Why does the note not get higher when I press my bow hard on the string?

April 4, 2011 at 04:50 AM ·

As I understand it, the note that comes out of my open string is set by two factors: its length and its tension (I don't think the thickness is a factor but could be wrong).

Why is it, then when I press on the string to play loud the note does not get higher?  Does the stretching of the string (making it longer) ballance the increased tension?  Or is the tension all in my head!! :)

ee

Replies (75)

April 4, 2011 at 06:11 AM ·

You're right.  The pitch stays the same when the string is pressed hard because the increase in tension is balanced by the increase in length, approximately.

(The basis in physics: the fundamental frequency of a vibrating string of a given mass is directly proportional to the square root of the tension and inversely proportional to the square root of the length.)

[EDIT: Incorrect.  See Bill's analysis below.]

April 4, 2011 at 09:01 AM ·

No, the pitch does in fact go up.  The change is just so small that you don't notice.

Try it on the g string, or better yet, try it on the c-string of a 5-string violin, and purposely use a lowish-tension string.  The change will be very obvious.

April 4, 2011 at 01:32 PM ·

Allan is correct and Y is incorrect here. And yes, you can easily make the g string sharper by pressing hard.

For a given stress and mass per unit length, the pitch (frequency) is inversely linearly proportional to length. That's obvious when you play fiddle--an octave is half the length of the string. However the pitch varies with the square root of the stress. Doubling the tension will double the stress but only increase the frequency 41%.

"mersenne's law"

April 4, 2011 at 03:07 PM ·

Thanks Bill.  Still can't hear it though - so practically speaking Y may be right for the violin.

BTW point is pressing on it with the bow while making a note though, which is not the same as pressing on it with your finger.  I can't detect an increase in the pitch.  Maybe I have to use a cello bow :o

April 4, 2011 at 04:16 PM ·

Bill, your statement of "Mersenne's Law" is correct.  However, in this case the mass per unit length is not constant.  It decreases as length increases, for a given mass of string segment.  Therefore the expression for frequency reduces to

Frequency = sqrt ( (T/L) / m ) / 2

which is what I stated.  See http://en.wikipedia.org/wiki/Vibrating_string

I said "approximately" because things are complicated by the after-length (total length greater than stopped length), flexing of the body, and elastic property of the string (steel, synthetic, gut, etc).

Now that's just theory.  I did a quick test on a violin, and the pitch did seem to go up when pressed hard, as Allan suggested, on the G, D, and A strings, but remained relatively constant on the E string, at least to my ears.

April 4, 2011 at 05:13 PM ·

" However, in this case the mass per unit length is not constant"

You are assuming that the string doesn't slide through the nut, and that the mass per unit length is therefore dropping infinitesimally as the string stretches.  In a well set-up fiddle you hope that the string is somewhat free. You add graphite there to prevent "hanging up" at the nut...in practice it is probably a 50-50 sort of thing going on. From a practical standpoint, your theoretical analysis is not correct. The mass of the string has not decreased--only the mass per unit length--infinitesimally.  Take any stringed instrument and mark the fingerboard at exactly 50% of the string length. Then push the string down to the fingerboard. The note will be sharp relative to the 2nd harmonic. This is due to the pitch rising from the stress rising with tension. The string lengthening most definitely does not balance this out. All steel-stringed fretted instruments have the bridge saddles set farther away than twice the harmonic, in order to compensate for this. I will agree with you that if you simply solve  Tension=4pi *r^2 *f^2 *L^2 * mass/(unit volume) and you arbitrarily increase the length 5% and the tension 5%, you will balance. But that is not what actually happens. The length doesn't increase as much as the tension!

In our case we are bowing, and so we stretch the string while bowing it. We actually have a slightly longer string, at a higher tension, when bowing, than the unbowed length. Even on a plucked instrument, the effective length and tension changes from the instantaneous pluck, to the sustain. The frequency drops. This is easily heard with good ears, and easily shown on a good frequency counter or strobe--you can even see it on some cheap electronic tuners.

In fact, if you "weld" the strings at each end to a solid immovable rigid base, and you push the string sideways, the tension will rise and the note will rise. Try it.

The reason the E doesn't change much is that it is a solid string and at its nearly maximum theoretical stress before breaking. Try pitch bending on a guitar and you will find that the E bends only a semitone, whereas the (electric, solid steel) g can bend over two semitones, or even three with really light gages.

Pitch change is proportional to the square root of the change in stress. When there is a much lower core stress, you have a lot more stress change to play with.

As a matter of practicality, the wound strings are not wound to absolute optimum core stress--in other words the cores of the wound strings are not right at the same stress as the e string. If they were, they would be more pitch stable under the bow pressure but they would also be much more likely to fail from being overloaded this way, as their core gages are very light and it takes very much less force from the bow to increase the core stress than on the e string where the whole cross section is carrying the load.

As an aside, it is bad form to quote wikipedia. It is not a reliable source for anything.

April 4, 2011 at 06:21 PM ·

If you bow fast with normal pressure (i.e. to play loud or project the tone) the pitch of the string can rise, noticeably so in the case of the bottom open string. You can hear the effect sometimes when a string quartet plays the last note or chord of a movement, with the pitch falling back to its natural level as the sound dies away. I suppose in theory a good quartet shouldn't allow that rise in pitch of the open strings to occur, but sometimes it does, so there you go.

Another trick that cellists can do with the open C is to force the pitch down by using a LOT of arm pressure (not speed), by as much as a full semitone. It's a graunchy sort of sound, not particularly attractive, and comes under the heading of party tricks I think, although some modern composers can doubtless find a use for it. You can do the same thing on a violin, as a fellow folk musician at a ceilidh demonstrated to me the other day when we were discussing the effect, but I don't recommend it, unless you're planning to change that string the next day!

April 4, 2011 at 06:41 PM ·

The note does get higher - I hear it all the time when I draw fast bow or apply more pressure, especially on the G string.  This is especially pronounced with lower tension strings, such as Warchal Ametyst, and Pirastro Tonica. That's probably why I'm not a fan of those strings - the pitch fluctuation drives me crazy!

Elise, if you really want to find out whether this is happening and you are not hearing it, this is one case that a chromatic tuner comes in handy.

April 4, 2011 at 06:50 PM ·

Let L=330mm

Let L1 = 50mm (distance from bridge to bowing location--I know, it is a bit far)

Let D = 5mm (how far the bow pushes the string down)

Solve pythagorean theorem twice and add the results. You get a string length of 330.294mm or 0.09% increase in length. And so the pitch, assuming 658 to start (just because of my numbers here) you would go down less than one hertz.

Now solve the increase in tension.

First approximation = fixed nut and bridge.

Steel e string, Young's modulus = 220 GPa.

cross section of string = 0.135mm radius--> area = .0573mm^2

Initial Tension = 85N , stress = 1.48 GPa

First approximation, (ignore poisson contraction effects) strain of  0.0009 = additional stress of 198 MPa for total stress = 1678 MPa.

Solve Sigma = 4*f^2*L^2*(mass/unit volume) and you get a pitch rise of about 6%.

Note that if we consider after-length and string sliding through the nut, that will reduce the pitch change, a little bit, but not enough!

The after-length and the poisson effect are 2nd order here. So the effect of string length change (dropping the pitch) is much less than the effect of tightening the string.

This should all be very obvious from any study of vectors, or of using a bow to shoot an arrow or pull a 4X4 out of a ditch---a small sideways force acting on a straight taught rope produces a tremendous increase in tension on that rope....

Of course I did this to an E string--which would never deflect 5mm. But it has a known stress, cross section, and density. Now applying what you know about strings to the G, string , you can see that the pitch rise is real. You know the tension is lower. But tension doesn't determine pitch--stress does--along with mass. So assume the stress is quite a bit lower. Maybe 800 MPa to start. 5mm seems reasonable for deflection. Maybe a bit less. You can see that you can get a good rise in pitch on the G-string. The better part of a semitone. Certainly a 1/4 tone with some strings. If you want a pitch-stable G-string, you want the stress of the core to be as close to the breaking stress of the core as possible. If it is a steel core, it would be close to the E-string stress. Additionally a higher tension (larger gage) string will just be that much harder for the player to load up. You will have to work harder to stretch it.  So a meathead player with light gage strings is going to get a lot of pitch rise on open G. Either change strings, or change brain :-)

April 4, 2011 at 11:38 PM ·

Are you guys and gal forgetting about speed (velocity ) in your equations?

It seems to me that you are adding speed along with pressure ,thus getting a rise in pitch.Try keeping the  same bow speed when adding pressure ,and you will notice that the pitch will go flat, not sharp.

Normal bow pressure and speed equals in tune note

increase in bow speed and pressure equals  a rise in pitch

Normal speed and increase pressure equals  decrease in pitch.

April 5, 2011 at 12:38 AM ·

Hey Charles,

slow speed bowing only lowers the pitch if you crunch it and create subharmonics. If you are bowing hard enough to raise the pitch, you better be bowing fast, or you will crunch.

April 5, 2011 at 12:48 AM ·

Charles - thats rather alarming.  You mean if I play a slow bow on a note and then a fast one the pitch will change???  Surely you jest, I'm having a hard enough time getting my finger in the right place than have to synchronize it with my bow speed.

I think that is the straw that broke the violin back - the instrument is actually too hard to play by any human.  Bring on the robots.  Or, failing that, the violin synthesizer - there you just need a few itterative subroutines....

April 5, 2011 at 12:51 AM ·

Pitch change is no problem when you are stopping the string. You automatically make the teeny-tiny adjustments required to make it sound right. This business only applies to open strings. (Except subharmonics on the G string which you can do stopped too if you try it out long enough.)

April 5, 2011 at 01:05 AM ·

As if proper intonation isn't difficult enough. :P)

April 5, 2011 at 04:35 AM ·

Elise, Bill,

There is a way to experiment with this: get the Peterson Strobe Tuner program and use it to measure the frequency. When I did that a few years ago, I found  that the bowed string has just a little (~1 Hz  for an A string) higher frequency than the same string plucked.

Bart

April 5, 2011 at 07:55 AM ·

Wow Bill.  Thats worth the investment!    Of course the question then is 'why is the bowed string higher?' is it the pressure, the tension (the bow grips the string and pulls it) the bow speed (which makes the pull stronger, see above) or the hot breath of the player melting the rosin?

:D

April 5, 2011 at 09:15 AM · You can hear the change in pitch easily when a child is using martele on the g string of their 1/4 size violin

April 5, 2011 at 10:34 AM ·

David Christianson

"As if proper intonation isn't difficult enough. "

David, I agree.

I can't understand why people just don't move their finger a fraction until the note is in tune?

Why do we have to have all this silly trauma and scientific arguments?

Just get on and play the damned instrument!!

April 5, 2011 at 11:13 AM ·

Actually, an understanding of this phenomenon is as critical to playing in-tune as is diligent practice.

-It's just that the OP had it wrong.

Tied to this concept is also string selection (gauges & overall tension) and bow tension.

There is even the issue of string height & scale length, as they can noticeably affect where you must place your fingers.

It's all important to a complete mastery of intonation.  - not that I will ever achieved it!

April 5, 2011 at 01:13 PM ·

Elise,

You ask why the bowed string sound higher. I don't know, but one idea isthat the bow acts to stop the string too, by introducing friction some way along the length of the string. That would explain why there was also some effect when I played pianissimo.

Funny: I've always thought of myself as a theory-minded person, but in this case other people have gone much deeper into the theory than old empirical me.

Bart

April 5, 2011 at 02:06 PM ·

Elise, Bart, I explained exactly why the bowed string is higher. Read my long-winded explanations above. The plucked string quickly decays to nearly the frequency related to the at-rest tension. A bowed string is rather significantly over-tensioned by the pressure of the bow. Therefore it vibrates at a higher frequency. The plucked string is only significantly overtensioned at the moment of releasing the plucking finger. It quickly decays as the energy is absorbed by the system and the tension drops back to the undisturbed tension.

April 5, 2011 at 02:41 PM ·

The rise in pitch noted with an increase in bowing speed is probably due in part to the "stick-slip" phenomenon. The bow grabs the string and pulls it to one side until the restoring force of the string overcomes the stick of the rosin. Then the string releases and whips the other way until its restoring force weakens and the bow grabs it again. Any practiced player knows this has a great influence on the tone and pitch. Bowing speed has to be added in to all the other variables, which increases the complexity of the calculations.

As to the question asked about why players just don't adjust their finger positions to correct the pitch, the answer is: they do! Someone once made the assertion that all notes on a stringed instrument like the violin start out of tune, but the player corrects so quickly that the off-pitch portion of the note escapes notice. I think that even in the famous slow-motion film of Heifetz playing an extremely rapid passage you can see him adjusting to correct the pitch. This was quite revealing because Heifetz was famous for his intonation.

April 5, 2011 at 02:58 PM ·

The more flexible the string the less you notice the raise in pitch. Try putting all steel strings on your fiddles and you will see how noticeable the pitch rise is when you pull the bow real quick and hard over the open strings.

April 5, 2011 at 03:12 PM ·

Prof. Bill, thanks for the physics lesson.  I stand corrected.

Peter wrote: "Why do we have to have all this silly trauma and scientific arguments?"

Because silly scientific arguments are easier than violin playing?  :D

April 5, 2011 at 03:51 PM ·

You got it YC! LOL...

April 5, 2011 at 04:36 PM ·

"Because silly scientific arguments are easier than violin playing?  :D"

I third that! :-)

April 5, 2011 at 05:01 PM ·

Virtually everything is easier than violin playing.

April 5, 2011 at 05:57 PM ·

Well, there is one thing harder...

..

...

....

not violin playing....

April 5, 2011 at 08:41 PM ·

Hi Bill,

It seems I failed to grasp the significance of your derivation; I'm sorry.

As a penitence I wrapped my brain around it, and came up with the following.

To a good approximation, the relative increase in length of the string, Delta L, is equal to

(Delta L)/L = 1/2 * D^2 /(L1 * L2) (following your naming for the variables, and introducing L2 = L - L1)

The increase in length is proportional to the amplitude squared.

After the same algebra you must have done, I get for the relative change in frequency f:

(Delta f)/f = (-1/2 + 1/2 * Y/Sigma  - nu)*(Delta L)/L,

where Y is Young's modulus for the string material, and nu is Poisson's ratio.

This takes both the lengthening of the string and the Poisson ratio into account. Compared to the increase in stress the other terms are negligible, as you said.

Putting in the numbers yields the same 6% you found.

But the effect is proportional with the D squared. Near zero D, one should find hardly any frequency increase. And that's not the case. So my tentative conclusion was that there must be other effects as well, for instance impediment of the string motion by the bow. I can produce a lower tone as well: no idea why that is so!

Incidentally, all this explains why as a child I got nowhere with rubber bands for strings on my cigar box violin: they are nearly impossible to tune before they break.

Cheers,

Bart

edit: oh dear, missed the last few posts. I'll concede to being silly.

edt II: silly scientific arguments can be fun, too

April 5, 2011 at 09:50 PM ·

Bart's post proves that those experts who state that music is good for maths just might be right! (Good stuff, Bart.)

The lower notes (notes below the fundamental) are variously called "subharmonics" as well as "weird growls" as well as other technical terms. How they work?  I don't know. Fun to explore it!

I can make them on my fiddle. It takes a lot of pressure, slow bow. I am usually up over the fingerboard somewhere. Though that may vary too. It seems to just suddenly "jump" into action and your arm muscles somehow learn the feedback mechanism to keep it going. (Sort of like learning to waterski the 1st time).

Your ideas about pitch rise close to 0 stretch is interesting. I'll have to think about that, too.

April 6, 2011 at 02:06 AM ·

So, all the above from Bill explains why one is told to tune by playing softly, not loudly w/ a lot of pressure?

April 6, 2011 at 02:48 AM ·

Very impressive Bart, but can you tie your own shoes :-)

April 6, 2011 at 07:14 AM ·

Smiley, LOL.

April 6, 2011 at 10:44 AM ·

Very nice Bart.  Thanks.  But can you pleae put that into english too (oddly, I can invent equations but I can't interpret them very well.. :-\ )..

Is my ear missing the tone change?  Or is this one of the wonders of the instrument that it has its own homeostatic tone mechanism?

April 6, 2011 at 03:03 PM ·

Hi Elise,

Thank you for asking. Equations are difficult to read as text. It was only after I had written Bill's equations in a normal layout that I understood what he meant, and that it was not too difficult after all. I had to look the Poisson stuff up and fiddle around (which reminds me) with it for some time. Most of it is very simple math, but it would become very complicated English if one wrote it out in words. Like:

The frequency equals two, divided by the length of the string, and again multiplied by the square root of the quotient of stress and density.

Shudder. I'd rather write Reverse Polish: ikswaineiW.

If you are interested I could write the derivations out in a word processor, math and all, and mail you the results.

When you tune your D string down an octave and then bow it, you will notice two things: the vibrations are much wider than normal, and the tone goes up when you play loud. With a Passione string I found a difference of a little less than a semitone (say 50 cents) between very soft and very loud bowing. That proves the effect exists.

With the string back up to its normal tuning the difference becomes too small for me to hear. The Peterson program claims that there is a difference of around 3 cents, but it is hard to distinguish that from random fluctuations in tone height, due to other causes.

Something tells me that this is a distraction. Next lesson is Monday, so I need to practice! I'm not complaining: it's a privilege.

Cheers,

Bart

April 6, 2011 at 09:42 PM ·

April 6, 2011 at 09:52 PM ·

Good catch Roland!

OK Bart, time to stop practising - there's an equation to tone!!

Sorry, didn't mean to put any pressure on.  If you know what I mean...

April 6, 2011 at 10:26 PM ·

In Simon Fischer's demo video, pressing hard (and no bow speed change) causes the pitch to go down a semitone, just as Charles Cook suggested. Any explanation on that?

April 6, 2011 at 10:51 PM ·

I'm amazed that Simon did that just Fur Elise.  Elise, you RATE!

@Bart, there was a guy in my college that was brilliant beyond comprehension.  In classes where everybody was completely lost, he would yell out the answers to problems before the professor finished solving them.  But, in spite of his brilliance, he had trouble finding his way around campus.  Hence, my remark about the shoe laces.

April 6, 2011 at 11:19 PM ·

My head hurts from reading all this, but I think I can answer why the bowed and plucked strings sound different.

The bowed string is distorted until the point where the friction of the bow is less than the tension of the string. This will be a farily narrow band of tension overall in the scheme of things.

The plucked string is distorted based on the physical angle and pressure of the plucking instrument (pick, finger, whatever). This will be a different note, unless carefully managed.

That said, the bowed string will be constantly snagged by the bow, and stay within fairly narrow tension limits as the bow slides across the string. The plucked string, however, will start from the maximum distension and with each oscillation, distort by an amount controlled by the tension and rebound characteristics of the string. Therefore, the sound will be less stable, approaching the nominal string tuning.

Sorry for not throwing out a bunch of math and physics, but I could dig it up if you want; I just would prefer thinking in analog terms instead of discrete terms.

April 7, 2011 at 12:38 AM ·

Ok Elise in English.  When you turn the peg to tune you are changing the tension of the string.  Higher tension = higher pitch.  When you press hard on the string with the bow, it has the same affect, higher tension therefore higher pitch.  The change in pitch is relative to the change in tension.  E string has higher tension so pressing on it has smaller relative change in tension compared to pressing on the g string.  Understand rubberband?

April 7, 2011 at 12:58 AM ·

Except for the affect/effect flub, I'd say Smiley has English dialed in better than any of us.

April 7, 2011 at 01:22 AM ·

Er, Smiley - I think you have just described the horse we came in on.... the point was that is what I expected - but its not what I hear.  The note does not change.  Bill (was it Bill or Bart or Ben or..) had the nice example of tuning down an octave and then you CAN hear a change with pressure.  The Fisher clip shows that you can hear the same thing if you shorten the string (by stopping).  Which raises the question whether the violin is the ideal length /note ratio to minimize the pressure effect:

Which also raises the question whether the pressure-tone effect can be detected on a viola or cello?

April 7, 2011 at 01:50 AM ·

I have a different question. Technically I suppose it could/should have its own thread. But it falls under the general heading of good strings gone bad.

Has anyone noticed that when a string has gone false, one of the indicators is that after you play it as an open string - and indeed, in a non-forceful way, just letting it ring out - the pitch changes as it rings. But here's the odd part: the pitch almost invariably goes up on a false string, whereas it stays pretty much level on a true string. Why should it go up? If the pitch is going to change at all on a string after you bow it and let it ring out, true or false, it ought to go down as it decays, no?

April 7, 2011 at 02:31 AM ·

OK, maybe I missed something -- too lazy to go back and read the entire thread.  What's the problem Elise?  Do you have an insatiable desire to change the pitch of the note by pressing down on the string?  Consider it a blessing that the pitch does NOT change.

I have a similar problem.  I make too much money.  As much as I try to make less, I keep making too much.  Can anyone help me with my problem? :-)

April 7, 2011 at 02:41 AM ·

"Which also raises the question whether the pressure-tone effect can be detected on a viola or cello? "

Viola's don't notice changes in pitch that are less tha a 5th ... (wink)

Joke:

Q:How can you tell when a viola player is out of tune?

A: As soon as you see the bow move ...

April 7, 2011 at 05:01 AM ·

That's a weird growl. (that was in response to Roland's post about the Simon Fischer video: the computer /Internet is playing tricks on me)

@Smiley: I understood your shoelaces remark the first time. No need to rub it in. Now where are my glasses?

April 7, 2011 at 11:22 AM ·

"Which also raises the question whether the pressure-tone effect can be detected on a viola or cello? "

I've never noticed on a viola:  Any pressure-induced change is always covered up by the Doppler effect -  Induced as I run away as fast as my legs can carry me.

"Thanks, I'll be here all week."

--------------------------------------------

But seriously:  The effect isn't more pronounced on larger instruments because the strings are proportionately thicker.

April 7, 2011 at 01:18 PM ·

OK so who has a piccolo violin?

Actually I still have my 1/2 from when I was 6.  Shudder to think that that violin is now at least a hemicentarian... Saturday experiment!!

April 7, 2011 at 06:05 PM ·

OK, here's an attempt to answer why the note doesn't go up. It has to do with relativity and our lack of complete understanding of the universe.

When the note is first initiated, it is new to the universe. However, the longer the note is sustained, the more the universe has expanded, so the string is actually longer for every instant. This increase in length should cause the note to decrease, however phenomenon of sound is always being redefined as the universe expands, and for some strange reason (still not completely explained, as the Higgs boson has not been yet discovered), the net effect is to have the apparent pitch increase.

April 7, 2011 at 07:01 PM ·

Roland, you lost me. I feel that we're drifting apart.

April 7, 2011 at 07:22 PM ·

Odd that, I had a hard time wity your equation but I understand Roland's explanation and can truly relate to it...

Particularly about the universe expanding - I mean just look below your rib cage...

April 8, 2011 at 11:16 AM ·

So - no takers on my question earlier?

I have a different question. Technically I suppose it could/should have its own thread. But it falls under the general heading of good strings gone bad.

Has anyone noticed that when a string has gone false, one of the indicators is that after you play it as an open string - and indeed, in a non-forceful way, just letting it ring out - the pitch changes as it rings. But here's the odd part: the pitch almost invariably goes up on a false string, whereas it stays pretty much level on a true string. Why should it go up? If the pitch is going to change at all on a string after you bow it and let it ring out, true or false, it ought to go down as it decays, no?

PS "Brooklyn isn't expanding" - Annie Hall

April 8, 2011 at 11:36 AM ·

I suspect noone answered because noone has a clue!  I sure don't.  But maybe if we approach the question from your last perspective we will come up with something useful...

April 8, 2011 at 01:46 PM ·

Raphael I will give it a go.

The more a string vibrates the higher the pitch.If you have a washing machine that is slightly off balanced, it will vibrate and shake at certain speed and be fine at other speeds. .If it is really off balanced ,it will shake violently at all speeds.The same principle can be applied to the worn string, excessive vibration may cause  certain frequencies or over tones to be amplified.

April 8, 2011 at 06:48 PM ·

Interesting. But keep in mind that I do most of my practicing in Brooklyn - which isn't expanding. So the laws of physics may be different here! ;-)

April 8, 2011 at 08:42 PM ·

I haven't got a clue: cannot even reproduce it on my own violin.

April 8, 2011 at 10:40 PM ·

Well DUH Bart, do you live in Brooklin?

April 8, 2011 at 10:53 PM ·

Bart - maybe you don't have any false strings right now. For my part, I couldn't reproduce Simon Fischer's Fur Elise trick. Maybe I couldn't bring myself to use enough force. Or maybe it's something in my quadrant of the space-time continuum.

April 8, 2011 at 11:28 PM ·

Raphael  I am sure you will get it in the next few day's. I teach this technique to my beginner students before they learn staccato and  to accent notes. I also use this technique to retrain intermediate players  who have poor control of accents and staccato. I feel they need to be able to separate speed from pressure so they will have more control.In the U tube video I posted earlier I use this bowing  technique to add more colour to the 1/4 tone slides.

April 9, 2011 at 03:46 AM ·

You guys are a total bunch of violin geeks.  No wonder I feel so at home here :-)

April 9, 2011 at 04:23 AM ·

Raphael - you're right, I did not have any false strings. But I made one by putting some Sellotape on my G string. After that it was false alright, but the tone still went down on pizz instead of up.

April 9, 2011 at 05:53 AM ·

Raphael,
I'll give it a go.

I would suspect one of the qualities designed into a quality string is a predisposition for the specific note of the open string. This would possibly be a tension predisposition. It would make it the range at and around the ideal note be an easier one to tune than say, a higher or lower pitch. You could test by tuning your strings down, rather than up, and see if they play false.

When the string turns false, it loses some of that elacticity at the magic tension; it becomes less pliable, and therefore does not hold the note as well for the full range of distortion it experiences.

Does anyone have ammunition to shoot the holes in this theory? I would be pretty suprised if my first salvo actually carries very far.

April 9, 2011 at 11:03 AM ·

Its simple reversion.  Once old or injured a sheep, pressured by a a predator, will run up the mountain side, not down it.  Its gut just does the same thing.

I have no clue about the synthetics though.  Maybe this is just a Baa-baa thing...

April 9, 2011 at 10:29 PM ·

I don't know. All I can say is that when a string is false, it consistently rings up as it decays when I bow the open string gently, and let it ring out.. Putting tape and pizzing may not be the same.

As far as the Fur Elise trick, the first couple of times a tried to replicate it was for only a few seconds each try. The the 3rd time I pretty much got it in my own way.

Now I must take a break from all postings for a little while - quite busy now with gigs.

April 12, 2011 at 08:41 PM ·

I will try to clarify some of these issues. Bill Platt's analysis is essentially correct (Bravo!), but there are a few misleading and erroneous comments in this thread.

The biggest bowed pitch rise occurs under the following conditions:

1. String with the least elastic core to maximize tension increase
2. Lowest frequency string to maximize bowed string vibration amplitude (displacement)
3. Open string to maximize bowed string vibration amplitude
4. Lowest string tension to maximize percentage tension increase
5. Low bowing force (pressure) to minimize the bowed string stick-slip "flattening" effect
6. Fastest bowing speed to maximize bowed string vibration amplitude
7. Shortest string length to maximize percentage tension increase (this seems to contradict #3, but I'll explain...)

A LITTLE BACKGROUND

The vibrating string differential equation which results in Mersenne’s Law as quoted above makes several simplifying assumptions and one of them is an infinitely small (zero!) amplitude of vibration. As Bill Platt and others have shown, the string length of a vibrating string increases over its rest length.

A bowed string vibrates completely differently than a plucked string. A bowed string consists of two straight line segments with the corner (or kink) travelling in a parabolic curve which forms the boundary of the blurry curve you see, once every vibration cycle. See http://www.phys.unsw.edu.au/jw/Bows.html for an animation of this Helmholtz or “stick-slip” motion of a bowed string.

FACTORS (as listed above)

1. String/core elasticity: if the string has very low stretch, the increase length when vibrating can increase the tension enough to cause an audible pitch rise. As others have shown, this tension increase has a much larger effect on the pitch than the increase in overall string length, which would lower the pitch. The stretch characteristics of a string is determined mainly by the material and the construction of the core. Gut, synthetics, and certain types of stranded steel cores have very high stretch. Solid steel core and certain stranded steel core strings have very low stretch.

2 & 3. String frequency: the bowed stringed amplitude (displacement) increases with lower frequencies. This can be understood from the geometry of the stick-slip motion. For the same bowing conditions (same speed and distance to bridge), the bow (hair) carries the string a further distance during the “stick” portion because each vibration cycle takes a longer period of time at a lower frequency. Therefore, it is easier to bow a string vibrating at lower frequencies to larger amplitude displacements and why the problem is always worst for the bottom string. This is the main reason a violin G has more pitch rise than a violin E.

Likewise, you can bow with a much larger amplitude on a open string versus a stopped string. Although the string length is decreased for a stopped note, the percentage string length increase is still less because any given bowing point is proportionally further away the bridge. See Bart Meijer’s equation above.

4. String tension: lower tension strings have a greater pitch rise because a given tension increase produces a greater proportional increase. The frequency is determined by tension, not stress, contrary to the statement above that “tension doesn’t determine pitch, stress does”. Stress is the merely the tension divided by the cross-sectional area and for most strings, the cross sectional area does not change enough under tension to be a factor, so tension and stress does vary together (Bill’s statement is not totally incorrect).

For wound strings, most of the tension is carried by the core. Pitch rise can be reduced by using a smaller core because a smaller core will stretch more, but that increases the stress. From experience, using a core above 60% of its breaking strength invites durability problems.

The main reason the violin E has low pitch rise despite its solid steel core is its high frequency (see #2), and not its high tension (though that helps).

Another factor is that lower tension strings sound less loud under the same bowing conditions, so the player has to bow with a larger string displacement amplitude for the same loudness, which contributes to the pitch rise. A lower tension string is also easier to bow to higher amplitudes, just as it is easier to pluck a lower tension string to larger displacements.

5. Bowing force (pressure): High bowing forces will cause a vertical deflection of the string, which increases the length of the string, and therefore its overall tension. However, the amount of static vertical deflection possible with the bow under normal bowing conditions is much less than the displacement from vibrations, so this effect is small compared to the bowing amplitude.

In addition, there is an opposite “flattening” effect, much studied by physicists. Under high bowing forces, the stick-slip mechanism takes longer and the frequency of vibration decreases slightly. This is the underlying mechanism for the trick described by Trevor Jennings and others. This flattening effect, less than a semitone, is different than sub-harmonics, also known as anomalous low frequency (ALF) tones, which can be an octave or more lower and used by some players: see Mari Kumura at http://web.me.com/marikimura/Site_2/main.html.

6. Bowing speed: it is easiest to use high bow speeds to produce the high vibrating amplitudes that maximizes pitch rise, rather than  bowing closer to the bridge, which requires higher bowing forces that are hard to control and contribute to the flattening effect. The minimum bowing force required to maintain Helmholtz motion increases rapidly as you get closer to the bridge.

7. String length: a shorter string length will result in a higher pitch rise because for the same string displacement, the string length and thus the tension will increase by a larger percentage. This seems to contradict #3. The explanation is that the shorter string will have a higher pitch rise if the two strings have the same frequency and tension, while an open string will always vibrate at a lower frequency than a stopped string. In addition, instruments with shorter string lengths usually use lower tension strings as well, especially children’s instruments, to make them easier to bow.

We can compensate for pitch rise to a certain extent by adjusting our fingers, but not completely. One cannot use fingers to reduce the frequency of an open string note. For stopped notes, the amount of pitch rise can change during a bow stroke, which is hard to compensate for. Many 6 or 7-string instruments make the lower strings a bit longer – this is only partially effective.

April 12, 2011 at 09:13 PM ·

Wow, Fan, thanks for posting!

I try to punt on the technical stuff (and Fan probably rolls his eyes from time to time), but Fan is the man. Click on his name for the bio, to get a sense of what he knows about strings and violin acoustics.

April 12, 2011 at 09:17 PM ·

I’m not convinced that all false strings exhibit a rising pitch trajectory after the bow leaves the string, but here are some possible explanations if it is true.

The bowing action (Helmholtz, stick-slip motion) forces the string overtones to be harmonic. When you lift the bow from the string, the string gradually transitions to its own natural vibration overtone frequencies. Even a non-false string can exhibit a rising pitch trajectory because the bending stiffness of a string (which depends on string construction) causes its overtones to be sharp relative to the fundamental, which could affect the perceived pitch.

If material is worn away where the fingers stop the string, that will increase the higher overtone frequencies more than the fundamental.

We also cannot discount possible psychoacoustic effects. Human pitch perception is highly context sensitive and the perceived pitch can change slightly with amplitude! (Different people can perceive the same thing differently as well.) As the note gets softer and changes in timbre, even if the vibration frequencies stays the same, it is possible the perceived pitch changes.

April 12, 2011 at 09:57 PM ·

Hi Fan,

Very nice to read an actual expert stringmaker's thoughts here!

One thing that seems unclear from your description, and which seems to contradict what I said, is as follows:

"This seems to contradict #3. The explanation is that the shorter string will have a higher pitch rise if the two strings have the same frequency and tension, while an open string will always vibrate at a lower frequency than a stopped string."

I know we are both saying the same thing but it can be difficult to put into words rather than equations. What I mean by " pitch depends on stress not tension" is assuming a monolithic string: the pitch, for a given mensur, will be independent of gage but dependent on the stress. In other words, the thick string has more tension, but the same pitch and same stress.

The corollary to this is the shorter string, kept at the same frequency as its longer cousin, all other things equal. The tension must needs drop, as will the stress. If you want to keep the same tension on a shorter string, the gage must go up relative to a longer string at same pitch; therefore the stress is lower on the shorter (monolithic) string. Or you can do a heavier winding...but as you point out, typically you don't make 1/2 size instrument strings thicker than full-size. We just seem to accept the flabbyness. That being said, I have often wondered whether you lighten the core more than the winding on wound fractionals, to keep the core stress up to a reasonably high level. (The 60% of sigma u idea is interesting--that matches my rough tests!)

Really interesting about the flattening effect. Now you have me really thinking. I've made the subharmonics a lot but I'll have to play with the flattening tones now!

April 13, 2011 at 02:56 PM ·

Hi Bill,

It is true that the frequency is uniquely determined by stress, for a string of a given length and homogeneous material. However, this is not a useful way of thinking about strings for me. Wound strings are not homogeneous material-wise so the stress depends on the specific implementation of the string.

In addition, physicists find it more useful to look at strings in terms of how fast a wave travels down the string. The frequency of a vibrating string is determined by the time it takes for a wave to come back to its original position after travelling down the string, reflecting from the bridge, travelling down the string in the opposite direction, and reflecting from the nut. The wave velocity of a string is squareroot(tension/massPerUnitLength) and occurs in Marsenne’s Law quoted by Y Cheung, though his original posting has a typo in it. Here is the corrected version:

Frequency = [1/(2L)]*waveVelocity = [1/(2L)]*sqrt(T/m) where L= length, T=tension, m=mass per unit length

For core loading, I know the breaking strengths of the available cores and sizes and I make sure there is a sufficient safety margin for the playing tension. I actually want to use the core at less than 60% of breaking if possible. I do not think in terms of core stress, nor do I pick a core to a target stress. Rather, the choice of the core is based on sound and playability factors. The core size is a secondary factor for pitch rise once the basic core material and construction are chosen.

Fractional size strings are almost always larger in diameter than their full size counterparts, despite their lower playing tension. Tension varies as the square of the vibrating length, for the same string and same frequency. If we use a full size string for a fractional size instrument, the tension drops more than we want. Therefore, fractional size strings actually need more mass per unit length, despite their lower playing tensions.

April 13, 2011 at 02:59 PM ·

Hi David,

Thank you for the kind words. You do a pretty good job of explaining technical things yourself, on the rare occasions you cross over to the technical side!

April 13, 2011 at 04:35 PM ·

re the issue of false and/or old strings ringing sharp:

I'm just guessing, but since such strings often have harmonics that are not correctly spaced, it's possible that this is what you are hearing.  In other words, the primary overtones might be slightly sharp (due to dirt, or uneven thickness, or uneven winding, etc )  and as the fundamental frequency fades away, these sharp overtones become more noticeable.

Or not, I don't really know.

It might also have something to do with Tartini tones.

May 4, 2011 at 12:21 PM ·

Hi Fan, and others. I also appreciate your professional input and expertise, and I just read your article in "Strings" magazine on the subject of false strings. I'm still left with a couple of questions.

When you said above, that you're not convinced that all false strings exhibit the rising pitch effect after the bow has left the open string - of course nobody could possibly try all strings. But what I can say is that I've experienced this effect innumerable times with different brands and types of strings. Sometimes I've noticed an effect where the string does not get specifically higher, but rather the 'after-sound', when the bow leaves the string, kind of swirls and spirals around in a less determined fashion. Anybody else ever experience this? I think I can understand how unevenness, wear etc. could bring out different overtones. I have more trouble accepting the idea that it might just be a matter of perception when this happens over and over again when a string has been on for quite some time, but not earlier.

Another thing I've noticed sometimes - especially with an E - is what I might call a 'false falseness', that is a temporary falseness when I first put on a string - especially of the swirling effect variety - which goes away after the string settles in. Why?

When do I begin to suspect that a string is false? Usually during the tuning process. If I'm having a lot of trouble getting say the D and A to co-operate into a clean 5th, I'll give each of them the 'after ring' test that we've been talking about. I agree with what you say in "Strings" that testing with 5ths is not the best idea. It's hard enough sometimes to tune the fiddle perfectly even when the strings are true, let alone to to play 5ths perfectly with stopped fingers. A much easier test is to play a minor 6th - e.g. in 1st position, 1st finger B on the A string and 2nd finger G on the E. Normally the fingers should be very close neighbors. This can vary with the thickness of our fingers, etc., and our ears must be the final arbiters. But generally this is true. When one, let alone both, of the strings is false, there will have to be some space between the fingers. Why this is true, I don't know, but I've found this to be so over and over.

Another phenomenon I've observed re tuning is open strings vs the natural harmonics - i.e. the first octave harmonic that divides a string evenly into 2 halves. I understand that natural harmonics don't always coincide with our more modern conception of consistant intonation, and that as we go along in the harmonic series, some overones flatten. Do I basically have that right? But I notice that most with the G, again, with various types and brands, and I don't know why. Say I get my open strings pretty well in tune, then I play the same string pairs an octave higher, with the natural harmonics in the 4th position area. The higher G will be most noticibly flat in relation to the higher D, when I play the 2 strings together. Why is this?

One last subject: in the "Strings" article, you mention the wolf note, and say that it occurs when the played note matches the instrument's resonant frequency. What about an instrument that has 2 or 3 wolf notes - can an instrument have more than one basic resonant frequenciy? Why are some wolf notes stronger than others? What about an instrument with no wolf notes? Also, I've noticed that say a violin has a wolf note typically on the C or C# above middle C. It will be less 'wolfy' with those same notes on the D. And by the time we get to the A, those notes will sound particularly good. Why is this?

Thanks!

May 5, 2011 at 03:50 PM ·

Hi Raphael,

You bring up many good points. I have observed some of the things you described. I wish I had time to do careful experiments and measurements to provide more definitive answers.

I agree that using minor sixths to detect false strings can be more reliable than fifths due to the sensitivity of our fingers to changes in relative spacing.

You are correct that natural harmonics do not match tempered (or most other) scales. It’s the same problem faced by natural valve-less trumpets or horns.

Acoustics researcher Knut Guettler has pointed out a several other reasons harmonics often sound flat. Most people prefer slightly stretched octaves and intervals, meaning an exact two to one frequency ratio sounds flat. Harmonics have less higher overtone content, making them sound flat in comparison to the overtone rich sounds of a normally stopped bowed string. Apropos to the original discussion on pitch rise, the open G-string suffers from more pitch rise than its harmonics or the D-string. All of this could explain why the harmonics of the G string sound flat compared to the D.

I only briefly touched on wolf tones in my Strings article on false strings. The editors improved my article, but introduced some minor technical inaccuracies. Yes, the violin body has hundreds of resonances, not just one, though less than a dozen that can be easily isolated at the lower frequencies below one kilohertz.

At the same time that the bridge transmits the vibrating forces of the string to the instrument body, the motions of the instrument body are transmitted back to the string via the bridge. A stable Helmholtz motion for a bowed string depends on the ends of the string being still. A wolf note can occur if this condition is not met, which usually occurs at the largest resonance of the instrument where there is the largest body movements. However, it is possible to have wolf notes at other resonances. Whether a wolf note actually occurs and the degree of severity depends on a many factors, including the exact behavior and mode shape of the resonance, the soundpost position, the bridge, the string, and other parts of the instrument (such as the tailpiece assembly) which could be vibrating at the same frequency as the wolf note.

The reason the wolf note is worse when playing the same note on a lower string is because the lower strings have more mass. This increases the coupling between the string and the instrument body, worsening the wolf effect. One remedy for reducing wolf notes is to use lower tension strings, which have less mass.

The point I was making in my false strings article is that instrument resonances, even if they do not cause recognizable wolf notes, can still detune a string for certain notes, simulating a false string. In rare cases, it is impossible to play the desired pitch, no matter where you stop the note!

May 5, 2011 at 04:10 PM ·

Very interesting. Thanks, Fan!

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