Tartini Tones and Under/Overtones

[David Burgess]

1 hour ago, JohnCockburn said:

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.

What is an amplitude variation, other than a greater or lesser variance in air pressure (when the conduction medium is air)?

These cyclic pressure variations, and the frequency at which they happen, are what the ear responds to, and what is interpreted as pitch. This includes the pressure variations which are generated by combining two tones, to produce a third set of pressure pulses, at a different frequency from either of the two which were combined to generate it.

[JohnCockburn]

For simplicity's sake, think of a pure sinusoidal sound wave entering your ear at a frequency of 440Hz. This will make your eardrum wobble backwards and forwards 440 times per second. This then gets transmitted to the basilar membrane of the cochlea, and your brain encodes the signal as having the pitch we know as A4.

As long as the eardrum continues to move back and forth 440 times a second, that pitch doesn't change. If you modulate the amplitude as you suggest, all that happens is that the maximum displacement of the eardrum experiences regular changes. But the eardrum still continues to move back and forth 440 times per second, ergo the pitch remains completely unchanged. 

 

 

[Bill Merkel]

John, do this thought experiment.  have a 440hz sine wave.  amplitude modulate it at some frequency.  then reduce the amplitude of the original 440 wave.  eventually all you have left is a wave of the modulating frequency

[David Burgess]

49 minutes ago, JohnCockburn said:

For simplicity's sake, think of a pure sinusoidal sound wave entering your ear at a frequency of 440Hz. This will make your eardrum wobble backwards and forwards 440 times per second. This then gets transmitted to the basilar membrane of the cochlea, and your brain encodes the signal as having the pitch we know as A4.

As long as the eardrum continues to move back and forth 440 times a second, that pitch doesn't change. If you modulate the amplitude as you suggest, all that happens is that the maximum displacement of the eardrum experiences regular changes. But the eardrum still continues to move back and forth 440 times per second, ergo the pitch remains completely unchanged.

You're not gettin it, and it might be my fault for explaining inadequately.

When two frequencies are combined, they can (under the right set of circumstances) produce a third third frequency, which can not only be heard, and measured with a microphone, but also wobbles the ear drum back and forth at this third frequency. (The eardrum can wobble back and forth at more than one frequency, simultaneously.)

[JohnCockburn]

1 minute ago, David Burgess said:

You're not gettin it, and it might be my fault for explaining inadequately.

When two frequencies are combined, they can (under the right set of circumstances) produce a third third frequency, which can not only be heard, and measured with a microphone, but also wobbles the ear drum back and forth at this third frequency.

Christ almighty. Yes of course, that's what we were talking about before you entered the realms of science fiction with your amplitude modulation nonsense.

[Bill Yacey]

By modulating an oscillator through switching it on and off is pulse width modulation, and the modulating frequency information can be recovered by low pass filtering away the high frequency carrier.  440hz being the carrier frequency in David's example, which would leave behind the low frequency modulating waveform. after the carrier was filtered out, albeit the resulting low frequency would be far below the audio band of frequencies.

This is the principle behind digital audio reproduction.

However, there isn't any frequency mixing taking place. Another analogy can be found in the doppler effect of an approaching train whistle; as the train moves closer to the listener, the sound waves are being compressed closer together within the time domain by the moving train. This causes enough phase shift to generate the raising of pitch heard by the stationary listener. If the train could be made to instantly reverse direction, the pitch change would reverse itself and drop in frequency. If the direction of travel is repeatedly changed back and forth, this rate of change would create a  sum and difference frequency in relation to the train whistle pitch.

Done fast enough it would create beat frequencies, and even faster, would be perceived as some distinct tones. The most readily heard tone - the sum or difference, will be dependent of where and if it falls within the audio spectrum.

[David Burgess]

4 hours ago, JohnCockburn said:

Christ almighty. Yes of course, that's what we were talking about before you entered the realms of science fiction with your amplitude modulation nonsense.

Doing a little backpedaling now, aren't you?

Volume (pressure) modulation is about the only way that the eardrum responds to frequency. And combinations of two tones can produce actual third frequency wobbling of the eardrum. That's similar to the behavior of microphones. A single microphone can signal multiple frequencies at the same time, not just one.

[JohnCockburn]

3 minutes ago, David Burgess said:

Doing a little backpedaling now, aren't you?

Not at all. Have you actually read my earlier posts in the thread?

 

[David Beard]

5 hours 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.

All hail.

[JohnCockburn]

1 minute ago, David Beard said:

All hail.

It's nonsense.

[Bill Yacey]

They have different physical laws in Europe.

[David Beard]

Perhaps I miss understand?

Difference tones are simple.  F1 - F2 = dF.

Essentially just an extension of beats. 

As a violinist, I grew up believing i'd learned that Tartini discovered using these actual difference tones in playing. And that people called such difference tones 'Tartini tones'.

Is this not the case?

[David Beard]

4 hours 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.

??excuse me??

There is no simple relation between the pressure wave frequency and motion of individual molecules.  Only the collective presure directly has the frequency.  Individual molecules of the medium will move move in response, but not necessarily simply and directly tracking the frequency as pulses of the wave pass through.

[JohnCockburn]

Just now, David Beard said:

Perhaps I miss understand?

Difference tones are simple.  F1 - F2 = dF.

Essentially just an extension of beats. 

As a violinist, I grew up believing i'd learned the Tartini discovered using these actual difference tones in playing. And that people called such difference tones 'Tartini tones'.

Is this not the case?

No, because beats arise through simple linear superposition of the component waves. There's no signal power at the beat frequency, just an amplitude fluctuation. That's why it wouldn't be seen in an FFT. There are no air molecules  oscillating back and forth at the beat frequency

Tartini tones require mixing of the 2 source wavelengths via a non linear medium. This leads to a difference signal that does have signal power, can move air molecules and can be seen in an FFT. The idea of Tartini tones being high frequency beats is wrong.

 

[David Burgess]

5 minutes ago, JohnCockburn said:

No, because beats arise through simple linear superposition of the component waves. There's no signal power at the beat frequency, just an amplitude fluctuation.

Amplitude fluctuation IS the signal power which is relevant to hearing.  Amplitude fluctuation is what wobbles the eardrum. Amplitude without modulation produces no sensation of sound, only something ranging between a weird feeling, and pain.

[Bill Yacey]

4 minutes ago, David Burgess said:

Amplitude fluctuation IS the signal power which is relevant to hearing.  Amplitude fluctuation is what wobbles the eardrum. Amplitude without modulation produces no sensation of sound, only something ranging between a weird feeling, and pain.

Just a change in atmospheric pressure.

[David Beard]

Air molecules vibrating back and forth??

We are talking fluctuating collective air presure, not vibrating molecules.  (Vibrating molecules = heat.  Periodically cycling presure wave = sound)

The air presure of waves is additive.  Beats do present a periodically cycling extra degree of low and high pressure as two waves of different frequency add their pressures.

If a listener, mechanical, mathematical, or human, fully recognizes that the periodically cycling extra peaks and valleys of the difference are completely dependent on the two basic waves, then the frequency of this cycle can be discounted and doesn't need to be reported/heard as a tone.

But the cycle of the difference tone is still physically present.

And, the fact that we hear these only tells us that or hearing system does include the rule 'discard presure cycles that sum from sine waves you're hearing at the same time'.

 

[Bill Merkel]

here's a frequency analysis of a file that's supposed to demonstrate a tartini tone.  in the plot there is just the two original tones visible at a level that would be audible. 

the file:  https://newt.phys.unsw.edu.au/jw/tartini-temperament.html

the frequency plot:

[JohnCockburn]

Wow. This is quite an impressive display of attempted collective bullying. As I'm being attacked on several fronts here, it'll take me a little time to respond. Don't take this as a sign of weakness 

[David Burgess]

5 minutes ago, JohnCockburn said:

Wow. This is quite an impressive display of attempted collective bullying. As I'm being attacked on several fronts here, it'll take me a little time to respond. Don't take this as a sign of weakness 

It's the Russians, trying to sow discord in the NATO alliance.

[Bill Merkel]

have i been shadow banned?

[JohnCockburn]

This isn't what Shunyata intended for his thread, so I'll start a new one. Probably tomorrow.

 

 

 

[Bill Merkel]

On 5/30/2020 at 6:54 PM, David Burgess said:

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

looking up some guitar tuner code just now, that particular code doesn't use an fft, but uses a comparator to square the input wave and then counts the duration of that squared wave.  if the threshold was set right, with a single note you'd usually get the fundamental or the octave above, same letter pitch.  from the same file, below you see 400hz and 600hz sine waves superimposed results in a periodicity of about 166hz.  that could easily be the frequency the tuner squares, depending on the threshold, and that may even be the pitch that you hear as a tartini tone in this case...  though there's apparently no significant component of that frequency in the spectrum, that periodicity is there...

 

[David Burgess]

Measuring the time between peaks.. interesting!

[Bill Merkel]

that's one way of measuring period, which is the reciprocal of frequency.  the main periodicity of a single note would usually be the fundamental or the first overtone because of their relative strength.  somebody should use two real pitches and see if gives a periodicity that corresponds to the expected tartini note