What is the third audible but unplayed pitch called when you play 2 strings at the same time?

January 13, 2019, 7:13 AM · What is the English term for the effect that if you play 2 strings together there sounds a another lower note that can (or at least could be) heard allthough it is not played? Like if you play A and E together you can hear a third lower note in the backround.

Replies (20)

Edited: January 13, 2019, 7:35 AM · Can't tell you what a musician calls it, but the physicist in me would say whenever you play two frequencies, you hear the sum and the difference.
Play A4(440) and E4(329.6) together and you should hear A2(110.4, the difference) and G5(769.6, the sum).
But that's if you play sinewaves. Play real notes and you'll hear the sums and differences of every overtone with every other overtone.
Play 440 and 441 and you'll hear 1Hz (a beat) and 881, but this 881 will probably be swamped by the overtones 880 and 882, although the differences between 880 and 881 and 882 and 881 will add to the strength of the 1Hz beat.

It's about whether a "mixer" is linear or non-linear. Mix two electronic signals with (linear) wires, and you don't get the effect. You only get it when semiconductors add nonlinearity. Our ears seem to be a nonlinear system.

It's not something I worry about - it's just the physics of the ears. In a way this response is pretty pointless (except that I'm revising out-loud), but there was another thread that mentioned the same thing, and I can't remember what it said, so I'm replying to jog people's memories.

January 13, 2019, 7:35 AM · Musicians often call them "Tartini" or "combination" tones. Physicists might call them heterodyne frequencies.
January 13, 2019, 7:50 AM · Yup - Tartini notes! Lots of fun to listen to....
Edited: January 13, 2019, 7:57 AM · Another term in use is 'difference' tones, for the reason that Andrew explained.
January 13, 2019, 8:06 AM · Modern radios used to be known as "Heterodyne sets", for reasons I could explain, but realise it's best not to, lol!
January 13, 2019, 10:05 AM · Thank you ver much, also for the explanation :)
January 14, 2019, 12:26 AM · Is this then always the case when we play double stops on the Violin?
January 14, 2019, 2:55 AM · So I tested with my violin and tuner.

And when I play A and E strings together, my tuner gives me A on the G string.

But Andrews post says A2, which is an octave lower than the A on the G string, (110Hz) am I correct?

So there must be something I dont understand. I found all the A s from wikipedia and I can barely hear the A 1110Hz.

https://en.m.wikipedia.org/wiki/A_(musical_note)

And I cannot hear it myself, but I maybe feel some extra vibrations with my hand from the back of the violin.

Edited: January 14, 2019, 3:44 AM · Well, I read on this forum that you can hear them, and I didn't see any reason to disbelieve that (in fact, I've heard them regularly in other situations, just not while violin-playing). If you play a straight A, you won't hear any of its harmonics individually (e.g. the 440 base sinewave - you won't hear that) - they merge into one roughly triangular waveform.

"when I play A and E strings together, my tuner gives me A on the G string." I don't understand what this means. Do you mean the D string?

The A2 (if created) is created in your ear, not in the violin; besides, if it were, it might be such a low pitch that the violin would attenuate it excessively - if you had an A2 string, that probably wouldn't vibrate in sympathy (well, it probably would, but only with the A440), but it depends on whether wood and string are 100% linear or whether there's an element of non-linearity in them.

When you play any note on a violin, the physical shaking will create extraneous (non sympathetic) vibrations in any part of the violin that is capable of vibrating. All these parts will have their own resonant frequencies which add tone to your sound. The vibrations will just be weaker than when they are sympathetic ones.

January 14, 2019, 3:57 AM · Andrew, I mean that if I play A4 and E5 that is A and E strings together, my tuner reads A3 which is the note A played on the G string ( first finger on the G string). I checked many times this and it happens only when the A and E strings are tuned just right with open fifths. And it happens with both mine and my daughters violin. How strange.

This all rised because our teacher said that if you play A and E strings together there is a lower note that can be heard and I understood it was from the G string.

January 14, 2019, 6:19 AM · Ah, E5, I wasn't thinking. You'll notice that I gave the frequency of E4.
e5 is about 659, so the sum and difference between that and A440 would be 1099 and 219 which are C#6 and A3
January 14, 2019, 6:46 AM · Incidentally, the theremin works this way - two very high pitches, one fixed and one moving. You just hear the difference tone as the others are very high.
January 14, 2019, 7:49 AM · Tartini Tones sounds better than Murph and the Mellow Tones.
January 14, 2019, 8:47 AM · Andrew, that clears it :) thanks :)
January 14, 2019, 9:40 AM · It's actually an interesting concept to have your tuner "hear" the Tartini tones for you.
January 14, 2019, 9:50 AM · Yes-- how could the tuner hear a tone that is a sum/difference created in your ear? Anyway, I don't think the ear creates sounds at all. Like the eye does not created images...
Edited: January 14, 2019, 10:46 AM · The tuner is nonlinear electronics, so it mixes.

The basic definition is, resistors, capacitors, coils are linear.
Any semiconductor is non-linear. That's a bit tricky, as integrated circuits contain resistors and capacitors made from semiconducting material which I'd say was linear, so you'll have to Google for a better definition if you're not happy. Probably anything that amplifies is non-linear, maybe that's it.

I infer that our ears are non-linear (our brain, if you prefer).

"the eye does not create images..." I hope this isn't going to turn into a discussion of the philosophy of perception - I got kicked off Delcamp for joining in with too many of them, lol! (Delcamp's loss, my gain)

January 14, 2019, 11:30 AM ·
January 15, 2019, 12:31 AM · I tried with 2 tuners, and finally I can hear the thing. Its a fluctuating wave of the A3 pitch. But the thing is I can only hear it if the A and E are played very loudly with the tuners, so no wonder I cannot hear it with the violin, its just too week a voice for my ears to hear. And its not an especially nice sound either.
Edited: January 15, 2019, 4:20 AM · That's why we have cellos and basses, to mask it all.

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