I'd like to be able to track my progress in keeping tempo during my practice, not only in working towards increasing my speed, but also the precision of my timing as I work on being able to play faster.
(How) Do people assess the precision of their tempo of their practice performance over time?
I started using librosa beat tracking to plot tempo of rolling windows of my practice performance, as well as reference material. The plots help me quickly identify which phrases that I rush or lag. I can also track the standard error of my tempo day-to-day to see if I'm improving.
librosa's onset detection helps me see if I'm ahead or behind the beat. Is there a quantitative way to summarize and track precision of practice performance so that I can see how/if my practice is improving?
Are there other/better tools or approaches to measure tempo and rhythm? I've seen that Yousician tells you if you're late or early as you play along, but I didn't see a summary of errors or performance. (And I want to practice with my own music.)
I realize that rhythm is only part of being able to play faster or more precisely, but I don't yet know how to measure or summarize tone quality, dynamics, or other aspects.... There's also the prospect of getting lost in the weeds dancing about architecture.... @Athenasius has a great summary of studies about perception of tempo changes providing some limits of necessary precision.