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Not taking into account human performance ability or human error, what is the max speed repeated notes can happen on a piano. Theoretically.

Write answer like this....32nd notes at quarter note = 124 etc.

I thought this would be the best place to post it, because you guys are familiar with how the lever system functions etc.

I don't think we know.

In physics, in the area of mechanical motion called dynamic computation, the maximum cycle can be calculated, but who wants to give it without being paid? I would do it for curiosity, but no I do not work for free.

I think that techs intimately familiar with player pianos may be able to give you a ballpark answer...

Assuming a hammer blow distance of 5cm and the fact that nothing can exceed the speed of light the answer is:

32nd notes at quarter note = 5,625,000,000.

Note that if you approach this speed and try to go even faster the notes will get louder instead of faster as the mass of the hammer increases.

Kees

I wonder what would happen if the rate of repetition approached the frequency of the string vibration?

But what about the time to get the key back into position so that it can be played again.

I'm wondering, to see if it is theoretically possible (I know it probably won't be able to be done) to play the chorus of this song on the piano.

chorus starts at 0:44 https://www.youtube.com/watch?v=l1zoxGDoU8o


It is 32nd notes at quarter note = 124, I've typed it into sheet music program and it sounds ridiculously awesome, just want to know if it is theoretically possible (even though it probably isn't practical)

Well, do the experiments, sislermi, and keep us apprised of results! See Just Steven's comments above.

You could use space-time warping to exceed speed of light. As Kees pointed out, hammer mass increases, this may warp your hammer flanges until they break.

Well. The human finger has a maximum of 6hz-7hz I've heard.

Some uprights can barely handle that.

Let's say a double finger repeat on a single key on a grand should be a minimum, so that's 12-14hz.

Using your notation, that's 32nd notes at quarter = 90bpm as a minimum.

The actual possible speed depends on many factors including friction, mass, etc.

I have heard pianists play the flight of the bumble bee which contains some repeated notes at a similar rate shown in your posted video.

I think finger speed is more of a limit than a properly done grand action. There are uprights that can't repeat that fast. And almost all uprights can't repeat that fast comfortably.

I ran a test on my own piano playing C2,C3,C4,C5,and C6, recorded at 96kHz. I was able to discern about 50 repetitions per key except for C2, where the waveform periods were too long to extract the attack portion. Here are the results

C6 50 repetitions in 4.574 seconds or 10.93 rep/sec
C5 53 repetitions in 5.061 seconds or 10.47 rep/sec
C4 47 repetitions in 4.583 seconds or 10.26 rep/sec
C3 56 repetitions in 5.428 seconds or 10.32 rep/sec

prout

Edit: math error

For me, there appears to be a limit on repetition speed imposed by the piano itself that I cannot exceed.

In high speed multiple repetitions - dit-dit-dit-dit...- as opposed to a single dit-dit, so to speak, the key is not released all the way but stays in contact with the finger, centered around the letoff point. You can feel the hammer pushing against your finger as it hits the repetition lever. It almost feels as if the hammer bounces back and forth between the string and the repetition lever in a manner where the pianist is simply adding energy to the system as positive feedback, rather than controlling the speed of the repetition, much like pushing a swing. It takes very little effort to keep the repetition going once you find the optimal frequency. But, once that resonant repetition frequency has been reached, you can't exceed it.

The speed of repetition is determined by how fast the jack can reset. Even then, there are differences in how we measure. The farther the key has to move, the slower the repetition. The slower the key moves, the slower the repetition. A very heavy key may repeat faster than a light one if it has to move a lot less distance. Hence, you could have a very light key with a very low back-checking repeat slower than a heavier key with a very high check, because the latter doesn't have to move very far to let the jack under the knuckle. The lighter key will accelerate faster under spring pressure, but the height of checking is a big factor in speed.

So, an action might be expected to repeat 18 times per second, which, though faster than fingers can move, is certainly needed for certain passages in which the hands gang up on a note. If I remember, Ravel wrote things into"Gaspard de la Nuit" that seem to reach the limit of a modern action in terms of repetition speed. I was recently asked to strengthen springs on one of our D;s for that performance. There were no problems, but I was in the audience and marveled that the piano held together, at all!
Regards,

The action need not reset. Consider bobbling or double striking hammers - they don't reset or sometimes even achieve let-off. I think max speed would be obtained by NOT pressing the key all the way and using all four fingers one after another in a swiping motion, just tapping the key, but very hard.

But how fast? I think there would be a sweet spot depending on how hard vs how fast vs how far the key is moved. There could be resonant frequencies of the strings and hammer/shank that would make the repetition at some speeds work better than others.

Here is a link to a thread that I remember talked about what Bill Joel was able to do in the song "Anger Young Man"

http://www.pianoworld.com/forum/ubbthreads.php/topics/1386654/1.html

And here is a link to the video: TRIGGER WARNING! Billy is playing a

https://www.youtube.com/watch?v=ErPywgiMb4k

[Edit:] Oh yeah, and if you alternated hands doing the four finger "swipe", like a dog digging a hole, you might really get it moving. I bet a drummer would be a natural at it.

I don't think a drummer, or the technique of drumming on a snare, for example, is transferable to acoustic piano technique. My limited experience with drums shows that the stick bounces off the skin. By simply keeping pressure on the stick/skin interface, the drum stick bounces at a rate determined by the distance traversed by the stick. The closer the stick is placed proximal to the skin, the faster the rate of repetition. The drummer is pronating the wrist at some fraction, probably an order of magnitude slower, of the repetition rate.

As I stated in my post above, the piano string/repetition lever interface apparently provides a similar resonant mode. Though, in this case, the pianist cannot continue the downward motion of the key and expect the hammer to bounce repeatedly off the string. He/she must release and re-attack the key, though over a very small distance in the middle of the key travel. The resonant mode created by the string vibration/repetition lever interaction limits the rate of repetition.

Billy Joel's repetition speed is almost precisely the same as my tests on my acoustic grand yielded.

Is there a drummer, ah, I mean a percussionist in the house? Wait! Isn't the piano actually a percussion instrument? Hmmm...

Reminds me of the story of the radio continuity announcer new to the classical music station.

He practiced composers' names diligently, and seeing that The Flight of The Bumble Bee was scheduled for Saturday, practiced all week saying "And now, The Flight of the Bumble Bee by Nikolai Rimsky-Korsakoff"

And on Saturday he said "And now, the Bum of the Flightl Bee, by Nikolai Rimsky-Korsakoff"......

While I was going on physics instinct in my explanation of drumming, I just searched and found a link to a drummer who explains basically what I said:

http://www.stewarthoffmanmusic.com/articles-percussion-techniques.php?id=50

Amongst other corroborating details, he says: "The less tension there is in the muscles of the arms and hands, the easier it is to respond to the bounce off the head. What's more, by incorporating the energy coming off the drum head into the stroke, the student's playing will become quicker, more fluid and relaxed."

Watch the video starting at 8 minutes. You will see almost no motion in the wrists but a very fast repetition. Neat.

Edit: I've noticed that, so far, no one has countered my theory that the repetition speed limit is based on a resonant mode in the string/hammer/repetition lever interaction.