Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Partial strength - hammer voicing or soundboard ?

You don't actually believe that the two frequencies (e.g., 174.6Hz and 220Hz) combine to form beats (i.e., that you tune to), do you?!?!?!?

Good evening again BDB. I approach partials as if they were a result of a "partial theory". This "partial theory", which may be totally wrong (if there is such a thing as truth), is sufficient to model and predict the motion of piano strings sufficiently well to tune a piano - by ear, or by ETD. It is important to understand that the "partial theory" is not "truth", nor does it need to be. It is, however, a convenient, common, theory that allows us to talk about tuning, temperaments, measurement of partials, and the like.

I hope you understand that I don't concern myself about whether or not partials exist. Until the theory fails and is replaced by a better theory, it works well enough for me.

On that basis, this discussion, regarding relative partial intensities, is valid.

Sure, I understand. There are several ways of looking at things. Partials are an abstraction that come from the Fourier series approximation of a periodic function. My only objection is to those people who think there are harmonic fairies magically making sine waves of all different frequencies hiding in a vibrating string, and they are what give a piano its characteristic sound.

Aside from the acoustic transmission of sound, one cannot forget that variations in the ear will color our perception. I have one ear more sensitive to hi frequency harmonics than another thanks to an MD rupturing one as a child. It can be helpful or frustrating in some tuning situations.

That's ok. You're not an aural tuner (I assume or you wouldn't be making these comments), so the idea is absurd to you. We, aural tuners, on the other hand, use these everyday to tune pianos. Of course we are going to choke on our coffee when reading comments like yours. Don't take it personally.

If you want to talk absurd, what exactly is gravity? I stick to the world? That just doesn't make sense to me, but I deal with it and use it every day to help me do stuff.

Have you seen my video on the harmonic series? You might find it interesting:

http://howtotunepianos.com/podcast-6/

It is not that I am not an aural tuner, it is that I came from a different tradition from most of you. My background was in mathematics, not the lore of piano tuning, which, all too often, is not very well integrated with physics and mathematics, nor with the relationship between the two.

Incidentally, I said an infinite number of sine wave generators because that is how many are needed to come arbitrarily close to most periodic functions. But two would do.

For the sake of a productive discussion, I'd start to remove the fairies from the picture.

I think that some form of "beat" or fluctuation can be noticed based only on one frequency by note, with fundamental also. But it is very faint. I doubt it can be mistaken with the stronger combination activity obtained with partials.

May be your comment, BDB, goes in line with my impression you tune mostly at fundamental level (unison, beat perception) which is possible but a little dull or "closed" in my opinion.

Your mathematics isn't necessarily well integrated with the physics of piano strings. Mathematics = physics. The assumptions and axioms you start from on the physics side determine the mathematics you use to quantify it.

There is nothing absurd about simultaneous sinusoidal periodic movements within the same string - your total bewilderment about it is in itself bewildering to most of us. Surely you can stretch your imagination far enough to see that it might be possible, even if you have an alternative theory? Certainly there is no justification for your persistent outrage at the mere idea.

Science is not nature, it mearly tries to describe it in useful terms so we can predict its behaviour.

Did you watch the video? There are four examples that show partials are not imagined, and string vibration can be thought of as a combination of sine waves.

I think I know what you may be getting at though.

If string vibration was indeed produced directly from individual sine tone generation, then the synthesizer algorithms of the 80's should have been able to accurately reproduce authentic sounds that could not be distinguished from the real acoustic.instrument, which of course is not true.

That said, PIanoteq and the GT2 (2?) are impressive in realism today.

The GT have even inserted the vibration we perceive in the keys when they are bottoming My brother, violinist , had a rehearsal with one, and told me after 54 minutes the "digital tone" is not noticed anymore, they could work normally.

In daily professional use, the sensors (rail) can worn out in +-10 years, and need changing. (not cheap, but unavoidable, anyway with the first models)


I do not understand BDB idea, partials cannot be dismissed, as they are responsible for the tone recognizing, different processes of tone production creating different ranges of partials hence different presence or absence of those in the final tone)

Their stability in piano tone, and predictability, can really be put in caution, hence the necessity to control what ETD's are proposing.

Hi BDB. I am trying to understand what you are saying. "Artificial" is a rather elastic word. Are you using it in the sense of "produced by man; not occurring naturally" or in another way?

BDB, I also come from the field of mathematics, and I fully understand what you mean when you say that harmonics are an artificial abstraction. I agree that could be said of harmonics. But not of partials. They are not the result of Fourier analysis of a periodic waveform, but rather the result of real physically separate modes of vibration in the string. This is evident from the fact that they can be excited separately by plucking the string in just the right place and lightly damping the string in another place. They are also not harmonics because they are not phase-locked to the fundamental as real harmonics are, and since the whole waveform is not strictly period.

Robert Scott,
Great explanation.

The string is a wave medium with specific dispersal rates determined by the elasticities and mass.

I think what BDB is saying is that the initial deflection of the string carries all the information that will be revealed over time. Of course the properties of the wave medium and it's boundaries change the shape of the initial deflection over time. So the sum total wave form of taut piano strings is non-periodic. But each separable component wave is periodic.

Exciting the string in different modes is not the same as the actual existence of partials as separate vibrations in a string.

What I really do not understand is why this is so important to people. I view beats as the results of combinatorics. Others view them as the creation of harmonic fairies. If it works for you, fine. I have posted recordings of my tunings. Most of you have not. If you want, you can make an appointment to drop by and experience my tunings in person.

There may only be limited circumstances where the difference matters. Since I view beats as the result of combinatorics, if the waveform varies, so do the beats. This means that voicing affects tuning. This is most evident in the bass, where softer hammers excite the string more closely to the fundamental mode, enough so that the coincidence of maxima and minima change, and the beats are better if the pitch is lower.

Oh, and there is the other fact that I mentioned somewhere else, about the speed of the hammer being bounced off the string being related to the frequency of the note. There are no harmonic fairies throwing them off any faster, although the characteristics of the hammers will make a difference.

So perhaps we could think (idealized of course) of disturbances of the piano string as ripples on a pond. There are many different periodic waves simultaneously that exist, with different parameters, pass through each other and, to the observer at a particular point, constructively or destructively interact.

Clearly there are relationships amongst the waves, as they acoustically couple (longitudinal and transverse waves for one) and are all affected by bridge bending, soundboard movement, which changes the instantaneous tension of the string.

Why the insistence on fairies, BDB? You are doing the discussion no favor by belittling it.

Any spectral analyzer, be it aural (frequency filter or analyzer, i.e. frequency domain) or visual (stroboscopic, i.e. time domain) shows modes to be present, simultaneously, in a string.

It also shows the beats of an (non-unison) interval to occur not between the fundamentals, but between the coincident partials. Just look at some of the spectrograms that Kees posted.

(Think about it: why would 174.6 Hz and 220 Hz beat at 7 Hz? Multiply the one by 5, the other by 4, and you have a 7 Hz beat. The beat is not happening at the fundamental!)

So if you have an instrument like an organ, which produces pure sine waves, there would be no beats between 174.6 and 220, and you could not tune it, because there are no partials.

Harmonics are a subset of partials. A Major third will beat at the 5 and 4 harmonic ( assuming the fundamental frequency is the first harmonic) in the same manner that it will on a piano. Organs ( including the Hammond C3 and B3 ) all have sound generators that produce, simultaneously, a multitude of harmonics - the pipe by its shape, and the B3 by multiple sine wave generators.

The point is that sine waves have no partials. Take two sine waves. They will beat, not because partials coincide, but because of combinatorics.