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My understanding is that each string on a musical instrument/chordophone has a "sweet spot", such that when a string is activated at that point, the "best" sound is produced.

Further, a string can be activated by a hammer (piano), bow (violin), tangent (clavichord), or plectrum (harpsichord, guitar).

  • For a given (possibly "ideal") string, is the "sweet spot" fixed, or is its position affected by the activation method?
  • What is the basis for that relationship (or lack thereof)?

The motivation for the question comes from imagining a keyboard instrument in which the action can be manipulated so that notes can be played with a hammer, plectrum, or tangent. Would each mechanism need to strike at the same point, or could the strike-point vary?


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  • have a check on where the hammers hit on good quality pianos, where the plecs operate on tines (Fender Rhodes) - as they, unlike violin, guitar, et al are fixed. Hopefully at the optimum point. If not, then there's an opportunity to improve those instruments..! Be interesting to have a movable hit point on a piano, though. Thought-inspiring question. +1. – Tim Dec 5 '20 at 19:05
  • From playing guitar, my opinion is that the timber of the note will change as you move up and down. It gets more "nasily" as you get closer to the bridge. And then I suppose it gets more sweet as you go towards the neck or even over some of the frets. For guitar for me, it is easier to rapid pick by the bridge and harder towards neck. I suppose the ideal spot would be the middle of the neck. But as this would make some notes unplayable, ergonomics and the idea, that the amplitude is largest there. It introduces the difficulty that the string to be plucked is moving up to a quarter inch. – marshal craft Dec 6 '20 at 11:08
  • As for harmonics, they can only be hit at very precise fractions of the necks length, depending on the note freted. – marshal craft Dec 6 '20 at 11:09
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According to this source there is a physical reason for where a piano wire is struck and the best location for plucking would be different:

After many tests throughout the history of the piano, it was determined that the best strike point is between 1/7 and 1/8 the length of the string. In general, it can be verified that if the point where a string is plucked (not struck) coincides with a node of any one of the vibration modes, that mode will not be excited. The most intuitive case is the fundamental of a string fixed at both ends. Its nodes are at the ends, which means that the greatest excitation of the fundamental will happen if the string is plucked exactly in its center, that is, at the antinode of the first mode. As the string is plucked further from the center, it vibrates less, and it is impossible to excite it by plucking right at an end. Likewise, if a string is plucked at 1/7 the length, the 7th mode is not excited, along with its multiple integers: 14th, 21st,.... In music, this phenomenon can be an advantage, since the 7th harmonic is dissonant to the tempered minor 7th. This fact has been utilized as a justification for the choice of strike point in the piano, and it is still affirmed in some relatively recent articles and books.

The report cites the following books for the paragraph I quoted above:

H.F. Olson. Music, Physics and Engineering. Dover, 1967.

C.A. Culver. Musical acoustics. McGraw-Hill, 1956.

E. Good. Giraffes, black dragons and other pianos. Stanford University Press, 1982.

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  • What if you want that harmonic? Or don't wat it? It wasn't clear from this why exactly that is the best possible choice – ggcg Dec 6 '20 at 20:30
  • @ggcg valid point for sure, however it does make sense that a 12-edo instrument – i.e. an approximately 5-limit instrument – avoids the first harmonic which doesn't participate in 5-limit harmony (IOW, the harmonic that would most prominently stick out without any matching in the harmonies). – leftaroundabout Dec 7 '20 at 10:59
  • That might explain the piano construction but the op is asking about everything – ggcg Dec 7 '20 at 11:17
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This is an interesting question. I'd refer to texts by Fletcher and Rossing on the subject as they are world leading experts in the physics of musical instruments. I can only tell you what I've learned from guitar playing, specifically classical guitar.

You should know that the brightness of the note produced by the string depends on where you pluck it (I am referring only to guitar and not hammered or bowed strings). So it is hard to say that any spot is "sweet" since that is somewhat subjective. If you wanted warm tones, al la Wes Montgomery, you would be wise to pluck at the mid point as that will accentuate the fundamental and kill a lot of the harmonics. If you wanted a very twangy tone you would want to pluck near the bridge as that will excite a lot of high frequency overtones and with considerable amplitude. So it would seem like you do NOT want to stay in one spot if you want variety and control of your tone. But who's to say which of those tones is "sweet"?

There are other factors to consider. By experimenting with the attack placement one may sacrifice other qualities like sustain and volume. So there is a trade off and I am not sure anyone has really studied this is detail but if anyone has it would be in Fletcher and Rossing's texts (if not originated by them). Various schools of thought are split on this in the classical guitar world. I recall Pepe Romero's book teaching that the strings should always be plucked at the same spot, just behind the sound hole in the direction of the bridge (I am pretty sure it was Romero, but could be Parkening) and that any other variations on tone could be achieved by varying the attack angle of the nails, pressure applied to the string, etc. In other words his method supports the idea that one gets overall superior sound in one place and that other variety can be achieved by controlling the attack parameters. However, not everyone agrees with this. I have seem video of Julian Bream where he will sometimes pluck over the finger board. It is also quite customary for Flamenco guitarists to play fast runs by plucking closer to the bridge but this is not for tone as much as the string feels stiffer there making it easier to bounce the fingers off the string, in contrast to feeling like a loose rope or wet spaghetti when plucked further in. Based on this you can see that there are other factors than sound that contribute to these decisions.

I cannot say for sure that Romero is correct (or the comment I have attributed to Romero) but in my experience it sure seems to be. When the hand drapes over the strings the fingers will lie across them diagonally, each finger touching the string at a slightly different place. This very fact makes it impossible to achieve consistency in placement, especially when playing chords. Perhaps they are in a small enough neighborhood about the sweet spot that it doesn't matter. My opinion is that this is true and it is a standard part of classical guitar training. But I have not seen objective data on this and would deffer to that.

The above does not likely hold as much for the electric guitar. While the basic string physics is all the same the amplification, sustain, and to some degree the tone, can all be controlled by electronics. With just a plain amp you can still hear the variety of tones generated by pick placement but the other issues that exist in generating a reliable note on the classical just do not exist for the electric. At the extreme I would guess that a large enough effect rack could make attack precision an unnecessary skill.

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    “At the extreme I would guess that a large enough effect rack could make attack precision an unnecessary skill” – sure it could, but doesn't necessarily. It depends on how the effects are used, and most guitar effects – even of the more extreme ones – do still respond to variations in string attack, though not in a 1:1 way. And IMO this should be made use of, too. Lots of amateur guitarists think that just replicating the guitar/FX/amp setup of their idols means they'll sound just as good, but usually this is far from true. – leftaroundabout Dec 6 '20 at 11:30
  • Thats the point if calling it an extreme. Like a limit point that is never really reached but getting close to it – ggcg Dec 6 '20 at 13:22
  • It sounds unintuitive, but distortion can magnify small details that are inaudible in clean signal. The position where you pick and the way you hold the pick certainly affect the result. – ojs Dec 7 '20 at 20:11
  • I am well aware of those facts, but again, as a limiting case once can flatten out the input signal so that none of those factors survive, then impose whatever spectrum you desire on the waveform. In theory (and I suspect in some practice) the player's actions, other than plucking a fretted note, can be removed. Thus making the guitar essentially a synth. – ggcg Dec 7 '20 at 20:43
  • What would the point of having a guitar instead of synth if you go out of your way to remove the one thing that makes it guitar? I understand that it's argument for argument's sake, but does anyone really do that and why even bring it up? – ojs Dec 8 '20 at 8:09
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My understanding is that each string on a musical instrument/chordophone has a "sweet spot", such that when a string is activated at that point, the "best" sound is produced.

As far as the violin goes your understanding is wrong. Putting to one side what is meant by "best", the three variables for violin playing are:

  1. Bow speed
  2. Contact point
  3. Bow weight or pressure

Juggling these three elements on any particular string produces different effects.

Generally speaking, close to the fingerboard you need light pressure and a fast bow. While close to the bridge you need a slow bow and more bow pressure. This is complicated by the length of the vibrating string. The more you shorten the string by placing a finger on it the closer to the bridge you have to play AND the less pressure you should apply.

Then there is the question of the way you (or the composer) wants the note to sound. The same note in different circumstances can call for a light, fast bow close to the fingerboard for the "best" sound in one part, a slow, firm bow close to the bridge in another and a moderate bow halfway between in yet another.

It is complicated, far more complicated than you would think.

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    Your opening statement validates the OP. What is being asked is whether or not the "sweet spot" depends on activation method. You seem to be saying there is no sweet spot because of the other variable in the activation method. That is confusing. – ggcg Dec 5 '20 at 20:02
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    @ggcg: there is no "sweet spot" - there are just "different spots". The question has an error built-in (i.e. assuming that such special spot exists). You can still say valid things about the problem (like: the total effect depends on more variables than just the contact point), but that does not make the question valid. The function in question does not have a limit, there's nothing you can approach. – fdreger Dec 7 '20 at 14:21
  • @fdreger, I agree that it depends on several variables but that doesn't mean that there is not a sweet spot. It depends on your criterion. The answer about piano tuning is on point. In classical guitar it is often taught that there is such a spot and it might be for the same reason as in the piano. But this answer seemed to be to have a built-in error too though I could be misinterpreting it. – ggcg Dec 7 '20 at 15:48
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    @fdreger "it depends on your criterion" is exactly what I meant: the sweet spot does not exist. There are spots that sound different, there are expectations (poeple expect certain instruments to sound certain way), there are trade-offs (guitar solo and the same guitar comping to a song), there are different spaces (e.g. resonating to different frequencies) and different effects you want to achieve (do you want a sound that is "mellow"? "sharp"? "surprising"? "similar to X"?). There's no more sweet spot for timbre as there is for pitch. – fdreger Dec 8 '20 at 10:01
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Hrmmm.

As a guitarist, where I pick gives me control over expression. To some extent, pickup placement replaces it for electric instruments, but even then, picking close to the bridge has an effect. I'd say that over the soundhole is the "sweet spot", but seeing that it's fretted, that moves, but even then, the unsweet spots can still be pretty sweet.

As a person who has progressed past the screech and is now a very bad fiddle player, is very much toward the bridge, but the need to have a waist so that the bow can angle confounds this. I'm sure there's other issues that I'm not experienced enough to know. Similarly, I'd expect that hammer placement on pianos, also pick placement on harpsichords, is more about where they can be mechanically placed than where they're musically optimal.

So I'd guess there's enough wiggle room for a few methods, depending on how high a note you're hitting. I wonder about the actuation, but that's not the question.

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This might be more an add-on on @Noah 's answer.

There is a fundamental difference between plucking and bowing:
For plucking, you basically get the string out of its "resting" state and then let the string vibrate. If you pluck it in the middle, the initial state will be more like a symmetric triangle whereas, the more you pluck it near one end, the more it will be like a saw. Even if the harmonic content won't stay the same over time, it is widely known in sound synthesis that the saw will have a greater harmonic content than a triangle. Basically because it's further from the sinusoidal shape of the fundamental. The more you pluck it near the end, the brighter it will sound.

For bowing the situation is different because you are continuously inputting energy to the string and the position where you now won't be a node or an antinode of the vibration: you can try with a rope attached on one end to a wall, and try to excite it with an up and down motion of your hand. If you manage to get it oscillate at its fundamental frequency, the antinode won't be located on your hand: the rope is more oscillating somewhere near its middle. It is also not a node, as you hand is moving. So, where you now is not the initial place of greater amplitude as it with plucking. There is also a lot of other factor like the input wave of the bow which might be close to a square because of the stick-slip mechanism which actually makes the string vibrate and also the feedback (mechanical) between the bow and the string, but that was not the point I wanted to make....

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