Giovanni Cecchi Study of Combination Tones
Has anyone else seen this yet?
If the existence of combination tones can indeed be proven, that ought to be significant for luthiers and researchers alike. I would, however, be interested to see a follow up experiment that included some old violins that didn’t sound so good and some examples of the best-sounding or most highly regarded violins by current makers in addition to good old violins and bad new ones.
If you ADD together the waveforms of two tones, this COMBINED waveform can be represented by two other tones that MULTIPLY each other, essentially modifying each other's amplitude.
"IF the existance..." I can assume that the difference and sum tones, the combination tones of double stops are real, and not a mental illusion, because I can hear them, and, if you run the two signals through an oscilloscope you can see them. In a broad philosophical sense, the universe is more likely to be real, and not an illusion or a computer simulation, because through our five senses, physical phenomenon obey laws, are predictable and consistent.
I saw the article, but it leads to a question: ok, so a third tone is made when playing two notes together—a double stop. But we don’t play double stops exclusively. How does it explain good tone from single notes?
@Joel - Our senses only give a us a partial and biased account of reality. In vision we're accustomed to accepting certain well-known phenomena as illusory. In audition I believe there's a greater tendency to assume that everything we hear is "out there" but in fact all the perceptual analysis and re-synthesis of sound objects is done "in here". Our hearing does a lot better job of deciphering sound mixtures than eyeballing an oscilloscope, but it's still vulnerable to deception.
I think the author’s theory is that the increased presence of Tartini Tones in a violin correlates to greater air resonance in the body, so a more resonant violin will sound better on individual notes as well, not just when double stops are played.
The sum and difference frequencies are produced in non-linear mixers, NOT in linear mixers. Your ears are non-linear mixers and "tartini tones" are produced in your ears.
I might have said this on this forum before, but our senses are very interesting. While studying electronics 40+ years ago, we were shown the maths of it - from the dimmest stars in the sky we can prove that our eyes are capable of detecting light at a rate of 8 photons per second, which is the same as persistence of vision, so our eyes are just able to detect one photon of light.
Can the 'Tartini-metric, hey, "Tat-met"' be far behind? A measurable quantity to boost the provenance - and value of violins? Will there be a stampede (OK, a legato walk) to make violins with bigger and better Tartini-metrics???
Shhhh, Elise. Auction houses might be reading this!
Don't worry, the last thing they want the buyers to learn is that the violin is lemon. You can sell lemonade by marketing its fruit, not using a scale of its acid ;) [Auctions work almost entirely by provenance - they are mostly scared of sound .... ]
I have long "believed" that combination tones have a lot to do with appreciation of one violin over another, and have spent tons of time studying it.
David, a quick glance at a frequency vs sound intensity (dB) plot of a single note will show considerable "noise" and small peaks MANY decibels below the intensity of the overtone and its fundamentals.
Carmen, thank you for your further comments.
I haven't studied this, but this is the first I've heard of an objective difference tone out of the violin (something that can be measured by precise linear equipment). Something must be nonlinear somewhere.
I have now read a whole thread about difference tones and nobody mentioned why Tartini "talked about them" as Carmen notes.
In other fields, these are called heterodyne frequencies. When I was flying remote control aircraft years ago, there were certain transmitter frequencies which we were not supposed to use at the same time, because the combination of the two would produce a third frequency, risking loss of control of another aircraft, which not only could result in crashing the aircraft, but also risk the safety of operators and bystanders.
If we define secondary tones as anything other than the fundamental or overtones of the note being played, my personal experience is that, yes, these can have a dramatic effect on the player's appreciation of the violin.
Carmen, your examples are of high frequency noise that has nothing to do with the notes being (or attempted to be) played, so I wouldn't call them a "tone" at all, and not secondary. Additional sounds, perhaps.
Don, aren't the overtone structures highly dependent on the underlying resonating properties of an instrument (or its parts)?
Sure, overtone charcteristics are extremely dependent on how the wooden box vibrates, and that is very much how "good" and "bad" are determined.
Indeed getting thirds and sixths in tune with combination tones means pure, un-tempered intervals, which are lovely, but tricky to integrate with tempered accompaniments. For example a Pythagorean third can be shrunk to a pure third from the top, from the bottom, or symmetrically..
Don, I'm not talking about fingered double stops. I'm talking about double stops built into the resonances of the instrument itself.
David, presumably you mean body resonances that are tuned in some way to each other. I think your mental model differs from how it really works. We can talk about this at VSA.
David, I am trying not to get too technical since this is probably not the forum for detailed discussion about the physics of vibration. But I might be able to briefly summarize what is happening.
Carmen, refer back to what I was saying about the string impulses acting somewhat like tiny impact hammer pulses. In that case, they will excite more resonances than just those of the string fundamental and harmonics.
It might help to think of someone sitting on a swing, and you give them a short push every time a metronome clicks. If the metronome and the swing natural frequency are close, you can get them moving well after a while. If the frequencies are far apart, you will be pushing at the wrong time to build up any amplitude... and after things stabilze, the swinger will only be getting a small swing, and it will be at the frequency you are pushing... not the natural frequency of the swing.
I know it can be difficult to wrap one's head around an impact consisting primarily of a fundamental frequency and overtones that are each an integer multiple of the fundamental.
David wrote: "In my opinion, understanding the small differences between an OK violin and a great violin will need investigation going beyond your chosen envelope."
In my experience, there is next-to-nothing on a violin that can be changed, without having SOME effect on sound and playing properties.
You can tune a Malibu forever, and it still won't behave like a supercharged Corvette.
Did I restrict this to adjustments? If you were under the impression that I did, what about adjustments to the thicknesses or wood properties?
I have to admit my bias. In the engineering world that I came from, we were mostly trying to suppress vibrations, not enhance them.
Carmen, I can accept no.2, but not no.1!
Christian, I stand corrected! >grin<
Carmen, interestingly enough, one of the major researchers in violin and guitar acoustics is a now-retired Boeing aircraft vibration analyst. He has said something similar... that while the final objectives are different, and might even be opposites, vibration is vibration.
This discussion has been archived and is no longer accepting responses.