Pianotech

If you google "Combination Tones" you will find a vigorous debate on this subject which started perhaps with the 18^th century violinist Giuseppe Tartini so they are sometimes called "Tartini tones." There is no debate over their existence. The debate is over their cause.

We are not talking about harmonics or partials whose cause we understand well. We are talking about pure or nearly pure sine waves (like the sound of a flute). On one hand you have those who say that when two sine waves of frequencies f1 and f2 mix in the air they produce the sum and the difference frequencies of f1+f2 and f1-f2. These sum and difference frequencies are supposed to behave just like naturally-occurring sounds when we hear them. In fact there are demonstration audio clips on-line that play two sine waves together and let you hear their difference frequency, such as 1500 Hz and 1000 Hz sounding together and then you hear the 500 Hz difference tone. You could then beat this difference tone with a separately-generated 501 Hz tone and hear a faint 1 BPS beat.

On the other hand there are strong scientific reasons against this explanation. One is what Don Mannino just observed. The difference tone is not detected by a spectrum analyzer, such as the one in TuneLab. So if it not really there, why do we hear it? The answer is the one that Kent Swafford mentioned and dismissed in his recent article in the Journal – that the difference tone is the result of non-linear intermodulation distortion in the playback chain. In favor of this view is the observation that the strength of the difference tone and any associated beats it creates is dependent on the volume of the sound in a non-linear manner. When you listen to normal beats in normal piano tuning, the strength of the beat decays gradually, exactly the same as the strength of the two notes that are producing it. As long as you can hear the two notes, you can hear the beat. But when a difference tone from two pure sine waves is involved, you need a certain volume level to hear the difference tone. Below that threshold you don't hear any difference tone at all, even though you can still hear the two individual tones quite well . This is the threshold at which something in the playback chain becomes non-linear.

What about Tartini? He did not have any non-linear electronics in the 18-th century. How was he hearing Tartini tones and using them to fine-tune violin double-stops? It turns out that the inner ear is also subject to intermodulation distortion which creates difference tones. It was noticed by Helmholtz that Tartini tones are not audible unless there is enough sound volume to drive the ear into its non-linear region. Also there is Don Mannino's example of the stained glass windows rattling out the difference tone. Anything that is loose and rattles is clearly responding in a non-linear manner and creating the difference tone right there.

What about the graphs of two pure tones producing clearly visible patterns? These are misleading since the pattern that they show is apparent to the eyes, but not to the ears. The real way to look at what the ear hears is to look at the graph of the frequency domain, not the time domain – in other words a frequency spectrum. In that case all you will see is two separate peaks, far apart, and nothing else. There is no evidence that the ear can detect the pattern that is seen on in the time-domain graph.

Perhaps it does not matter how they are produced. Difference tones are a perceptible phenomenon and would produce the same effect on the sound of a musical instrument regardless.

If you google "Combination Tones" you will find a vigorous debate on this subject which started perhaps with the 18^th century violinist Giuseppe Tartini so they are sometimes called "Tartini tones." There is no debate over their existence. The debate is over their cause.

We are not talking about harmonics or partials whose cause we understand well. We are talking about pure or nearly pure sine waves (like the sound of a flute). On one hand you have those who say that when two sine waves of frequencies f1 and f2 mix in the air they produce the sum and the difference frequencies of f1+f2 and f1-f2. These sum and difference frequencies are supposed to behave just like naturally-occurring sounds when we hear them. In fact there are demonstration audio clips on-line that play two sine waves together and let you hear their difference frequency, such as 1500 Hz and 1000 Hz sounding together and then you hear the 500 Hz difference tone. You could then beat this difference tone with a separately-generated 501 Hz tone and hear a faint 1 BPS beat.

On the other hand there are strong scientific reasons against this explanation. One is what Don Mannino just observed. The difference tone is not detected by a spectrum analyzer, such as the one in TuneLab. So if it not really there, why do we hear it? The answer is the one that Kent Swafford mentioned and dismissed in his recent article in the Journal – that the difference tone is the result of non-linear intermodulation distortion in the playback chain. In favor of this view is the observation that the strength of the difference tone and any associated beats it creates is dependent on the volume of the sound in a non-linear manner. When you listen to normal beats in normal piano tuning, the strength of the beat decays gradually, exactly the same as the strength of the two notes that are producing it. As long as you can hear the two notes, you can hear the beat. But when a difference tone from two pure sine waves is involved, you need a certain volume level to hear the difference tone. Below that threshold you don't hear any difference tone at all, even though you can still hear the two individual tones quite well . This is the threshold at which something in the playback chain becomes non-linear.

What about Tartini? He did not have any non-linear electronics in the 18-th century. How was he hearing Tartini tones and using them to fine-tune violin double-stops? It turns out that the inner ear is also subject to intermodulation distortion which creates difference tones. It was noticed by Helmholtz that Tartini tones are not audible unless there is enough sound volume to drive the ear into its non-linear region. Also there is Don Mannino's example of the stained glass windows rattling out the difference tone. Anything that is loose and rattles is clearly responding in a non-linear manner and creating the difference tone right there.

What about the graphs of two pure tones producing clearly visible patterns? These are misleading since the pattern that they show is apparent to the eyes, but not to the ears. The real way to look at what the ear hears is to look at the graph of the frequency domain, not the time domain – in other words a frequency spectrum. In that case all you will see is two separate peaks, far apart, and nothing else. There is no evidence that the ear can detect the pattern that is seen on in the time-domain graph.

Perhaps it does not matter how they are produced. Difference tones are a perceptible phenomenon and would produce the same effect on the sound of a musical instrument regardless.

Wow! Didn't expect to get so many interesting responses! Thanks, all!

Peter – Regarding your last post, YES! Regarding your first, I'll try to attach a recording I just made between a recorder alternating a B5 & C6 along with a pennywhistle playing a very sharp G5. The difference tones are much louder in my ear, but they are still audible on the recording, albeit faint. I'll try to make a better recording this week just to see what I can pull off in my plethora of spare time (yes, sarcasm...but now I'm curious.)

Ed! Do you happen to remember these flute duets?!? I would LOVE to play them with a student of mine. Our flutes put out the loudest difference tones I have ever heard!

I also believe one can hear amplifications of overtones and can now hear them quite well, sometimes to my annoyance. I started hearing them louder when I started practicing overtone singing in my car. Simply hearing them created by my own voice made me much more aware of them in the piano. It's occasionally useful, but mostly annoying. I'll have to look that article by Galembo up! Thanks!

The thing that's been catching my attention lately isn't coming from one string by itself. Amplified harmonics from one string are fairly obvious to me. I'm pretty sure most of what I'm hearing is a reaction of tones from one string to other tones in the room or another string. They are getting annoyingly loud.

Edward – Really interesting about the Rhodes. I've only seen one twice.

So, the fundamental is sometimes vibrating but you can't hear it? I hadn't thought about that before.


I'm pretty sure I can NOT get a reading on a difference tone with my ETD. I've gotten readings on what I thought might be summation tones but that may not be in fact what they were. I'll double check that this week with my 440 & 441 tone bars. I can easily record them so they can definitely be picked up by a mic. My understanding is that there are different kinds of them, and that some are only in our ears and others are definitely in the air (or other medium) around us. Some are around us but can't be detected or noticed by everyone.

Jim – Yes. Especially for those of us who have a softer grasp to reality. ;-)

Richard – I don't see that as off topic. Like you said, we're dealing with these all the time whether we know it or not trying to get an end result. I have a problem right now (Ed knows about this one) in which a church pianist can suddenly hear the first second or third overtone on many of the strings when others can't. It's driving her crazy. We don't have a solution yet.

Don – I've heard them with organs many times and am pretty sure they are recordable. I'll try that this week at our college. I bet my simple phone recorder can pick them up. I'll try the combination tone, too, just because I've never tried it. If I fail, nothing lost. ;-) I have definitely recorded them on flutes. I'll try to either find that recording or reproduce it...easy enough to do with music students all around. As you and Ed pointed out, they don't show up on ETD's. I've never tried on an oscilloscope but am assuming it would be the same? I know you can record them, but have no deep understanding of it.

Robert – You half lost me, but as you pointed out, they happen regardless of the cause. My understanding is that there are different types with more than one cause. When you say "frequency domain" (as opposed to time domain), are you talking about what shows up on an oscilloscope? Sorry I couldn't follow it all.

John – really cool experiment. The second to last paragraph is what I would have expected & it's cool you actually did it. Regarding the last paragraph, I'm not sure I would have predicted that but I'm not surprised. I bet the perception can be different with different people, too.

The only reason I'm calling what I'm hearing difference tones is that they sound exactly like other difference tones I hear, so I'm assuming that's what they are.


So...the answer to my first question seems to be that this isn't necessarily due to age and that I'm just going to have to deal with it. LOL!

Wow! Didn't expect to get so many interesting responses! Thanks, all!

Peter – Regarding your last post, YES! Regarding your first, I'll try to attach a recording I just made between a recorder alternating a B5 & C6 along with a pennywhistle playing a very sharp G5. The difference tones are much louder in my ear, but they are still audible on the recording, albeit faint. I'll try to make a better recording this week just to see what I can pull off in my plethora of spare time (yes, sarcasm...but now I'm curious.)

Ed! Do you happen to remember these flute duets?!? I would LOVE to play them with a student of mine. Our flutes put out the loudest difference tones I have ever heard!

I also believe one can hear amplifications of overtones and can now hear them quite well, sometimes to my annoyance. I started hearing them louder when I started practicing overtone singing in my car. Simply hearing them created by my own voice made me much more aware of them in the piano. It's occasionally useful, but mostly annoying. I'll have to look that article by Galembo up! Thanks!

The thing that's been catching my attention lately isn't coming from one string by itself. Amplified harmonics from one string are fairly obvious to me. I'm pretty sure most of what I'm hearing is a reaction of tones from one string to other tones in the room or another string. They are getting annoyingly loud.

Edward – Really interesting about the Rhodes. I've only seen one twice.

So, the fundamental is sometimes vibrating but you can't hear it? I hadn't thought about that before.


I'm pretty sure I can NOT get a reading on a difference tone with my ETD. I've gotten readings on what I thought might be summation tones but that may not be in fact what they were. I'll double check that this week with my 440 & 441 tone bars. I can easily record them so they can definitely be picked up by a mic. My understanding is that there are different kinds of them, and that some are only in our ears and others are definitely in the air (or other medium) around us. Some are around us but can't be detected or noticed by everyone.

Jim – Yes. Especially for those of us who have a softer grasp to reality. ;-)

Richard – I don't see that as off topic. Like you said, we're dealing with these all the time whether we know it or not trying to get an end result. I have a problem right now (Ed knows about this one) in which a church pianist can suddenly hear the first second or third overtone on many of the strings when others can't. It's driving her crazy. We don't have a solution yet.

Don – I've heard them with organs many times and am pretty sure they are recordable. I'll try that this week at our college. I bet my simple phone recorder can pick them up. I'll try the combination tone, too, just because I've never tried it. If I fail, nothing lost. ;-) I have definitely recorded them on flutes. I'll try to either find that recording or reproduce it...easy enough to do with music students all around. As you and Ed pointed out, they don't show up on ETD's. I've never tried on an oscilloscope but am assuming it would be the same? I know you can record them, but have no deep understanding of it.

Robert – You half lost me, but as you pointed out, they happen regardless of the cause. My understanding is that there are different types with more than one cause. When you say "frequency domain" (as opposed to time domain), are you talking about what shows up on an oscilloscope? Sorry I couldn't follow it all.

John – really cool experiment. The second to last paragraph is what I would have expected & it's cool you actually did it. Regarding the last paragraph, I'm not sure I would have predicted that but I'm not surprised. I bet the perception can be different with different people, too.

The only reason I'm calling what I'm hearing difference tones is that they sound exactly like other difference tones I hear, so I'm assuming that's what they are.


So...the answer to my first question seems to be that this isn't necessarily due to age and that I'm just going to have to deal with it. LOL!

Wow! Didn't expect to get so many interesting responses! Thanks, all!

Peter – Regarding your last post, YES! Regarding your first, I'll try to attach a recording I just made between a recorder alternating a B5 & C6 along with a pennywhistle playing a very sharp G5. The difference tones are much louder in my ear, but they are still audible on the recording, albeit faint. I'll try to make a better recording this week just to see what I can pull off in my plethora of spare time (yes, sarcasm...but now I'm curious.)

Ed! Do you happen to remember these flute duets?!? I would LOVE to play them with a student of mine. Our flutes put out the loudest difference tones I have ever heard!

I also believe one can hear amplifications of overtones and can now hear them quite well, sometimes to my annoyance. I started hearing them louder when I started practicing overtone singing in my car. Simply hearing them created by my own voice made me much more aware of them in the piano. It's occasionally useful, but mostly annoying. I'll have to look that article by Galembo up! Thanks!

The thing that's been catching my attention lately isn't coming from one string by itself. Amplified harmonics from one string are fairly obvious to me. I'm pretty sure most of what I'm hearing is a reaction of tones from one string to other tones in the room or another string. They are getting annoyingly loud.

Edward – Really interesting about the Rhodes. I've only seen one twice.

So, the fundamental is sometimes vibrating but you can't hear it? I hadn't thought about that before.


I'm pretty sure I can NOT get a reading on a difference tone with my ETD. I've gotten readings on what I thought might be summation tones but that may not be in fact what they were. I'll double check that this week with my 440 & 441 tone bars. I can easily record them so they can definitely be picked up by a mic. My understanding is that there are different kinds of them, and that some are only in our ears and others are definitely in the air (or other medium) around us. Some are around us but can't be detected or noticed by everyone.

Jim – Yes. Especially for those of us who have a softer grasp to reality. ;-)

Richard – I don't see that as off topic. Like you said, we're dealing with these all the time whether we know it or not trying to get an end result. I have a problem right now (Ed knows about this one) in which a church pianist can suddenly hear the first second or third overtone on many of the strings when others can't. It's driving her crazy. We don't have a solution yet.

Don – I've heard them with organs many times and am pretty sure they are recordable. I'll try that this week at our college. I bet my simple phone recorder can pick them up. I'll try the combination tone, too, just because I've never tried it. If I fail, nothing lost. ;-) I have definitely recorded them on flutes. I'll try to either find that recording or reproduce it...easy enough to do with music students all around. As you and Ed pointed out, they don't show up on ETD's. I've never tried on an oscilloscope but am assuming it would be the same? I know you can record them, but have no deep understanding of it.

Robert – You half lost me, but as you pointed out, they happen regardless of the cause. My understanding is that there are different types with more than one cause. When you say "frequency domain" (as opposed to time domain), are you talking about what shows up on an oscilloscope? Sorry I couldn't follow it all.

John – really cool experiment. The second to last paragraph is what I would have expected & it's cool you actually did it. Regarding the last paragraph, I'm not sure I would have predicted that but I'm not surprised. I bet the perception can be different with different people, too.

The only reason I'm calling what I'm hearing difference tones is that they sound exactly like other difference tones I hear, so I'm assuming that's what they are.


So...the answer to my first question seems to be that this isn't necessarily due to age and that I'm just going to have to deal with it. LOL!

Wow! Didn't expect to get so many interesting responses! Thanks, all!

Peter – Regarding your last post, YES! Regarding your first, I'll try to attach a recording I just made between a recorder alternating a B5 & C6 along with a pennywhistle playing a very sharp G5. The difference tones are much louder in my ear, but they are still audible on the recording, albeit faint. I'll try to make a better recording this week just to see what I can pull off in my plethora of spare time (yes, sarcasm...but now I'm curious.)

Ed! Do you happen to remember these flute duets?!? I would LOVE to play them with a student of mine. Our flutes put out the loudest difference tones I have ever heard!

I also believe one can hear amplifications of overtones and can now hear them quite well, sometimes to my annoyance. I started hearing them louder when I started practicing overtone singing in my car. Simply hearing them created by my own voice made me much more aware of them in the piano. It's occasionally useful, but mostly annoying. I'll have to look that article by Galembo up! Thanks!

The thing that's been catching my attention lately isn't coming from one string by itself. Amplified harmonics from one string are fairly obvious to me. I'm pretty sure most of what I'm hearing is a reaction of tones from one string to other tones in the room or another string. They are getting annoyingly loud.

Edward – Really interesting about the Rhodes. I've only seen one twice.

So, the fundamental is sometimes vibrating but you can't hear it? I hadn't thought about that before.


I'm pretty sure I can NOT get a reading on a difference tone with my ETD. I've gotten readings on what I thought might be summation tones but that may not be in fact what they were. I'll double check that this week with my 440 & 441 tone bars. I can easily record them so they can definitely be picked up by a mic. My understanding is that there are different kinds of them, and that some are only in our ears and others are definitely in the air (or other medium) around us. Some are around us but can't be detected or noticed by everyone.

Jim – Yes. Especially for those of us who have a softer grasp to reality. ;-)

Richard – I don't see that as off topic. Like you said, we're dealing with these all the time whether we know it or not trying to get an end result. I have a problem right now (Ed knows about this one) in which a church pianist can suddenly hear the first second or third overtone on many of the strings when others can't. It's driving her crazy. We don't have a solution yet.

Don – I've heard them with organs many times and am pretty sure they are recordable. I'll try that this week at our college. I bet my simple phone recorder can pick them up. I'll try the combination tone, too, just because I've never tried it. If I fail, nothing lost. ;-) I have definitely recorded them on flutes. I'll try to either find that recording or reproduce it...easy enough to do with music students all around. As you and Ed pointed out, they don't show up on ETD's. I've never tried on an oscilloscope but am assuming it would be the same? I know you can record them, but have no deep understanding of it.

Robert – You half lost me, but as you pointed out, they happen regardless of the cause. My understanding is that there are different types with more than one cause. When you say "frequency domain" (as opposed to time domain), are you talking about what shows up on an oscilloscope? Sorry I couldn't follow it all.

John – really cool experiment. The second to last paragraph is what I would have expected & it's cool you actually did it. Regarding the last paragraph, I'm not sure I would have predicted that but I'm not surprised. I bet the perception can be different with different people, too.

The only reason I'm calling what I'm hearing difference tones is that they sound exactly like other difference tones I hear, so I'm assuming that's what they are.


So...the answer to my first question seems to be that this isn't necessarily due to age and that I'm just going to have to deal with it. LOL!