BDB, you of all people should know better. You are only deceiving yourself if you really think it is possible to make single, double and triple octaves all be beatless simultaneously. If that were possible which it is not, then why do technicians who go for beatless triple octaves get expanded single and double octaves as a result? Why can't everyone do what only you claim to be able to do?

Maybe because I have trained myself not to listen to extraneous sounds.

I have six shows to tune for before the end of the week. Over 5000 people will get a chance to decide for themselves.

The distinction that Bill is drawing is not one that the 5000 people are likely to hear. Nevertheless, it is measureable and demonstrable. Sure, you can make all the various types of octaves very close to zero-beating - so close that no one, not even the artist, will have any cause for complaint. But they will not all be zero beating at once.

I did not say they were zero beating. I said that they sounded like they were beatless. You can always claim that there is a beat, because nothing is as accurate as we can imagine is possible mathematically.

I tune the way that I tune because musically it makes sense to do it that way. If someone else wants to tune so it makes sense mathematically, they are welcome to do so. They can tune for mathematicians. (Although I have probably tuned for a lot more mathematicians than they are ever likely to tune for!)

BDB, this was your statement, "I do not understand how anyone can claim they tune so that the intervals sound wrong, and get away with it." Who do you think is "getting away with tuning intervals that sound so wrong"? My customers describe the octaves I tune as "pure" yet I know they are not. When I asked Owen Jorgensen how the octaves I tuned for him at the convention in Dearborne sounded, the response was "perfect", yet I know that only the triple octaves were beatless. Just what do you think I am "getting away with"?

I've made my entire living as a full time piano technician now for over 30 years with only small amounts earned from other activities. Do you really believe I am fooling all the people all the time? Couldn't it it possibly be that your octaves are really about the same as mine but you believe that you are the only person who knows how to tune a piano correctly and no one else does? I never even think about any mathematics while tuning. My goal in tuning is not to fool anyone but to provide for an optimally tuned piano.

Here are figures from the two pianos I tuned this afternoon. The first is a very low inharmonicity piano, the second very high.

Low inharmonicity: C4 (1st partial) 0.0, 2nd ptl: 0.8 4th ptl: 4.4, 8th ptl: 20.8

High iH: C4 1st ptl, 0.0, 2nd ptl, 2.6, 4th ptl: 6.8, 8th ptl: 22.5

In the first example, if you tuned C4-C5 as a 2:1 octave, the C5-C6 also as a 2:1 octave, the double octave would be slightly narrow but only with a slight beat but if C7 were also tuned from C6 as a 2:1 octave, the triple octave would be so narrow as to beat rapidly. So, that couldn't be what you do, could it?

For your triple octave to be beatless or at least, if you are fooling people into thinking it is beatless, it would have to be tuned about +20 cents. If you tuned C5 at 0.8 and C6 at 4.4, there would be at least 15 cents width in the C6-C7 octave and that would beat very rapidly. You couldn't "get away with that" now, could you?

If you tuned C4-C5 as a 4:2 octave, it would still sound pure and if you tuned C5-C6 as a 2:1 octave, that would certainly sound pure but you would still end up with about a 15 cent dilemma for C7 for the triple octave to "sound" pure.

In the second example, you would have a far more difficult problem. The second example is most likely to be more like all the Steinway concert grands you tune for all the shows in all the halls we have all heard about, time and again. So, you must be doing something other than what you describe. On one hand, from your descriptions of what you do, the only conclusion I can come to is that I do not understand how you can tune intervals that sound so wrong and how you can get away with it. But then you chime in with the accusation that just because I do not know how to do it does not mean that it cannot be done.

Then, you change your story a bit so that you say you don't really tune the intervals correctly after all, you just fool people into thinking they are correct. You just fool people into believing that what is impossible becomes reality but only when you do it. 5,000 people will confirm it yet this week. They'll all sign an affidavit to attest to it.

Just why is it that you feel compelled to condemn what other technicians do and put yourself up as the only person who can tune a piano correctly? Couldn't it be that what you do is what any other ordinary piano technician does day in and day out? Couldn't the problem be that you just don't really know exactly how to describe what you do, so as a defense mechanism, you choose to tell everyone else how badly they tune pianos and put yourself up as the only one who knows what is right? I know, you don't have time to describe to all the idiots on here just what you do. But you did have time to write 10,633 posts so far, most of which have contributed nothing to anyone.

You do have the potential to contribute something of substance, real advice, real information and from time to time, I have seen it and been grateful for it. But when I see pure baloney, I don't take very kindly to it. What you said a few posts back was just that, pure baloney. So, next time you feel the urge to write pure baloney, think twice because you may find yourself scrambling to justify it and you will only dig yourself into a deeper hole.

I wish you would actually read what I said. I have not criticized anyone else's tuning. I have merely explained what I am listening for when I tune octaves, in very rough terms.

We have gone through this before. I explain what I am doing, and then some people come and say, no, that is not right, if you do it that way, you will be off in one way, while other people come and say, no, that is not right, if you do it that way, you will be off in exactly the opposite way. That merely convinces me that my explanation is valid.

By the way, I recently posted pictures of beating sine waves. There is a lot to be learned by looking at pictures like that, yet nobody commented on them. I am curious why nobody though them to be interesting.

BDB:

Yes, I agree. There is too much of “My way is right!” and not enough of “Oh, why do you do it that way?”

I did not comment on the diagrams because I had seen that sort of thing many, many times and not just about piano tuning. It is important, but not new.

Bill:

Your figures show only the partials for one note on each piano. To know, mathematically, what the beating with the partials of other notes might be, you must first know what the frequency of the partials of the other notes are.

Hopefully by the end of the week I will make a computer application available that will calculate the beat rates for an entire piano given the iH curve and the tuning. It could be used in a discussion like this to determine, mathematically, just what all the different beat rates are. It will not do "swartz" comparisons, though.

Well, the interesting thing about the diagrams is not whether you had seen them before or not. Rather, you should be asking yourself, "What is wrong with this picture?"

BDB:

I stared at the pictures for a few minutes, didn't notice anything, and then looked at a blank wall to consider what I might be missing. Lo and behold, the afterimage was Osama Bin Laden!

Hi Ron,

Thanks for the illustration in figures. The illustration is crystal clear in its own right, and I could understand it pretty well. However, it still doesn't quite explain Bill's passage in relation to F3 vs F2. Lets break it down to details.

(1) Bill uses F2 vs A4 on keyboard and F2 vs A4 on fork. If the beats sound similar, then A4 on keyboard equals A4 on fork.

(2) Bill uses F2 because F2 has a coincident partial with the 1st partial of A4, which means A4 at 0.00 cent.

So far so good

(3) Bill says if you use F3 vs A4 as a means of testing, if the beats between F3 vs A4 on keyboard and F3 vs A4 on fork sound similar, then A4 on keyboard is likely to be flat.

Why ?

(4) Bill explains that this is because F3 does not have a coincident partial with 1st partial of A4; instead it has a coincident partial with the 2nd partial of A4.

Now, can you see where I am coming from ? The connection between point (3) and point (4) is a 'BIG LEAP'. Of course, (3) is correct, and (4) is also correct. But how do they connect ? So in a way, (4) is more of a conclusion, not so much an explanation.

I'd be grateful if someone could plug the gap

If I borrow your figures, that the 2nd partial of A4 is 1.73 cent due to inharmonicity, by using F3 to test against the 2nd partial of A4, does that mean we're 'forcing the 2nd partial of A4 to 0.00 cent' ? This is where more confusion creeps in.

How do we 'force' a 2nd partial to 0.00 cent ?

Since we cannot change the pitch of A4 on fork, the only time that F3 vs A4 key and A4 fork beat the same is when F3 beats to the 2nd partials of both A4 key and A4 fork. So how can A4 key be flat of A4 fork ?

Look closely at the first part of this statement, and I think you've got your answer. By the actions you describe, you've just tuned the 2nd partial of A4. You haven't tuned A4.

Bingo ! I think I'm almost there.

But but how does tuning 2nd partial of A4 affect the 1st partial of A4 ? Did we do anything to 'force' the 2nd partial of A4 to 0.00 cent and in turn 'pushed' 1st partial to minus 1-2 cents flat ?

Think of the partials as a ladder with uneven rungs. The rungs don't represent pitch, but a cents measurement from the math expectation. Each string has it's own unique ladder. (well many may share verrrrry similar ladders...) What you have is the DNA of that string represented in cents. The ladder rung spacing doesn't change with tuning, just the position of the whole ladder up or down. If A4 partial one is set on 0.0, the other partials are usually positive. Now move the whole ladder down so that the 2nd partial stops at 0.0. (Down 1.73 in the example) What ever that amount was, will also show a lowering of the first, as well as all the other partials, because you can only move the whole ladder via tuning... So the A4 first partial ends up 1.73 cents flat.

Does that help, or muddy the field even more?!?

Ron Koval
chicagoland

Cashley, once again, it is not my method but something I learned very long ago from PTG. Others have made the same error. I even saw a top technician from Milwaukee demonstrate the way you said using F3 at a regional seminar and another top tuner from Los Angeles who was there stood up and said, "If you do it that way, you'll lose 6 points on your tuning exam pitch score!" The response from the instructor was, "Aw, dat's for youse (sic) perfectionist guys!"

At the time, I didn't really understand the problem either. This was back in the very early 1980's. Even the top Steinway concert technician, Chapter and PTG organization president at that time did not really understand coincident partials. Pure knowledge of basic facts have come a long way since then and are known to a broad base of technicians now. There is no denying that PTG was uniquely responsible for spreading that knowledge to a very broad base of piano technicians whether they ever were members, whether they were ever RPTs or not. Again, this is NOT my method of which I am writing. It is common knowledge now some 25 or more years later.

I had always heard that a tuning fork had no second partial, that it was a "pure" tone, fundamental only. If that were true, when you play F3 and the fork together, you would hear no beat at all because F3 has no coincident partial with A4 but it does with A5. So, I tried it today. I played F3 (on a nice, restored Steinway A originally manufactured about 100 years ago) and the fork. At first, I didn't hear any beat as I expected. Then, I detected a faint beat.

I tested the fork with my SAT III set on A4 and got a strong reading as expected. The SAT III has no signal strength indicator as some other ETD's have and the SAT IV has but you can still perceive from looking at the fuzzy pattern that it is receiving a very weak signal which it did when I switched the SAT III to octave 5. The fork did have a second partial but it was very weak and had no inharmonicity at all. The fork certainly had no detectable 4th partial.

So, the same problem comes up as with an electronic tone that has a second partial but no inharmonicity. If you play F3 and the fork and hear a beat, it is a beat created by the weak second partial of the fork which has no inharmonicity. When you play F3 and the A4 of the piano, the A4 string does have inharmonicity. You are comparing two different frequencies. If you make the F3-A4 M10 of the piano beat exactly the same as the F3-fork M10, your A4 is likely to be flat by whatever the amount of inharmonicity is between the first and second partial of A4 (which is usually between 1 and 2 cents).

In most cases, this would not really be very important at all but if you are trying to take the PTG tuning exam, each 0.1 cent beyond the 1.0 tolerance will cost you 1 point. I have seen this happen when people used an electronic tone (but I have also, amazingly seen someone get a perfect 0.0 reading with one). To have a fork that really reads 0.0 with an ETD is more or less hit or miss. To actually tune the A4 string aurally by whatever method or technique that would really read 0.0 is actually quite rare. Anywhere within 1.0 cents is still considered a perfect score and anywhere within 2.0 cents is still considered superior.

The internationally accepted specification for Standard Pitch is A4 at 440, plus or minus 1 cycle per second which translates to +/- 4.0 cents. In most situations, even concerts or recordings, that would still be ok but on the PTG tuning exam, +/- 4.0 cents would yield a score of 70 which would be 10 points below passing. Ultimately, on a PTG tuning exam, your A4 must read within +/- 3.0 cents to pass. If, upon your first attempt you are beyond that specification, you are given a second chance but upon that second chance, if your A4 is still greater than +/- 3.0 cents, the entire exam is failed, no matter how well you may do in other parts of the exam. So, it is important to have a well calibrated fork and know the right procedure.

So, having said that, this is not something to get all too worried about. If you had been using F3 and it seemed to work for you, now, I hope you understand why but it is not really correct. The correct test note to use is F2 because as you have already understood, the 6th partial of F2 is coincident with the first partial of A4.

Incidentally, you can also use the test note, B1 because the 7th partial of B1 is coincident with the first partial of A4. If B1 is already at or very nearly tuned to where it ultimately should be, the B1-A4 double octave and minor 7th interval will beat very rapidly and will thus provide for a very exacting test.

Unfortunately, at the PTG tuning exam, B1 will be detuned by an amount that makes that test useless. Therefore, in the case of the PTG tuning exam, it is best to use F2 (which will also be detuned) and adjust temporarily F2 either flat or sharp from where it is detuned to create a widened M17 that beats as rapidly as you can still discern. This will be your most precise tool to tell you that you have matched the A4 of the piano to the tuning fork. The very first step however remains to tune the A4 of the piano to a solid, beatless unison with the fork. The F2-A4 test should merely confirm that or at the most, reveal only a slight discrepancy which takes an extremely fine adjustment to correct.

I could understand that part about moving the ladder down and thus causing the 1st partial to be 1.73 flat. I understood it the first time you wrote with all the figures. The part which i'm still scratching is this:

What did we do to cause the 2nd partial to be 0.00 cent ? How does the method of employing F3 to test A4 on both key and fork cause the 2nd partial of A4 on the key to be 0.00 cent ?

By using F3 as a testing key, didn't we cause 2nd partial of A4 on key and 2nd partial of A4 on fork to coincide ? OH ! OH ! I think I got it. Because A4 on the fork is perfect at 0.00 without the complication of 1.73 cent caused by inharmonicity. Am I right ?

Cashley, the tuning fork produces a relatively pure tone, unlike strings. Not much of the vibrating energy goes into overtones and they die out extremely fast. When measured with extremely sensitive spectrum analyzers, the strongest overtone of a tuning fork occurs around 6 1/4 times the the fundamental frequency which is close to 2 1/2 octaves above it. For practical purposes, the second partial is so faint and dies out so quickly that the fork serves its purpose well for tuning a note to its fundamental pitch.

I think you have got it, Cashley. The error would occur not when you tune the unison with the fork to A4 but when you cause both the F3-A4 M10 (where the coincident partial is at A5 not A4) and F3-fork M10 (where the coincident partial is also at A5, the fork's second partial but has no inharmonicity) to beat exactly the same. If you do that and you compare again the A4-fork unison, you may (and should, technically) hear a very slight beat in that unison which would indicate that the fork and A4 are not a perfect match.

If this error is made, the reason for it is that you have compared two different sets of coincident partials which are perhaps close but not exactly the same. As I mentioned, the inharmonicity between the first and second partial of the A4 string is usually between 1 and 2 cents. On a typical exam piano such as a 5'9" Yamaha, Kawai or Young Chang, I often find it to be 1.0 to 1.5 cents. A very large, well scaled piano may have inharmonicity of a little less than 1 cent. A small console or spinet may have inharmonicity of 2.0 to 2.5 cents at the most.

There are a few things you can do to prove this both aurally and electronically. First, sound the tuning fork and with the ETD reading on A4 (first partial), carefully calibrate the ETD to where it reads exactly 0.0 if it does not already. (They rarely do unless they are at a specific temperature where the fork produces exactly 440. If the ETD is a pocket PC version, it must have also been precisely calibrated to a reliable source. The SAT has a quartz crystal internal calibration which is supposed to insure an exact calibration but even those can develop some problem with the calibration mode. At a PTG exam, the examiners are required beforehand to check calibration of their devices because when the pitch score is carefully measured, 0.1 cents error in reading that score can mean the difference between passing and failing).

Tune A4 reading on A4 (first partial) to the ETD. Now, sound the fork and A4 of the piano and you should hear a steady, beatless unison. Now, set the ETD to A5 and play the A4 of the piano. It will indicate that the pitch is slightly sharp. Measure that amount by pressing the cents up button until the pattern stops. It will probably be between 1.0 and 1.5 cents. The pitch of A4 has not changed but the partial which is being read has. Whatever that figure is, it is the amount of inharmonicity between the 1st and second partial of the A4 string.

Now adjust F3 so that you hear a rapid beat between the F3-A4 M10, making sure it is a widened interval, not narrow. You may make the interval faster than you usually hear it. The faster it is but can clearly be heard, the better because the faster it is, the better you will be able to hear any discrepancy. Next, Adjust F2 similarly so that the F2-A4 M17 beats very rapidly.

Now that you know that A4, the ETD and the fork all agree perfectly. Perform the interval tests. You should hear that the F2-A4 M17 and the F2-fork M17 beat exactly the same. Then perform the F3-A4 M10 and the F3-fork M10 comparison. You should hear that the F3-A4 M10 beats a little faster than the F3-fork M10. This would cause you to want to flatten A4 slightly to get both to beat exactly the same. Using the figure that you found for the inharmonicity between the first and second partial of the piano's A4 string (usually between 1.0 and 1.5 cents) put the ETD again on A4 reading on A4 (the first partial). Reset the ETD flat by that amount (-1.0 to -1.5 cents). Carefully retune A4 to that setting.

Now, perform the F3-A4 and F3-fork test. The test should indicate that both intervals beat exactly the same. However, if you now perform the F2-A4 and F2-fork test, the F2-A4 M17 will beat slightly slower than the F2-fork M17. If you sound the fork and play A4 on the piano, you will probably hear a very slow and slight beat. This will prove that using F3 is the wrong test note and will often cause a slight error to the flat side if you do. You will also probably notice that any time you play the F3-fork M10 that the beat you hear is considerably fainter than the F2-fork M10. Also, if you sound the fork and calibrate it exactly to the ETD, you will see a strong pattern on the ETD. If you then switch the ETD to A5, the pattern will be far weaker but there will be no difference in inharmonicity as there was with the A4 string.

I hope that finally clears up any questions you have had about this matter.

Should that be F2-A4 M17?

Looking at this question, I think it would be relevant to confirm the basics:

• The first partial of A4 is the fundamental frequency (440 Hz).
• When you turn the tuning pin, you are simultaneously changing the frequencies of all partials of the string.

Understanding these statements, I think you would come to the conclusion that the question doesn't make sense, because tuning the 2nd partial doesn't "affect" the 1st partial. Instead, turning the tuning pin affects both (all) partials simultaneously.

Kind of like attaching clothes pins to a bungie cord and then stretching it back and forth and watching their positions move. You wouldn't say that moving the 2nd clothes pin affects the first. Stretching the end of the bungie cord affects the position of both.


I think when Ron originally said "force" the 2nd partial, he meant "tune A4 such that its second partial is beatless with some pitch reference."

Yes, thanks, Monster, I caught the error in time to edit it.

I think when Ron originally said "force" the 2nd partial, he meant "tune A4 such that its second partial is beatless with some pitch reference." [/quote]

Cashley, look back at my last long post again. If you tune A4, reading on A4 (first partial) to 0.0 but then switch the ETD to A5 (second partial), the device will indicate that the same pitch is now 1.0 to 1.5 cents (usually) sharp. You haven't changed the pitch of the string but you are reading a higher partial, so it will inevitably be sharper.

If you then tuned A4 read on A5 (second partial) to 0.0, it would cause the first partial of A4 to be flattened by whatever amount of inharmonicity there is in the second partial. It is not possible for A4 to read 0.0 on both the first and second partial (or any higher partial) at the same time. Only one partial can be 0.0.

Essentially, when you use F3 as the test note, you are tuning the second partial of A4 to 0.0. Therefore, the first partial will be flat of 0.0, categorically, by definition, scientifically speaking.

What can happen, of course is that your aural tuning is just a little imprecise and your perception of whether the test note F3 yields two intervals that beat exactly the same is also a little imprecise. You could end up with A4 being within a tolerance of 1 cent but only by default.

I recall two instances during tuning exams: one was by a very skilled tuner who had practiced everything to the hilt, new all of the concepts, etc. He got scores of 100 in several categories. However, he used an electronic fork for the pitch and was quite surprised and disappointed by his score of 94 (the very six points that the instructor 25 years ago had warned about). The strong second partial with no inharmonicity confused his ear and caused him to tune the fundamental of A4 flat by the amount of inharmonicity there was in the second partial of A4. His second partial of A4 was perfectly in tune with the second partial of the electronic tone. Boy was he mad about that!

The other instance was a person struggling with the exam and who failed the temperament and midrange badly. But using a cheap, electronic metronome, that person managed to tune A4 to a perfect 0.0 which I had never seen happen before with anyone at all. That person apparently got the pitch as good as that person could and it just happened to fall right where it should. It was kind of like a first time bowler rolling a strike or an amateur golfer getting a hole in one.

So, don't worry too much if you still find this all to be a bit confusing. Just use F2 for the test note, not F3 and also try the things I mentioned in my next to last post. If you are preparing for the tuning exam, just follow the steps, keep practicing and you should be able to tune the pitch aurally within tolerance.

The note F3, by the way, is the test note which proves the A3-A4 octave is a 4:2 type. If you use F2 for that octave, it will be a 2:1 type. Again that is not MY method, it is just what I know and is common knowledge today for experienced and well educated aural tuners.

Bill, your welcome. That just helps to comfirm that I'm on track. Am going through the RP course and this is all spelled out there. I'm still trying to fully grasp the 2:1, 4:2, 6:3 stretches and on what pianos are they applied to.

Also if when a note is struck and the frequency changes from the attack through sustain and decay... at what point do you call it correct?

That is a very good question and the reason that among tuning examiners, there is always the possibility of a +/- 0.3 error on any given reading. My teeth clenched when I first saw that suggested but it has been proven to be true. That does not mean that EVERY note is sloppily read, it just means there can be an error, particularly in the case you mention.

What examiners do in such a case is to try to "catch" the reading within the first few seconds after playing the note. The note is always struck very softly for a reading, never loudly. When there is drift or oscillation, all three examiners confirm the best possible reading.

One thing that examiners do in a case where a pitch may mean the difference between pass or fail is to cover the "cents" display so that it cannot affect the examiners judgment. All three examiners watch the display very carefully and all three agree when the pitch as been read as best it can be. Then, the "cents" display is uncovered and the results are recorded.

Tuning examiners make every possible effort to make unbiased decisions. When an error is detected electronically, it can always be proven aurally except in the case of the stability test where there is no aural reference point.