Tartini Tones and Under/Overtones

[Shunyata]

I dont want to get into a discussion of whether Tatartini tones are real or not, but...

I have I 100 yr old violin that plays wonderfully strong Tartini Tones and when I play thirds, my tuner actually registers a note a fourth lower than the root.

I have another new violin with weak Tartini Tones and when I play thirds, my tuner registers the the root.

What aspects of the violin build control this behavior.  Or is it just age and playing in?

[Michael Darnton]

Just a guess: that the fundamentals in the two component notes need to be strong to form the third note. Individual notes do not need strong fundamentals to be perceived as that note*, so the fundamental is not necessarily always present. Different instruments would be different in this quality, and that would explain the difference. 

*[For instance the notes of the first position on the G string are usually quite lacking in fundamental.]

[JohnCockburn]

Would you expect an interval of a 3rd to give a TT a 4th below the root?

[David Burgess]

4 hours ago, Shunyata said:

I dont want to get into a discussion of whether Tatartini tones are real or not, but...

I have I 100 yr old violin that plays wonderfully strong Tartini Tones and when I play thirds, my tuner actually registers a note a fourth lower than the root.

 

That's interesting, since I mostly can't find Tartini tones on a high-level FFT, even those which most people can clearly hear. The way this was explained to me is that the processing in a typical FFT program will separate and identify the component tones, but will not necessarily process and render them in the way the human ear and brain do.

It would be interesting to know how the programming in your tuner gets around that.

[JohnCockburn]

9 minutes ago, David Burgess said:

That's interesting, since I mostly can't find Tartini tones on a high-level FFT, even those which most people can clearly hear. The way this was explained to me is that the processing in a typical FFT program will separate and identify the component tones, but will not necessarily process and render them in the way the human ear and brain do.

It would be interesting to know how the programming in your tuner gets around that.

The usual explanation is that TT's arise because of the non linear response of the ear.

An intermodulation distortion kind of thing.

As I said above, I don't think this 4 th below the root is a TT for an interval of a 3rd.

[David Burgess]

59 minutes ago, JohnCockburn said:

The usual explanation is that TT's arise because of the non linear response of the ear.

Which to me is a little weird, since TT tones can be mathematically calculated, and the calculations correspond very well with ear/brain impressions.

[JohnCockburn]

3 minutes ago, David Burgess said:

Which to me is a little weird, since TT tones can be mathematically calculated, and the calculations correspond very well with ear/brain impressions.

Yes, they're simple to calculate. Just the difference frequency between the 2 notes of the interval. I don't see where the weirdness comes in?

 

[Shunyata]

My newer violin that lacks the Tartini Tones, has heavier plates.  I wonder if it isn't flexible enough to strongly generate cleanly differentiated, dual frequencies and the resulting Tartini tones.

On my current in-flight build I am paying more attention to the plate flexibility, and to keeping the weight down.  It will be interesting to see if it has stronger Tartini tones.  I hope that some of you have additional ideas i can explore.

My tuner is just a cheapo Korg CA-1.  Not sure what the circuitry is picking up.  But my instructor uses the effect to reinforce proper tuning of third and sixth intervals.  When the tuning is right, the Tartini Tones kick in and you can see the tuner flip.

[David Burgess]

52 minutes ago, JohnCockburn said:

Yes, they're simple to calculate. Just the difference frequency between the 2 notes of the interval. I don't see where the weirdness comes in?

 

The weirdness, to me, comes in because some very experienced violin researchers have claimed that fiddle tone doesn't behave linearly. I disagree, but what do I know? I might not even have a good understanding of what "linear" means in the acoustic engineering realm.

[David Beard]

49 minutes ago, Shunyata said:

My newer violin that lacks the Tartini Tones, has heavier plates.  I wonder if it isn't flexible enough to strongly generate cleanly differentiated, dual frequencies and the resulting Tartini tones.

On my current in-flight build I am paying more attention to the plate flexibility, and to keeping the weight down.  It will be interesting to see if it has stronger Tartini tones.  I hope that some of you have additional ideas i can explore.

My tuner is just a cheapo Korg CA-1.  Not sure what the circuitry is picking up.  But my instructor uses the effect to reinforce proper tuning of third and sixth intervals.  When the tuning is right, the Tartini Tones kick in and you can see the tuner flip.

A key to producing the Tartini tones is stability of pitch.  The pitch needs to be clean and stead.  Perhaps the one violin is somehow moving in and out of the pitch center?

[JohnCockburn]

3 hours ago, David Burgess said:

The weirdness, to me, comes in because some very experienced violin researchers have claimed that fiddle tone doesn't behave linearly. 

i don't think that's necessarily relevant.

[JoeDeF]

It is my (limited) understanding that tartini tones are created by nonlinearity.  That nonlinearity could be in a mechanical object like the instrument or your ear, but I have read that air can behave in a nonlinear fashion.

Difference tones don't tend to show up in measurements.  As a mental model just for visualization, I think of two colored lasers being beamed into a fuzzy lens that partially outputs the mixed waves, yielding a third color.  If you take a picture of the lasers with a clear lens (measurement instrument), you only get a picture of the two colors, not the mixed third one.  Again, just a mental model.

In pianos, I do tend to hear difference tones most loudly when there is some defect in the soundboard structure.  I assume that the defect creates a more nonlinear condition.  In fact, when I hear them prominently, I usually start to look for soundboard cracks, loose ribs (braces, more like a series of bass bars), the soundboard separating from the inner rim, etc.  I often find such a defect, though not always...which is a very roundabout way of saying that you could inspect your violin's interior very carefully for any small gluing defects, etc.  If you like it as it is, I guess you wouldn't want to "fix" them, but it would be interesting to know if they are there.

[JohnCockburn]

4 hours ago, JoeDeF said:

It is my (limited) understanding that tartini tones are created by nonlinearity.  That nonlinearity could be in a mechanical object like the instrument or your ear,

agree

 

4 hours ago, JoeDeF said:

Difference tones don't tend to show up in measurements. 

disagree, depending on circs

[Michael Appleman]

"Tartini tones" or false fundamentals are a very real thing. You will not find them on FFT analysis, because they are psycho-acoustic phenomena, like the fundamental of the open G string (and other lower notes up to about C) on the violin. Our brains "hear" them, because we're being fooled into perceiving them by the combination of overtones we are actually hearing. 

I use them intensively in my own practicing, my teaching, and in evaluating violins. They inform me about the envelope of overtones I'm producing, the temperament of my intonation, and the types of overtone envelopes a given violin produces at different bow pressure/speed/contact point combinations.

[David Burgess]

In my radio-control model helicopter days, there were certain radios which could not be operated at the same time, because the combination of the two frequencies would produce a third frequency, and interfere  with operation of a helicopter operating on that third frequency. In group flying situations, we had to refer to a list of frequencies which could and could not be operated together, to prevent loss of control and crashing or injuring people. We called these heterodyne frequencies, and I think the tartini tones are essentially the same thing.

While an FFT doesn't show these, they will show on a sound recording when you expand the wave file enough to see the individual waves. When certain frequencies are recorded together, there will be regular recurring spots where two of the waves occur at the same time, combining to make a large wave. One can count these large waves on the time scale, and that will be the frequency of your "tartini" tone, or heterodyne tone. These air pressure pulses are "real", in the same sense that all sound consists of air pressure pulses.

I hope that makes sense, and isn't incorrect. It's early, and I'm only on my second cup of coffee.

I don't have an explanation for what's going on with the OP's violins and his tuner, but my guess is that the tuner is somehow counting pressure pulses, rather than processing via conventional FFT.

[JohnCockburn]

Theory tells you that you should detect combination tones including difference (Tartini) tones whenever the two originating tones go though a non-linear system. This could be, for example, the human auditory system. But it doesn't have to be. A nonlinear (ie distorting) amplifier would also do the trick. So it's not an exclusively psycho-acoustic phenomenon. In a stringed instrument, I guess it's also possible that the non-linearity of the sound generating  process itself could produce the TTs. I think this might be quite an interesting thing to study. Don't know if anyone has done this.

You can see Tartini tones in an FFT spectrum, if the required nonlinearity is present.

[David Burgess]

I'll try running another explanation up the flagpole, and see if anyone salutes:

Most of us can hear obvious "beats", when two strings on a piano are almost at the same pitch, but slightly off. As the pitches are moved closer to unison, the beats become slower. As the pitches are moved farther away from unison, the beats get faster.

When the pitches move far enough away from each other, the beats become fast enough to generate an audible pitch of their own.

[JohnCockburn]

38 minutes ago, David Burgess said:

I'll try running another explanation up the flagpole, and see if anyone salutes:

Most of us can hear obvious "beats", when two strings on a piano are almost at the same pitch, but slightly off. As the pitches are moved closer to unison, the beats become slower. As the pitches are moved farther away from unison, the beats get faster.

When the pitches move far enough away from each other, the beats become fast enough to generate an audible pitch of their own.

no, my explanation is the correct one. Beats and combination tones have a different origin, and the former don't require nonlinearity. You can never see beats in an FFT because they are just an amplitude fluctuation.

We can start throwing equations around if you like 

[notsodeepblue]

42 minutes ago, JohnCockburn said:

...

You can see Tartini tones in an FFT spectrum, if the required nonlinearity is present.

Do you mind if I ask by "see" whether you mean "infer from" (after post-processing of the fft, in the case of a tuner identifying the pitch of a digitised soundwave) or literally "see" (will be visible as a maximum)?

[JohnCockburn]

1 minute ago, notsodeepblue said:

Do you mind if I ask by "see" whether you mean "infer from" (after post-processing of the fft, in the case of a tuner identifying the pitch of a digitised soundwave) or literally "see" (will be visible as a maximum)?

visible as a peak

[David Burgess]

28 minutes ago, JohnCockburn said:

no, my explanation is the correct one. Beats and combination tones have a different origin, and the former don't require nonlinearity. You can never see beats in an FFT because they are just an amplitude fluctuation.

 

What is sound, or a pitch, other than a pattern of amplitude or air pressure fluctuations?

This is what microphones pick up, as do our ears, and these can also be seen in the visual waveform of a recording track, as can "beats".

[JohnCockburn]

10 minutes ago, David Burgess said:

What is sound, or a pitch, other than a pattern of amplitude or air pressure fluctuations?

This is what microphones pick up, as do our ears, and these can also be seen in the visual waveform of a recording track, as can "beats".

In a sound wave of a given pitch, or frequency, the air molecules are vibrating back and forth at that frequency. Changing the amplitude of the wave means they vibrate back and forth to a greater extent, but still at the same frequency. The frequency of the air pressure fluctuations stays the same, irrespective of amplitude fluctuations.

[Don Noon]

While I understand that "true" Tartini tones need non-linearities in either the generating or detecting systems in order to be present, I wonder if a listener's perception of fast beats (at the Tartini frequency) are that easily distinguishable from a real Tartini tone.

[David Burgess]

43 minutes ago, JohnCockburn said:

In a sound wave of a given pitch, or frequency, the air molecules are vibrating back and forth at that frequency. Changing the amplitude of the wave means they vibrate back and forth to a greater extent, but still at the same frequency. The frequency of the air pressure fluctuations stays the same, irrespective of amplitude fluctuations.

Yes, but that's not what I'm attempting to describe. If you take a 440 A, and increase volume of every third wave, you will also be generating a sound (or air pressure peaks) at a frequency of 146.6. That would sound as a D natural.

You could also take an G major triad (for example) and volume-pulse it 440 times per second, and hear an A. How easily perceptible either of these examples would be, would depend on the amount of volume fluctuation, as well as whether the generated frequency falls into the normal overtone series of the primary notes (which would make it more difficult to distinguish aurally).

[JohnCockburn]

1 minute ago, David Burgess said:

Yes, but that's not what I'm attempting to describe. If you take a 440 A, and increase volume of every third wave, you will also be generating a sound (or air pressure peaks) at a frequency of 146.6. 

 

No, you wouldn't. You'd be generating an amplitude variation at that frequency. Which isn't the same thing. Maybe the most helpful way to see this is to consider an analogy between light and sound. I'll explain when I come back from taking the dog for a dump.