I think the perception of tension comes from tensing muscles we do NOT need for tone production as well as from using the muscles we do need for tone production inefficiently - most typically by continuing to tense after the string has been released.
From piano studies, which we can use to get some insight, both issues occur much more with amateur players than expert pianists. So we can deduce that minimizing both issues is necessary and desirable. From here on I will focus on the second issue.
You mention tempo, but another variable which brings up these issues is dynamics - playing louder requires more force, and that makes even expert pianists be a bit less efficient in their strokes.
Anyway, let's look at this figure from a 2007 paper on piano key strokes; just read "string" in all instances of "key":
Let's say string release occurs at the moment of maximum string displacement (I am oversimplifying things but I think the concepts apply well and can give us insight). The idea is that the finger force should be turned off as soon as this occurs, thus minimizing unneeded tension per stroke. That impulse area (finger force with time) is very focused and precision-timed in expert pianists, with immediate relaxation after it is not needed.
This also works in our favour when a sequence of fast successive strokes is needed (i.e. when we need to play at fast speed): imagine several of these shapes next to each other, getting closer and closer as speed is increased. At some point they will start to overlap, especially if the trailing branch after string release is wide. But the more we can play like experts with immediate release after the force is not needed, for each stroke, the closer the successive strokes can get without overlapping force production.
The perception of this, if done with time precision and efficiency, is that you can play very fast scales while still feeling like your hand is not doing much at all and has virtually no tension in it - even at loud volumes. (The perception of tension is probably some time-average or cumulative measure of the finger forces).
Based on this, a couple of things to try:
- Decouple loudness from speed - muffle your strings (e.g. a sock) so that loudness is not a goal, and play a fast scale. This let's you learn to experience that tempo does not necessitate large or excessive tension (we are using loudness as a proxy for finger force magnitude since the two are coupled).
- Play without a muffle but stop after every few strokes and be conscious that your muscles are not continuing to fire/be tense. This can start from just one stroke at a time; then two at a time, etc. However, for each stroke play them as if they are part of very fast scale and/or very loud. The idea is to learn to feel and diagnose if you continue to tense after it is not needed (i.e. after the string is released) and to teach yourself to turn the force off immediately after string release. Actually, I believe this is what 'speed bursts' are supposed to be like as an exercise; though their other purpose is to prime your CNS and yourself psychologically that you can move that fast.
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