# Harp Innovations



## Enthalpy

It's among the nicest instruments. A harp makes seducing and familiar music that would sound aggressive or esoteric on a violin. Harpists manage to play difficult pieces on the diatonic pedal instrument, so why not.

But the harp plays too softly for a symphonic orchestra and has more drawbacks. So here are some thoughts, of random quality as I don't play the instrument.

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At present harps, the strings pull strongly the soundboard, but it must deform easily and be light to radiate the sound. This needs soundboard materials that store much deformation energy per volume and per mass unit, including at the bridge. First put there
scienceforums

If trusting an R^1.5/E figure-of-merit, *yew Taxus baccata would outperform spruce, sycamore and beech*. Yew already made longbows and mandolins. *Steel Fe-Ni18Co9Mo5Ti and titanium Ti-Al6V4 would outperform aluminium* used by Camac at the bridge. Profiled dense materials can make light parts within limits.



Code:


Material   Pedantly        Resistance    Young    Merit
---------------------------------------------------------
Spruce     Picea abies          70         12       49
Sycamore   Acer pseudopl.       95         10       93
Beech      Fagus sylvatica     115         12      103
Yew        Taxus baccata       105          9      120
Aluminum   AA7075              480         72      146
Titanium   Ti-Al6V4            830        114      210
Steel      Fe-Ni18Co9Mo5Ti    2000        190      471
---------------------------------------------------------
                              R MPa      E GPa   R^1.5/E

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A bigger improvement would *copy the genial pianoforte construction* where the strings don't pull the soundboard. They only make a zigzag around bridge pins and pull on a frame instead, enabling a much lighter hence louder soundboard. Suggested there with sketches for the diatonic and the rare chromatic harps:
scienceforums and next two messages



















The Chinese Konghou uses already this construction. Hear the nice sound, deep at low notes as hoped
XqT7nfXTp5c at 15s - Pc2mD5vAhww at 14s - 04oWysYCN0o - Gv0DOFkhFm4 at 21s - UbYA_K9QoWc
The symphonic orchestra equivalent would drop the second row of string and add the contrabass octave.

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The same *materials and shapes should improve the stress-free soundboard of a harp* or a piano
talkclassical

The standard is Spruce _Picea abies_, but Kiri _Paulownia tomentosa_ could outperform it.
The plate can have machined integral ribs, or ribs glued at the faces, or both.
Sandwiches of balsa and spruce or graphite are computationally lighter, but how do they sound?
Marc Schaefer, aka Enthalpy


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## Monsalvat

I disagree that the harp plays too quietly... it isn't terribly loud, sure, but it projects well enough that with the right orchestration, a harp solo can be clearly heard in a concert hall. Why fix what isn't broken in the first place? I'm imagining the _Adagietto_ of Mahler's Fifth with a much louder harp and it doesn't make sense.

Sorry for the jargon in this paragraph. I'm just focused on the materials here, not the rest of the design. Are you talking about _resilience_, where you wrote _resistance_? That is the maximum elastic strain energy, in SI units expressed in joules per cubic meter, which is dimensionally equivalent to the pressure units you have listed in your table. I don't think that's really a relevant parameter here, since the harpist shouldn't be stressing the harp enough to get close to the yield point. Assuming linear elastic behavior for most materials, the resilience is σε/2 (at yield), and with σ=Eε we get a resilience of σ²/2E at yield; so the two material parameters in your figure of merit are not independent. The strain energy stored in the harp has to be equal to the energy imparted on the string by the player, minus the strain energy stored in the string; the actual capacity of the material to store strain energy is not relevant as long as plastic deformation is avoided, because there isn't that much energy to be stored. The player should not be getting anywhere near the yield point.


Enthalpy said:


> If trusting an R^1.5/E figure-of-merit


Where does this come from and why should I trust it? It seems totally arbitrary. Rubber would outperform every material in your list, I'm guessing, since it has a low elastic modulus (tricky to define, since rubber exhibits nonlinear elastic behavior) and a high resilience. But I don't think a harp made of rubber would be good for anything other than the trash heap. I don't think this problem can't be reduced to just one figure of merit, since there are many competing factors here. Certainly the sound one would expect depends on more than just the stiffness and the resilience!!


Enthalpy said:


> but how do they sound?


And _this_ is the ultimate question. The burden of proof would have to be on a prototyper to _make_ such an instrument with the modifications, before it can be determined if they are an improvement or not. It's easy to conjecture, but ultimately my skepticism is grounded in the fact that I've heard modern harps and don't really have a reason to believe that these design changes would improve a harp. Hearing one could provide such a reason, since that is the ultimate test.


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## mbhaub

Well, invest your money in a new harp factory and build this supposedly superior instrument and let's see how it goes.

The modern harp has been developed over the past 150 or so years and I think it can safely be said that the design is finalized. The harp is one of the most difficult instruments to master and my harp teacher told me that if you don't start at a very young age and grow up with the instrument you cannot hope to be a virtuoso. (I took several lessons on it for the sole purpose of getting a better grasp on how to orchestrate for it.) The standard concert harp is what most students learn on and there is no way they would be willing or able to change designs. In some ways they're like pianos and a harpist can play on any good instrument, not necessarily their own, because they are all put together the same way: string placement (and colors!), pedal configuration, etc.

How far the harp has come can be illustrated by looking at some 19th scores where there are two harps that often don't play at the same time, mostly because they're tuned differently. But modern harps can re-tune much more quickly and both parts can be played by one person.

Changing any instrument runs risks and there's no guarantee of success or acceptance. Sometimes traditions are just too ingrained.


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## pianozach

mbhaub said:


> . . . The modern harp has been developed over the past 150 or so years and I think it can safely be said that the design is finalized . . .


I doubt that. Innovations in instrument construction and design happen. 

Pianos have been continually developing ever since their invention. 





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ychef.files.bbci.co.uk





Guitars have certainly evolved. There have been plenty of 20th Century innovations for woodwind instruments.

Harps though? I don't know. Why not a carbon fiber harp? Camac has been using carbon fiber to lighten their harps for years and they also use a fairly different action design. Andrew Thom has been making harps from aluminum and carbon fiber for years, some makers use other materials to make a more thinner, more resonant soundboard that withstands the pull of the strings. Heartland Harps have been making very light folk harps entirely of carbon fiber and are now working on a pedal harp.

But why are the pedals still noisy?


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## Enthalpy

Hi Montsalvat, thanks for your interest!



Monsalvat said:


> [...] with the right orchestration, a harp solo can be clearly heard in a concert hall. [...] the _Adagietto_ of Mahler's Fifth with a much louder harp doesn't make sense.


Many existing scores are not written properly and the harp is inaudible. We won't rewrite Wagner and so many more. But a louder harp would solve that.

For composers and arrangers who orchestrate properly, a louder harp would give more possibilities.

Making jokes about the harp like "pp means Press Powerfully" is nice. Fixing it would be even better.

The harp plays softly with ease, so a louder instrument could still play the whole repertoire.



Monsalvat said:


> [...] Are you talking about _resilience_, where you wrote _resistance_? That is the maximum elastic strain energy, in SI units expressed in joules per cubic meter, which is dimensionally equivalent to the pressure units you have listed in your table.


Yes, the maximum elastic strain energy σ²/2E. I've read other definitions of resilience elsewhere, related to impact strength.

Where did you find the Greek letters? Apparently you used the character "squared", but are there exponents too? I searched for all that.



Monsalvat said:


> I don't think that's really a relevant parameter here, since the harpist shouldn't be stressing the harp enough to get close to the yield point.


It's indirectly relevant, in that the cumulated string rest tension can't be reduced, but the table must deform easily under the string vibration. The combination of both tells that the table must store deformation energy under the rest tension of the strings. I suppose the musician adds little energy to that.

And... Harp tables do sometimes break, because the manufacturer wants an easy deformation for loudness, which implies a limited resistance. Visually, the static deformation is impressive. Manufacturers give a guarantee of X years against table explosion, sometimes it serves indeed.



Monsalvat said:


> [...]Where does this come from and why should I trust it? It seems totally arbitrary. Rubber would outperform every material in your list, I'm guessing, since it has a low elastic modulus (tricky to define, since rubber exhibits nonlinear elastic behavior) and a high resilience. But I don't think a harp made of rubber would be good for anything other than the trash heap. I don't think this problem can't be reduced to just one figure of merit, since there are many competing factors here. Certainly the sound one would expect depends on more than just the stiffness and the resilience!!


Agreed. That figure-of-merit is only a part of the story. Sounding materials need more qualities than that. Yew having made mandolines suggest it has acoustic qualities.

I determined the R^1.5/E three years ago. If I remember properly, it compares the stored energy at identical maximum force and volume, adapting the width and thickness to the material.



Monsalvat said:


> And _this_ is the ultimate question. The burden of proof would have to be on a prototyper to _make_ such an instrument with the modifications, before it can be determined if they are an improvement or not. It's easy to conjecture, but ultimately my skepticism is grounded in the fact that I've heard modern harps and don't really have a reason to believe that these design changes would improve a harp. Hearing one could provide such a reason, since that is the ultimate test.


Agreed again, experiments decide. But computations are useful to detect what direction can make sense, ideally by how much to change, before prototyping. Experimenting without a clear intention is rarely fruitful.

Consider a piano. The musicians gives about as much energy in a piano key and in a harp string. But the piano is much louder. A difference is the far better piano soundboard.

I provided links to the konghou, which has a soundboard parallel to the strings, though not as perfect as on the piano. It does bring a deeper sound. Pins on the bridge like the piano has, rather than string angles, would improve further.


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## Enthalpy

Hi mbhaub, nice to read you!



mbhaub said:


> Well, invest your money in a new harp factory and build this supposedly superior instrument and let's see how it goes.


My money... Err, well. But maybe I create a factory for percussion instruments. Small parts of machined metal, I can produce them myself if I access machines, the investment is small, and I have ideas for such instruments. They don't need to dry wood for years neither. By the way: if you see an invention from me on the Web, it's because I don't plan to develop it myself.



mbhaub said:


> [...] The standard concert harp is what most students learn on and there is no way they would be willing or able to change designs.[...]


Nice about the vertical soundboard is that *the playing technique is the same*. Pedal diatonic instrument, and so on.



mbhaub said:


> Changing any instrument runs risks and there's no guarantee of success or acceptance. Sometimes traditions are just too ingrained.


Yes, that's the case with any innovation. Music instruments are special in that they demand a very long learning, and they must play existing music too. The chromatic harp was an obvious improvement, but it couldn't play the glissandi of existing scores. It isn't dead though: more and more musicians play one, with 6+6 strings rather than 7+5, with a smaller range, and they play completely different music, not the scores written for the pedal harp. How big will this movement grow?


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## Enthalpy

Hi pianozach, thanks for your comments!



pianozach said:


> Innovations in instrument construction and design happen. Pianos have been continually developing ever since their invention. Guitars have certainly evolved. There have been plenty of 20th Century innovations for woodwind instruments.


As an extreme example, airplanes had not evolved decisively for millenia. And then came the Wright brothers and co, who showed that improvement was still possible.

Instrument makers tend to be rather small, from 1 to 50 people. Yamaha and the Steinway Group are exceptions. Some makers afford acousticians and researchers, most don't. Then you have acoustics, which is an incomplete theory, and its predictions often disappointing. It takes really good physicists who are musicians too.



pianozach said:


> Harps though? I don't know. Why not a carbon fiber harp? Camac has been using carbon fiber to lighten their harps for years and they also use a fairly different action design. Andrew Thom has been making harps from aluminum and carbon fiber for years, some makers use other materials to make a more thinner, more resonant soundboard that withstands the pull of the strings. Heartland Harps have been making very light folk harps entirely of carbon fiber and are now working on a pedal harp.


I strongly believe that most highly stressed parts of a harp would or do benefit from recent materials. But don't underestimate wood, a very high-perf material.

The soundboard is much more difficult. For instance plain carbon fibers make bad soundboards, either heavier than spruce or resonating lower, which gives a horrible sound. But with a carbon-balsa-carbon sandwich, the numerical comparison gets favorable. Time to try and let the ears decide?



pianozach said:


> But why are the pedals still noisy?


The action is badly difficult to design and build properly. The natural fork must stay immobile when the pedal moves the sharp fork. The movement (seven pairs of!) must pass to many strings within a curved part. I tried to think at a different mechanism and didn't find one shortly. I admire Erard's design. With minor adaptations, it still serves over a century later.


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## Enthalpy

Monsalvat said:


> [...] Where does this [figure-of-merit] come from? [...]


The picture gives a rationale for my sigma^1.5/E *factor-of-merit for a harp's soundboard materials*, including the bridge. It tells the deformation of the soundboard that resists a given force by the strings, if the thickness adapts to the accepted stress. This shall indicate how easily the strings move a survivable soundboard, hence how loud the harp is. Though, I did not check by how much the strings stiffen the soundboard.

This factor-of-merit gives no importance to the mass nor resonant frequencies. The lowest soundboard resonance being around 55 to 70Hz without the strings, the factor-of-merit is valid for the low fundamentals. A concert harp reaches down to 31Hz.

Other effects may produce a metallic or plastic sound, not considered here.

I compute with a cantilever beam, as this one is simple, and all shapes use to give the same material's factor-of-merit.








Or without maths, we could say: yew _Taxus baccata_ gave longbows a bigger deformation energy released quickly, like a harp needs, and yew made mandolin soundboards, so yew might make harp soundboards. Yew's factor-of-merit is nearly as good as aluminium's, which Camac uses at some bridges.

My soundboard parallel to the strings must bring more than minor modifications to the existing soundboard design. For it, spruce _Picea abies_ is a better choice, or perhaps kiri _Paulownia tomentosa_.


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