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Topic: Piano low A string and the fundamental frequency? (Read 9981 times) previous topic - next topic
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Piano low A string and the fundamental frequency?

I have some questions, and I'm hoping someone can help me out.  I'm not an audio engineer and I may mangle the terminology, so I want to apologize for that right up front.

Anyway, here's the situation.... Recently a friend recorded some individual notes on his 5' 1" Steinway baby grand (Model S) using his Roland R-26 recorder and the built-in mics. And then, using iZotope RX4, he produced a very interesting spectrogram, which he showed me. Focusing on the spectrum of the lowest note on the piano (a low A), which did not seem to show any acoustic energy in the 27.5 Hz range, my friend remarked, "Supposedly, the lowest note on the piano is 27.5 Hz, ... but we're not really hearing anything 27.5 Hz on that lowest note, or the first harmonic, either." Indeed, his spectrogram did not seem to show any sort of distinct horizontal band at the expected 27.5 Hz or at 55. Hz.

My friend also sent me some information from a book called, "Pianos Inside Out", and on p. 105, the author, Mario Igrec, analyzes the sound of a low A on a slightly longer Steinway Model A (6' 2") piano, and Mr. Igrec writes, "Notice ... an absence of well-defined first and second partials -- expected around 27.5 and 55. Hz." (Mr. Igrec's audio recording and analysis was apparently carried out using the built-in mic of an Apple iPad 2 and n-Trak Tuner, v. 7).

Really? In a low A on the piano, there's nothing going on at 27.5 Hz? Or even at 55 Hz??  I've been pondering this and wonder if this is really true, and if so, why? 
Is there something about the low strings, especially in a small piano, such as a Steinway Model S or A, that really does not vibrate at the fundamental frequency of 27.5 Hz of the low A? Or even at the first harmonic, 55 Hz?

Or is there possibly something about the audio equipment, such as a cut-off in the low-end sensitivity of the R-26 microphone in that range that would make it appear as if there is no acoustic energy at the fundamental frequency of 27.5 Hz? (Note: My friend says he did not have the low-cut filter engaged.  I have no idea about the specs and settings for Mr. Igrec's iPad, his iPad's built-in mic, and the n-Trak Tuner software.) 

Could someone please help me make sense of all this....

PS: Also, I have recorded the low A from a different, and much larger piano -- a 9' Yamaha CF concert grand. The link to that audio is here if anyone is interested. To attempt a somewhat equal comparison with my friend's initial test recording, I recorded this piano using a similar set-up: another Roland R-26 and the built-in mics.  Can someone tell me if there is something significant going on at around 27.5 Hz in this sample?  I think so, because when I look at the waveform in Audacity, I can count approximately 28 distinct oscillations per second.

Piano low A string and the fundamental frequency?

Reply #1 –
Depends on the piano I guess. You can find recordings of A0 that show energy at 27 Hz, but the higher harmonics are usually louder.

"I hear it when I see it."

Piano low A string and the fundamental frequency?

Reply #2 –
Quote from: Japanofile on
Anyway, here's the situation.... Recently a friend recorded some individual notes on his 5' 1" Steinway baby grand (Model S) using his Roland R-26 recorder and the built-in mics. And then, using iZotope RX4, he produced a very interesting spectrogram, which he showed me. Focusing on the spectrum of the lowest note on the piano (a low A), which did not seem to show any acoustic energy in the 27.5 Hz range, my friend remarked, "Supposedly, the lowest note on the piano is 27.5 Hz, ... but we're not really hearing anything 27.5 Hz on that lowest note, or the first harmonic, either." Indeed, his spectrogram did not seem to show any sort of distinct horizontal band at the expected 27.5 Hz or at 55. Hz.


His observed results are pretty typical of my experiences. I have yet to find a piano with useful response at 27 Hz, and I've recorded more than a few highly regarded concert grands.

In fact I find it to be  very common for bass instruments of many kinds to produce far more energy in their harmonics than the fundamentals, in those cases where there even is readily discernible energy in the fundamental.

Piano low A string and the fundamental frequency?

Reply #3 –
Our ears don't mind...
http://en.wikipedia.org/wiki/Missing_fundamental

I guess the fundamental of the string itself is 27Hz, but it's not efficiently transmitted by the instrument.

Cheers,
David.

Piano low A string and the fundamental frequency?

Reply #4 –
Hmm... maybe your friend and you forgot to disable the LCF (HP filter (@ 100, 200 or 300)) or the mic specs are not good enough for low frequency area?

Piano low A string and the fundamental frequency?

Reply #5 –
My friend sent me the link to a discussion on the Piano World forum entitled "The Missing Fundamental", and in that thread there are several posts by Delwin Fandrich, a Piano Research, Design & Manufacturing Consultant, that seem to do a good job of explaining this issue.

Piano low A string and the fundamental frequency?

Reply #6 –
Just listening to a piano it's pretty obvious that there's not much deep bass energy.    For example, you can often feel the bass from an electric bass or kick drum in your body, but you don't get that from an acoustic piano. 

The lowest note on a standard electric bass is around 40Hz but it sounds & feels a lot "deeper" than a piano.    With Audacity you can generate test tones, so you can generate a 27Hz tone to see what it sounds like...  If you've got the woofers to reproduce it!

Piano low A string and the fundamental frequency?

Reply #7 –
Quote from: 2Bdecided on
Our ears don't mind...
http://en.wikipedia.org/wiki/Missing_fundamental

I guess the fundamental of the string itself is 27Hz, but it's not efficiently transmitted by the instrument.

Cheers,
David.


And not many mics are 'flat' to 27 Hz. My AKG C-451 (cardioid capsules) are about 6dB down in that area judging by the manufacturers response plots.

G²

Piano low A string and the fundamental frequency?

Reply #8 –
Quote from: DVDdoug on
The lowest note on a standard electric bass is around 40Hz but it sounds & feels a lot "deeper" than a piano.    With Audacity you can generate test tones, so you can generate a 27Hz tone to see what it sounds like...  If you've got the woofers to reproduce it!


Thread with upload: http://www.hydrogenaud.io/forums/index.php?showtopic=105844

Piano low A string and the fundamental frequency?

Reply #9 –
Piano key A0 (freesound.org sample) shows energy at 27 Hz.
"I hear it when I see it."

Piano low A string and the fundamental frequency?

Reply #11 –
Quote from: Japanofile on
In a low A on the piano, there's nothing going on at 27.5 Hz? Or even at 55 Hz??  I've been pondering this and wonder if this is really true, and if so, why?
A piano hammer strikes the string at about 1/7th of its length. The main reason is to reduce the amount of the 7th harmonic, which doesn't sound very nice. The fundamental is the loudest when the string is hit in the middle, but that would require very long hammers, so to simulate the effect I plucked the lowest string of my piano somewhere in the middle and voila, there is your fundamental in the FFT.
Pianostring27.5HzHammered&Plucked.wav

BTW, I stumbled upon this nice animation about the effect of hammer position.

Piano low A string and the fundamental frequency?

Reply #12 –
Nice explanation. However, in the Wolfram article, in image 4/5 the spectrum bars should be not of descending height, but rising, like you alluded.

Piano low A string and the fundamental frequency?

Reply #13 –
Hmm, it looks fine to me. The explanation on the webpage:
Quote
Snapshot 4: If the hammer is placed very near the end of the string, all the harmonics are present in very nearly the same amount. Violinists exploit this phenomenon when they bow near the bridge of the violin—a bowing technique called "pontecello". The resulting timbre, rich in higher overtones, is very "glassy" or strident sounding.
IME when a string is hit close to one end, the sound will be brighter but also softer, which doesn't show in the graphs. Apparently the shown amplitudes are relative to the fundamental, not absolute.

Piano low A string and the fundamental frequency?

Reply #14 –
Yeah, makes sense, but... what I said was because of the hammered note in your piano recording. The harmonics get progressively louder until the 5th is reached then drop again. The series of harmonics then reaches a local minimum at the 8th. Then, local minimums at multiples of 8 which suggests the string was hit at about 1/8 of its length.
But maybe the very LoF attenuation of the first few harmonics is from the mic.

Piano low A string and the fundamental frequency?

Reply #15 –
Quote from: Hex144 on
local minimums at multiples of 8 which suggests the string was hit at about 1/8 of its length.
Very good observation ! I've noticed that too, but didn't dig further until you asked
The 1/7th position that we've learned at piano class might be correct in theory, but piano builders do listen and choose a good compromise between sound quality and mechanical stability. On a piano tech forum I found:
Quote
On the larger Steinway grands, the strike proportion for the first 20 notes is 1/8. After the break, the proportion will be more like 1/9 and at note 88 something like 1/16.
The theory makes sense: strike the string at the location where undesired harmonics have a node to minimize their amplitude. I've found an explanation why this doesn't (always) work:
Quote
However, studies have demonstrated that this argument is not completely valid. In the piano, the string is not plucked but struck, meaning one cannot assume that the interaction that begins the vibration is instantaneous. The hammer-string contact time is brief but long enough to form harmonic standing waves in the shorter section of the string (see figure 4.5). Assuming that the strike point is exactly 1/7 the length of the string, the standing waves constitute the harmonic series of a frequency seven times greater than the entire string, which are precisely the supposedly eliminated harmonics (7, 14, 21...). As the hammer loses contact, all these are propagated across the rest of the string, and the final result is that all vibration modes are present in the string.
[/size]Sorry if this is too much off topic for this forum

Piano low A string and the fundamental frequency?

Reply #16 –
Quote from: xnor on
Piano key A0 (freesound.org sample) shows energy at 27 Hz.



The FFT before me suggests that the 27 Hz fundamental is 25-30 dB below the strongest harmonic, and there are a large number of strong harmonics.

My eyeball analysis is that the fundamental is totally masked by the harmonics. IOW, inaudible.

Piano low A string and the fundamental frequency?

Reply #17 –
Quote from: Kees de Visser on
Quote from: Japanofile on
In a low A on the piano, there's nothing going on at 27.5 Hz? Or even at 55 Hz??  I've been pondering this and wonder if this is really true, and if so, why?
A piano hammer strikes the string at about 1/7th of its length. The main reason is to reduce the amount of the 7th harmonic, which doesn't sound very nice. The fundamental is the loudest when the string is hit in the middle, but that would require very long hammers, so to simulate the effect I plucked the lowest string of my piano somewhere in the middle and voila, there is your fundamental in the FFT.
Pianostring27.5HzHammered&Plucked.wav

BTW, I stumbled upon this nice animation about the effect of hammer position.



The recording above appears to show two notes that are very different. Which is what?

Piano low A string and the fundamental frequency?

Reply #18 –
First one is hammered.
"I hear it when I see it."