Piano World Home Page Forums Our Most Popular Forums Digital Pianos - Electronic Pianos - Synths & Keyboards How much low frequency power does a piano have?

You know when you are following a thread up to a certain point and you suddenly hit a point where you are hopelessly out of your depth?

I have officially reached that point...

I think you are probably correct. It is fascinating how complex and still mysterious is the ability to perceive pitch, especially the ability to discriminate between two very close pitches, when not played together.

There must be a 'learned' component to pitch perception given the complex harmonic and inharmonic structure of most pitches. By that I mean that we learn to hear the oboe, the flute, the violin, as individual instruments even when playing in unison. A person who has never heard any of those instruments would likely hear a single source sound.

Is it fair to call the missing fundamental an illusion?

If it were an illusion the note without the fundamental would sound the same as the one with. With the fundamental present the sound is generally 'fuller'.

Seems quite easy to pick out the point at which the fundamental goes lower than the soundboard resonant frequency when playing note by note down the piano.

Assigning a pitch to the sound seems more a case of identifying the repetition rate rather than specifically picking out the lowest sine wave.

It could be an illusion in that the missing fundamental can really be missing and we still hear it, because our brain wants us to hear it, possibly for some evolutionary survival reason.

But, I argue that the mechanical structure of the ear (in all its complexity of drum, bones, cochlea) is inherently non-linear, which means that it distorts the sound causing actual additive and subtractive interactions between the partials, which means the fundamental is actually created by the mechanical structure of the ear.

Try my experiment on your DP - play C5 and E5 simultaneously. You will hear G4. The ratio C5:E5 is 4:5, yet we hear G4, which is in the ratio G4:C5:E5 = 3:4:5.

Non-Linear mixing (addition and subtraction of two or more frequencies) is actually used all the time in radio electronics and audio.

In radio, it is used to convert a high frequency radio signal to a constant low frequency signal for efficient amplification. It is also used for frequency multiplication. A sine wave is fed to a non-linear amplifier which produces multiple harmonics above and below the sine wave. The desired harmonic is put through a band-pass filter and amplified.

I mentioned guitar amps and speakers are designed for non-linear operation. There is an emphasis on the second harmonic, which interacts with the fundamental pitch creating the octave below. The result is a rich, warm sounding guitar.

It is not the complexity which cause non-linearity, but some kind of saturation, or important displacements. The sound is about very small displacements. This makes me think the ear should be generally quite linear, but I have no proof about it.

The stereocillias could vibrate with high displacement (compared to their size). But This wouldn't change their bandpass, only how they vibrate if they vibrate. They would vibrate with harmonic distortion, but this won't change the fact that they vibrate which is what it is measured. Then no impact.

Here is a paper abstract on the non-linear functioning of the vertebrate auditory system.

"Abstract
The vertebrate ear is highly nonlinear. This is rather surprising since its vibrational amplitudes are so minute in response to normal sound pressures. Generally, one might expect a stable mechanical system to respond linearly when disturbed slightly from its resting state. Thus the nonlinear properties of the peripheral auditory system are of considerable interest inasmuch as they can provide valuable insight into the underlying transduction process in the ear. The two most prominent nonlinear properties are inter-modulation distortion and two-tone suppression. Their characteristics have been studied extensively in the mammalian auditory system by a number of investigators. To provide a comparative view, a series of electrophysiological experiments were conducted in order to determine the nonlinear behavior of the anuran’s peripheral auditory system. The results have interesting implications regarding the origin of nonlinearities, as well as the mechanical basis for frequency analysis, in the vertebrate inner ear in general. Before presenting these findings, several relevant studies of nonlinearities in the mammalian auditory system are summarized, followed by a brief review of the anatomy of the anuran’s ear."

The paper references significant research into non-linearity of the auditory system by Moe, Plomp, and especially Zwicker.

Clearly intermodulation distortion in the physical process is the cause of our ability to sense the 'missing fundamental'. The research on this subject is huge.

edit: another source: non-linearity

This seems to be compatible with I have said. Thanks for the sharing. Unfortunately, the article is a little expensive if one just want to satisfy its curiosity. I won't know why I was wrong.

It seems odd that such minute displacements give rise to non-linearities. However, we have looked at only pitch. The real non-linearity is in our perception of loudness.

The researchers all seem to argue that the non-linearities are the result of some evolutionary advantage.

One interesting point is that the original idea, that pitch perception occurs by some form of rudimentary mechanical/neural time-variant Fourier analysis in the cochlea, has been discarded, since our ability to sense precise pitch occurs in a time interval that is less than the Gabor Interval required for such precision.

The ear is a truly amazing organ.

I got so bored tonight I actually read through this stuff . . . . .Yamaha's brought out a new range of pianos nobody's interested in . . .guess I'll have to just . . . practice. Sad isn't it?

It is fascinating how threads often meander far from the desired trajectory. However, we often learn stuff on the way.

Yes, prout. Lots of interesting stuff here sometimes, despite the divergence from an OP's topic.

There's one thing I'd like to add ...

The posts here (and the cited paper) speak about the physical causes of sound, But there little here about the psychological portion. The relationship between the two is at the same time the most interesting and the most difficult.

My point is this: Perception is entirely in the mind. And that's where we live. We don't live in a reality world. We live in a perceptual world.

Reality has air vibrated by physical objects. But reality has no sound. Only the mind has sound.

Reality has electromagnetic waves, and the eyes respond to some of those. But reality has no light, and no color. Only the mind has light and color.

Everything we think we know is really just perception. We build a cognitive model of reality beginning in childhood, and we tend to think that perception is reality. It is not.

Appropriate inquiry can deduce real, meaningful relationships between reality and perception. Often those relationships are simple and sensible ... which leads us to believe even more that there is a direct relationship between the two. But often those relationships are complex, bizarre, and even nonsensical. In the end these inquiries reveal that reality is not at all what we think it is.

The cited paper on the subject of the "missing fundamental" is just one example of that. Optical illusions offer more examples. But if you study modern physics you'll find examples much more profound. Ones that make optical illusions and missing fundamentals seem like minor anomalies.

Well said.

I have spent my life immersed in physics, electronic design, astronomy and music. I love how theories give us a schematic means of comprehending and predicting behaviour in the universe without actually 'seeing' the underlying reality.

We need words like 'sound', 'colour', and such as descriptors of our mapping of the external world to our mind. Sound waves propagating through clouds of galactic hydrogen is one way to create stars. We would not hear the sound, yet it is the simplest way of thinking about the mechanism.

My vacuum tube designs allow me to think of electrons flowing from cathode to anode. My MOSFET designs allow me to think of holes flowing from source to drain. Yet, the 'reality' is that there are no physical electrons, or holes, just wave functions that collapse when I try to measure them, and all that activity is just a 'disturbance in the force', or so the latest theories would have me believe.

I think the discussion about the use of subwoofers for digital pianos is missing something.

To me, the biggest reason to use a subwoofer is to ensure the quality of the frequencies you get. By only high passing the signal to the main speakers near the sub's low pass frequency, you ensure less work (and even better, less lower frequency work) for the main speakers. This will generally improve the sound of the higher frequencies (whatever was passed to the lowest amp and driver for the main speaker). Also, the low frequencies can often be more faithfully reconstructed by a quality subwoofer than by a quality main speaker.

But subwoofers seem to be generally more expensive when "quality" and spl matching, like getting a brand's matching sub to their pair of studio monitors, so you might interpret the above as requiring higher quality (more expensive) subwoofers than main speakers.

Sorry, following a tangent from the OP.

Yes, off-loading the main amps is a good thing. However, it can be devilishly difficult to get a smooth crossover, both in amplitude and phase, and this tends to occur right around the place where you want the best low end response for a piano.

Agreed.

My audiophile colleague carefully limits the bandwidth to each of his horns-drivers. But he has a massive amount of equipment, measuring gear, time, and expertise.

For regular people like us, the engineer who built my speakers just told me to try integrating the subs both ways to see what sounded best in my room.

Running full bandwidth to both the monitors and subs sounds much better than any crossover scheme I tried. Some of that was luck; room measurements showed the monitors dropped off steeply around ~70hz, just where the sub picked up. . .

Right, the crossovers at around 80Hz are pretty close to the bottom end of the piano's bulk power.

Perhaps better for piano is going with a tri-amped main speaker. This is what I have currently rigged up. No sub, but for each main speaker a low driver and amp good from about 35 Hz and taking up to 650Hz, a mid driver/amp from that to 2kHz, and a high up to ~15kHz to a slow rolloff. Sounds a lot better especially for separation of all voices across the keyboard than the same brand's bi-amped lower-tier model I briefly used. But it could definitely just be due to other overall quality improvements.

Are you saying that without external crossovers (bass management) the monitors happened to naturally drop off in your room around 70Hz? Nice

Yes. I suppose you could say there is a "natural" crossover but that is pure luck.

Of course extensive measurements, careful sub placement, and an ideal room helped. Fact that smaller monitors "don't" reproduce sub frequencies and that good subs "only" reproduce sub frequencies also helped.

Getting round discs inside a few rectangular boxes to replicate long strings inside one big funny looking piano box requires a lot of vodoo science. . .

Thank you for your excellent in-depth analysis, spread out over several very informative and thorough posts, which points to this conclusion.

A little over a year ago I was trying to figure out "where the goal posts are" so I could build a gig-worthy speaker for my son, who plays DP. I came to the conclusion that the fundamental and first overtone were too low in energy to be audibly significant for A0 and A#0, and that the lowest frequency where there was arguably significant energy was at the first overtone of B0, around 62 Hz.

But I would trust your analysis over mine!

Just so happens that imo 62 Hz is also where the goal posts are for a good bass guitar cab, that being the first overtone of B0. While the bass guitar itself does produce significant energy at the lowest fundamentals, reproducing those lowest fundamentals is not necessary for pitch perception, and may even be undesirable (steps on the kickdrum, interference with FOH speakers, turns into a wall of mud on stage and out in most venues, and imposes a significant size/weight/cost penalty).