String Instruments

[Enthalpy]

Elements for the soundbox of the grand cimbalom suggested here on August 25, 2019.

Modelled as 1.2m*0.55m, the soundboard is a quarter-wave broad of the lowest C=65.7Hz, so piston move would give it 5.6mohm*F² = 24ohm radiation resistance and 1m/s rms (arbitrary for comparisons) would displace 0.66m³/s rms and radiate 10W.

0.15m depth provide 0.10m³ and 0.61µF or j0.25mS at 65.7Hz. The same 0.66m³/s create 2.6kPa in the box whose 1.9m² dissipate 6*10^-9*SP²F^0.5 = 0.63W by conduction, far smaller than the radiation. Conduction losses would accept a shallower box even at this bass.

The unstressed soundboard of Picea abies (Norway spruce) weighs some 3.5kg with bracings, bridges and strings: the 0.66m² piston has 8H inductance. The Helmholtz resonance can be at F#=93Hz where soundholes add 12H, tiny margin. For the resonance, the soundbox could be slightly shallower, like 0.1m over the musician's legs, with a thicker opposite face, where the table is higher.

The metal frame being outside, only the soundholes vent the box. 338 holes, D=1mm h=2mm, achieve L=12H R=0.64kohm so Q=27 from these losses. Other figures can tune the resonant frequency and amplitude to please the ear. The holes can make up one or several rosaces, for instance facing the public.

The spreadsheet evaluates resonant frequencies for a 1.2m*0.55m ribbed table of Picea abies held flexibly at all edges.
CimbalomBracings.xls
Tuned arbitrarily for 140Hz, then about a fifth between the low resonances. The ribbed table weighs 3.3kg/m² and outpaces sound in air above ~500Hz. Paulownia tomentosa should enlight the table, and varied rib height spread the resonances better. Soundposts could vibrate the back plate too to provide interleaved resonances.

Marc Schaefer, aka Enthalpy

[Enthalpy]

On 7/21/2019 at 10:37 AM, Enthalpy said:

I've seen no [aluminium] alloy beyond the eutectic 12% Si.

RSP Technology uses rapid solidification and sintering to produce alloys with unusual compositions and properties. They have improved and widened their product sprectrum
Precision equipment at RSP Technology

A frame with 11.6ppm/K from their RSA-453 (Al-Si50) would match carbon steel strings perfectly, better than cast iron does. E=110GPa for 2500kg/m³ are 1.67* better than steel and cast iron, as good as TiAl, wow.

Many hypothetical string materials need nearly the same frame expansion as carbon steel: Maraging, martensitic stainless (optionally with precipitation hardening).

Strings of CoCr20Ni16Mo7, Duplex stainless or nickel superalloys would be stabilized by 13.6ppm/K from the RSA-443 (Al-Si40) and RSA-441.

Strings of austenitic stainless (optionally with precipitation hardening) would be stabilized by 17.3ppm/K from the RSA-4019 (Al-Si20 etc) and RSA-461.

The elongation at break is worse than brass. The parts I made of RSA-708 didn't break by falling on the floor and could withstand significant deformation by hammer.

Last time my employer needed an ultra-strong rod from RSP, he just paid and got it. Some 30€/kg are a hurdle for music instruments. I haven't seen tubes nor exotic profiles from them, so a frame should use rods, or waste costly material, or convince RSP to experiment.

Marc Schaefer, aka Enthalpy

[Enthalpy]

I suggested to replace Picea abies (spruce) with lighter Paulownia tomentosa (kiri) at the table of bowed instruments too, here on
March 05, 2019

Koto luthiers reportedly don't get their Paulownia tomentosa from a company that selects the trees and quarter-saws them. They season the pieces in 2 years and carve plates along the L and T directions. Though, the length-to-width ratio of the violin family fits the L and R directions from quarter cuts.

To balance the instrument, the back should be lightened too. Presently of Acer pseudoplatanus (sycamore), it sounds less strongly than the table if I read properly violin frequency responses, so it would need a bigger change than the table.

• Replacing Acer pseudoplatanus with Picea abies at the back would change more than Paulownia tomentosa does at the table.
• For instance some Pinus have intermediate properties, but they are not available in music instrument quality.
• Thinner Acer pseudoplatanus can be stiffened by a bass bar or bracings that pass under the sound post.

The replacements must keep the resonant frequencies, not the thicknesses nor the mass. The frequencies depend on E_L and on E_R, not so simple. Maybe two different thickness ratios can be computed, from the ratios in E_L, E_R and rho between the materials, and some mean value used for a first prototype.

The bass bar should change like the table; bending it would matter more with Paulownia tomentosa. The width could be kept and the height scaled like the table thickness. The anisotropic stiffnesses act differently on the bass bar, so the height needs further tuning.

Replacing only the table and bass bar in a first prototype would already tell the effect and whether the back needs improvement too.

Marc Schaefer, aka Enthalpy

[Enthalpy]

I had suggested it on January 27, 2019 07:39 PM and followings
scienceforums
and the ancient Chinese Konghou harp has already soundboards parallel to the strings.

How loud is the Konghou? It seems to work very well. Hear the exquisite sound
XqT7nfXTp5c
I like immediately this music from the opposite side of Earth. Because a harp carries it?

The low notes sound deep, better than the Erard-style harp
Pc2mD5vAhww - E1aUfdLSi64 - 04oWysYCN0o - Gv0DOFkhFm4 - UbYA_K9QoWc
that's what I expected from the bigger and more flexible soundboard.

Introduction: the instrument abandoned for centuries was revived and modernized around 1980
QReFNf4RzAM
7 notes * 5 octaves, right and left identical. Double-movement pedals identical to the Erard design.

Erard-system harpists can play the Konghou immediately
1oO_oCAlWxM - ZuUrtGTfWoM
so European and US luthiers should make harps with vertical soundboard before all musicians prefer the Konghou.

Equalling the range of the concert harp is a matter of resistance and stiffness, and the tall Konghou soundbox helps, while the neck can be taller at the centre. Steel gains a bit over wood.

I had proposed a single-strung instrument instead. Stress halved, and the harpist sees better, but the soundboard is shallower at high notes.

The Konghou's bridges stress the soundboard far less than the Erard-style does. My proposal to imitate the piano or to pull at the board's end injects no side force at all. This enables a lighter and louder soundboard.

Edited March 24, 2020 by Enthalpy

[Enthalpy]

It may still seem exotic because unusual, as I proposed it only on
July 28, 2019 here
but a self-tuning harp will be that profitable:

• Imagine the sensors, motors and electronics sell for 42€ per string, totalling 2000€.
• A professional harpist who doesn't waste 2*15mn tuning a day saves his orchestra 400€/year. 5 years ROI.
• Over 6 years with that instrument, a harp student who saves 15mn tuning in 3h training becomes a paid professional 0.5 year earlier. Gain is 10* the cost.

Edited May 2, 2020 by Enthalpy

[Enthalpy]

The piano could play flageolet by adding limited hardware.

It need a set of artificial "fingers" that touch the strings slightly at mid-length, or a 1/3 etc if this improves anything. Maybe of durable elastomer like PU or SI, or of hard material covered with felt. An additional pedal could move them simultaneously.

Accuracy seems easier if each finger nears its strings spontaneously up to a stop and is lifted by a collective part.

Addition to existing instruments looks feasible.

I suppose the luthéal had the capability
scienceforums
The added expression is useful and of reasonable complexity, so we could generalize it.

Marc Schaefer, aka Enthalpy

[Enthalpy]

I suggested here on January 22, 2019 to replace the violin family's purfling by graphite fibres glued on the wood
scienceforums

Though, the purfling makes the table's and bottom's rims more bendable. Or rather, the groove makes the wood more bendable, and the purfling doesn't add significant stiffness. This is more important at the table and bottom's ends, where the fibres arrive perpendicular to the bracings.

Imagine the groove removes one half of the wood thickness over 1.25mm: there, the table and bottom bend as easily as 1.25mm/(0.5)³=10mm extra length. Suppressing the groove raises a violin's resonances a bit, perhaps by a semitone. It also makes the table and bottom less mobile.

So I propose, if replacing the groove by graphite fibrers on one or both faces, to make the table and bottom thinner in this region. Numerically, this shall keep the sums of L/e³. With random figures, 1.25mm/(1.3mm)³ + 5mm/(2.6mm)³ could become (1.25mm+5mm)/(1.9mm)³.

[Enthalpy]

The holes in the box of an instrument (F-holes, for the violin family) must fit many constraints.

1. Their inductance knowingly tunes the Helmholtz resonance, together with the volume. The inductance depends on the width too: a narrow long hole needs less area.
2. Air friction at the rim usefully dampens the Helmholtz resonance. A narrow long hole is more efficient, a rosace even more. Too little investigated.
3. They give the plate flexibility. Little at the guitar, much at the violin family.
4. Their shape shall alleviate the stress concentration.

I tried a cello with three pairs of round holes instead of two F-holes, which neglects the points 2 and 3. The lowest resonance was brutal, and the next ones too high. I hated the sound, some customers liked it.

The strings of the violin family press strongly on the table, and holes nearby concentrate the bending and shear stress where fibre orientation is unfavourable. Elongated holes with sharp ends worsen it, as known in mechanical engineering. Despite being narrow, the F-holes provide a big radius at their bent ends and they shelter the tips where the holes reduce the stress. Violins built three centuries ago, with a higher bridge meanwhile, still play.

Few shapes fit this job. An other instrument retains the bent ends, but as a C shape instead. Would longers holes and the more mobile table make louder violins? Sound quality would need a thicker bass bar and other re-adjustments.

Marc Schaefer, aka Enthalpy

[Enthalpy]

A motorised tuner exists for guitars since 2012 or earlier, and nobody tells me a word.

Tronical produces it, others maybe too
tronicaltune
and some guitar manufacturers integrate it under their own name
Gibson
It's available separately too, for 250€ or 300€ at Tronical.

Many people own a guitar, but a decent musician tunes his guitar quickly and not so often. Harps would need a tuner badly, as I suggested in this thread.

250€ for 6 strings seems expensive. That would scale to 2000€ for 47 strings, but costs and prices aren't proportional. 1000€ seem attractive to save 15min every day, and my previous computation tells that 2000€ are quickly profitable for a professional harpist.

The motorized tuning hammer I suggested previously should be cheaper but slower.

A harp needs perfect reliability. Some strings break if tuned a semitone too high, and if several strings are too high, the table may break. So the instrument must distinguish the strings and tell if a pedal is engaged. Involving the harp maker in the development seems better.

[Enthalpy]

The violin family has a long bass bar that is glued under the table and passes below the left bridge foot. It's usually made of Picea abies (Norway spruce). Most luthiers give the bass bar tension: its ends are typically 1.5mm away from the table's curve when the centre touches it. The bass bar is then glued with a permanent elastic deformation of both elements, said to drop over decades.

The bending force of the bass bar alone is around 10N. The strings press about 0.40*400N=150N on the table, so the help by the initial tension is unimportant.

This paper finds that 1.5mm bass bar tension raises some violin's resonances by a semitone, and 3mm tension by a full tone
SkrodzkaLindeKrupa
which definitely changes the sound of a violin. Damping is unaffected.

That study observes a 10dB increases in the 4-5kHz violin's response
CroenAtwood
and that stress doesn't change the resonant frequency of two wood stripes glued together. This is consistent with a linear behaviour of wood.

It seems paradoxical: stress doesn't change resonant frequencies, but tension does.

==========

My incomplete explanation: wood is anisotropic, and the fiber orientation in the bass bar differs with and without tension.

A phone book is easy to bend when the pages are loose, impossible when pressing the pages together. In wood bent elastically, shear stiffness hinders the fibres from gliding reversibly against an other. Picea abies has little shear stiffness: G_LR is 20* smaller than E_L, the stiffness of fibre elongation. Hand computation fails at the shape of a bass bar, but if a beam's length is less than 20* its thickness, shear matters more than elongation. Same if a beam's centerline deviates more than 1/20 from the fibre direction, or if the section varies faster than 1/20. The bass bar is in these cases, the table too.

In the "Favourable" zone, tension orients the fibres nearer to the section's centerline and upper edge. The bending angle is small and unknown to me, the upper edge has a bad orientation, this zone is thick and short, and we speak about a semitone hence 12% stiffness, so I won't risk figures.

In the "Doubtful" zone, tension orients the fibres away from the centerline, wrong direction. But it also lets the bar's fibres meet the table's fibres with an angle, which improves the stiffness of both elements. I'll risk figures even less.

One could try anisotropic FEM modelling. I'd prefer someone to devise experiments, maybe with a simplified "table".

==========

Be my explanation of tension effect right or wrong, the present shape misuses the properties of Picea abies. So can the bass bar improve by using the material better? Not to raise the resonances, but to make the bar lighter and the instrument louder.

Acer platanoides and others bring a bigger G_LR but are denser. I trust luthiers to have tried and abandoned them.

Paulownia tomentosa seems favourable to bass bars and tables, little thicker than Picea abies. I have no figure for G_LR, and is it available quarter-sawn? One guitar luthier is enthusiastic.

Assemble plywood from Picea abies and hide glue. The usual +1/2 -1 +1/2 plies, or +1/2 -1 +1 -1 +1/2 etc, but not the usual +-45° directions. Rather +-1/10 slopes, resembling the bass bar and the table.

Keep the bass bar high, make it narrow where it was thin (keep wide ends for the glue). At identical h³W, the bar is lighter, and the fibres are less cut.

Make a laminate beam from Picea abies and hide glue. Bend the centres of the stripes, glue the stripes applied on a pattern, cut a bass bar out of that, narrow preferibly to thin.

Make a narrow beam of Picea abies, add few graphite fibres on the top and tilted at the sides where stiffness needs them. Spread them more than sketched. Graphite fibres alone aren't as efficient as sounding wood, but over a light kernel they are better. If possible, I'd prefer hide glue over epoxy, for known damping and ageing.

Make a truss of Picea abies operating in the fibre direction. How much work?

Make a T-profile of Picea abies, with the top well oriented and the centre thin. Adjust the top's thickness.

==========

This setup would measure the flexibility to let a new bass bar reproduce an existing good one:

It should use a real table, sorry for that, as glueing the bass bar on a model beam would be inaccurate even for a comparison. If mounting the table upside down, a narrow bar might buckle to the side.

The positions of the weight, supports, measurements need precision. A milling machine would be perfect, with stops for the table and the weight, or a 3D printer if controlled accordingly. The deflection has to be significant. More support positions, further inwards, possibly with a heavier weight, give better measures near the centre. One could even move the supports at constant distance from the deflection point.

Once the lighter bass bar gives the same stiffness, the resonances are too high, so the bass bar must be trimmed to the desired frequencies.

==========

Trimming the resonant frequencies may hopefully be done at the table with bar, without the rest of the violin, by glueing temporarily a frame, about as heavy as the bottom plus rim and neck, where the ribs use to be. This won't reproduce perfectly the violin's resonances, as the enclosed air and the interactions are missing, but let compare with a known good bass bar. Such frames would also let reproduce good bottoms and good tables without the bar, better than when these elements are alone.

Marc Schaefer, aka Enthalpy

[iNow]

Different species of wood have different grain structures and orientations. If you could produce a few EXACT replicas of the body but using DIFFERENT species of wood, that might offer a way to validate / nullify your hypothesis.

[StringJunky]

49 minutes ago, iNow said:

Different species of wood have different grain structures and orientations. If you could produce a few EXACT replicas of the body but using DIFFERENT species of wood, that might offer a way to validate / nullify your hypothesis.

Making instruments from the same tree will produce different results because even a single tree is not homogenous. There's a luthier on a guitar forum with an engineering bent been doing it for decades and he can't get his guitars to sound the same. There's a fair bit of BS about using different woods to get different sounds... there's too much crossover between species. You have to find the piece of wood -of any kind - that fits your target sonic envelope.

Edited April 16, 2021 by StringJunky