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How much low frequency power does a piano have? #2647315
05/26/17 02:28 PM
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Attached is a analysis of how we tend to hear non-existant low frequency fundamentals based on their harmonics.

But I would like folks to see the frequency response graphs of two acoustic pianos playing a C2 (the second C up from the bottom). In this case, notice how little fundamental is actually being created by the piano. (at around 60Hz). This leads me to question the desire for sub-woofers.

Your interpretations are most welcome.


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Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647321
05/26/17 02:48 PM
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Subwoofers focus mostly on the tactile element of low frequencies.


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Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647327
05/26/17 03:06 PM
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To an extent, it depends on how you recorded the sound; most cheaper microphones don't have a linear response and generally underestimate lower frequencies. Having said that, I certainly agree with your central point and interpretation; a subwoofer may be fun and if people enjoy having one then absolutely fine, but it's not really going to sound like an acoustic piano; too bass heavy.


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Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647333
05/26/17 03:11 PM
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I hate to be the bearer of bad news, but the video is incorrect.

The 'missing fundamental' really is 'missing' (very weak actually, due to the inability of the piano soundboard to resonate below its natural resonant frequency under load). We hear the 'missing' fundamental because our ears comprise a non-linear system. Amplifiers and speakers also comprise a non-linear system. Radio frequency mixers that convert one frequency to a much lower frequency take advantage of the careful design of a non-linear system. If you have heard a real Theremin, you have heard the ultimate in non-linear systems.

I have recorded and analyzed four simultaneous sine waves - 130, 260, 390 & 520Hz. The FFT analysis shows no energy at any frequency other than the four sine waves. The noise level is at -180dBFS so way below the graph which runs from 0.2Hz to 48kHz and -10dBFS to -150dBFS.

[Linked Image]

Here is the .wav file of the four tones. I don't hear any energy at 65Hz on my ATH-M50x headphones running through a Roland Quad-Capture DAC/ADC at normal volume.

Sorry.

It is important to understand that, while the piano does not produce significant energy below about 60Hz on an S&S D and at even higher frequencies on smaller pianos, we actually do hear the fundamental as it is created in our ears.

You can try this on your DP. Play C5 and E5 simultaneously. Listen carefully and you will hear G4. You may need to turn your head a little on way or the other, but you should hear it faintly. Two sopranos or two flautists playing those same notes near each other can produce a painful G4 to their ears and others near them. This note does not exist except in your head.

I wonder if MatLab is not set up properly for the desired results. Here is an image of the second partial (130Hz) and the sum of partials 2 through 7 (shown as sine waves of decreasing amplitude). The resulting waveform of SUM:P2+P3+P4+P5+P6+P7 is still clearly based at 130Hz with no evidence of anything at 65Hz.

[Linked Image]




Last edited by prout; 05/26/17 04:32 PM.
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Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647334
05/26/17 03:13 PM
05/26/17 03:13 PM
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What size are these pianos? If you're playing a 9 foot grand, you'll have a lot more deep bass than if you're playing a spinet.

Re: How much low frequency power does a piano have? [Re: anotherscott] #2647351
05/26/17 03:40 PM
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There's no doubt a bass speaker/subw increases the bass response, assisting the on board speakers but they have a tendency to colour the rest of the sound too.
To do the job properly, you need a volume gradient tool, supposing one exists (not an equaliser) or a piano with 88 keys volume control.


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Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647361
05/26/17 03:54 PM
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Great video.

Good subwoofers can add a lot of "depth" to action movies and some music. To your point, a high-performance subwoofer adds "less value" to the typical digital piano system. But a subwoofer still provides some low fq information that monitors are incapable of reproducing.

Integrating a subwoofer to a room and to speakers is tough and can take a lot of time. There are some threads here noting the advantages and disadvantages of two subwoofers. Also use caution with cheap, unsealed subwoofers.

One personal data point - I spent months trying to "seamlessly" integrate a subwoofer into my audio system. It was a labour of love with calibrated mics and lots of trial-and-error. Finally it sounds great (e.g. I don't notice the sub, ever). However, I still am struggling to get this same audio system to sound "right" with my digital piano; the sub is particularly problematic. So for now, I am most happy playing piano with some nice, big open-backed headphones.

==> "Big" monitors and a well set-up room can be a great sounding, inexpensive, easy solution for a digital piano.

Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647376
05/26/17 04:35 PM
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It is a well-known fact, that on most grands the strings are too short to produce fundamental frequencies for notes of lowest octaves.

Sorry, but I don't understand what is this all about. PianoMan51, do you want to supplement acoustic grands with subwoofers? Are you serious?

Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647389
05/26/17 04:55 PM
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When I switched from film projection to digital in my theatre, I got a complete new sound system to go with the new projector and associated gear.

To configure the sound system, a cinema tech puts microphones in the auditorium that are hooked up to a laptop, then sits there and plays the most ghawd-awful sounds at various volume levels.

At one point during the initial setup he was playing one channel at a time with alternating shrieks and buzzes, and he mentioned to me that in some old theatres he's had the plaster on the ceiling fall down at this point when configuring a new sound system for the digital conversions due to vibrations that were never present with old systems that simply don't have the dynamic range of the latest gear. Apparently cinema subwoofers have been known to shake the bolts out of seats, too.

All of this is stuff that you want to find out about and eliminate before you have an audience in the room, of course. smile


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Re: How much low frequency power does a piano have? [Re: Iaroslav Vasiliev] #2647392
05/26/17 05:04 PM
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Originally Posted by Iaroslav Vasiliev
It is a well-known fact, that on most grands the strings are too short to produce fundamental frequencies for notes of lowest octaves.

Sorry, but I don't understand what is this all about. PianoMan51, do you want to supplement acoustic grands with subwoofers? Are you serious?


I don't think PianoMan51 is suggesting the addition of subwoofers. He is explaining a well known and very interesting psycho-acoustic phenomenon. It explains why, even on a spinet, we can sense the decreasing 'pitch' of the notes as you play a descending scale, or when you play a single C1 and then C2 and are able to hear the lower 'pitch' of the C1, in spite of the fact that the energy of the first partial is exceedingly small.

It is my opinion that it is not our sensing of the 'missing' fundamental (though it can be heard weakly), but that we get used to the unique quality (meaning relative partial amplitudes and Inharmonicity) of each note and map that uniqueness to a position on the keyboard.

Here is A0 on my M&H BB. There is a reasonable amount of energy at 27.05Hz. Notice however that the main energy is above 60Hz. My piano's soundboard resonates right on C2.

[Linked Image]

Last edited by prout; 05/26/17 05:17 PM.
Re: How much low frequency power does a piano have? [Re: Iaroslav Vasiliev] #2647399
05/26/17 05:20 PM
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You guys are two or three steps past me. I think, at least I think I do, that I meant to calm down the talk about how we need sub-woofers for DPs. Sure, having some real power at 31Hz may feel wonderful, but real pianos don't product very much power below 100Hz.

I guess I should have been more explicit.

If you click on the top of the embedded screen you can go directly to youtube and see a bunch of other things this fellow has done.

But I am intrigued by the results shown by Prout. Why does his show a strong fundamental from A0 while the youtube I posted shows almost none? Hmmm. This may be interesting.

Last edited by PianoMan51; 05/26/17 05:24 PM.
Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647401
05/26/17 05:26 PM
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Originally Posted by PianoMan51
You guys are two or three steps past me. I think, at least I think I do, that I meant to calm down the talk about how we need sub-woofers for DPs. Sure, having some real power at 31Hz may feel wonderful, but real pianos don't product very much power below 100Hz.

I guess I should have been more explicit.

If you click on the top of the embedded screen you can go directly to youtube and see a bunch of other things this fellow has done.

But I am intrigued by the results shown by Prout. Why does his show a strong fundamental from A0 while the youtube I posted shows almost none? Hmmm. This may be interesting.


You are quite correct. There is little energy even on a 9' grand below about 60Hz and little energy below 100Hz on small pianos.

My concern is that the video is propagating mis-information.

Cheers

edit: You were editing while I was writing. My 7' BB has a huge soundboard, and a very wide tail, allowing for the bass bridge to be well away from the rim while still aloowing for relatively long strings. This allows much greater energy transfer to the bridge and results in a bass that is as deep and loud as most 9 foot grands.

Last edited by prout; 05/26/17 05:29 PM.
Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647406
05/26/17 05:59 PM
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Originally Posted by PianoMan51
You guys are two or three steps past me. I think, at least I think I do, that I meant to calm down the talk about how we need sub-woofers for DPs. Sure, having some real power at 31Hz may feel wonderful, but real pianos don't product very much power below 100Hz.

So lets move the discussion to how we can fix real pianos to output powerful low frequencies - shaking the audience in their seats with Rachmaninov 3,2. ;-)


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Re: How much low frequency power does a piano have? [Re: JoeT] #2647407
05/26/17 06:05 PM
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Originally Posted by JoeT
Originally Posted by PianoMan51
You guys are two or three steps past me. I think, at least I think I do, that I meant to calm down the talk about how we need sub-woofers for DPs. Sure, having some real power at 31Hz may feel wonderful, but real pianos don't product very much power below 100Hz.

So lets move the discussion to how we can fix real pianos to output powerful low frequencies - shaking the audience in their seats with Rachmaninov 3,2. ;-)


Make a bigger piano with longer strings and write new music that capitalizes on it. laugh

Re: How much low frequency power does a piano have? [Re: prout] #2647471
05/26/17 11:18 PM
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Originally Posted by prout

My concern is that the video is propagating mis-information.


Prout-

My take on the video is that it supports what you are saying. The maker of the video is clear that there is very little energy of the fundamental produced, but attempts to show why our ear perceives the existence of the missing fundamental, possibly as a result of the sums of the harmonics which do exist repeating at a frequency similar to the missing fundamental's frequency.

I remember we had a discussion about this a while back on the forum when we remarked on how good (including having enough bass response) the 5" JBL LSR305's sounded, despite their seeming inability to produce the lowest frequencies of the piano. I resolved then to buy the 5" monitors at some point in the future rather than dealing with the extra size and expense of the LSR 308's.

Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647475
05/26/17 11:47 PM
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I've been playing a lot with headphones lately, but when I play with a subwoofer, it's hard to get a very realistic sound. It sounds boomy, but not quite like a piano. I'm going to try the Yamaha HS8 monitors and ditch the subwoofer.


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Re: How much low frequency power does a piano have? [Re: Tom Fort] #2647525
05/27/17 07:40 AM
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Originally Posted by Tom Fort
Originally Posted by prout

My concern is that the video is propagating mis-information.


Prout-

My take on the video is that it supports what you are saying. The maker of the video is clear that there is very little energy of the fundamental produced, but attempts to show why our ear perceives the existence of the missing fundamental, possibly as a result of the sums of the harmonics which do exist repeating at a frequency similar to the missing fundamental's frequency.

I remember we had a discussion about this a while back on the forum when we remarked on how good (including having enough bass response) the 5" JBL LSR305's sounded, despite their seeming inability to produce the lowest frequencies of the piano. I resolved then to buy the 5" monitors at some point in the future rather than dealing with the extra size and expense of the LSR 308's.


Actually the video attempts to show that the addition of harmonically related sine waves produces the octave below the fundamental. This is not true, either mathematically or physically. EDIT: I was wrong.

My pictures above show what actually exists as recorded and measured using lab grade equipment. We hear the octave below because our ears distort the sound. It is possible to design an amplifier/speaker to also distort the sound in the same way. Guitar amps do this (especially vacuum tube based) very well and produce a wonderful rich, deep bass that the guitar itself cannot produce.

Any size driver is capable of producing any frequency. Headphone drivers are very tiny and yet easily produce 25Hz if properly designed.

The key is the amount of air that is needed to be moved to reproduce realistic and accurate sound in the space where your DP lives. Given that the amount of energy produced by an 9 foot grand at 27.5Hz is very tiny compared to the amount of energy produced by a pipe organ at the same frequency, it is logical to spend one's money on buying the most accurate, that is neutral, speakers you can afford and are capable of producing realistic sound levels in your playing space. The LSR305s seem to fit the bill, especially as they allow you to adjust the response curve for wall proximity, IIRC, which is good, given that few concert grands are placed against the back wall in a concert hall. They are placed in essentially a free field.

Last edited by prout; 05/27/17 09:06 AM.
Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647527
05/27/17 07:43 AM
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Iaroslav Vasiliev Online content
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Originally Posted by PianoMan51
You guys are two or three steps past me. I think, at least I think I do, that I meant to calm down the talk about how we need sub-woofers for DPs. Sure, having some real power at 31Hz may feel wonderful, but real pianos don't product very much power below 100Hz.

I guess I should have been more explicit.

If you click on the top of the embedded screen you can go directly to youtube and see a bunch of other things this fellow has done.

But I am intrigued by the results shown by Prout. Why does his show a strong fundamental from A0 while the youtube I posted shows almost none? Hmmm. This may be interesting.


As anotherscott correctly stated, on big grands with long strings there is a lot more deep bass. You should have known that, PianoMan51, before going two or three steps ahead of us. smile That's why 9-foot grands are so adorable and that's why (almost) everyone would like to have one. Besides long strings add dark (bass) color to other notes because of resonance.

People who have been playing different grands for a long time can easily distinguish if fundamental frequency is present or missing. The illusion of missing fundamental breaks with listener's experience. And that's why many people would like to use subwoofer with their digital pianos - to simulate the sound of 9-foot grand. That's basically a good idea, but as others have mentioned here, it is very difficult to match subwoofer sound to monitors in most acoustic environments, especially on low volume.

Last edited by Iaroslav Vasiliev; 05/27/17 07:56 AM. Reason: misprint
Re: How much low frequency power does a piano have? [Re: Beakybird] #2647528
05/27/17 07:48 AM
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Originally Posted by Beakybird
I've been playing a lot with headphones lately, but when I play with a subwoofer, it's hard to get a very realistic sound. It sounds boomy, but not quite like a piano. I'm going to try the Yamaha HS8 monitors and ditch the subwoofer.

I would recommend 8' Mackie's. I believe they have much better bass than Yamaha's.

Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647530
05/27/17 08:01 AM
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Originally Posted by PianoMan51
You guys are two or three steps past me. I think, at least I think I do, that I meant to calm down the talk about how we need sub-woofers for DPs. Sure, having some real power at 31Hz may feel wonderful, but real pianos don't product very much power below 100Hz.

I guess I should have been more explicit.

If you click on the top of the embedded screen you can go directly to youtube and see a bunch of other things this fellow has done.

But I am intrigued by the results shown by Prout. Why does his show a strong fundamental from A0 while the youtube I posted shows almost none? Hmmm. This may be interesting.


Actually, the fundmental is not that strong. It is a visual illusion caused by the y axis being in decibel amplitude rather than linear amplitude as was shown in the video. In my case the P1 (27.05Hz) is 24dB below or only 0.06 the amplitude of P4 (115.17Hz).

Re: How much low frequency power does a piano have? [Re: prout] #2647541
05/27/17 08:55 AM
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Thanks Prout, that clears up my cognitive dissonance!

Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647547
05/27/17 09:04 AM
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Mea Culpa. I must sincerely apologize to PW for my contribution to mis-information. The addition of sine waves, as shown by the video posted by PianoMan51, is indeed accurate. My own tests using the technique shown in the video produce the same results. The octave below (missing fundamental) is clearly heard on my headphones.

My knowledge of the math has now been enhanced. That being said, the graphs and pictures I have posted above are accurate and do represent observed reality.

Here are graphs of the sum of 4 sine waves - 120Hz, 180Hz, 240Hz, and 300Hz, all 60 Hz apart and of decreasing amplitude. The top sine wave shown is 120Hz and the next one is the sum of the four sine waves. This produces a 60Hz 'fundamental', clearly seen and heard. However, if you look at the FFT analysis of the same .wav file, you will see that there is NO ENERGY at 60Hz, only at the 4 sine wave frequencies. You may hear it, but it isn't there.

[Linked Image]
[Linked Image]


Last edited by prout; 05/27/17 09:27 AM.
Re: How much low frequency power does a piano have? [Re: Iaroslav Vasiliev] #2647552
05/27/17 09:29 AM
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Originally Posted by Iaroslav Vasiliev
Originally Posted by PianoMan51
You guys are two or three steps past me. I think, at least I think I do, that I meant to calm down the talk about how we need sub-woofers for DPs. Sure, having some real power at 31Hz may feel wonderful, but real pianos don't product very much power below 100Hz.

I guess I should have been more explicit.

If you click on the top of the embedded screen you can go directly to youtube and see a bunch of other things this fellow has done.

But I am intrigued by the results shown by Prout. Why does his show a strong fundamental from A0 while the youtube I posted shows almost none? Hmmm. This may be interesting.


As anotherscott correctly stated, on big grands with long strings there is a lot more deep bass. You should have known that, PianoMan51, before going two or three steps ahead of us. smile That's why 9-foot grands are so adorable and that's why (almost) everyone would like to have one. Besides long strings add dark (bass) color to other notes because of resonance.

People who have been playing different grands for a long time can easily distinguish if fundamental frequency is present or missing. The illusion of missing fundamental breaks with listener's experience. And that's why many people would like to use subwoofer with their digital pianos - to simulate the sound of 9-foot grand. That's basically a good idea, but as others have mentioned here, it is very difficult to match subwoofer sound to monitors in most acoustic environments, especially on low volume.


I looked at some other analyses by the same guy. See the youtube below. I wasn't really interested in how we hear, but rather in the surprising lack of fundamental in the low end of acoustic pianos. When I read closer, I agree with Prout's statement that smaller pianos have little power below 100Hz, and large pianos have little power below 60Hz. This can be seen in the youtube below.

If you can accept that, then we can move into the ideal sound transducer for piano alone. This is where I look at the typical frequency range of decent studio monitors, not 'tiny', but not X-Large. They typically are reasonably flat down to 60Hz. This should be plenty for acoustic piano reproduction. And as Prout states, the emphasis should be on mid-range quality.

My own experience is with the Baldwin SF-10 (7' semi-concert grand), which I chose over the 9' because the added bass resonance interfered with crisp jazz bass lines. I bought this 30 years ago.

For Digital Piano players I can think of two reasons why they might want to buy a sub-woofer. The first is that their current transducers don't go to 60Hz. The second, and more unpleasant, is they don't want their DP to like a real piano, but rather want their DP to sound like some idealized piano in their dreams. Everyone has their own tastes.

For the first case, get a good set of studio monitors, and set them up as near-field, in the traditional triangle pattern. You will love this.

For the second case, go wild baby. It's your sound and you can do what you want. But as a pianist for the last 55 years, I can tell you that even a 2 or 3 dB of bass boost in a recorded piano sounds unnatural to me.


Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647558
05/27/17 09:40 AM
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The problem of the missing fundamental is not related to the length of the string. Because of the copper wire, a short string does vibrate at a low frequency.

However, the mechanical impedance of the soundtable is high at a low frequency, then, the lower partials doesn't produce a lot of sound.

Bigger grands have a larger soundboard and are able to produce lower partials.

"Physics of the piano" is a interesting book to read. wink


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Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647578
05/27/17 10:44 AM
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The video PianoMan51 posts just above is interesting in that it shows how little energy is produced below about 100Hz. The presenter tries to argue that the idea of superior clarity in European pianos over other pianos is inconclusive. He does not mention, however, the differences in the use of muting felt in the area between the bridge and the hitch pins.

On many pianos the felt extends over every single string. This reduces non-tuned sound from competing with the tuned strings. On many other pianos the felt extends only over a portion of the lower keys and is left off in the treble. On these pianos the unmuted portion of the strings vibrate and produce noise. In the Steinway, for example, the noise is untuned and adds brilliance to the sound, not clarity. On other pianos, the unmuted portion is carefully tuned to either the fundamental, fifth above, octave above or 12th above. This adds clarity to the sound.

It is my opinion that both either muting all the non-speaking portions of the strings or tuning them adds to clarity. I think is actually seen in the video. The S&S is shown to be the noisiest.

Re: How much low frequency power does a piano have? [Re: prout] #2647586
05/27/17 11:05 AM
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I don't understand what part of your earlier statement you're taking back.
Originally Posted by prout
I must sincerely apologize to PW for my contribution to mis-information. The addition of sine waves, as shown by the video posted by PianoMan51, is indeed accurate. My own tests using the technique shown in the video produce the same results. The octave below (missing fundamental) is clearly heard on my headphones.
If you linearly add pure sine waves at frequencies 2f, 3f, 4f, 5f, etc, the result contains NO energy at 1f. This is what I think you said earlier, and it remains true. So what exactly are you retracting?

If one does find some output energy at 1f, it's because either:
(a) the original sine wave sources were impure, containing some energy at 1f
or
(b) the mixing was non-linear, and the non-linear mixer products have produced harmonic and intermodulation distortion, some of which will be at 1f

But I don't think you intended to introduce these anomalies into the discussion. So wuzzup with the retraction?

Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647589
05/27/17 11:23 AM
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@MacMacMac : we could add :

(c) we can ear missing frequency because of an ear illusion due to the way our brain process the decomposed sound.

We have an article about the missing frequency : https://en.wikipedia.org/wiki/Missing_fundamental


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Re: How much low frequency power does a piano have? [Re: PianoMan51] #2647607
05/27/17 12:20 PM
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Originally Posted by PianoMan51

If you can accept that, then we can move into the ideal sound transducer for piano alone. This is where I look at the typical frequency range of decent studio monitors, not 'tiny', but not X-Large. They typically are reasonably flat down to 60Hz. This should be plenty for acoustic piano reproduction. And as Prout states, the emphasis should be on mid-range quality.

I see. No, first of all I don't accept that. Even though fundamental is significantly weaker (on large grands it is -25 db for A0 compared to strongest sound component according to book "Acoustics and the performance of music", p. 71), it is still there. And such low frequencies are very perceivable, even on tactile level.

Besides it is very arguable question if near-field monitors can match the sound of subwoofer (even if they are flat down to 60Hz). Many people will tell that it's a completely different experience, maybe because of different sound diffusion in space.

Re: How much low frequency power does a piano have? [Re: Frédéric L] #2647620
05/27/17 01:11 PM
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Yes, that's the whole point:
Originally Posted by Frédéric L
We could add :
(c) we can ear missing frequency because of an ear illusion due to the way our brain process the decomposed sound.
This is missing from the charts given earlier. The charts can only show physical waveforms. They cannot show perceptual results.

Re: How much low frequency power does a piano have? [Re: Iaroslav Vasiliev] #2647622
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I think you're onto the right point.
Originally Posted by Iaroslav Vasiliev
Even though fundamental is significantly weaker (on large grands it is -25 db for A0 compared to strongest sound component according to book "Acoustics and the performance of music", p. 71), it is still there. And such low frequencies are very perceivable, even on tactile level.
My take is this: You don't lose much if your speaker response drops off below, say, 60 Hz.

But you do lose something. Not much, but something.

Still, I wouldn't add a subwoofer. Big bass doesn't move me.
These are pianos, not bass guitars.

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