Tuning Fork Disagreement: Newsletter Challenge (01/02/08)

Several possibilities come to my mind (not all are serious):

1. Tommaso realized he had tinnuitis (ringing in the ears), and this had fooled him.

2. Giovanni realized he was using the wrong tuning fork.

3. Tommaso plays a different instrument and doesn't know how to tune a piano. He thinks that because he is an expert at his own instrument, that makes him an expert on other instruments.

4. The pitch changed as Giovanni continued playing the key. The strings played by that key are worn out and need to be replaced.

5. Tommaso is on drugs. He come down off his high during the second five second listening period.

When Tommaso was passing by, Giovanni was checking the different keys on the piano board to see which key matched the tuning fork. What Tommaso heard was the key that did match the tuning fork, Giovanni then pointed out that the key he was playing was not the correct key, so when Giovanne played the correct key that should match the tuning fork he agreed they did not match.

Regards JD.

I think that you are right. At least as far as the challenge question goes.

Pianos contain multiple strings per key or note. When you tune the piano with double or triplet strings you do not tune all strings to the exact same note. Rather, you tune the center string slightly sharp from each of the others to provide a richer tone. If the blend of notes are not correct it will produce an undesired effect and you could get a note that sounds off-key.

Also, during the tuning process you need to mute the companion strings to that key or you get two notes. If one string has a longer and louder sustain it will override the other string as it decays. It can get pretty frustrating trying to tune multiple strings without damping the others.

Pros take years to lear the techniques by practicing and practicing.

In re to Europium's reply #4 and Anonymous's reply # 9, I am sold, guys. You know your stuff. Now, can we get back to talking about the harmonics of Black Hole's accretion discs, please?

A trick of sound called sympathic vibrations can allow the piano to set the tuning fork to vibrating if the frequencies match. In this example the key was not inducing the vibrations on the fork.

Also keep in mind that most of the keys on a piano use more than one string so if only one of the strings slips it will cause a distortion in the note. To tune the piano correctly one needs to silence all but one string on a key and start tuning each string individually. After the first string is tuned the other strings can be added in and tuned to match the first.

As usually, too many possible answers, too little information or limiting parameters.

When two frequencies 'interfere' with each other, they produce two new frequencies, one frequency being the sum of the two and the other being the difference between the two. It is the difference frequency that is the give-away. What Tommaso heard was a low-frequency 'throb' that was the difference between the tuning fork and the struck note in the five seconds while standing there, and concluded that as there was a difference between the note coming from the tuning fork and the other coming from the string and, therefore, that the piano was not precisely in tune.

As europium has correctly pointed out, the strains in a piano frame as it comes up to pitch from tensioning the strings are a significant fraction of the overall strength of the frame. So, changing the tension in one set of strings will adjust the shape of the frame slightly, and in so doing it will alter the pitch of the other strings, particularly near the centre of the frame where dimensional distortion will be the greatest. For this reason, a piano tuner will revisit the other strings periodically during the tuning process and give them a gentle 'tweak', as well as the one under primary consideration.

It takes a long time to tune a decent piano really well, and even then its pitch will change slightly as the ambient temperature changes; it changes the stresses in these components thereby altering the vibration frequency of the strings; the tuning.

Of course, Tommaso and Giovanni were both perfectionists and the propsect of buying an electronic keyboard instead was far beneath them....

My question is this, would a high quality electronic/electric piano sound just as good or better (being ALWAYS in tune, by definition I believe) than a medium quality home-type (vertical or spinet) that might de-tune somewhat naturally over time?

Well, it depends. A perfect 5th, or 7 semitones, is 1.5 times the root frequency. 2^7/12 = 1.4983070768766814987992807320298, which isn't quite 1.5. So it depends upon whether the http://en.wikipedia.org/wiki/Equal_temperament tuning or the http://en.wikipedia.org/wiki/Meantone_temperament tuning method is being programmed.

For the piano in René's humble café, it probably doesn't matter, as everyone puts cheese in their ears while Edith sings. Plinky plinky plinky, plinky plinky plonk....

Hello PWSlack,

Although there is a very slight change in net tension overall, it is rather the extreme tension of each string that causes the string to behave acoustically more like a metal bar than the idealized, infinitely-thin strings we find in physics textbooks. Where idealized strings produce perfect, integer-multiples (harmonics) of the fundamental, metal bars do not. In a piano string, even a slight departure from equilibrium stretches the string slightly. This effect, coupled with a real string's non-zero thickness, causes the overtones to depart from a purely harmonic relationship to the fundamental.

Cheers!
-e

easie said:

Decadence

Jstacat

What about Doppler?

Maybe it was in tune, but in the wrong octave?

Yes, but the combined sounds of the piano string and the tuning fork are not perceived as variations pitch, but as variations in loudness as the sound waves from each alternately reinforce and cancel.

I thought I clearly explained that the beats were a variation of loudness. Where did I even hint that the notes were perceived as variations in pitch

The beats occur with a frequency which is the difference of the 2 notes

"I thought I clearly explained that the beats were a variation of loudness. Where did I even hint that the notes were perceived as variations in pitch."

-----

Your hint is supplied by the fact of your response itself to the Newsletter Challenge, which asks why Tomasso perceives a change in pitch. But if your answer is not to the question posed by the Newsletter Challenge - and apparently it is not - then what question are you answering? The Challenge question does not ask why Tomasso perceives a change in volume, but why he perceives a change in pitch. If you are not even hinting, as you say, that the notes are perceived as variations in pitch, shall we then consider your answer off-topic?

"Your hint is supplied by the fact of your response itself to the Newsletter Challenge, which asks why Tomasso perceives a change in pitch."

C'mon "e"! Go back and re-read the original question! To0 lazy? OK, I will paste it here:

Giovanni was tuning his piano using a tuning fork when his friend Tommaso stopped by. Tommaso listened for five seconds and then confidently told Giovanni that the key was in tune. Giovanni disagreed. After about five more seconds, Tommaso was forced to agree that the key wasn't in tune afterall. What happened to change Tommaso's mind?

The question does NOT ask "why Tomasso perceives a change in pitch", but "what happened to change Tommaso's mind, and Lleros is clearly correct that with more time, Tommaso was able to hear the same thing that Giovanni had been hearing, i.e. amplitudinal beats with a long period caused by the extreme closeness of the two audio frequencies but not perfectly in tune (which would have an infinite period based on the calculation Lleros clearly stated.

You are usually better than that "e"!

You're absolutely right. My bad. I should wait until after my morning coffee before making assumptions. Usually by then I'm too busy jumping to conclusions, but it keeps me in shape.

I suspect that when he said "the louder part" and "the softer part" he was referring to loudness, not pitch.

OOPS -- caught this in the edit window. You've already been chastised for your woeful behaviour. No need for me to rub your face in a senior moment.

Ignore what I said above. But which?

I believe this is the correct answer!

:-))

cheers

RF_G

I think you are right !!! It couldn't be something as simple as listening more carefully or longer.

I think that when the fundamental note is struck and compared to the tuning fork, in the first 5 seconds the pitch may sound like a match.

As the fundamental note sympathetically excites the harmonic over and under tones and the strings at different octaves, the decay rate is shortened if the fundamental note is off by 1 Hz or even a fraction of a Hz. This rapid decay could be caused by phase cancellation or dissonant damping.

From this, if the instrument is not still resonating after 10 seconds the string or strings are not in tune.

Looking forward,

Tomqwest

Having played piano, cello, clarinet, and spoons I have to agree with your beat answer. it was how we tuned our instruments. (But 1 beat every couple seconds was as good as my ear could discern!)

Hi GW.

I play the violin, and when the tuning fork is struck the string that is to be tuned will vibrate at the same frequence when it is in tune, it is called sympathetic vibration!
Spencer.

I was always able to get the sympathetic vibration and still have a beat. It didn't seem to have a particularly high "Q" test.

I see the same thing in tuning variable speed drive systems, the forcing function does not have to be spot on the resonant frequency to excite the resonance.

I play guitar, but I don't ever tune it. Am I supposed to? I thought those knobs were for when the strings start buzzing on the frets, you crank a knob a few times 'till it stops buzzing. I wondered why my kids go outside when I reach for the axe!

Guitar players are never in tune... And we like it that way!!!

Actually the trick with the harmonics can be used to test the tune of a piano. For instance if you gently depress the "C" key on a piano such that the hammer does not strike the strings, and while holding it, sharply strike and quickly release the "C" key one octave lower, you will hear the note you are holding ringing. This is again an example of sympathic vibration. If the note is out of tune you will not hear the held note ringing.

Lleros MaHarg, I did not understand your calculations of the constant ratio between two successive half-tones (13th root of 2):(1) ????? In my humble opinion, it should be instead 12th root of 2 i.e, approximatively 1,059463... Perhaps the difference of tuning two contiguous half-steps using your formula would not be immediately perceptible, but considering a range of various octaves, I am not so sure...

Dear Slimac,

My apologies, you are correct, 13 notes to an octave counting the first note and the last one (an octave above). 12 half note eqally tempered intervals in between.

Ratio between half notes is (12th root of 2):(1) with ratio.

It certainly stirred a hornets nest, got the musicians out of the woodwork, excellent multi discipline discussion. Should be more challenge questions like this.

It's all freshman physics, with a small component from my cello playing days, plus a bit of logic

Lleros

Most interesting is the applied science, obserations from practical application, and the theory from the musicians. ( Is this not true engineering, that is applied science?)

I am not disagreeing with your explanation and I will say that i am in agreement with the bulk of it.

However being a musician and having tuned several instruments and have had a piano tuned several times I believe what Giovanni was listening for are whats called Cross-tones. This is the effect that happens when to instruments are just barely out of tune. They are more of a pulsing that happens at a faster rate when the to instruments are at their farthest point of tuning and a much slower rate to the point where perfect tune in made and there is no more pulse.

For a close approximation of this phenomenon take 2 identical wine glasses and fill them half full with water. alternate ring them and keep the tone going as long as you can. if they are exactly the same fill and structure you will hear nothing in the background if they are slightly off you will hear the pulse of which i am speaking. gradually add or remove water from one glass and you will make the pulse faster or slower. Slower means closer to tune faster means farther from tune. Best to do this with your eyes closed and concentrate on the combination of sounds and the extra tone they make not the individual sounds.

I watched a blind man tune our piano when i was a child and I sat quietly for hours as he did so. (no easy feat mind you) He educated me as to what to listen for and demonstrated it many times during the tuning of our piano. At the 5-10 second mark if the long duration pulse is not heard then the string being tuned is now correct.

As stated by previous posters Tomasino... Tommas...tom...the other guy did not wait long enough to have been able to hear this pulse before making his decision as to the state of the tuning of this particular string.

Just a note: If you have a piano and want to have it tuned. If the tuner is not blind find another. Their perception of sound is much more acute than that of a person who can see. Plus its really cool to watch them do their thing without being able to see a thing.

As you appear to be a person who has done this in practice, I'd like to ask you a question: do you observe this length of cross-tone (or beat) when comparing a note on the piano to a note from the tuning fork? (I've no difficulty with the idea that you can hear this when comparing different strings that are below middle C, as the sound is relatively similar and decays at a similar rate, but I fear there could be problems when comparing with a tuning fork)

Thanks

Fyz

I can't help but notice that your post number is the second harmonic of Llero's. Spooky.

I think "beats", "beat," or "beat frequency" are the more common terms to indicate what you refer to as Cross-tones. Granted, I don't have any real data to support that, but in my experience, everyone tunes by listening for "beats", assuming lack of perfect pitch.

I agree much of what you say here. But, while many (most?) string players believe that they play to harmonics when a piano is not involved, this is not actually correct.
The most obvious demonstration of this would be the use of major and minor thirds. The "equivalent" harmonic relationships would be 1:25:1 (major third) and 1.2:1 (minor third). That is about 0.059 of an octave, or 0.7 of an average semitone. But I for one (when unaccompanied) play the difference between a major third and a minor third as a large semitone.
A secondary piece of evidence is the difficulty when instruments play one fifth apart. If the notes played separately sound "in tune", the sound when put together will often be terrible; I believe two factors are at play here - first, the 1.5:1 frequency relationship makes difference notes extremely audible, and second, the usual size at which we play a fifth is relatively close to the factor 1.5.

BTW, although I expect that your answer to the challenge will be the formal answer, I'm not certain that it is completely realistic. I'd appreciate your comment on the following:
Assuming the tuning fork and piano note to be somewhere between 440- and 512-Hz, they will both decay very significantly over a few seconds - possibly sufficiently that you it will be extremely difficult to detect a beat with a period of more than about three or four seconds. What could happen is that the levels are initially so disparate the general decay in amplitude hides the beating effect; then, as the note decays the levels become sufficiently similar that the beat is larger than the general decay.
This is of course purely theoretical - I would prefer to make a practical check, but my piano is due to be tuned in about four weeks, and its pitch is not close enough to my tuning fork to confirm whether I could detect a beat period of 5-seconds** or more in the presence of un-cancelled overtones and decaying levels.
The same does not of course apply to the difference in pitch between the multiple strings that make up the notes - they will have similar amplitudes and decay together, and the results will certainly be extremely audible

**N.B. that this represents a frequency difference of < 0.05%, or less than 1/24 of a tone

Regards

Fyz

When tuning my guitar, the beating of the strings can also be seen as the amplitude of the vibration varies. When the two strings are closely matched, the amplitude varies only slightly and over a very long period. Being tone deaf, the visual aspect helps me alot.

Another amusing way of tuning the guitar is by puting a tiny piece of folded paper on the string and then tuning it with either another string or a tuning fork. The paper literally jumps off. Can be a pig to get it out of the guitar afterwards.

While I like the explanation that Lleros MaHarg gave us (and I will remember it for some applications), it is something that only somebody dealing with THIS situation would know (excuses, Lleros, if you just came to the answer by pure abstract thinking -I am only an engineer ).

I am still waiting for the explanation of the one who published the puzzle.

While I like the explanation that Lleros MaHarg gave us (and I will remember it for some applications), it is something that only somebody dealing with THIS situation would know (excuses, Lleros, if you just came to the answer by pure abstract thinking -I am only an engineer ).

I have to disagree with you Indel. The explanation the Lleros gave regarding audio beats is basic physics, taught at the freshman or sophomore level in any Engineering school, in fact, even in High School Physics, and should be common knowledge for any engineer, not just "somebody dealing with THIS situation". I, and I am sure several others had reasoned this out as well, but Lleros beat us to the punch and posted first. Usually, I do not like to post the same answer as someone else who has nailed it, except to give credit by agreement and defend the answer if needed ("e", please note!)

Now, when it comes to his mathematical description of the frequency relationships of piano notes to the scale and to other instruments, well that is a cat of a different color. That would require some specialized knowledge of the physics of the piano, other instruments, and some music theory as well. But he only brought that up in relation to other posts, not to his original, and IMHO, correct answer. We could have just as easily been talking about a guitar string. In fact, I have used the zero beat method, as well as sympathetic vibration in tuning guitar strings from a tuning fork or from a piano.

Zero beating also has applications other than strictly musical or audio frequencies. Zero beating is a tried and true method of tuning a radio to match the frequency of another signal for optimum communication, often used by amateur radio operators (Hams) and others, especially back in the day before digital tuning when all you had was an analog dial and your trusty BFO (Beat Frequency Oscillator)

Bottom Line: You don't need "pure abstract thinking" (whatever that is!) to come up with or to understand his answer, even if you are "only an engineer"!

I agree with you in all you have said about audio beats. Actually, not only audio – Lissajou, eye pattern, you name it…

What I was saying was a bit self-criticism and a kind of (un)hidden envy for people who have time for "abstract thinking" i.e. things they are not involved with in their immediate professional life.

I know, this is how the great ideas have been "brewed", but I am just a humble worker who spends his spear time with stock market, tv action movies, some home improvement,

In one word (actually two - to avoid another correction) an ordinary engineer.

Further to the guitar example, a common method for tuning the instrument is to tune the "A" string, e.g. with the help of a fork and then play the A on the "E" string (5th fret). Both should have the same frequency, so you can tune the second string by eliminating the beat.

Of course You will repeat the same process with each newly tuned string and the one immediatley higher in pitch.

Beat is your friend, I believe it is indeed the right answer.

I think the frequency of the tuning fork and piano key were very close to sync and it took a few seconds for the low frequency difference beat to be heard by Tommaso.

Why post this? It just reiterates, with no explanation, what Lleros so eloquently illuminated in post #11.

Don't "guests" read before posting?

And why post this? So we have 2 (now 3) rather than just one post that ads nothing new?

Don't members have better things to do than criticize guests? Perhaps the guest though his post was more succinct than Llero's excellent explanation.

Touché, Ken. The count is now up to 6 gratuitous postings (counting yours of course!).

I will try to limit my future responses only to important, crucial, vital, essential, indispensable, necessary, needed, needful, or required postings!

STL,

I like your postings, they give depth to the discussion, but consider the fact that we are more experienced at this. More than likely the newcomer is reading the question and just hits the very first reply button he sees, without reading any of the comments already posted. They may be preceiving the intent of the forum is to see how many different postings come up with the same thing. Preception is in the eye of the beholder.

Please keep posting your insightful experiences but please ease up on the new guys.

Perhaps Tommaso struck the octave keys and heard they were at the proper frequencies and compared them to the tuning fork frequency as well as that of the "tuned" key.

if the string being tuned is either new or very old, that is not having been tuned in a long time, when the string is stretched for tuning it will inevitably return to its original position this will cause a change in pitch. The string held the proper frequency for 5 seconds after an additional 5 seconds the string stretched changing the pitch. This is the result of being a new string or very old string. This happens frequently when tuning stringed instruments. A pitch can change over 10 seconds depending on the condition of the strings.

The mention of five seconds twice is the give away here. Beating. As the piano string and pitch fork vibrate at slightly different frequencies, the volume appears to change.

Most probably this is due to the Diopler Effect.

Since Giovanni was tuning the piano we can assume that he was stationary.

As Tommaso was passing passing by most probably he was walking towards Giovanni when he listened to the turning.

On the next five seconds most probably he was also stationary.

Perhaps Tommaso is completely tone-deaf and regards the question "is it in or out of tune" as a 50:50 gamble. Alongside with his acute amnesia he is unable to remember his previous choice, so when asked 5 seconds later it is another guess.

With the rules of probability and given the outcome at time t=0, with another non-weighted flip of the coin at time t=5seconds, his answer has changed.

Now add different decay rates that represent different decay rates for the tuning fork and for the piano string. Say set the decay to -6-dB at 2 seconds for the piano and at 1-second for the fork respectively. (I think that would be thetas of about 693m and 346m). You won't get a clear beat there

Now a second experiment: have the frequencies coincide exactly but in antiphase, start the piano 6-dB greater than an electronic reference, and set the decay of the piano to 6-dB at 7 seconds (theta ~ 100m) and the electronic reference at constant amplitude. Same frequency signals, but there is a clear minimum.

I believe this shows that the beat method is not suitable for observing frequency differences unless the amplitude decay times are sufficiently similar. This is clearly the case for comparing the sounds different strings of the same pitch, but more than five seconds per beat seems highly unlikely when comparing a piano note against a tuning fork as implied in the question (and inferred for the answers)

I'm quickly swinging through here, (so forgive my possible too quick read of your response, but I've tuned pianos, and find LLeros explanation right on the money (at least in terms of it's being a good response to the question, which I assume is simply trying to get at the beat frequency concept.) I'd say that one beat every 4 seconds is about my limit for detection, but others could do better.

Excellent, experience-based post. Kudos, Ken!

Actually, if you have access to a suitable instrument, you'll not find it hard to hear beats at even 30 seconds (on a single note from the piano), particularly in the lower-mid regions where the strings are in pairs and the destructive interference is pretty-much complete. But tuning to that accuracy is a different matter, and opportunities to hear such things in music are, to say the least, limited.

The situation when comparing a string with a tuning fork is completely different, however. So either it's a badly-posed question, or the beats are much faster but only become audible to Tomasso as the sound levels of the piano and the tuning-fork become similar - after about six seconds.

By the way, if I had my 'drathers, I'd have a tuning fork that was about 441-Hz, and tune to the known error - that way you know which direction to adjust.

OK, since some of our guests are having some fun with this thread I'll have a go as well!

Giovanni was tuning his piano using a tuning fork when his friend Tommaso stopped by. Tommaso listened for five seconds and then confidently told Giovanni that the key was in tune. Giovanni disagreed. After about five more seconds, Tommaso was forced to agree that the key wasn't in tune after all. What happened to change Tommaso's mind?

It seems that Giovanni and Tommaso, besides being music lovers and excellent piano tuners, are also hit-men and members of the local Mafia. And as usual, when Mafiosi want to settle an argument, weapons are drawn. Well, it seems that Giovanni ("The Tuner") got the drop on his buddy Tommaso ("Tommy Two-tone"), and, staring down the gleaming barrel of a shiny chrome-plated Colt .45 ACP automatic, Tommy was "forced to agree" with his friend and change his mind. The five seconds were exactly how long it took Tommy to decide if it was worth finding out whether or not his Looney Tunes "buddy" would pull the trigger or not if he continued to disagree!

The "beat" frequency (f1-f2) was ~0.1 Hz. Tommaso needed to wait a full 10 seconds to hear it.

The first thing that struck me, was the Doplereffect. This question is for realistic, accurate ENGINEERS, not for shaky, sensual MUSICIANS.

So, after looking through al the dilldalling forerunners, I was glad as I came to the Guest with the diopler, - there is still hope for the engineers.

However, I dare not ask for his/her age.

Maybe someone needs their dioplers changing? 4mph is not large enough to create a discernable change in pitch, and the sounds would be coming from much the same direction, so their relative pitches would be essentially unchanged. Obviously, Tomasso has to be relying on beat notes.
When moving, he'd hear level variations just from the reflections, so he's more likely to think the piano is out of tune when it was actually correct. Plus "stopped by" presumably means just that.

Now THERE is a guest (#68, not #66) with something worthwhile to say, as opposed to #66 who seems to just grab onto anything that, sort of, sounds right to him, and he gets to make fun of "shaky, sensual MUSICIANS" and calling people with other answers "dilldalling forerunners" (I guess that includes you, too, Fyz! ).

Call it unkind (and I have been called worse ), but personally, I would like to see more from guests like #68 and less from those like #66. I hope #68 comes back and registers with his own screen name so we can become more acquainted and appreciate his contributions. Guests like #66 can just, well...GO AWAY!

By the way, #50 wrote "diopler", when I am sure he was referring to the "Doppler effect", and not "diopter", which is an optical measurement. I am hoping that #66 just repeated the mistake for comic effects (which I am pretty sure is what #68 did when he repeated it as well). At least that part of his post was amusing!

Normally, I try not to be nitpicking on speling misteaks <grin> but it might be a bit indicative here. Perhaps more posters should use the spell-check function. Both "Doppler" and "diopter" were offered by the spell-checker as alternatives to "diopler".