Enthalpy

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Everything posted by Enthalpy

  1. Enthalpy

    String Instruments

    Hello everyone and everybody! Some string instruments have parts, notably a fingerboard, commonly made of ebony: some Diospyros species, sometimes a Dalbergia species Fingerboard , Ebony , Diospyros , Dalbergia on wikipedia Ebony has drawbacks: the trade and travel of many Diospyros and Dalbergia species is restricted, even as components of an instrument; it takes many years to dry before processing; and it's expensive. Replacements were proposed, including hard rubber "ebonite", which has only 1/10th the stiffness of ebony and maybe not the resistence to abrasion. My suggestion is a polymer loaded with short graphite fibres with random orientation. They are hard and stiff (1/2 to full ebony lengthwise Young's modulus, transverse outperforms), some resist abrasion in plain bearings, they slip well and feel soft. Many are readily available, like POM and PEEK. Turning and milling tend to blunt the cutting tools quickly, faster than metals but slower than aramide fibres do. I suspect sanding roughens their surface, while planing and scraping have better chances. Worth a try? Marc Schaefer, aka Enthalpy
  2. Enthalpy

    String Instruments

    The best musical strings are still made from gut, possibly spun with metal wire. Gut is often replaced with PA11 polyamide or with metal, but nothing provides the crispy, profound and long sound of gut, for reasons not fully understood. Strength per mass unit is mandatory, very low mechanical losses too, density and bendability are useful, and I believe elastic strain matters. "Catgut" is one sheath of the lower part of the intestine of sheep, sometimes goats or cows, after mechanical and chemical processing which I understand leave only the collagen, in fibres oriented essentially lengthwise gamutmusic.com and web.mit.edu The upper part of the intestine made sausage casings, but for decades collagen widely replaces it because the process is simpler wikipedia Similarly, it would be nice to make musical strings of collagen, where at some process step collagen would be a homogeneous melt or solution, to obtain more easily strings of repeatable properties. The cited Wiki paragraph, brief and not quite clear about it, mentions: "It is widely used in the form of collagen casings for sausages, which are also used in the manufacture of musical strings." but I've never heard about a musical string made of collagen, far less a good string, so there must be hurdles. Yarn from collagen exists already and serves for medicine. Citing subchap 2.4 of: Biomaterials Science: An Introduction to Materials in Medicine By Allan S. Hoffman, Frederick J. Schoen, Jack E. Lemons "Reconstituted collagen is obtained by enzymatic chemical treatment of skin or tendon followed by reconstitution into fibrils. These fibrils can then be spun into fibres..." Gut is a raw material long enough for strings, but to spin fibres, tendon seems an interesting alternative. Or continue with gut if the strings are better. Wiki suggests that the exact spinning method is paramount to stretch and orient the macromolecules and transform weak polyethylene into ultra-strong Dyneema and Spectra Polyethylene fibre and Gel spinning at Wiki it seems logical: the lower exit temperature in gel spinning keeps the order acquired by the macromolecules in the spinneret. Whether this achieves strings as good as gut? Marc Schaefer, aka Enthalpy
  3. Enthalpy

    String Instruments

    Musical strings stretch the strongest materials to their limit. The string sound speed sqrt(sigma/rho) is 300 to 500m/s in music instruments, and where a string must be shorter, it is spun with metal wire over a thinner core that is still extremely stressed. Examples: Violin E. 662Hz, 325mm, 430m/s. Plain steel, 7850kg/m3 needs 1455MPa tension, and many E strings are overspun with aluminium wire. Was gut in the past, then estimated 1000kg/m3 needed 185MPa. Harp Eb. 625Hz, 287mm, 359m/s. Plain gut, 1320kg/m3 needs 170MPa. Harp Gb. 2973Hz, 78mm, 463m/s. Plain polyamide, 1040kg/m3 needs 223MPa. Piano C. 4186Hz, 48mm, 402m/s. Plain steel, 7850kg/m3 needs 1268MPa. Plucking or striking the string increases the stress further, in addition to bends at a knot, bridge or nut. For strength, polymers are drawn to wires, which stretches the macromolecules. Hardened high-carbon steel is cold-drawn to harden further. roeslau-draht.de >1720MPa for D=5mm to >2790MPa for D=0.28mm. I mean, wow. ========== Is different steel possible? Austenitic stainless steel exceeds 2000MPa by cold-working. Quality Strings alleges it's abandoned because it cracked more easily when flattened qualitystrings.com but I experienced the opposite with 2000MPa cold-laminated band: notches kill carbon steel band while the 17-7 alloy can be bent flat with a hammer after short tempering around 180°C which improves both the resilience and the proof stress. Tempering uses also to reduce the vibration losses, which I suppose were the real disadvantage. I doubt 17-7 attains 2700MPa but it retains more strength at bents and knots than carbon steel does. Duplex stainless steel behaves much like austenitic. Precipitation hardening austenitic stainless steel hardens by aging after cold-working, easing the effort. The PH 15-7 Mo spring alloy is documented to 1800MPa only but mechanical uses probably didn't exaggerate the cold work enough. Martensitic and ledeburitic stainless steel behaves much like carbon steel. PH 13-8 precipitation-hardens to 1400MPa, so prior cold-drawing may give a good hardness. Maraging steel is seducing. 18Ni12Co5Mo1Ti bring 2400MPa by aging, even at big diameters, with much resilience worth more than brittle 2800MPa. 50% reduction hardens the 18Ni9Co5Mo1Ti from 1900MPa to 2400MPa for instance diccism.unipi.it A violin or a piano afford easily the 50€/kg. Maraging would not rust, even at finger contact, but it can trigger allergies if bare. ========== Other alloys? The cobalt alloy CoCr20Ni16Mo7 similar to maraging steel resists corrosion better than needed. It can trigger allergies if bare. Its strengthening by cold work is documented matthey.ch 1920MPa @60% reduction, 2290MPa @90%, can increase further. Thicker strings of lighter metal may sometimes be better. A violin E string thicker than 1/4thmm would be more comfortable, it might be less prone to hiss and stick better to the bow. Thicker piano bass strings would carry the heavy copper wire in a single layer, which some manufacturers prefer pianopricepoint.com Titanium alloys resist corrosion. Ti6Al4V, Ti6Al6V2Sn, Ti10V2Fe3Al attain by ageing 1100MPa, or the same sound speed as 1950MPa steel, and the same elongation as 2050MPa steel. The equivalent of 2600MPa demands 1470MPa from titanium, hopefully obtained by cold-working. A titanium core of identical mass would be 1.7* stiffer than steel against bending, which has no consequence at a piano bass string. Exotic aluminium alloys attain 810MPa, for instance the RSA-707 made by RSP by rapid solidification and sintering. Same sound speed as 2200MPa steel. Maybe this one, or more common ones like AA7075 (480MPa), attain by cold-working 950MPa, the equivalent of 2600MPa steel. Cold-rolling brings the AA5456, which would resist finger corrosion, to 432MPa at 60% reduction and 487MPa at 80%, so more is possible. High-Pressure Torsion brings AA7075 to 1000MPa and the corrosion-resistent AA5083 to 900MPa nature.com while High-Pressure Sliding, better suited to wires, brings AA7075 to 700MPa researchgate.net they apply to titanium alloys too, but I've seen only the superplastic properties. Metal matrix composites improve the strength-to mass ratio of metals, but they tend to increase the E modulus too, and I suppose they dampen more. ========== Polymers? Polymer ropes of aramide, polyester or polyethylene are lighter than steel at identical resistance cousin-trestec.com exceeding 1000 or 1500m/s sound speed, equivalent to 18 000 MPa steel, but they sound "poc" when plucked. I suppose that braiding, impregnation and cover create damping by friction. Just twisting, possibly twice as in a steel rope, must be better. Polyamide musical strings are monofilament (and don't equal gut sound by far). Polyester and polyethylene get strong by fine extrusion, so quite possibly they must stay multi-filament and keep lossy. How would metal-spun Dyneema sound, properly assembled and stretched, no idea. Ropes thrive to minimise the strain, but musical strings need elastic elongation. That's one simple property where gut outperforms polyamide. The stiffer para-aramide uses to make ropes and meta-aramide fluffy heat-insulating material, but yarn exists too teijinaramid.com Meta-aramide has 1/4th the strength of para-aramide as a fibre. If it retains that factor as a string, it attains 500m/s, and more if twisted rather than braided. So meta-aramide strings can be worth trying. If needing an impregnation, natural rubber is the elastomer with smallest losses. Tennis rackets and other sport goods need strings with similar qualities as music instruments. Meta-aramide may improve them. Marc Schaefer, aka Enthalpy
  4. Enthalpy

    String Instruments

    Usual wolf killers seem to use banal elastomers between the string and a metal mass, so they would dampen all frequencies, their relative effect being best felt at the strongest resonance. Schleske's damper is allegedly tuned, and his measured response curves support the claim. He doesn't tell on his website how the damper is built despite having sold several, secretive thing. Just elastomer and a mass is conceivable, but for a stable resonant frequency, I'd prefer an all-metal design which looks easy at 100Hz using small parts in flexural mode. Strings vibrate between the bridge and the holder. They shall not resonate there and get some damping organic wrap from the manufacturer, but they receive movement from the speaking part of the string, over the bridge sitting on the table and the bottom, whose stiffness is limited as they shall vibrate. Some violin workshops even let musicians pay to remove the damping material from the strings there. This changes the sound, and some customers even believe it improves. ========== Erratum to the figures in my message of February 14, 2019 03:09 AM. Was Now ------------------------ 50mm 36mm (drawing) 14mm 22mm (drawing) ------------------------ 20mm 10mm 6.0kN/m 12kN/m 4.4kN/m 10.8kN/m 50mm 36mm 14mm 22mm 4.0kN/m 10.3kN/m ------------------------
  5. Enthalpy

    String Instruments

    Luis & Clark manufacture graphite fibre cellos and other instruments luisandclark.com as do some competitors. One amazing record by Scott Crowley 5SRDj9xGAoM on Youtube the détaché starts quickly and neatly, without the noises so common with celli. The musician and the strings matter a lot, but the instrument too. The timbre is extremely clear. This strikes me less at a cello, which I don't play, as wooden instruments too have quite a clear sound. The timbre is also hollow. Most musicians owning a graphite cello comment "useful under temperature contrasts" or "sturdy and easy, nice for students" but "won't give up my wooden instrument". Records of (carbon) graphite fibre violins exist too on Youtube, and they sound just like one expects: badly clear, hollow, with very uneven intensity. No, thanks. From manufacturing videos, the body is just a couple layers of fabric. Then graphite can't compete with wood, as explained here on December 30, 2018. To the very least, it would need a sandwich, for instance with a balsa core, to achieve a decent velocity for flexural waves. Copying a violin's dimensions with an isotropic fabric isn't reasonable neither. Hi StringJunky, thanks for your interest! This works. Several ways exist to kill the wolf tone, with varying selectivity. Some instruments exhibit the instability over 3-4 semitones, which prevents tuning the offending frequency between two semitones. Then you have the worry of unusual tunings (for baroque music, or to play with some historic or detuned instrument), of glissando, portamento... A more selective approach puts an extra mass at the best place on the table. It's also a shift of the offending frequency, but it doesn't affect all the notes. The more common approach puts a damper on the string, between the bridge and the string holder, where the string isn't supposed to resonate. This one reduces the resonance instead of shifting its frequency. But it acts on all notes. Martin Schleske claims to taylor a resonator that dampens only the instrument's offending resonance schleske.de/en his curves support the claim. This would be the best targeted intervention, working for all tunings and leaving intact the rest of the response. The setup I propose is more for research than for an actual instrument. It aims to reproduce my claimed mode split without using a resonance, so if a wolf tone is observed, this will favour my explanation. Or disprove it.
  6. Enthalpy

    String Instruments

    To check the explanation I proposed for the wolf tone, the experimental setup could look like this. At left a bridge is flexible laterally, at right it's a steel string. Here at least the vertical modes of the string are harmonic thanks to the boundary conditions and the uniform lineic mass. Horizontal compliance lowers the string's horizontal mode by adjustable 4Hz from E=165Hz. This results from the equivalent of 20mm extra length, that is horizontal 6.0kN/m side stiffness of the imperfect node. The string's non-speaking length keeps its damping yarn and it can be 75mm to have no common low harmonic with the speaking length (I checked only the vertical modes). The stiffness of these 75mm with 120N string tension leaves horizontal 4.4kN/m obtained from the tweaked bridges. 1mm is the maximum lateral deviation of the non-speaking length of the string at the tweaked bridges. ========== The flexible wooden part (left on the sketch) uses stiff glue. Mind the wood's orientation. The height of the thin section adjusts the frequency drop of the string's horizontal mode. At right on the sketch, a violin E string of 0.25mm unspun steel serves as a pseudo-bridge. Some 12.6N tension would resonate the 100mm at 902Hz to avoid common harmonics with the cello string, but more tension may be better, and additional reasonable damping looks useful. The violin string is bent sharp pemanently. The mere tension of the four 100mm sections brings 0.5kN/m horizontal stiffness, and the adjustable 2*14mm width of the Lambda shape 4.0kN/m more. A reasonably sturdy wooden frame, not displayed on the sketch, holds the upper V made of violin string. ========== If a wold tone appears in this setup with no soundbox resonance, it will favour my explanation. Many cello strings are ferromagnetic, useful to excite each mode separately. A repetition rate of the wolf tone near the frequency difference between the modes would be a further argument. Both variants of the setup let adjust the frequency difference. Marc Schaefer, aka Enthalpy
  7. Enthalpy

    String Instruments

    The wolf tone is a sound instability that can appear on celli and double basses, rarely on violins de.wikipedia (audio) en.wikipedia - schleske.de/de - schleske.de/en theories exist, essentially a strong body resonance that couples too much with the string. These theories match some observations but fit others imperfectly. A string can and does vibrate in any perpendicular direction, plus all the combinations, which includes elliptic modes. If the bridge is stiff, all modes have the same frequency. But if the soundbox resonates strongly, the bridge is more mobile, which lowers the string's frequency, and more so in one direction decided by the soundbox' behaviour. The string modes split in two that have different frequencies and can beat. The split may be more common at celli and double basses because their bridge is tall and narrow, so body resonances matter more to the string in the transverse direction. I suggest to inject this mode split in the current theories. Some experimental checks: If the wolf tone persists when a single string remains on the instrument, try unusual bowing directions, observe if they have an influence. Will that be convincing? On a hauling cello, use a capodastro, check by an actuator if the string has split modes and if their frequency difference matches the beat when bowing. Build a pseudo-instrument with a string but no soundbox, where the bridge is stiff in one direction but flexible in the other, for instance steel wire in V shape, or flat wood aligned with the string, preferably at 45° with the bow. Check if the wolf tone appears with the mode split but without any body resonance. Measure both modes, check if the instability's frequency is the difference of them. Pluck the string, compare with the bow. Marc Schaefer, aka Enthalpy
  8. Enthalpy

    String Instruments

    Estimated bridge stiffness required by my two harp designs with vertical soundboard. From the previous message, the bass strings should feel about 200kN/m, and if the bridge is to spread the side movements over +-0.1m, R~1MN/m2. The bridge must be stiff enough for that: EI~100N*m2. Beech (E=12GPa) needs W=e=18mm. If it sounds decently, 1D graphite (170GPa) on wood needs e=1+12+1mm W=7mm, a bit lighter. Medium and trebles need different dimensions. ========== At its column end, the bridge could be anchored with elasticity so the lowest strings feel a good stiffness and move the soundboard at the higher strings too. The unstressed soundboard can hold at its top ridge under the bass strings, and be free at the bottom. ========== Imagine that the narrow tall soundbox contains 0.03m3=210nF with the unstressed soundboard. The lowest H2 has 62Hz and we don't hear fundamentals lower. For arbitrary 1Parms in the box, the power radiated by the small source is 0.15µW while conduction to 0.6m2 box wastes 0.03µW, so it's big enough for that. Air elasticity pushing on equivalent 0.2m2 at the bass bridge portion adds 200kN/m stiffness, the full stiffness goal, so the box could be slightly bigger or the soundboard smaller. If the equipped soundboard brings 150g equivalent inertia and the bass strings too, air elasticity resonates them near 130Hz. Fluffy material in the box can dampen this resonance. My designs have leaks around the soundboard, say 1mm*1.6m wide and 15mm long. At 62Hz and for 1Parms in the box, inertia limits them to 0.14m/s and 0.2dm3/s compared with radiated 0.08dm3/s. The leak intensity improves with the frequency squared and the box volume, and it's nearly in phase quadrature anyway, resembling more a Helmholtz resonance around 100Hz, combining with the previous 130Hz to make 160Hz. The leaks waste power by viscosity. For 1Parms at 62Hz hence 0.14m/s it's 16µW. This reduces the strings' decay time. The box volume improves this loss, holding the soundboard where possible too. Frequency improves all this quickly. At 140Hz, radiation equals viscous losses. Marc Schaefer, aka Enthalpy
  9. Enthalpy

    String Instruments

    The soundboard of the usual concert harp, 8 to 10mm thin (my mistake) and 580mm wide, can't resist alone the traction of the low strings. The midrib (=bridge at present harps) does it there by holding at the pillar, but this makes the soundboard very stiff under the bass strings. The bass strings also resonate longer than needed, so a more compliant soundboard could be louder. Imagine that the soundboard flexes by 0 to 10mm under the 15 lowest strings that pull each mean 500N, that's roughly 1.5MN/m, neglecting all angles. Badly stiff. ========== Tone wood isn't flexible at identical bending resistance. Accordingly, the luthier Camac replaced at least the lower end with an aluminium bar. 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 NiCoMoTi 18-9-5 2000 190 471 --------------------------------------------------------- R MPa E GPa R^1.5/E Steel would give more flexibility than aluminium. This lowers the resonances consequently. Thickness, and optionally profile, that vary with the position, can increase the soundboard's flexibility only at its wide but underused lower end. Or if keeping wood, a wider thinner end of yew (it made longbows and mandolines) should outperform spruce and sycamore. Additional parts can resist the force and give more flexibility than a straight bar, for instance a transverse bar. The soundboard must be thin to accept the deformation. The midrib's end can pull the soundboard low until the strings pull it up. The position of the midrib's end can be adjustable, at the factory or while the musician tightens the strings. I'd have stops at the midrib's end to protect the soundboard. ========== Kurijn Buys made seducing proposals for the harp's soundboard: Kurijn Buys' report (in French) decouple the soundboard from the column, build it from composite materials to resist the string's pull but be flexible, prestress it, among others. ========== My two versions of vertical soundboard are far more flexible. Over 180mm for the same 15 lowest strings, spruce 3mm thick and 200mm high contributes only 2kN/m bending stiffness, and 40MPa allow 27mm deflection. If fastened 200mm lower, the 7500N cumulated tension contribute 38kN/m, whether this tension is in the string extra length or in the soundboard. This oriented compliance lets a string swing slower, but only in the transverse mode. For a string tightened with 770N, this acts like 20mm extra length over 1.27m or 0.8% pitch mismatch, so the beat half-period is 0.8s, shorter than the exponential decay time. Around 5* stiffer, or 200kN/m, would be better in this register: fasten the strings 40mm below the bridge rather than 200mm, or add wood springs at the bridge. The unstressed design needs abundant bracings for adequate resonances. +-45° orientations may protect the soundboard better against in-plane traction by the musician. The tensile soundboard has a big wave speed parallel to the strings. 14MPa tension and 400kg/m3 give it 190m/s, so a half-wave in 200mm height give a lowest resonance at 470Hz without bracings. Resonances need only bracings perpendicular to the strings. But since this soundboard moves like a flat sheet, its base concentrates the bending stress and may demand some protection. My two designs seem to have design margins everywhere, including for thicker soundboards. With a radiating area similar to the present harp, but movements about 7.5* bigger, my designs should be 17dB louder, as much as 50 present harps. Could that be a first step towards the gaffophone? fr.wiki and google Marc Schaefer, aka Enthalpy
  10. Enthalpy

    String Instruments

    Le Carrou used already a shallow chimney at one hole to indentify the Helmholtz resonance. How much would tall chimneys at harp holes bring? I take 100mm height at the holes Le Carrou measured. The narrower soundbox end isn't that deep, but it adds its own inductance. D131 (16.2H) // D120 (18.6H) // D111 (21.1H) // D89 (30.2H) = 5.1H which resonates the soundbox' volume at 154Hz, same as the soundboard at this harp model hence useless. This improves if doors shut some holes. 3mm elastomer are worth 2.2m air. The soundboard's compliance contributes too. With chimneys at the lowest holes (could be elsewhere), 2 holes resonate at 118Hz and 1 at 86Hz. Arbitrary 1Parms at 118Hz in the box would radiate 1.9µW, conduction would waste 0.1µW and viscosity >0.1µW, elastomer doors contribute, for Q<68. A rosace or narrow F-holes would increase the viscosity losses, as would leaving a single hole open with a shallower chimney. Fluffy material, as in loudspeakers, can dampen too strong resonances of the long air column in the almost-closed soundbox. Marc Schaefer, aka Enthalpy
  11. Enthalpy

    String Instruments

    A 237th check tells me eventally that the volume of the harp's soundbox isn't 0.2m3. It's nearer to 0.03m3, depending on the model, giving it 210nF capacity. This needs updates to my February 03, 2019, 11:33 PM message. Acoustic measurements of a harp exist there Le Carrou's thesis (mostly in French) The measured soundbox has 5 elliptical holes (table 3.1), of which I keep the 3 lowest. I assimilate their inductance to a disk of same area, which acts as a cylinder of length (0.3+0.3)*D: D131 (7.1H), D120 (7.8H), D111 (8.4H) total 2.6H to estimate the Helmholtz resonance at 216Hz. Le Carrou attributed it 172Hz rather, after subtle arguments since his fig 3.8 provides no obvious logic, probably because the soundbox isn't short. For instance, the strong resonance that appears at 190Hz with holes closed has lambda/2=0.9m, shorter than the soundbox. Can soundbox' resonances be brought usefully below 154Hz, the measured lowest soundboard resonance? I suggest resonating doors tuned to 123Hz, 99Hz, 79Hz, 63Hz. Of Acer pseudoplatanus, they could measure approximately 170mm*60mm*1.3mm, 190mm*70mm*1.4mm, 200mm*90mm*1.2mm, 210mm*100mm*1.1mm - or rather thicker with an adjusted mass in the middle. The last hole would resonate at 50Hz in Helmholz mode with 48H inductance resulting from an 185mm*85mm*0.8mm elastomer membrane. ...Maybe. The resonating doors need a non-absorbing airtight fastening. A harp that radiates low frequencies like a plucked contrabass may sound denatured. Marc Schaefer, aka Enthalpy
  12. Enthalpy

    String Instruments

    A sheet of elastomer can be a door for a harp's hole. Very few mm suffice to stop the air by inertia. It's easily silent and airtight. Strings could hold the door (or patch) at round hooks at the soundbox. The patch could even hold in the hole by a firm fit. I suppose the viscoelastic properties don't matter as the patch moves little. Polyurethanes resist wear best, while perfluoroelastomers are immune to chemical degradation. Of course, the finished patch must be nice. ========== Strings can also go through the soundboard of a loud chromatic harp as suggested here on January 20, 2019. The springs of January 27, 2019 02:30 PM apply, oriented stiffness as on January 27, 2019 04:32 PM too. Marc Schaefer, aka Enthalpy
  13. Enthalpy

    String Instruments

    Harps have presently big holes in their soundbox that let mount the strings from behind the soundboard. Though, the first role of a soundbox is to enclose the rear wave of the soundboard so it doesn't cancel the front wave. Many people are concerned with these holes, some proposed covers, mobile to access the strings, or even controlled by a pedal, but all this is abandoned. So how critical is the leak? At high frequencies, the soundbox' volume and capacitance builds little inside pressure, and the holes' inductance is big, so the rear wave doesn't exit, and the holes have no effect. Near the frequency where the holes' inductance resonates with the box' capacitance, the rear wave can be stronger than the front one and produce a stronger net sound, as for a violin's Helmholtz resonance. At lower frequencies, the inductance doesn't stop the rear wave which weakens the front wave - here the holes could be detrimental. A harp can emit a Cb=30.9Hz but we don't perceive fundamentals so low, only the harmonics above roughly 80Hz, and a soundboard also radiates the low frequencies badly. As grossly estimated from pictures - an acoustic measurement would be better: The soundbox is 1.6m long while lambda/4=1.1m at 80Hz, so it's not far from a lumped constants case: tweaking a bit suffices. The soundbox has 0.2m3 = 1.4µF, mostly near the bass strings, so I keep it fully. The 5 holes are 0.25m high each but I cumulate only 1m as a lumped constant. The walls are thin so the inductance results from cylindrical spreading between mean w=120mm to W=500mm: L = 1.225kg/m3*(2/pi)*Log(0.5m/0.12m)/1m = 1.1H (inside+outside). As much as 0.11m air thickness. The resonance is 128Hz very approximately. The loss is 4dB at 80Hz, not much. It worsens at lower frequencies that we perceive less. But around 128Hz, the resonance by the soundholes amplifies the sound (I didn't estimate the Q factor). So there's nothing damning in these convenient openings. Can we improve this? Doors strengthen the radiation at 80Hz but waste the resonance at 128Hz, possible explanation for the mixed opinions when they were tried. Shifting the resonance to 80Hz or slightly lower should be better - maybe. Make the soundbox bigger. Under the medium strings, it could be reasonably wider and deeper. Significant contribution, but it won't double the capacitance. Make smaller holes? No, harpists need big hands. Close every second hole with a door. Their seals shall absorb the vibration, but not too much. Put membranes on the holes. A 950kg/m3 material, 140µm thin, would double the inductance of 0.11m thick air. I doubt they can be silent (hear a sudrophone...) and durable too. Add chimneys to the holes in the box. If 0.11m long, they double the inductance and shouldn't hamper the hands' activities. They can broaden at depth. They would also strengthen the Helmholtz resonance, for good or bad, more so with rounded edges. Close some holes with resonating doors. Keep 3 from 5 effective holes open, the Helmholtz resonance drops to 100Hz. Let a door resonate mechanically at 80Hz, the other at 65Hz. Made flat of Acer pseudoplatanus, they must be around 2.3mm and 2.8mm thick, to be experimented, then adjusted individually at production. The doors can be bigger than 250mm*120mm and thicker. The holes are small at celtic harps. Chimeys or resonating doors would keep the resonant frequency and allow bigger holes. Marc Schaefer, aka Enthalpy
  14. Enthalpy

    String Instruments

    The chromatic harp is nearly extinct: it isn't taught for decades, the last instruments were built three-quarter century ago, most remaining ones are in a bad state. As one drawback, it is less loud than the concert harp, for which some simple reasons exist. The added strings add mass, stiffness, and they pull stronger at the soundboard. The strings pull excentred at the soundboard, which may or not need extra thickness, but for sure the soundboard is harder to move from an excentric point. My two arrangements solve that, with strings pulling in line with the sounboard or not at it. They need pairs of soundboards, one for each plane of strings (which I possibly swapped). Then a chromatic instrument would be as loud as the diatonic one which hopefully improves over the present design with flexed soundboard. The soundboards have some directivity at high notes and harmonics, so tilted reflectors that double as protective covers shall direct all notes in the same direction, essentially forward. The (cover-) reflector may apply to the diatonic versions too. Marc Schaefer, aka Enthalpy
  15. Enthalpy

    String Instruments

    Here's a glipmse at a harp with unstressed soundboard inspired by the pianoforte, whose strings make only a zigzag at a bridge and continue to a frame. From descriptions of playing techniques, the musician must access the strings near the bridge too composingforharp.com but only the left hand reaches the lowest 10th, and the right hand stops even earlier near the soundboard, so I believe the soundboard can extend over the bridge at the right side of the two bass octaves; where it extends much, its rim can be attached. The soundboard can also extend deeper below the bridge in the medium, as depicted. Could the bridge be curved to run higher in the medium? This would put the strings' middle on a more regular curve, possibly ease playing, but change the musician's habits. The unstressed soundboard is much thinner than at present harps. It can be fastened at a position different from the strings. Abundant bracings, plus the bridge and possible bass bar(s), keep the resonances high enough. The bridge is a copy from a piano with the gliding layer and precise nails and wedges, reduced at the bass and much more at the treble. The bass strings too must extend below the bridge for compliance, hence between the left and right pedals. Opportunity to extend the soundboard too. A truss can improve the protection of the thin soundboard, protect the musician's legs against the nails, and close the traction-resisting section. Besides wood, fibre composites may perhaps constitute the soundbox' shell and the truss, or even cast metal, especially magnesium alloy, thin and with ribs - not only for this instrument. The soundbox being as narrow as the neck and pillar, folded or disassembled feet and pedals would make an instrument thin and easier to transport. Marc Schaefer, aka Enthalpy
  16. Enthalpy

    Hear a Qanun

    Depending on where you have lived, you may not have heard a qanun up to now... The kind of zither is common from Armenia and Turkey to Iran and Syria and beyond. Music on Youtube: NplUDKSwvQU, "The Seven Gates of Damascus" xL1QRZ1nfro "Syrian Dreams" e351z9H5MB8 audition for a graduation Allegedly the instrument was formerly played by men only... Maya Youssef is a fabulous composer, and to my untrained ear she plays very well too. Explanations about the instrument: h81283r_cJ8 including the piece "Breakthrough" wikipedia Enjoy!
  17. Enthalpy

    String Instruments

    The arrangement of symphonic orchestras fooled me, but harpists show their front to the public, slightly from the right side. So, the soundboard pulled at its edge by the strings, as depicted here on January 27, 2019 07:39 PM, shall better radiate to the left and have its soundbox at the right.
  18. Enthalpy

    String Instruments

    The next step is obviously to design a harp inspired by the piano arrangement: the strings run next to the soundboard parallel to it and make only a zigzag at a bridge to and end at a frame without pulling the soundboard. The arrangement resembles the previous message, so much of the description and the many advantages applies. Better, the soundboard can more easily extend higher than the end of the bass and medium strings to be bigger and louder. Details should come. Marc Schaefer, aka Enthalpy
  19. Enthalpy

    String Instruments

    Guitars have an ultra-thin soundboard, around 1mm, made possible because their strings pull parallel to it, not perpendicular. So here's a harp whose strings pull parallel to the soundboard. 20mm thickness resist (often) the perpendicular pull over some 250+250mm width, so for a parallel pull, a 2mm thin soundboard should suffice even at the bass strings: we're getting somewhere. Abundant bracings are necessary to keep decent resonant frequencies. The strings pull at the upper end of the soundboard, at least at the treble end, so that both hands reach the strings. The soundbox' shell doesn't touch the soundboard near the strings, but it passes close to the bar there to reduce sound leaks. No access is needed through the shell, so acoustical experiments shall decide if the shell has openings. I'd have a truss of non-resonating material over the radiating side of the thin large soundboard as a mechanical protection, and to make stronger and stiffer this part of the harp's frame stressed by the strings. Its holes let insert the strings. Closing the cross-section between the strings would help mechanically. A cover, removed to play, would protect the soundboard further. The soundbox can be narrower than presently, which helps the transport. Consider foldable or removable pedals and feet. Inverting the neck, with the strings at right side, may make the harp even thinner. Marc Schaefer, aka Enthalpy
  20. Enthalpy

    String Instruments

    Strings can be fastened at the bottom of the soundbox, and the extra length be stiff, if the contact with the harp's soundboard decouples the vertical movements and transmits the horizontal ones. The left attempt uses rolls. These must move with the slightest force, which isn't trivial and may exclude any sliding guide. It also demands a smooth sleeve around the spun strings. The right attempt has flexible parts. These must stay horizontal when tuning the string: glide easily, small zigzag. Notches guide the string transversally in both cases. Marc Schaefer, aka Enthalpy
  21. Enthalpy

    String Instruments

    I confirm that strings fastened directly at the bottom of the soundbox are too stiff, hindering the soundboard's vibrations. Good reason not to do it up to now. The tension of the metallic bass strings bends present soundboards visibly, by >1mm, but 600N on 250mm extra length of a string with D=1.1mm steel core stretch it by 0.8mm only. This vertical stiffness added to the in-plane stiffness of the soundboard would hinder the perpendicular vibrations. The extra string length needs elasticity. I didn't check if the gut treble strings bring enough elasticity naturally. ========== This spring example gives elasticity to the string extra length and adds little mobile mass. Meant for an Eb=78.1Hz string, 1.27m spun metal, 770N tuned, 19.6g/m. 3850N tension in 400µm*10.5mm L=80mm cold-rolled steel (possibly split in two to pass the string, or replaced by steel wire(s), D=2.2mm cold-drawn) strain it by 0.35mm, contributing 2*3.5mm at the string. The mass is 4*2.6g, acting as 3.5g at the string. If someone can solder high-carbon steel, fine; if not, the band ends can be clamped together with many screws, or maybe a wedge. 7700N compression in Do=14mm e=1mm L=160mm AA7075 tube strain it by 0.42mm, contributing 4.2mm at the string. The mass is 4.1g, acting as 1.0g at the string. 11mm strain is more than a soundboard's deformation presently. 4.5g mobile mass is less than 40g per string for a present soundboard that needs 20mm wood to stand the traction. With that spring, a lighter soundboard looks possible. ========== Can the spring be lighter? The Lambda shape of strong material is a good start: as in a longbow, it's light and uses at a lower speed an elastic material that can be heavier. The Lambda is lighter if less flat. Cascading several Lambda brings the slowing factor. If the Lambda don't bring enough elasticity, the added elements (a tube previously) can be nearly immobile to add less inertia to the string. ========== I had imagined that the soundboard's deformation could cause most detuning, but after seeing experimental data about polyamide and gut strings, it's less clear. Elasticity created by metal parts could maintain a more constant tension in polyamide and gut strings when these lose stiffness at heat. The tension drop might even be adjusted to compensate the reduced mass of the speaking length. Springs are then useful for medium and treble strings too, even if the extra length is elastic enough, in which case the springs can be heavy. Marc Schaefer, aka Enthalpy
  22. Enthalpy

    Woodwind Materials

    Hello everybody! The material used for the walls of woodwind instruments, and its real, perceived, imagined or absent influence on the sound and ease of playing, has been and is the controversial matter of recurrent discussions that I gladly reopen here. The air column is the essential vibrating element of a wind instrument, the walls are not, but this is only a first analysis. The walls are commonly made of wood (sometimes cane, bamboo etc.), metal, or polymer aka plastic, which manufacturers call "resin" to look less cheap. Mixes exist too, with short reinforcement fibres or wood dust filling a thermoplastic or thermosetting resin ("Resotone" for instance). I'm confident that long graphite fibres were tried too, as fabric, mat or in filament winding. The choice results from marketing, tradition, weight and manufacturing possibilities (a tenor saxophone is too big for grenadilla parts), cost - and perhaps even acoustic qualities. ========== Plastic is a direct competitor for wood, as the possible wall thickness, manufacturing process, density, stiffness, shape possibilities, are similar. As opposed, the density of metal restricts it to thin walls made by sheet forming an assembling, but permits big parts. Manufacturers typically use plastic for cheaper instruments and grenadilla for high-end ones - some propose cheaper wood in between, possibly with an inner lining of polymer. Musicians who own a grenadilla instrument disconsider the plastic ones; I never had the opportunity to compare wood and plastic instruments otherwise identical, so I can't tell if the materials make a difference, or if grenadilla instruments are more carefully manufactured and hand-tuned, or if it's all marketing. Two polymers are commonly used: polypropylene for bassoons, and ABS for all others, including piccolos, flutes, clarinets, oboes. These are among the cheapest polymers, but 10€/kg more would make no difference. They absorb very little humidity, but some others too. More surprising, they are uncomfortable to machine: POM for instance would save much machining cost and (my gut feeling) easily pay for the more expensive material. But ABS and also PP absorb vibrations while others don't, which I believe is the basic reason for this choice. They limit the unwanted vibrations of the walls. As a polymer that dampens wall vibrations, I should like to suggest polyketone https://en.wikipedia.org/wiki/Polyketone it's known to make gears more silent than POM and PA, its glass transition is near ambient temperature, its density and Young modulus resemble ABS, it absorbs little humidity. Still not widely used, it can become very cheap. Its creep behaviour and ease of manufacturing are unknown to me, but ABS and PP aren't brilliant neither. Marc Schaefer, aka Enthalpy
  23. Enthalpy

    Woodwind Materials

    One musician confirms that his French system bassoon reaches high notes easily Pw3WcvcJslQ on Youtube he demonstrates an E, one octave higher than the Sacre du printemps, 4 octaves and a small fourth over the lowest Bb. Or if you prefer, near the oboe's conventional limit. The narrower bore of the French system surely helps. The reeds are a bit smaller too hence faster, but I doubt they limit the instrument. The tone holes differ, obfuscating the comparison. And Buffet Crampon still uses dense wood Bassoon model at BC presently Dalbergia Spruceana (amazonas palisander, amazonas rosewood) amazon rosewood at wood-database.com whose 1085kg/m3 and EL=13GPa are twice as much as for maple used on Heckel system bassoons. ER, ET and damping would be as significant. The video's author tells "lots of advantages" [to the French system]... except that it's even less loud than the Heckel system, and the fingerings are worse.
  24. Enthalpy

    String Instruments

    Violins and their relatives get a "purfling" at the rim of their table and bottom Purfling at Wiki to protect the table and bottom against cracks. Some sources add "and to ease the vibrations" despite the purfling is glued in the groove. Maybe preimpregnated graphite filaments could replace the sandwich of precious wood there. They would be stronger and much faster to install, if possible on the wood without a groove, which would ease modifications. Some clarinet makers reinforce already the ends of the grenadilla joints with graphite filaments instead of metal rings. The matrix shouldn't absorb vibrations: no polyester, but epoxy maybe, preferably warm hardened. Or can hide glue, ubiquitous at luthiers, impregnate graphite fibres? Several continuous turns of thinner filament at the table and bottom's rim would leave no weaker zone. I believe it's optically acceptable to run straight where the table and bottom have angles over the glued corner blocks; add black paint if preferred. Or cut the filament there. Marc Schaefer, aka Enthalpy ========== In the messages on January 20, 2019, I drew the cones (displayed green) that shall hold a string much bigger for visibility. They would be as small as possible to reduce the inertia and damping. The second variant, with a single part displayed green, seems to need more mass.
  25. Enthalpy

    String Instruments

    At a harp, the strings pull about 10kN directly on the soundboard. The soundboard must be thick, which loses sound strength. Nevertheless, soundboards sometimes break. Could the soundboard's deformations cause most detunings at the harp? Gut strings don't detune so badly at violins, but strongly bent wood may be more sensitive to humidity and temperature than stretched gut. The other instruments do it differently. The violin family only bends the strings by roughly 1/10th over the soundboard, so the force is much smaller, and only 1/100th of the soundboard's compliance acts on the strings' tension. Strings make just a sidejump at the piano's bridge but exit parallel to their arrival, so no net force results, only a torque. I suggest to copy that. Maybe the soundboard could be parallel to the plane of the strings, but this seems inconvenient at the treble strings at least, which are very short and played with both hands. On the sketch, the strings pass through the soundboard, making just a small zigzag there, and they hold at the bottom of the soundbox. A small tube, of alumina or other hard material, probably notched, can protect the soundboard (including the bridge) from the string fed through and transmit the vibrations. A small tilt suffices, as the maximum deflection of the string suggests. Powder of graphite or MoS2 would linder the sudden tension releases, and piano bridges have a special black material for that purpose. The instrument's foot may need modifications, possibly more depth. If an added frame holds the strings' bottom, it might pass between the left and right pedals towards the column. A full-loop steel frame gives the steel-stringed piano stable tuning. I have a feeling (and didn't check as usual) that this idea was already tried and abandoned, possibly because the extra portion of the many strings (which must be precisely parallel) is too stiff and hinders the soundboard's vibrations. Though, this construction works at a piano which has more strings and where the extra portion is short too. I should come back with proposals for fast added compliance in some directions. Marc Schaefer, aka Enthalpy