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

With the difference in amplitude between the tuning fork and a piano string it would be very difficult to hear the "beats" caused by their different frequencies. The end of a tuning fork is generally placed on a resonating surface, such as the sound board to give it more volume. Even with the added volume it can be very difficult to use "beats" to determine the correctness of pitch due to the characteristics of the overtones on piano strings. On most pianos smaller than a full sized grand the overtones will be sharp in comparison to the fundimental pitch. This tendency increases as the strings get smaller and the tension becomes greater. For this reason piano tuners use their ear instead of the "beats" when using a tuning fork to find the starting note to tune on the piano. Subsequent tuning is done to that string and the tuning fork is no longer used.

FYI about tuning pianos. Because of the sharp overtones previously mentioned most pianos need to be "stretch" tuned in order to sound good. This means that the strings are tuned by ear to the overtones of the octaves below. If your piano tuner doesn't know how to do that you probably won't get a good sounding tuning job. Often the lower strings on a piano will have overtones that cause beats when the fundimental pitch is in tune. Piano tuners need to be able to hear these things and make the best compromise for optimum sound. In fact the whole tuning system for the piano is a compromise called "equal temperment". Equal temperment is a tuning system designed to allow musicians to change keys and sound equally good in all of them. Other tuning systems can tune perfectly to one key and sound good in a few, but have limitations when going beyond that. In equal temperment the interval of a perfect fifth inherently has three "beats" every five seconds. So equal temperment is inherently slightly out of tune, but the best compromise.

Well, now that we've found out what Giuseppe did for tuning that particular cord, I am trying to understand the process of tuning. We tune with a fork on 440Hz (I think that's the "la"), and it plays to the perfection (that is with a less than 0.1Hz deviation). How about the other 12 full and half tones in a gama? Do we use other 12 forks? Wikipedia mentions something but if anybody can make it clearer...

I used to do it pretty much like this , except that I didn't have an electronic tuner. I'd use an A tuning fork, and would tune that as perfectly as able. Then I would tune up and down in a series of fourths and fifths (up from c to g, up from c to f, down from f to b flat, etc.) by ear. I'd double check that the octaves were OK (by beat -- technically a good tuner might disagree.) Most notes have three strings tuned in unison (by beat), so there is a lot of fiddling around that goes on. Then I'd play it a little to see how badly I did, and I'd be done.

It would take a about a whole day, partly because I didn't know what I was doing, and because I'm not a professional, so only tuned my own (and parent's) pianos: I didn't get much practice. I think a good tuner can do it in 2-3 hours.

The link is does not cover the one issue that is relevant to us, of course - the issue of beats between a tuning fork and a piano. Over the years (mostly before Korg or the like were remotely economic) I've adjusted everything from harpsichords to organs, but have never touched a piano**. I wouldn't be 100% certain, but my recollection is that I've never detected a beat between a tuning fork and any other instrument with a duration longer than about a second. However, that would be a great deal closer than the difference (around 3-Hz, I think) that I could tune by pitch.

Of course, this would imply that the logical, plausible and much-praised answer given by Lleros MaHarg is simply incorrect. I plan to check this when our pianos are next tuned, but by then the challenge will be obsolete. In the meantime, would you care to state your view in black-and-white?

**This is on the basis that, if the error is large enough for me to think it worth adjusting (intrinsic irritations being so large) I would need to tune the whole instrument so that all the strings settle together. This would be way beyond both my expertise and my patience so that all the strings settle together

The link is does not cover the one issue that is relevant to us, of course - the issue of beats between a tuning fork and a piano.

Fyz, you miserable, pedantic twit: the article does indeed mention "beats" in tuning one string against another, (which applies, by extension, to tuning one string against a tuning fork -- unless, of course, one accepts the ludicrous, fancy-schmancy reasoning you put forth earlier). A piano string acts like a bar, as does a tuning fork.**

BTW, usually one verb per clause is sufficient. Your "The link is does not..." could read "The link does not..."

In the meantime, would you care to state your view in black-and-white?

Only in an approximation thereof. On my monitor, black is far from a true black, and white is a crude approximation too. Here in the colonies we use what we call "color" monitors, but in the UK and other third world locations, I assume the green screen monitors we used 25 years ago must be the norm.

OK. Enough silliness: I realize I can no longer find my tuning fork and piano tuning stuff. (I wonder if, when I bought my first synthesizer I was so enamored that I sold the tuning stuff or gave it away, thinking that pianos would disappear altogether by 1988.) We have a couple violins, a cello, and a couple guitars here, however, and I tried the guitar just now, and would say that one beat every four seconds is about my limit... but that has a lot to do with the fact that the volume decays to the point that I can't hear the beats, I think. I could try the cello, but I know that I am not sufficiently skilled to bow it for any length of time without the pitch changing (because of tension changes from changes in bow force), and when plucked, I don't think it sustains any longer than the guitar.

When tuning a guitar, I always listen for the beat frequency, and generally tune by stopping the strings to play what is commonly called "harmonics" (as if you don't ordinarily). Otherwise, when a string is pressed to a fret, its tension increases, and the pitch changes, so the open tunings will be incorrect.

But in simple terms, when I've tuned pianos, I initially listened for beats between fork and string, and then tuned by fourths and fifths (and octaves and unisons) again by beat. Tempering was also done by beat frequency -- in other words, a particular detectable beat frequency was desirable, rather than striving for no detectable beat. But again, I was not a pro tuner, so maybe my tunings would sound awful to others. I think that at 440, the fundamental dominates in this beat frequency assessment. In the low bass notes (c 55 Hz), I'd think the second harmonic must, but that is just gut feel. (I'm guessing that you are really tuning 55Hz using 110 hz for the beat frequency, in which case, your percentage accuracy would be better than expected. I'm thinking aloud here, and my contention might seem ludicrous, if I thought about it.)

All this stuff is just a series of crutches for lack of perfect pitch. If I didn't have a tin ear, I could just start in the middle, work out in both directions, and then back in toward the middle, setting each string to the right pitch purely by ear. I do have perfect color pitch, however. Pantone frequently calls me to check their colors.

** I'm kidding here, of course. I always find your posts informative, and sometimes even vaguely correct. ***

*** I'm kidding here about the vaguely correct part - they are often spot on. ****

**** and BTW, you'd get a kick out of this thread, which reminds me a little of Bill Clinton's, "Well, that depends upon what you mean by 'is'." Much of it has to do with the existence or non-existence of a compound.

"I think arrogance is fundamentally unpatriotic, and is a major contributor to our being despised around the world to an extent never matched in my lifetime*."

And some Americans have a propensity for confusing pride with arrogance, when in fact they are being arrogant to do so! I would like to know where you get the data to back up your statement about Americans being despised around the world "to an extent never matched in my lifetime", unless you are a newborn babe. I believe we were despised significantly more in the late 60's and early 70's with significant failures in our relationships with Third World countries (despite the beginnings of Detente with Russia and China), but then maybe you are in the under 30 crowd, and can be forgiven such naiveté . There is an excellent article in the Wikipedia on Anti-Americanism if you would like to learn more about the long history of the subject (going back to pre-colonial times, believe it or not!)

Granted, Bush's policy to "go it alone" in the Iraqi invasion (with the exception of notable support from Britain and a few other allies), rather than trying to obtain approval for UN-sponsored action, did not win us any friends in Europe. Also, the subsequently hard road we have traveled to try to get the country back on its feet economically and institute democratic (note, small "d") reforms against a backdrop of chaotic violence by factional in-fighting and anarchistic and suicidal insurgents, which required us to take some extreme and distasteful measures, also led to some ill-will in other countries. Internally and likewise, Home Security measures have had some political activists (forgive the irony here) up-in-arms, although a preponderance of Americans welcomed the security actions by "the current administration" as necessary to protect us from terrorism. Funny, what they called "threats to liberty" have been standard policies in Europe for decades. I well remember machine-gun toting soldiers in German airports and long lines for Passport checks back in the 1980's. Britain's Official Secrets Act and other "draconian" laws have been enforced with a vengeance since Islamo-terrorism raised its ugly head there many years ago.

Sure, there are thousands of Mujahadin in the middle east and elsewhere who despise us. After all, their religious leaders have taught them we are "the Great Satan". But in general, and I won't say everyone loves us, but we are well thought of by probably most of the over 1 billion Chinese people, millions more in India, Pakistan, Africa, Latin America, etc. who would love nothing more than to come here to escape life in their miserable countries. Of course many of these people do distinguish between the acts of our Government and the American people. They really don't recognize that, because of our political system, for the most part, the two are not that different. In 2004 President Bush won by a (sometimes) slim, but distinctly positive margin in MOST of the 50 US states!

In fact, one of the biggest problems for the powers that be in many totalitarian countries which "despise' Americans is that many of their own people, especially the young people, LOVE Americans and American culture. But these pro-American voices are bullied into silence, fearing retribution through imprisonment and torture.

Of course, many of the French hate us. They have never forgiven us for helping "defeat the Hun" in World War I, liberating them from Nazi Germany in WWII, trying to contain Communism in Southeast Asia where they had failed miserably, and most of all, taking the lead from them in world politics and helping make the English language, ironically, the lingua franca of the modern world. Granted we have not accomplished all that we have by ourselves, but with the help of valued Allies, which also proves that we can't be so universally despised as the picture you are trying to paint. I have even read reports that the PEOPLE of Iran, not the mullahs and the religious leaders, don't hate us at all and in fact hate their own government much more, which is why President Bush (and hopefully his successor) will never bomb Iran.

And you say we have recently TRASHED our constitution? Well, if that is so, we have a cure for that, called the Supreme Court, but I have not seen any evidence to that effect, only opinions like yours.

But your last statement, or footnote, was the giveaway:

"*But there is hope. The country is swinging back to more reasonable leadership, with approval ratings for the current administration in the low 30s.

Low 30's? Better check your data. I agree, his approval ratings are not stellar, but since when does 35.6% count as LOW 30's? Can you spell, "SPIN"?.....sure, I knew you could! I mean, I am not a big fan of the Prez either, but JEESH! I actually thought his brother Jeb (former Gov. of Florida) would have made a better President!

C'mon, Ken. Let's keep politics OUT of CR4, "off-topic" or NOT!

If anyone agrees with this sentiment, post a "Hear, hear!" or an "Amen, brother!"

Although I consider myself a middle-of-the-road Independent with conservative leanings, and not a true-blue Republican, I expect to be attacked by Bush-hating, knee-jerk, party-line Democratic liberals like Ken for the statements I have made above.

I just glanced though your post, but after I finish a reread of War and Peace, I'll read through more of it.

but then maybe you are in the under 30 crowd,

Don't I wish!

when does 35.6% count as LOW 30's?

Last I checked, it was 34.999.

If anyone agrees with this sentiment, post a "Hear, hear!" or an "Amen, brother!"

Hear, Hear, Here, Here

Apologies for my over reaction. This was more to the excessive volume of praise and lack of development of other comments than to the original contribution itself - I should have known better. I should indeed have said "improbable" rather than "wrong". The problem of course is not the specific answer, but that the scenario of the question is distorted.

Therefore, I add your new scenario "Giovanni had raided the physics lab and was using a low-frequency tuning fork" to my list of plausible answers.

Returning to the original question, I think the realistic scenario (based on historically standard tuning techniques) would be that, as all the wedges had been removed, Tommaso thought Giovanni was doing a final check, whereas he was actually just starting the second run through, so when Giovanni sounded the next notes he could hear how far the tuning had progressed. Unfortunately, that would impy that the question didn't really belong in this forum, as it is not be a "technical" answer!

BTW, your solution to the detuned piano is terrific if you can do it**. As I used to perform classical and early romantic music using period instruments I have worked with wooden-frame pianos and their somewhat frustrated players. We just tuned the instruments to each-other; in some cases, the winds and the keyboard could not be aligned, so one or other had to transpose. Happy days.

**Either:
the stringing needs to be parallel, or at least spaced without sudden discontinuities - which is not universally the case even with wooden-frame pianos; or
you need to make major modifications to one key at each discontinuity - quite a job if you are to keep the "touch" reasonable

Regards

Fyz

Lleros MaHarg - especially in his post #17, clearly illustrates he is the most knowledgeable respondent to this 'puzzle'.

I suppose it is about time I presented my thoughts as solutions rather than as critique.

Solution1:
Giovanni allowed the piano note to die away, and re-sounded the tuning fork. When the sound intensities reached similar levels, Tommaso could hear that there was a clear beat note at about 2-Hz.

Solution2:
The tuning fork died away, and after about seven seconds Tomasso could hear that there was beat between the strings that Giovanni was trying to synchronise (I don't know why Giovanni had sounded the tuning fork at this point - perhaps Tommaso asked him to).

Solution3:
Giovanni knew that he had only just adjusted the key, and the fact that the note sounded in tune when Tommaso first heard it meant that it would drift out before too long.

Take your pick - but without more evidence I wouldn't go with detecting 0.1-Hz beats between a tuning fork and the piano. (And in any case, I would definitely consider the note to be unusually well-tuned if the beats between piano and tuning-fork were below even 0.5-Hz.)

Another possibility is that the piano has tuning issues. In older pianos the tuning pins slip and cause the piano to go out of tune quickly. The large block of wood that the pins sit in will wear over time and not hold the pins tight causing the slippage.

Maybe he needs to replace the piano.

This phenomenon is know as "false waves". Occassionally strings will give rise to what are called forth waves or beats that are similar to the real ones. To the untrained ear these are indistinguishable from the real ones. "False waves" are often caused by a twisted string or a fault in the string caused by imperfect drawing of the string wire. Also, it is noted that naturally occurring "false waves" do occur in low bass tones as the result of harmonic overtones. Close attention to the beats will help the listener distinguish the difference. Also, inexperienced tuners can use mutes to help dampen the effects of the overtones.

Since Tommaso was a friend, and assumed inexperienced as a piano tuner, he was not able to quickly recognize the "false waves". He needed an additional 5 seconds to detect the "false waves".

Would a mime be as well qualified for the dampening chores?

The difference is pitch was very small so that the beat note generated between the very slight difference in frequencies had long period (>10 s) so that the 5 sec listening interval was not sufficient to establish the off-tune state.

With the extra listening time the beat note was verified and hence Tommaso changed his mind and announced the off-tune state for certain !

Clearly, to ensure that 2 frequncies are "spot on" requires an infinite amount of time !

I learned plenty from our expert piano tuners. So here is a question. In electronic coupled tuned circuits there is an effect, called pulling. If two (or more) tuned circuits are individually tuned quite close, but not identical, the one providing the oscillatory energy can pull and lock the other into perfect synchronisation. When after that observation one, the the other is dampened, and their resonance measured, the difference is observable and measurable.

Since the piano has lots of 2 and 3 string groups for every tone, is this effect observed, or it has no significance in stringed instruments?

Yes there are significant effects, but not quite in the way you suggest - at least not between strings at the same pitch. The mechanism you propose is forced oscillation, with one resonator having large amplitude and the other small. We should not expect this in a piano, because the whole point of having multiple strings is so that equal(lish) energy can be delivered to each string, so they can contribute greater volume than would a single string.

But there are still two relevant coupling effects - the shift in the natural frequency of one string due to the movement of the adjacent string, and injection locking.

First, consider the shifts in natural frequency: these do not relax the tuning accuracy required.
Because the hammer causes the strings to move (at least initially) in the same direction, stopping one string from vibrating will increase the restoring force on the adjacent string, and hence its frequency. If you have groups of three strings, the shift this will cause on the centre string will exceed the shift on the outer strings - so the centre string of a group should always be tuned sharper than the other two (when tuning with only one string vibrating). As stated above, this is essentially a linear process, and does not affect the accuracy that is needed to keep the strings in sync

Then there are injection effects. These are a result of the frequency of the strings being dependent on their amplitudes. If the the strings are vibrating at very similar but still different frequencies, I think that the amplitude of the string at the lowest frequency will initially fall faster than that of the others (which may well increase). Now, I believe that the vibration frequency of a piano string tends to increase with amplitude of vibration, so this would actually make the phases diverge more rapidly - at least during the critical initial period. If this effect is significant, it will get worse as you play louder; on the other hand, I may have the sign wrong...

Fyz

After any given time, The tuning fork , or the string being tuned would have equalized thru Harmonics ,So listening at a later time would have given the desired results! The Same Note!

Hammers on the piano made of same metal an thickness as the tuning fork, that could help. Interchangeable string accuators metal for tuning, wood with felt for song, music.