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I am not familiar with your term "shared lower note". What you seem to be describing is properly called a "difference tone". "Beats" and "difference tones" are the same phenomenon.



No. If E5 is sounding at 661 Hz, and A4 is sounding at 440 Hz, then the difference tone would be at 221 Hz, 221 being the difference in the two frequencies.



True. Beats (that is, subsonic difference tones) are heard at the levels of the "coincident partials".



As I said, beats are heard at the coincident partial levels. Difference tones are sometimes audible, but they are not heard "at the fundamental"; they simply form notes heard at a frequency of the difference between the two fundamentals.

Right?

Hello again,

OK, I think your posts answer my question. Yes, difference tone is the concept I was looking for. In my A4-E5 example, the difference tone would not wobble, but simply shift frequency to 221 Hz.

So far, so good. But what I do find interesting, is that this E5, being part of a tri-chord, would only beat at 1 Hz with its unison partners, while it beats at 2 Hz with A4!

I would have thought that if E5 is 1 Hz out-of-tune within its unison, then it would be 1 Hz out-of-tune with any (pure) interval.

It seems I was mistaken.

Not that I'm a pinao tuner, not even an aspiring one, but I do find the concepts fascinating (especially coming from a scientific background including Maths and Physics) and would like to learn more.

Regards,
Mark

Mark:

Are you asking what happens if you are sounding 440 with 660 and 661?

Hi Jeff,

No, not really.

I'm asking what beats I will hear (at which pitch, and how many beats per second) if I sound 440 and 661.

Then, in a separate "experiment", I'm asking what beats I will hear (at which pitch, and how many beats per second) if I sound 660 and 661.

In both cases, 660 has been de-tuned to 661, and it seems that in the first instance, this causes a beat of 2 b.p.s., while in the second case, it causes a beat of 1 b.p.s.

That's what's puzzling me: that a note which is 1 Hz out-of-tune can cause beats of different beat rates (depending on which note I use to test it).

Regards,
Mark

I'm not 100% sure it would not wobble.

That is, yes the frequency should stay constant at 221. But the amplitude of the 221 tone should also vary at a different frequency. I'm not sure how detectable this is in piano, in some electronic applications it is a problem. (I'm not a piano tuner. I am a musician and I easily hear beats. Beats are a good sign, they mean I'm getting close! <g>)

"(I'm not a piano tuner. I am a musician and I easily hear beats. Beats are a good sign, they mean I'm getting close! <g>)" You've crossed the line; now there is no turning back!

Maybe I can give this a try...

First, be careful about your assumptions.



You are assuming that the tones will have overtones. Not all tones have overtones. Not all tones have all the overtones of the series. Not all tones that have overtones have harmonic overtones. So the question, as you have asked it, is not completely answerable.

However, remember that the beats sounding between tones of 440 Hz and 661 Hz will be the beats between coincident partials, if present, and not that of the fundamental frequencies.

Really, I think you already answered your own question -- harmonic partials, if present, are located at whole number multiples of the fundamental frequency. Therefore, any change in frequency of the fundamental will cause a larger change in the overtone frequency by a factor equal to the partial's place number in the partial series. That is, change of 1 Hz in the fundamental will cause a change of 2 Hz in the second partial, 3 Hz in the 3rd partial, and so on.

So, a frequency change of 1 Hz in the fundamental causing a 2 Hz change in the beat speed of coincident partials is not really a conundrum at all; it's just the way partials work in relation to the fundamental.

Roger,
Do not be discouraged by those who would pull up the ladder by which they themselves ascended. I have a graduate trainee who can tune beautiful unisons as a byproduct of correcting strings disturbed by string seating and leveling. From there, octaves were easy and 5ths naturally followed. She still cannot hear the beat rates of maj. 3rds, let alone minor 3rds and so she is using 5ths and octaves to set a scale as was taught years go and a creditable job she does too, within these limitations. She will begin to hear these faster beats when she needs to, maybe even tomorrow.....In the meantime, she already has a good grasp of voicing and regulating and has hung a set of hammers already after starting her training only a month ago. Develop your eye for straight lines even spaces and hammer traveling and shaping while you are working on your hearing skills. These skills are just as important. Why do we still teach tuning as though it stands alone???
Don't get hung up on one single aspect of piano technology.
Oh, and make sure that you are listening to the interaction between either single strings or really good unisons...poor unisons will mask these faster beats.

good on yer.

On further reflection, How about tuning nothing but really good unisons and octaves for a while,maybe some slightly narrow 5ths. Your hearing will be so 'atuned' to absolutely still notes that any rapid disturbance between the notes of other intervals, (maj.3rds and 6ths) may become even annoying to you... .just a theoretical rumination based on previous teaching experience. Tuning a good unison that stays there while you tune another note from it is also the first step to solid tuning. Lose the temperament strip, at least for a while, and tune from complete unisons. Many experienced fine tuners do not use a temperament strip, if for no other reason than to keep their unison tuning in good shape, It might work for you. R

That's how we are taught in the Randy Potter course. Tune unisons, unisons, unisons... then hearing beats will come alot easier, it's what you were trying to eliminate in tuning unisons. Perfect unisons are suppose to be the hardest to tune.

Arthur Reblitz: Piano Servicing tuning and repair Has a wonderful section on tuning and he says tune octaves first. With exercises it is very good for beginners and good tuners alike.
Leo

I know this is quite an old post but I thought I'd throw in a few more cents to further add more intricacies.

The other aspect is that every individual person is setup and tuned in to different overtone partials. So you may hear the first partial beating but I might be able to better hear the 3rd partial beating. The size of your head, ear canals, if you've damaged or destroyed any of your hearing, etc. all factor into what types of overtone is heard more clearly to you. That isn't to say you can't learn to hear other overtones, there are just certain ones that your ear may be drawn to.

There is the phenomenon of an undertone as well but that is more associated with singing.

This topic is encouraging me as I only tune octaves after setting the middle octave from a tuner. One thing I have not seen mentioned is whether you use the damper pedal while tuning octaves.The way I prefer is to keep the damper pedal down and sound the two notes an octave apart. I was sounding the lower note first , then the higher one. But then sounding both together seemed to work better . I`m not sure of the reason . Mainly by keeping the damper down the beats will keep sounding as I move the tuning lever . That way I don`t have to worry about stretch tuning as it will happen naturally .

Learn to hear beats on other intervals. Fourths and fifths barely beat at all, so if you hear them prominently, you are off. You can check that in different octaves. You can also use different octaves with thirds, to make sure that they do beat at the same rate. All of these checks make your octaves sound more accurately, and they develop your ear so that you get better and better.