I've come to realize that the ability to switch between subdivisions is not modeled by a logistic function, but instead by an exponential decay function like the blue one below.

Once again, t represents the amount of time spent practicing, but here y represents the amount of time it takes to lock in the new rhythm after changing which subdivision is being used.  The first few times I tried jumping from 8 subbeats to 9, it took a few measures before I could play the 9 notes at a consistent speed, but after working at this for a while, it got to the point where I could make the change instantaneously. In other words, as t approaches infinity, y should (hopefully) approach 0, which would indicate that I'm actually absorbing the concepts rather than just stumbling through them.

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Week 28 total: 26 hours
Grand total: 659 hours
Required pace: 538.5 hours (+120.5)