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Well, I think everyone who knows anything about soundboards recognizes that the mass and stiffness of the board are two of the most important parameters that affect the sound of the piano. Clearly, selecting rib stiffness is an essential part of the design process. Of course, it is by no means the only one. The bridges also are a significant contributor to both soundboard mass and stiffness, and beyond that there are a large number of other factors that determine the tone and sustain of any particular piano. To suggest that it is not useful to know how rib width and height affect the rib's stiffness and mass is truly beyond my understanding--truly.

I design systems and subsystems for a living, and therefore know better than many who post in these pages that the performance of any system is due to the combination of many components that combine in ways both simple and complex to the behavior of the system as a whole. In any system, some components are crucial and play a large role in the performance of the system, and other components provide more subtle qualities. The ribs in a soundboard assembly are an example of a highly consequential part of the soundboard design. BTW, I find your analogy to chess, as stated, particularly inapt.

Trying to figure your math - for your "original rib cross section" - no stiffness ratio indicated - if I understand how you arrive at the same numbers for 'new rib and new rib any size' Id say the number should be 1.4046???

The stiffness ratios compare the 2 modified ribs to the original rib. To think of it another way, the stiffness of the original rib has been normalized to 1.

Roy123,
Thanks for your engaging discussion.
Your rib calculator is not useful because you will then be making changes without a purpose. I've studied hundreds of soundboards, mostly compression soundboards, and I have seen many makers try different things. Rather than isolate and analyze a single rib, it would be far better to the study rib structures of the assembly of different makers. Otherwise, a rib could be too small or too tall, or just have too much mass, or not enough mass. How would you know without the knowing the context of the entire structure? You can't go by one soundboard either, I've seen two Original Steinway M's with entirely different structures. Which one is correct? Or maybe neither? How would you know? Not by looking at a single rib. And regarding stiffness of a single rib, you can make a big change by just slightly sanding on the scalloped region. That should be in a stiffness equation since it has such a large effect. Another large effect on stiffness is the relationship of rib shape to scallop length and the bridge location on that rib. You take the same rib and change the other two factors and you have different stiffness. You take the same rib, same scalloping and just change the bridge location and you have different stiffness. No two pieces of wood a behave the same. You can have the same Height, Width and length and different stiffness. So i hope I have shown that there is much more involved..

When it comes to soundboard performance, your entire language is off. When an individual learns to belly from someone with a lifetime of experience, the discussion isn't mass, stiffness, or impedance. Its more procedural, craftsmanship skills, and experience that brings out the soundboards potential. I have made many improvements this year in my attempt at maximizing a soundboards potential- I find most soundboards are just too heavy. These days (using my software that has 4 years of development) I can successfully remove 5 lbs of weight and maintain structural integrity. I recently removed 8 lbs from a Mason and Hamlin. Many rebuilders I know and follow, just copy the original or, they make it worse by increasing the weight to size ratio, often just by reducing size. I never liked the idea of a 6 foot grand that acoustically performs like a 5 foot grand.

Also, I think there is more of an acoustical performance way of thinking, rather than an engineer structural way of thinking that makes a difference. I think this is the core of our disagreement.
Over the years, I have focused on things like how does the sound of a solid bridge differ from that of a laminated bridge? How about a maple cap vs.a Beech cap? What do the different woods sound like. I have heard the effects of Spruce versus Cedar panels. How about the sound of a Douglas Fir Panel? I can tell you it has an amazing dark timbre. Its just not in the awareness of the public. Another one is if the soundboard has a closed sound versus an open sound? What frequency should its fundamental tone be? How can it be manipulated to improve performance? What are the changes in performance of moving the acoustical centers? Here's a neat one, changing a rib with a thud sound (when bounced on the floor) to having a ringing tone.

Soundboards are suppose to enhance sound. They are not buildings, bridges, or floors with joists. Those have different goals.
-chris

All uninspired self gratifying bologna.
Soundboard assemblies that differ from yours are not buildings, bridges or floor joists, get over it.
Have you ignored the fact that most everyone that does this work is wrong with the exception of you?
Books included. I should be humbled.
And boards do not enhance sound. they try to bring out The full potential of the input energy and most usually fall short to some degree or another - that is except yours, right? Superior, right?
I just cannot take you seriously.

Thanks for your thoughts Gene,
But your thinking is a bit fuzzy.
Since this is a piano forum, i'll ignore the personal attacks and address your piano related query.

You said:
"And boards do not enhance sound."

Then in the same sentence you said:

" they try to bring out The full potential of the input energy and most usually fall short to some degree or another"

That's practically the definition of enhancement Gene.

-chris

Enhance in Webster’s is to heighten and or increase, to augment.
Essentially to make more of what’s there by adding something.
The energy coming out of the board cannot be more than the input.

Finger moves key that moves hammer that moves string then bridge, board and air.
Energy losses for every interaction.

It’s a fallacy to divorce yourself from the way I react to you.

Gene,

Of course the input of energy is transduced . But, its going from being an inaudible energy to an audible energy. Hence, its volume is enhanced. Amplification would be adding energy. Which is not the case.

-chris

I specifically said sound, not volume.
But you can be right Chris, its ok.

I have bolded and numbered a few things so I can respond to them
(1) Oh, so changing the stiffness of a rib is a change without a purpose? Need I say more?
(2) Yes, the entire rib structure is what counts, but the entire rib structure comprises a number of constituent parts--most importantly, individual ribs. You can't change or analyze the whole structure without considering its components.
(3) Yes, there is tons more involved, which I explicitly stated. I never claimed otherwise nor would anyone with any domain knowledge.
(4) If so, then I think there's lots of opportunities that are being missed. Thinking about procedures, skill sets, and experience sounds like a good way to make a soundboard that hasn't had the benefit of new and creative thinking.
(5) Indeed? Then you should be extraordinarily interested in how the cross-sectional aspect ratio of a rib can greatly decrease weight while maintaining or increasing stiffness.
(6) IMO, this statement is just goobledygook. The acoustical performance arises from the totality of the structural design. To think they are separate from each other simply ignores the reality that a soundboard is a structural, mechanical assembly, which is both subtle and therefore complex in its design. There are no fairies in there, and no magic--it's all science.
(7) Who said they were buildings or floors? Not I nor anyone else with any sense or understanding. However, to pretend that the totality of the soundboard in its structure, design, and execution is not what produces the lovely sound we're all after is REALLY missing the point.

But for the sake of discussion let’s include power as opposed to volume.
Hammer hits string and all of the tone, partials, harmonics and even power is in the string.
Then all of this stuff gets into the soundboard that only moves air.
Certainly the sound and power from the strings is altered so it’s more audible but the board does not add anything, it tries to get 100% of the string energy out as moving air that gets into our ears.
My point is that no soundboard does this perfectly, 100% efficiently. That includes power. We hear a volume change but the power is less as it moves across the system.

Roy123,
Thank you for the response.
My answers in bold.
(1) Oh, so changing the stiffness of a rib is a change without a purpose? Need I say more?
(2) Yes, the entire rib structure is what counts, but the entire rib structure comprises a number of constituent parts--most importantly, individual ribs. You can't change or analyze the whole structure without considering its components.
(3) Yes, there is tons more involved, which I explicitly stated. I never claimed otherwise nor would anyone with any domain knowledge.

You answered your own questions here. 3 answers 2, 2 answers 1

(4) If so, then I think there's lots of opportunities that are being missed. Thinking about procedures, skill sets, and experience sounds like a good way to make a soundboard that hasn't had the benefit of new and creative thinking.

Talk about goobledygook?

(5) Indeed? Then you should be extraordinarily interested in how the cross-sectional aspect ratio of a rib can greatly decrease weight while maintaining or increasing stiffness.
Cross sectional area all by itself is useless. You seem to think that the bridge is always in the center of a rib, and you don’t take the scalloping into consideration. Because of the offset of the bridge and the asymmetrical load being placed on the rib, means acoustically, the rib should not be the same cross section across its length. Thus making it low in value as an analysis factor.

(6) IMO, this statement is just goobledygook. The acoustical performance arises from the totality of the structural design. To think they are separate from each other simply ignores the reality that a soundboard is a structural, mechanical assembly, which is both subtle and therefore complex in its design. There are no fairies in there, and no magic--it's all science.
Do you think everything you don’t at first understand to be goobledygook? You can’t seem to bridge the gap between mechanical function to acoustical performance. Here’s a video in which you can watch a master violin maker enhance the sound of the violin for the artist in front of a crowd. And you won’t hear the words mass, stiffness or impedance. And he was a physicist!!! https://www.youtube.com/watch?v=c8-rOvWeV8k&t=16s

(7) Who said they were buildings or floors? Not I nor anyone else with any sense or understanding. However, to pretend that the totality of the soundboard in its structure, design, and execution is not what produces the lovely sound we're all after is REALLY missing the point.

My point is that using the same math that is used to engineer floors and buildings , fails to produce a highly efficient wooden sounding board. That requires an ear.

-chris

My point is that using the same math that is used to engineer floors and buildings , fails to produce a highly efficient wooden sounding board. That requires an ear.

That’s more like an uninformed and totally biased opinion.
I think your point is consistent with things I tell you about that you misinterpret as attack.
Being superior and making people out to be wrong who don’t do compression crowning the way you do.

As I said, there are many considerations in designing a soundboard. You mentioned the value of compression-crowned boards as being more stiff. Higher aspect-ratio ribs are another way to increase the stiffness of soundboards without adding mass. Understanding the incredible sensitivity of the rib's stiffness to its height might provide a better understanding of the effects of scalloping, which could be useful.
There is no gap between the mechanical design and the acoustical performance. To think otherwise is a profound misunderstanding on your part. A soundboard is its structure, its structure is the soundboard. It's structure is utterly and 100% responsible for its acoustical performance. Where else would its acoustic capabilities come from? Some magical realm? I agree that it may be extremely difficult to map the mechanical structure to the acoustic performance, but many technologies are complex and difficult to analyze.
Also, yes, the same math that applies to floor design applies to soundboard design. It is the mathematics of the analysis of mechanical structures. In addition to that math, the soundboard designer should also understand the math that describes the transduction of mechanical vibrations into the production of sound. Engineers who design speakers usually understand that math quite well. The difference is the end goal. Floors are designed to safely support some defined load, and soundboards are designed to efficiently transduce the mechanical vibration of the strings into pleasing sound.
Everything I'm trying to say can be summed up simply. The soundboard is a mechanical structure. All aspects of its design, including its constituent parts, determine how well it will function as a transducer to produce a desired result.

I will give you the last word. I don't know how to express my thoughts any more clearly than I already have, though others may be able to do a better job than I.

Roy123,
You said:
There is no gap between the mechanical design and the acoustical performance. To think otherwise is a profound misunderstanding on your part. A soundboard is its structure, its structure is the soundboard. It's structure is utterly and 100% responsible for its acoustical performance. Where else would its acoustic capabilities come from? Some magical realm?

Everything you write makes sense on the surface, but the misunderstanding is not on my part, but rests on your shoulders. That's why you keep referring to "that it must be magic". No math, or analysis of the structure, can explain why one board sounds awful, and another identical board sounds great. In the video i presented, Fry didn't make any structural changes to improve the tone. Its not magic Roy123, but a deeper understanding. You may be well regarded in your field of expertise (engineering?) but that doesn't necessarily lend itself to another branch of expertise. Musical instrument Acoustics is most likely a sub- branch of Acoustics and that is a lifelong study in itself. Most of the changes that are made to improve the acoustical performance of a sounding board are subtle and often can't be detected by the eye. Again referring to the video, Fry mentions a drop of lacquer in a critical area can be tool. Just a scrape or two made a huge difference.
The piano soundboard may not be as subtle as that due to its size, but the ideas are the same. Steinways Diaphragmatic soundboard is an example.
The engineering is good up to a point. And I understand that belief, because the industry as a whole has a mass production mindset. Often the acoustic manipulations are not done on a piano soundboard. But what a difference they make.
-chris

So if i understand this correctly: Chris’ Unique in depth knowledge of the acoustics of a piano soundboard that exceeds that of an engineer’s or other rebuilders amounts to dripping lacquer on the board, trimming it with some tool, pounding it and watching for ideal sand patterns, all while unloaded?
I’ll stick with engineering.

I made my first soundboard in 1978. I am proud of the soundboards I produce and the advancements that I have made. I will defend them when challenged, and amaze anyone who hears them.

Unlike Gene, who cannot defend his product and must resort to name calling and snarky comments, when he feels threatened by others accomplishments.

-chris

Chris, I have never challenged your soundboards. If you recall I complemented you on your production of 50 boards per year, told you that you must do good work if you do that many, also stated my respect for anyone in this business who tries to make a better piano.
Besides, I could not criticize your product because I have not encountered it/them, that would be unethical - I’m certain you can understand that, no??
I do have much experience with the problems with compression crowned boards and if you re-read my posts, my criticisms are based on that process.
What I have challenged is your claim to superiority and you just don’t get the message.
I have defended my product just fine, only to be told by you that everything I do is wrong or it cannot be done or I’m building floors and bridges as opposed to soundboards. no reasonable dialogue could be expected as a result.
Like I told you Chris, you cannot divorce yourself from how I react to you.
You need to reflect on yourself just a bit. Possibly just a little humility??

Gene,
When I mentioned Compression soundboards are superior to RC&S boards that was 500 posts ago. You've been a BULLY and STALKER ever since.

The mention was not generalized.
And now the victim angle.
I’m outa here.