I started learning to play the saxophone in my mid-30s, and now I play in the horn section of a ska band. A good horn section plays together and hits its notes in the right place in the song. That requires practice.
But, how do you improve with practice? There has to be some kind of mechanism that helps you learn when you played too early or too late and to adjust the timing of what you play in the right direction so that eventually your notes come at the right place.
There are a few ways this could happen. One is that you might base your feedback on whether the song sounds right when you play where you do. You could detect whether your playing coincides with the playing of other members of the horn section.
A second thing you might also do is to actually have a mechanism that is keeping track of the time intervals between notes you play and gives you feedback about whether you played too early or too late. Your brain could then use that feedback to adjust when you come in the next time you play the song.
This mechanism of judging errors in time intervals was explored in a paper in the March, 2017 issue of the Journal of Experimental Psychology: General by Basak Akdogan and Fuat Balci.
In most of the studies, participants were given training on two time intervals. A study might use 2.1 seconds and 4.2 seconds or 1.5 second and 3 seconds. Across studies, the intervals varied between 1 second and 6 seconds. One of the studies had participants only train on a single interval.
To train on these time intervals, they saw a blue square appear on the screen for that interval. Then, they pressed a button on the keyboard and the square reappeared. They pressed a second button when the time interval they just experienced elapsed, and the square disappeared.
After that, participants rated whether they thought they pressed the button early or late and how confident they were that they pressed it early or late.
Across all studies, participants were actually quite accurate at distinguishing between trials when they pressed the button early and trials when they pressed it late. The researchers used a technique called signal detection analysis to determine that people were good at differentiating early from late trials and that they were not really strongly biased to say that they were early or late.
These results suggest that we have a timing mechanism that is helping us to determine the length of intervals (of at least a few second). This mechanism then coordinates with our activities (like pressing a button or playing a note on the saxophone). This ability to recognize when we are early or late is valuable information for the system that helps us to learn when to respond. When we are early, we can delay our response a bit the next time. When we are late, we can shorten our response. In this way, performance on tasks that require timed responses can improve.
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Akdogan, B. & Balci, F. (2017). Are you early or late?: Temporal error monitoring. Journal of Experimental Psychology: General, 146(3) 347-361.