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Application of Spectral Analysis to Pianos #2960117 03/24/20 07:57 PM
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PaintedPostDave Offline OP
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I have not posted here in long time mostly because I prefer to post on forums where the responders do not have pseudonyms but since many folks are now experiencing self-imposed isolation perhaps the attached video might be a welcome diversion from CNN.



Stay well.


Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/
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Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960125 03/24/20 08:29 PM
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Hi Painted Post Dave,

What a nice surprise to see you here. It has been a long time.

Thank you for posting!


Rich Galassini
Cunningham Piano Co.
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Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960135 03/24/20 09:29 PM
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Hi Rich. Hope you and Cunningham’s Pianos are well.


Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/
Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960178 03/25/20 12:44 AM
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Originally Posted by PaintedPostDave
I have not posted here in long time mostly because I prefer to post on forums where the responders do not have pseudonyms but since many folks are now experiencing self-imposed isolation perhaps the attached video might be a welcome diversion from CNN.

That was 1000x better than CNN.
Low bass notes from a piano will always have weak fundamentals, because the soundboard can't couple them to the air. (But also consider your microphone's frequency response.) After several centuries, piano makers haven't figured out what loudspeaker designers solved almost immediately: Low-frequency emitters need an enclosure to either trap or phase-shift the back-side radiated sound, or it will cancel the front-side sound.
The bass strings themselves do vibrate strongly at the fundamental. I proved this with a high-speed camera, and also by electromagnetic induction to measure string velocity directly.

Regarding the "sharp" C8, we should expect the upper-end notes to be high, as a product of the stretch tuning that's required to match fundamentals to the harmonics of lower notes all across the piano's range. For the same reason, it's not unusual to find low-bass fundamentals and second partials a little flat.

From the studies I've done, the partial frequencies don't drift as the sound decays away, but the partial amplitudes do decay faster than the fundamental.


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Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960242 03/25/20 10:18 AM
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I assume that for the A4 and C8 you were measuring a single string of the choir? I read somewhere,but cannot now find it, that the spurious peaks are caused by standing waves that are faster than the fundamental period. Could this be correct? Surely the inharmonicity would result in the partials of C1 being lower than their harmonic not higher as you illustrated?
Ian

Last edited by Beemer; 03/25/20 10:19 AM.

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Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960256 03/25/20 11:22 AM
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This is a very good presentation.

Thank you very much for sharing.

I will be looking forward for the next session.

Re: Application of Spectral Analysis to Pianos [Re: Beemer] #2960284 03/25/20 12:25 PM
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Originally Posted by Beemer
I assume that for the A4 and C8 you were measuring a single string of the choir? I read somewhere,but cannot now find it, that the spurious peaks are caused by standing waves that are faster than the fundamental period. Could this be correct? Surely the inharmonicity would result in the partials of C1 being lower than their harmonic not higher as you illustrated?
Ian

If the unisons are well tuned, this method of spectral analysis does not require damping down to a single string. In fact, if a unison is out of tune and the analyzer has enough resolution, you can see the multiple peaks. Additionally, different strings in the choir can produce slightly different partial frequencies even if their fundamentals are the same - again, you can see this if the analyzer has enough resolution.

The phrase "standing waves that are faster" doesn't make sense. Standing waves are just that - standing.

Inharmonicity always produces partials that are sharp. It is due to the mechanical stiffness of the string effectively increasing the bending spring constant as wavelengths become shorter. Generally, the longer the string, the less the degree of inharmonicity, so larger pianos have an advantage, at least in the bass-tenor range.


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Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960362 03/25/20 04:53 PM
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By standing wave I am referring to the mention of reflected wave from the bridge. I agree with you comment about inharmonicity. I guess I'm confused over the need to lower tuning for lower notes according to the Railsback curve.
Ian


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Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960384 03/25/20 05:57 PM
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Roy123 Offline
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Hi Dave--great to have you back. I have a few technical questions. Given your sample rate of 44 kHz, I assume you're using a sound card to capture the audio. Yes? What portion of the waveform are you using to make the spectral plots? I assume you're not using the whole recording, but eliminating the "noise" at the beginning and cutting things off before the sound decays severely, but maybe that's not true. Are you using the pwelch function to create the plots, or did you write your own function(s)?

A previous poster suggested that the reason for the low power in the bass fundamental tones is due to the soundboard being a dipole radiator. Dipole radiators have been thoroughly analyzed in the world of hifi speaker design, and one could compare the expected power vs frequency of an ideal dipole radiator and the results from the piano. I suspect additional factors are strong contributors to the weak bass fundamentals. For example, it is well known that cantilever bridges contribute to poor low-frequency transduction. One can almost guarantee that other aspects of the soundboard also contribute.

Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960412 03/25/20 07:14 PM
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I should mention one other thing about bass reproduction. For an audio transducer, be it a speaker or a soundboard, the diaphragm needs to be in the mass-controlled region rather than the spring-rate controlled region in order to reproduce sound with equal efficiency across the bandwidth of interest. This means that the frequency of the spring-mass system formed by the diaphragm and its suspension must be lower than the lowest frequency to be reproduced. This is surely not the case for the bass end of the piano. If it were, the piano would sound more like a bass than a piano. Nevertheless, it's important to keep in mind that below resonance, the diaphragm's sound output will decrease by 12 dB per octave. By the time one gets down to A0, the there's no doubt lots of volume lost from just this one factor.

Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960476 03/25/20 10:53 PM
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Ed McMorrow, RPT Offline
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I believe when one hears a good fundamental in the lowest octave of a piano, one is hearing combination tone effects where the balance of energy in the partials is such that it triggers a sensation of the fundamental either in the brain and/or combined with the ear.

When I first read about combination tones, I though this can't be real. But my first time creating and experiencing one occurred when I was experimenting with the tone generating system of a Rhodes tine piano. I "voiced" some notes very mellow and when I played a fifth those notes formed in the lower portions of the compass, I heard a note an octave below the bottom note of the fifth I was playing. Spooked the heck out of me.

I am interested what the learned OP and commentators think of this representation.


In a seemingly infinite universe-infinite human creativity is-seemingly possible.
According to NASA, 93% of the earth like planets possible in the known universe have yet to be formed.
Contact: Ed@LightHammerpiano.com
Re: Application of Spectral Analysis to Pianos [Re: Ed McMorrow, RPT] #2960538 03/26/20 05:28 AM
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Originally Posted by Ed McMorrow, RPT
I believe when one hears a good fundamental in the lowest octave of a piano, one is hearing combination tone effects where the balance of energy in the partials is such that it triggers a sensation of the fundamental either in the brain and/or combined with the ear.

When I first read about combination tones, I though this can't be real. But my first time creating and experiencing one occurred when I was experimenting with the tone generating system of a Rhodes tine piano. I "voiced" some notes very mellow and when I played a fifth those notes formed in the lower portions of the compass, I heard a note an octave below the bottom note of the fifth I was playing. Spooked the heck out of me.

I am interested what the learned OP and commentators think of this representation.



I'm sure you are right Ed. My little experiment here was to check the frequency response of the (actually quite nice but necessarily size limited) speakers on my computer and pure sine waves of the lowest piano fundamentals are so rolled off they are completely inaudible, even with volume at max. Yet when I listen to recordings of actual piano bass notes I can hear them clearly and to my brain they sound as if the fundamental is fully present, even though it is completely missing.

There are similar tricks that can be done with colours and vision as well.

Re: Application of Spectral Analysis to Pianos [Re: Ed McMorrow, RPT] #2960737 03/26/20 03:26 PM
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Originally Posted by Ed McMorrow, RPT
I believe when one hears a good fundamental in the lowest octave of a piano, one is hearing combination tone effects where the balance of energy in the partials is such that it triggers a sensation of the fundamental either in the brain and/or combined with the ear.

When I first read about combination tones, I though this can't be real. But my first time creating and experiencing one occurred when I was experimenting with the tone generating system of a Rhodes tine piano. I "voiced" some notes very mellow and when I played a fifth those notes formed in the lower portions of the compass, I heard a note an octave below the bottom note of the fifth I was playing. Spooked the heck out of me.

I am interested what the learned OP and commentators think of this representation.



Hi Ed,

You're correct--the effect of inferring a lower note that's part of a harmonic series has been documented in the literature. What affect that has in the piano is a good question. The difference in the sensation of the bass is amazingly different between what one hears in a D for example, and a short grand.

Re: Application of Spectral Analysis to Pianos [Re: Roy123] #2960857 03/26/20 10:19 PM
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Ed McMorrow, RPT Offline
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Thanks Roy123.

I can report that using the softer wire from Paulello as core wires in the bass is allowing me to get some amazing depth of tone in small pianos.

In the past I used thinner standard modern wire wrapped to the max for the low notes in small pianos. The pitch sounds much less indistinct that way than the standard scales, but the sustain and warmth are at low levels. The sense of fundamental was only present right after hammer impact.

Now with the Hybrid Wire Scales Protocols, (HWSP), I am getting long sustain of the fundamental, warmth and clarity. I have an Aeolian era 1979 Chickering 501 that is a stunning grand. I like it as much as playing much bigger pianos.

But I have no model to describe for how I know what result I am going to get. I know too little about how we perceive difference tones to really document how I get the results I am getting. I have just done it by careful guesswork. I can repeat the general success in each piano I apply the HWSP.

I have read that tuning Tympani's also involves difference tones. I have always thought of the piano soundboard as a little similar to a tympanic membrane. Without the resonant cavity of course.


In a seemingly infinite universe-infinite human creativity is-seemingly possible.
According to NASA, 93% of the earth like planets possible in the known universe have yet to be formed.
Contact: Ed@LightHammerpiano.com
Re: Application of Spectral Analysis to Pianos [Re: PaintedPostDave] #2960868 03/26/20 11:09 PM
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Chernobieff Piano Online Content
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Hi,
I am a real person and not a pseudonym or robot.

Is it possible to try different piano hammers(soft, hard, soft shoulders, hard tips etc) to see the different analysis?

Thanks,
Chris


Chernobieff Piano Restorations
Lenoir City, Tennessee U.S.A
www.chernobieffpiano.com
grandpianoman@protonmail.com
Re: Application of Spectral Analysis to Pianos [Re: Ed McMorrow, RPT] #2961001 Yesterday at 01:51 PM
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Originally Posted by Ed McMorrow, RPT
When I first read about combination tones, I though this can't be real. But my first time creating and experiencing one occurred when I was experimenting with the tone generating system of a Rhodes tine piano. I "voiced" some notes very mellow and when I played a fifth those notes formed in the lower portions of the compass, I heard a note an octave below the bottom note of the fifth I was playing. Spooked the heck out of me.

I'm a little surprised that you don't encounter difference tones like this more frequently.
Every radio receiver today relies on the principle. Any time you superimpose two frequencies, and nonlinearities are present in the signal path, some amount of the difference and sum frequencies is produced.
By the way, I only recently noticed we are both in the Seattle area. It would be lovely to meet some time - after the epidemic passes, of course.


First love: Kawai GX-6
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Re: Application of Spectral Analysis to Pianos [Re: Roy123] #2961007 Yesterday at 02:27 PM
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Originally Posted by Roy123
For an audio transducer, be it a speaker or a soundboard, the diaphragm needs to be in the mass-controlled region rather than the spring-rate controlled region in order to reproduce sound with equal efficiency across the bandwidth of interest. This means that the frequency of the spring-mass system formed by the diaphragm and its suspension must be lower than the lowest frequency to be reproduced. This is surely not the case for the bass end of the piano. If it were, the piano would sound more like a bass than a piano. Nevertheless, it's important to keep in mind that below resonance, the diaphragm's sound output will decrease by 12 dB per octave. By the time one gets down to A0, the there's no doubt lots of volume lost from just this one factor.

This is a very good point, and certainly contributes to the fundamental attenuation. This behavior is common to all resonant systems, even if they are well damped - as I presume a piano soundboard is. (I tend to think of physical systems in terms of their electrical analogs, as that's the domain I routinely work in, and LCR circuits behave just as you described - substitute inductance and capacitance for mass and spring.)
On my 7' Kawai GX-6, the rolloff point appears to be around 55Hz (A1), while on the RX-2 that I had previously it's a few semitones higher. But below that point, fundamental amplitude drops precipitously; at E1 it's about 20dB lower.
I've had success picking up much more of the fundamental with a microphone, if I place it in the tail of the piano and close the lid. So we have evidence that both resonant rolloff and dipole effects are important.


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Re: Application of Spectral Analysis to Pianos [Re: MarianneØ] #2961140 23 hours ago
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Ed McMorrow, RPT Offline
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MarianneO, I would be honored if you would visit my shop in Mukilteo. I always enjoy visiting with skilled and knowledgeable people. Call/Text to 425-299-3431 is best. My website is down, sorry.


In a seemingly infinite universe-infinite human creativity is-seemingly possible.
According to NASA, 93% of the earth like planets possible in the known universe have yet to be formed.
Contact: Ed@LightHammerpiano.com

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