The Process Of Designing An Electric Upright Bass: Headstock

Usually you only get to see the finished product; the tip of the iceberg that is pushed out of the safe development-stage and then exposed to the real world.
For those who want to take a peek under the shiny surface, I plan to write a series of articles to illustrate the deliberation processes during the design stage. In this post I discuss the headstock of my upright bass.

Upright Bass Headstock with Pegbox and Scroll

Why not Headless?

As you can see, I have chosen quite a traditional pegbox design. This might seem a bit odd at first. Because when designing an electric upright bass from scratch with absolute freedom, ‘carte blanche’ as it comes to the shape of the headstock, this is probably the least innovative idea… And moreover, when assumed that low weight and compact size are some of the major design axioms for an electric upright bass, why would you make a headstock with pegbox and scroll at all, why not a headless bass like for instance Steinberger or Washburn Mark King bass guitars?
Well, the first part of the answer is quite simple; a headless neck is still a rather experimental path of design. This means you severely sacrifice the freedom to choose strings specifically designed for acoustic upright basses.

Upright bass string with silk winding at both ends
Upright bass string with silk winding at both ends

Together with a choice for the tailpiece, the standard ¾ string length gives the prerequisite of string length above the top nut, and therefore more or less a given (remaining) distance from top nut to the tuner peg for each string. At the headstock end, acoustic upright bass strings are often thinner. This allows easier winding around the pegs (usually wound with a material like silk). So there is also a minimum required length above the top nut.
Conclusion; the string choice together with the tailpiece, dictate the positions of the tuners and so dictate the boundary conditions of the headstock design.

Glitch

Why not a bass guitar style headstock?
While I easily dismissed the headless neck with rational reasoning (limited string choice), I can’t dismiss the bass guitar style headstock so easily; actually it can probably even be made smaller and lighter than the acoustic double bass style pegbox design.

Generally I am blessed to find myself in the comfortable position that my personal taste aligns with ratio, so that ratio can be used to justify certain design choices. But as it comes to the headstock, a strange glitch in my brain takes over; while I have no problem furiously redesigning the whole intrument and turning every stone to find the optimal lightweight solution, the headstock somehow doesn’t allow me to do that, like magnet poles repelling: every ‘improvement’ disproportionally substracts from the beauty of the archetypal shape. And there is no compromizing; I am also unable to produce the ones that have a pegbox but where the scroll is beheaded, or – to complete the lugubrious horror cabinet – have some molten stump for a scroll, as if it stopped growing while still in some kind of embryotic stage. So there you have it; it’s not all rational Form Follows Function.

A scroll all the way it is, including – as tradition dictates – designing my own ‘signature’ version.

Ancient Meme

The instigator of this glitch is an inspirational history teacher (mr Kwak), ever since this lesson, I have a weak spot for the scroll:
In ancient Greece, they built most houses from wood. Using wood for a column introduces a problem; the top end of the columns gets exposed to sun and rain, so the end grain has the tendency to crack, tear and rot. This of course weakens the structure. So the Greek sealed the top of the column with leather slabs as a raincoat. The excess overhanging leather would then curl up into a scroll. The stone scrolls of Ionic columns are an abstract artistic interpretation of these leather slabs.

Disclaimer; searching the internet, I cannot find confirmation for this very plausible explanation. I don’t know if this is the scientific consensus among historians, but the other explanations I found (mimicking vegetation, ovaries etc), to me seem less plausible as a primary inspiration for the shape. But then again, I am a luthier, not a classicist.

"Ionic" wooden column covered with leather skin to prevent end grain from rotting
“Ionic” wooden column covered with leather skin to prevent end grain from rotting

Renaissance

Late Renaissance /Baroque violin family luthiers like Antonio Stradivari (1644 – 1737) and Giuseppe Guarneri (1698 – 1744) recycled the scroll shape. This was an era where not only they ‘rediscovered’ Greek and Roman history, which broadenend the perception and concept of time, but also where expeditions (had) sailed around the world to discover ‘new’ land, where science and mathematics revealed the laws of nature, be it the heliocentric worldview (Galileo Galilei 1564 – 1642) or the microscopic world (Antoni van Leeuwenhoek 1632 – 1723).
For luthiers living there and then, the worldview hugely expanded, in xyz, in time, and in wealth. I can imagine the infinite mathematical spiral shape of the scroll resonated in such an era where the limits of imagination lay beyond the horizon.

And so this is why I want my bass to have a scroll; passing the art meme as a link in the chain, an ambassador for past and future. Because I like the idea of passing the scroll as an ancient art meme and – not least – I like it aesthetically.

3 axis cnc portal machine
My self designed and pieced together 3 axis cnc portal machine

When to CNC or not to CNC?

CNC stands for Computer Numerical Control; programmable mechanical machines; robots. You can use a cnc machine to replace some of the handwork. It is like MIDI, complete with a similar discussion on artistic value; you can have a real person playing a live concert on an e-piano, and record a midi file of that. When you play back that midi file on that same e-piano, it is the-same-but-not-the-same as the original. This is – I guess – why musicians have audiences. The audience wants to witness the act of playing.

I understand the romantic idea that artisan handwork adds value. As it comes to lutherie, I suspect many people imagine, or want-to-believe this romantic scenery of a Geppetto-like crafts(wo)man in a picturesque workshop, where a permanent golden hour sun shines through the diamond grid window, covering pretty much all shades of brown – from the dark shadows behind the purring cat to the bright freshly curled up woodshavings. Perfect for dreamy soft focus photography, this image of what ‘a luthier’ is. The very implication that there could be anything other than handwork going on here introduces a perspective that could break the magic of this cosy nostalgic narrative.

Pencil tracing and bandsawing of the headstock contour. The wood is wedged because it is a 'pie part' of a tree trunk. The front is wider than the back.
Pencil tracing and bandsawing of the headstock contour. The wood is wedged because it is a ‘pie part’ of a tree trunk. The front is wider than the back.

Reality Check & Meditation?

Zooming in to the real world however paints a different picture. The making of a headstock by hand actually consists of pencil tracing templates onto a piece of wood and then using (hand)tools to remove the excess wood. The first time-consuming step is to get the tracing exactly in place on a piece of maple. This is tricky to get right because of the wedge shape. Once the contour tracing is in place and roughly cut with the bandsaw, the actual handtool work of the contour is rather simple, but not too simple; it has a meditational quality to it.

The meditational experience I think arises because the mental concentration level is high but steady. As you use very sharp tools to carve away in small increments, you do not overload the mind into stalling. You can just ‘keep up’ so to say, which makes the experience satisfyingly continuous and seamingly effortless. Some would call it flow, or in the zone.

However – and this is the reality check that might disappoint the romantic, for all other operations than carving the contour, the constant checking and marking off of dimensions (symmetry) that gradually increases as work progresses, interrupts this experience of flow. And as you come closer to the deepest surfaces, the interruptions become a plain frustration factor; no flow at all (at least, that is my personal experience).
I find carving out the deepest part of a pegbox bottom not a pleasant chore. I confess I ‘cheated’ with the drillpress the very first time already. Not so much impatience, more “there must be a better way to do this”.

3d Template

When making a headstock, there is no real interaction with the wood tonewise. It are the dimensions that are leading, the end result is fixed dimensionally, beforehand.
I don’t think the instrument is more valuable if I have three days of frustrating handwork with gouges, chisels etc. When all goes perfectly well I could, with a lot of experience, match the same level of dimensional precision a cnc machine delivers. But I will never outperform it in speed and efficiency.

Another way to see it; a skilled luthier working in series, delivering constant quality on ‘flow-autopilot’, is like a biological cnc machine. Handwork is based on templates that are made in advance, the same set of templates is used for multiple instruments. Instead of a pencil tracing a template, the cnc machine traces a 3d template path. Handwork on a headstock does not make the instrument sound or play better. (it would make it a lot more expensive though).

Play

On the other hand, when making the tonal wood parts of the resonating body, the dimensions are contingent on the bending and resonance properties of the wood. This makes handwork – a real person steering every step of the process – the superior method. There is a responsibility, but no dimensional outcome to comply to, the procedure forms along the way, through interaction. As a novice I used to measure and control every step; I recorded tapping sounds and did Fourier spectrum analysis. Nowadays I just bend, flex and tap the wood and know from experience when to stop sanding off thickness.
There is concentration and involvement, just like a sailor who reads the elements to define the course, it is never the same.

I think this possibility of play is the source of my motivation to do this myself, by hand. This play, the involvement, the duration and the fast fluid ‘measuring’ during the job also gives the comfortable experience of flow.
To me, handcarving a headstock following strict templates is a chore, making the tonal wood parts of the body by hand is play.

Perspective

Just like handwork, working with cnc is very much a learning process. For the first cnc machine I built – back in the DOS based Windows95 era – I used the guide rails of architect’s drawing table, put some steppermotors on it and wrote code by hand. Since then I have built 3 new machines, each machine a step better. Because I have been working with cnc for so long, experienced the challenges and pitfalls, had my big and small victories, I have grown a passion for it. This is of course a totally different perspective than that of a customer who might expect traditional artisan handwork. The way I see it, working with cnc is a craft of its own, just as carving by hand is.

Chain of Events

There is another dimension to cnc machines I would like to promote. Previously I mentioned the experience of flow. I would like to incorporate this state of mind in the processes in my workplace. Luckily, I get a similar state of mind when watching my cnc machine carve out a piece I designed myself. It is like witnessing a live performance. I set up the chain of events in the program. The program unwinds; pressing ENTER kicks the first domino stone, leading to a slow but inevitable reveal.

Separation

The deeper concept here, is that there is a clear separation of information, ground material, energy and the machine. It might seem grotesque but bear with me; ever since the birth of the universe, matter, information and energy have been spreading out. An endless chain of cause and effect. Interacting, arranging and rearranging into different compositions, to after 13 billion years finally meet in my workshop (of all places). Some of it enters as electricity via the wall outlet; some of it comes as the chunk of maple I carried in myself; there is the cnc machine and… there is this package of information; the program I wrote to harness electricity, cnc machine and maple to form the headstock.

The huge advantage of this seperation of information into a program detached from my brain (and the sharp tools detached from by muscles), is that the information in the program does not decay or mutate, and you can use it anytime. All the actions that would otherwise be done by hand, are ‘extracted’ to a program. This program defines a very specific chain of events inside my workshop. In other words, I extracted the craftmanship, condensed and redefined it inside the program; the program is a translation of handwork; different language, different grammar. Although I let the cnc machine do its dance and so bypass labour of my brain and hands, it doesn’t feel like cheating at all; there is pride here, of – yes – craftmanship.

All Things are Delicately Connected

BTW, a major principle here is, that apparently, the program makes this particular chain of events that produces the headstock, the path of least impedance; it happens because the program impedes other possibilities.
Of all the possible arrangements the laws of nature in the universe allow to happen, carving the headstock was apparently the most likely chain of events to occur. Mind you, this includes the existence of the program, which in itself is a branch of the same majestic 13 billion year old chain of events. Welcome to the frontwave of now where you read about these events. All things are delicately connected.

I suspect the percieved effortlessness, the steady ‘natural’ pace of the cnc machine, is somehow connected to the experience of flow; like with the minimal effort of a kid on a swing, resonance occurs where impedance is minimal.

Craftmanship

Designing and making a headstock with a 3-axis cnc machine is not for beginners. Even though I thought I had over the years gained quite a good insight in – and feel for – what the limits of wood and tools were, still I sacrificed some mill flutes and pieces of maple while trying to find the optimal program and workflow for this headstock; how to get these very narrow tracks inside the scroll so deep without jittering the tool tip or without clogging the track with wood shavings and breaking the mill flute; how to precisely clamp in the workpiece in the cnc machine to mill the other side(s) in slightly tilted angles; this requires a lot of expertise, not to mention trial and error.

In my design, the whole headstock is comprised of 11 different cnc programs, 6 different mill flutes types and 5 clamping setups. After all this, it still has to be chiseled at some inner corners and after that sanded and finished.

I hope that by reading this article, you have come to appreciate and understand my choice for cnc machining the headstock, and understand its benefitial role in the workshop; they excell at repetitive work where precise dimensions are paramount, I find it a welcome innovation.

Upright bass headstock with scroll
Silhouette of the headstock, glued to the hollow carbon neck (top nut is not yet installed)

The Process Of Designing An Electric Upright Bass: Tuners

Usually you only get to see the finished product, the tip of the iceberg that is pushed out of the safe development-stage and then exposed to the real world.
For those who want to take a peek under the shiny surface, I plan to write a series of articles to illustrate the deliberation processes during the design stage. In this post I discuss the tuners of my upright bass.

Density

One of the main reasons to buy an electric upright bass, is transportability. While compact size evidently leads to lower weight, I found that simply making it smaller is not enough to reach a comfortable weight for easy shoulderbag-ish transport in for instance a subway or at an airport.
The catch is that an acoustic upright bass with its large hollow volume, actually has a very low density because the instrument is mostly air, while an electric upright bass is mostly solid.

High density parts like tuners are a logical choice to start reducing weight and so gain transportation comfort. A set of 4 tuners for an acoustic bass from conventional manufacturers – like Rubner or Sloane – weighs around 0.8-1.2kg. When the goal is to design an electric upright bass of say, 4kg, conventional tuners alone would make up at least one fifth of the total weight. So it is worth investigating this. 

Of course there are already tuners that are lightweight, these are for bass guitars. However, – and I fully realize this is a nonlogical overruling ‘however’- I like the classical headstock with scroll too much to compromize on this headstock shape. I simply want lightweight tuners that fit a double bass’ pegbox type.

 Searching the internet for lightweight sets of upright bass tuners, I didn’t find something that meets my desires. So I started experimenting…

Brass Tuner Experiment:

The first lightweight solution I designed, was a set of brass tuners (see below). This set was based on a conventional set where I bored out the pegs and replaced the baseplate with a self designed and produced version. The weight of the set of 4 tuners was 650 grams:

Not bad, but it just didn’t feel right to buy a finished product, strip it, and have this large amount of waste material from it.
Second to the waste, there was the relatively large amount of work. If you are an employee working for a company, you need to make yourself unmissable so you won’t get redundant. For me – working alone – the aim is to make myself as missable as possible; the production process may take time, but preferably not my time.

Sadly, making the brass baseplate was very time consuming; the brass blank bar went through the procedures of predrilling; 3 different clamping positions and cnc programs per baseplate; a saw line; post drilling; countersink… Here each new clamping procedure really eats away time while also the chance of error increased. This led to even more waste (and loss of job satisfaction).
Last but not least, the loud sneering noise of brass milling made the workshop sound like a catfight in a busy abattoir; inspirational enough to perform a genuine kill your darlings, and loop the timeline back to the quiet, erased drawing board.

Diverge and deliberate

It might sound like lame design textbook language, but nonetheless I find it a valuable cliché, that for a systematic design process, you first determine the basic function. In this case ‘Setting a string under tension’ and start from there.

You can set a string under tension in many different ways, but I understand and agree that in the evolution of basses the worm drive mechanism won. The quintessential property of a worm drive is that it transfers rotation in one direction only; you can make the cog rotate by turning the worm screw, but the other way round – turning the cog to rotate the worm screw, will not work. Perfect for tuning strings. BTW, in engineering the common way to see a worm screw, is as ‘a cog wheel with one tooth’.

Wormgear animation
Wormgear (source: Wikipedia)

I also find the ergonomic operation of tuning with the left hand while plucking the string with the right comfortable to do. The high gear ratio – as opposed to simple 1:1 pegs on cello’s or violins – allows smooth and precise tuning. Also the blades of the tuner keys provide easier operation than for instance a micro knob like you find on tail piece fine tuners.
So after this deliberation exercise it is re-established; the worm drive is and stays my basis for the design of the tuners. 

Stripping the Tuner Baseplate

A worm drive with a baseplate like I had on my brass set, is relatively easy to install, because the position of the cog relative to the worm screw is fixed. But it isn’t the option with the lowest weight.

Also, the design with a baseplate takes a lot of forces which are – as engineers tend to say – undetermined; like a table with 4 legs instead of 3, it is one too many. This makes it unpredictable what the actual load of a particular leg is. In other words, an even load for every leg is statistically not the most probable distribution of load.

What you want, is a simple and clear scheme of forces. In the design I prefer, the peg+cog sit in the pegbox. The pegbox is holding the peg, while the worm screw with the tuning key prevents the peg from unwinding.

Worm prevents peg from unwinding

When the peg rests on a baseplate, it is unclear which partion of the load is held by the wooden pegbox via the pegholes and which part of the load is held by the screws with which the baseplate is attached to the pegbox. It may even vary over time if the wood of the pegbox holes wears out and the load then takes the path of the baseplate. Then the forces at play change a lot, also in direction. This is why I chose to hold the peg in place with bearings inside the pegholes in the wooden pegbox. A baseplate is not necessary.

Load Distribution

To prevent the tuning pegs to jam like those of a violin or cello, the friction is almost eliminated using an Igus bearing especially designed for static load at the cog-side, and a brass ring with a tiny axial bearing at the opposing side of the pegbox. This makes the pegbox is holding the peg; the peg is an axle.
As a consequence, the load on the saddles via the worm screw is mostly axial and actually one of the two saddles is taking almost all the load (there is a small momentum also, which makes the non-compressed saddle pull away from the pegbox).

fusion 360 deformation simulation of axial force on a schematic worm wheel between two saddles
Fusion360 simulation of axial force on a schematic worm wheel between two saddles

So the two saddles that hold the worm screw and tuning pegs have a very different load. In a computer simulation (Fusion360) I tried to map the stress and deformation patterns. This just as an indication to see what is going on, not so much to get reliably quantized results (I could have, but that would demand a lot more input data I didn’t have, like the bending stiffness of the worm screw. In the end it turned out that the minimum practical shape was already strong enough, so cutting edge engineering was not necessary).

How About High Grade Plastics?

Conventional tuners are worm drives made from metal, usually brass for the cog and steel for the worm screw. This is because brass is self lubricating, and steel is strong. This combination is a major advantage because you don’t need oil. But brass also has a very high density (= heavy), even higher than steel.

There are also strong plastics with self lubricating properties, like pom (Polyoxymethylene). Fundamental design question; is metal necessary?

Choosing a plastic like pom would lower the weight by factor 8 and keep the desired self lubricating properties. Pom is also regularly used for gears. But… Since the tuners of a bass are gears that most of the time have a static load, I expect that the teeth and worm made out of pom will probably deform (creep) over time (decades). Also UV light and dirt might make pom degrade.

You can’t glue or mold pom easily if at all, so then you need to take a solid and remove material until you have the shape you want. The production process would become expensive, probably using a cnc lathe in several procedures to make the cog plus peg out of one cylinder piece. The most economical basic shape out of which you can produce the cog +peg on a lathe would be an extruded plastic cylinder, where the production process may cause rest tensions due to faster cooling of the outside. All-in all, I think using pom for the worm gear is a dead end.

Brass… Plus

Let’s zoom in on the boundary conditions. The parts that need to be metal are actually only the surfaces that are susceptible to wear and creep. It is possible to reduce the solid brass cog wheel to a brass toothed ring with a composite plastic filling. But a ring is not practical; how do you make this ring while keeping it precisely round, how do you transfer the torsion forces from ring to the core that has the peg attached to it? How can you center the ring in further processes? Production is probably safer and stronger, more reliable and easier (=cheaper & better) when when you hollow out a solid cog wheel. To exactly match the centers, you can use the same clamping for the center(ing) hole and the toothed ring.

So, I found a supplier that makes very precise worm drive sets. The hollowed out cogs are excellent for glueing on a carbon fiber reinforced peg, so then cog and peg become one solid body.

worm drive with hollowed out cog wheel
Worm drive with hollowed out cog wheel

Tuner Saddles

The worm screw has a steel axle, a D shaft actually, I want this axle to sit in two omega shaped saddles. Since I am already working with carbon reinforced epoxy resin, this might seem an obvious choice. The huge advantage of epoxy resin is that it is a liquid. This means you can mass produce parts by simply pooring the resin into molds. So, no problem then when using epoxy instead of pom?
Well, contrary to pom, fiber reinforced epoxy is not a low friction material, which would mean the D-shaft of the worm screw would not run smoothly and therefore would wear out fast. So just like with the worm gear, only the contact surfaces need to be wear resistant and low friction.

I found low friction bearing inlays that could withstand long term (axial!) loads without deforming, made from sintered bronze. I can position the sintered bronze shaft bearings in the epoxy mold before pooring in the resin. And because sintered bronze – which is actually a porous kind of bronze – is impregnated with oil, it does not adhere to the epoxy. This makes it easier to recycle the materials.

sintered bronze bearings for the worm wheel
Sintered bronze shaft bearings for the worm wheel

Making the Tuner Saddles

The saddles are a rather straight forward omega shape. The aim is to have high precision parts while keeping the production time and energy consumption at a minimum. To achieve this, I used the cnc machine to make a master dummy out of phenol formaldehyde resin. With this dummy I made a bunch of rubber molds. This concludes more or less the complete preparation for the production line of the saddles.
To make the omega saddles, I just have to (re)fill these rubber molds with carbon reinforced epoxy resin. Mass production and easy to scale up:

The Tuner Key Shaft

The only part of the tuner key that needs to be metal is the shaft, because of the sintered bronze bearing in the saddle. For the rest of the key I can use molded carbon fiber reinforced epoxy resin, which makes that color and method are consistent and production is also relatively easy to scale up.  

Boring out the D-shaft
D-shaft boring

It is not really as easy as this line of thought suggests. The torsion of the epoxy tuner key wings when winding the string, needs to be coupled with the steel D shaft. To achieve this, I bored out the D-shaft and glued in a Ø4mm carbon rod. Drilling a 4mm hole into a ¼ inch D-shaft requires perseverance to master.

1/4 inch D-shaft bored out with 4mm hole
1/4 inch D-shaft bored out with 4mm hole

Carbon Epoxy Tuner Keys

I can apply the same recipe – or style even I used for the omega saddles, to the wings of the tuner keys; use molds. So I milled out the key molds out of phenol formaldehyde resin. The mill path lines are just 0,2mm apart, which makes it somewhat resemble wood grain. Actually this wood grain appearance was not planned, but because I didn’t have a short mill flute, I had to resort to a longer one. The longer mill flute has a bit of jitter at the tip which made path somewhat irregular, wich makes it look more ‘biological’ wood grain (I think most designers feel the urge to sand the mold to a smooth finish, but I actually really like that you can see the details of ‘how it’s made’ in the finished product).

It was quite a challenge to find the right filling method, because it is a deep mold with a small opening. With some frustration, trickery and skill development I managed to control the molding process to such a degree that incapsulated air bubbles are prevented.

Tuner Cog Wheel and Peg

The hollowed out cog wheel will form a one-piece part together with the peg. Again, same idea; fill a mold with the cog and carbon reinforced epoxy resin and let it cure.

Ultralight Upright Bass Tuners
Ultralight Upright Bass Tuners

Some Numbers:

The set of ultralight tuners weighs only 360grams (4x ±90gr).
The gear ratio of the cog-worm gear is 1:27. This means it takes 54 half turns (27 full turns) of the tuner key to achieve one revolution of the peg where the string is wound around. The (average) diameter of the (tapered) peg is 14mm, add to that 1x the thickness of the string say 2mm, then per full revolution of the peg, you reel in ( (14+2)*pi)/27 = 1.9mm. So when changing strings it will take around one second to reel in 1mm, 6cm per minute. This ratio provides enough precision for accurate tuning.