Last Year I was Mostly...

Not got round to posting an update for a while, but over lockdown I was able to get some ideas out of my head and put some left-over parts them to good use. 

Driver Checking

This has nothing to do with the DVLA, but instead is a simple speaker measurement unit based on an Arduino with a separate AD9833 DDS which can give a sine shaped output. The Arduino controls the DDS frequency and its ADC allows speaker voltage and current measurement. The frequency is swept to find the points of maximum and minimum impedance. It's not the most accurate, but better than doing it manually, and gives reasonable results when compared to manufacturers data. This may allow me to find a new use for any unknown drive units hanging around...

I have Celestion BL10-200X drivers in my 4x10 cab, here's the measurements of my 4 drivers (A, B, C & D) when I took them out with my assistant to repaint the front.

 Mfr   A   B   C   D

fs 73.0 61.3 69.2 65.9 72.5    Hz

Re  5.8  5.84  5.86  5.84  5.83   Ohms

Qms  3.58  3.31  3.09  3.13  3.12

Qes  0.56  0.46  0.51  0.49  0.54

Qts  0.48  0.40  0.44  0.43  0.46

Speaker D seems the closest to the published specs.

Here it is checking out an old 8" Soundlab 8LUX driver.

And the results are in:

fs 36.4  Hz

Re  7.15 Ohms

Qms  2.35

Qes  1.13

Qts  0.76

New Tunes For Old

In June 2021 I wanted to create a bass tuner to fit in my main amp. The Arduino just didn't have enough grunt for this, so I tried an ESP32 module and a 128x64 graphical LCD display.

Inside it uses the u8g2 display library with a modified Haichi Maru font to produce the smiley faces. The tricky stuff samples the signal at 4kHz, uses 512 point FFTs plus some filtering and topped off with Gaussian interpolation courtesy of the nice people at CERN. Such a name dropper! It's just a better way of working out where the real peak should be given the height of the ones either side.

I didn't want any buttons so the tuner just responds to a reasonably constant note. When the input signal is quiet it waits patiently, smiles and pokes its tongue out. 

Once a consistent note is played it switches to the tuning view - the aim is to get the line horizontal, at which point the triangular markers are filled.

If it decides someone is playing (ie the notes keep on changing) then it cycles through oscilloscope, speaker and frequency views for amusement. Well it amuses me anyway.

LFO 

Over Christmas 2021 I decided to redesign the LFO section on my synthesiser that was built in 2007. It has worked well for several years, but when changing the duty cycle with ramp based waveforms, the frequency changes too. This limits the usefulness of the control as the interaction makes setting up awkward. My assistant took a keen interest.

In the centre position the duty was 50:50 as expected, and the current charging / discharging the main capacitor is equal in magnitude at that point. To put some numbers on it to help understand what's going on, the charging and discharging current could be +2mA and -2mA, equating to 1s rise and 1s fall to give a period of 2s or frequency of 0.5Hz. 

Moving the threshold from the mid 50:50 point to 90:10 gives +0.4mA and -3.6mA. The rise time will be 5 times slower at 5s and the fall time almost twice as fast 0.9s. Together these give a period of 5.9s which is a frequency of around 0.16Hz. It does give the right duty cycle, but the frequency is now much lower.

There is no easy way to keep the frequency and duty cycle independent, but there is a flakey analogue way that will vary with temperature and phase of the moon, so we'll go with that. Going digital in the middle of an analogue synth doesn't seem right...

Captain's Log (Amp)

To keep the same frequency, the above duty cycle needs to provide a charge current of +1.1111mA and a discharge current of 10mA. This gives a rise time of 1.8s and a discharge time of 0.2s. These still give an overall period of 2s (0.5Hz) and the right duty cycle. A reciprocal relationship is needed here (100/90 = 1.111mA and 100/10 = 10.0mA). Log amps here we come...

From school maths (A * B) / C can be calculated using logarithms: Antilog( logA + logB - logC ). Once the log and antilog amplifier circuit blocks have been made, the rest is straightforward adding and taking away.  

Seeing as I was passing by I also improved the sine shaping and made the duty cycle able to be controlled by the other LFO.

When controlling the VCF it can now cycle from wob wob wob to bow bow bow without changing the rate significantly. Sooooo much more usable than the old one.

 

The Finishing Touches

 Bouncing along

After a successful wind-up, the completed spring was slid onto the main tube. A 90 degree bend made at the bridge end allowed the coil to be anchored by passing the wire through the last fret position hole (drilled earlier for guidance). Each coil was nudged into position before fastening at the head end using a bicycle brake cable clamp-bolt. Finally the entire spring was glued to the tube with epoxy resin to prevent it wandering about. This was a bit messy and a fair bit of IPA was used in cleaning off the excess before it set.

Tuners

Conventional closed gear tuners were used. These are normally fitted into the headstock which is around 15mm thick. The stainless tube is only 1.5mm thick and is curved! To get around this (quite literally) four circular aluminium spacers with OD = 30mm, ID = 16mm and length 24mm were sawn into 16mm & 8mm lengths then shaped to fit either side of the tube wall. 

It took a fair bit of whittling to match the tube shape. The tuners were then fitted to the tube using these spacers to sandwich it all together. The smaller convex spacer is on the inside. The small wood screw that normally prevents the tuners turning under tension is replaced with an M2 bolt that also passes through the main tube wall and clamps both parts of the shaped spacer.

Bridge

The separate parts of the bridge were assembled into fixed and adjustable sub-assemblies. The fixed part is bolted to the body tube and the adjustable part is clamped to this using M6 x 75mm bolts. This allows +/-4mm of height adjustment and a certain amount of sideways wiggle too. Angled holes were drilled into the taller end part of the bridge for the strings to pass through before sanding and polishing. 

The string grooves were cut into the saddle, and a horizontal groove cut underneath to allow space for the piezo pickup (see below). A drawback of this single saddle style of bridge is the limited intonation adjustment. I'm over it already...

Pickup

As this guitar is based on a tube, the strings cannot 'fan-out' from the nut to a larger bridge spacing without causing the action to increase significantly too. The spacing at the bridge is kept to be nominally the same as at the nut to prevent this increase in the action height and therefore requires a very small pickup too.

The smallest pickup I could find was for a Ukulele. Even this was too long so it had to be dismantled. The individual piezo elements measured around 7.5 x 1.2 x 1.2mm. 

The first attempt sounded wrong using 3 elements. The middle element must have been too high causing The E-string end to be very weak. The centre element was removed second time around and with just two elements it sounded peachy! 

Altogether Now 

I'm very pleased with the spiral frets - they are no more difficult to play than straight ones. I deliberated over shimming the zero fret to make it slightly taller but actually got round to it. A truss rod was not required as the neck is an inherently stronger shape and shrugs off the string tension without showing any signs of curvature at all. A properly set up bass neck does actually have a slight bow to accommodate the string as it vibrates back and forth. This cannot be achieved here.

I've never used piezo pickups before and the sound covers the full audio range regardless of cable length. A common-place wound inductive pickup will have an electrical resonance that can be worsened by excessive cable capacitance. This can be caused by a long or a cheap cable. Above this resonant peak, which can itself add a bit of sparkle in the right place, the output drops noticeably reducing the amplitude of higher frequencies. The piezo pickup is in essence a capacitive pickup and additional cable capacitance makes very little difference. 

The tonal character of a stainless steel tubular body, new strings and a piezo pickup system result in an extremely bright sound. This can be tempered by adjusting the playing position of the right hand to give a fuller sound. The same trick can be done on a conventional guitar but due to typical body shapes only a small range of playing positions seem feasible. On the tubular bass, there is no body or other points of reference, so the right hand can carry on up the fret board giving almost hollow synth-like tones.

Other than that, to be honest, it's a complete nightmare to play 😮 The string spacing is very tight for the right hand, and the picking hand has to reach round under the tube for the higher strings. 

Ergonomics were not that high on the list of important considerations.

It has stretched the concept of guitar construction in a new direction, but also reinforced that conventional guitars are good examples of incremental development. That being said, with a D-shaped tube and some welding, a more familiar neck and body could be crafted giving rise to an instrument that would have more universal appeal. 

But I like the prototype - it still looks like an exhaust pipe from a Lamborghini Murcielago 😊

The Spring Winder

The Spring Winder is based on the usual method of a rotating former and a wire dispenser moving along its length. For an ordinary spring, the wire would be moved at a constant rate, but for a fret-spaced spring it needs to be fast at one end and slow at the other. A linear actuator was obtained as they are popular in 3D printers. They are built from readily available extrusions with a stepper motor driven lead-screw. The spring length needs to be roughly 700mm, so a 1000mm actuator will allow some breathing space.

An Arduino Uno was purchased as I really wanted to try one out! No additional programmer box or pricey software is required, just a USB A-B lead and a (free) download of the Arduino IDE. The built-in functions make pin operations straightforward and makes it a great introduction to programmable hardware.

After successfully blinking a few LEDs on and off, the main circuitry was developed to PWM control the winding motor and use a DRV8825 module to run the stepper motor. An LCD alphanumeric display was also added to show useful info. 

The winding former was estimated to be 30mm when using 1.8mm diameter stainless steel wire and a 50mm inside diameter. The winding speed was set at a fairly pedestrian 12rpm and the position of the winding former is monitored by a rotary encoder. 

The whole fixture was built on a combination of plywood and MDF measuring about 1200mm x 400mm x 45mm and uses pillow block bearings to constrain the winding former and a brass clamp to provide wire tension. The first winding motor tried out didn't have enough torque, so a larger motor was sourced connected to a chunky 36V/10A PSU. To negate the effect of loading on the motor speed, the PWM controller uses a small amount of current feedback. 

The main software loop takes the rotary encoder count, calculates* the new actuator position and sets the number of actuator steps so that this can be achieved. Using the micro-stepping facility of the DRV8825 module gave a nice round 100 steps per mm and worked up to a maximum rate of 8000 steps per second. If the quantity of steps are not completed within 30ms an error flag is set and the loop repeated anyway. The slow (~12rpm) winding speed ensures that this overspeed condition does not occur. This process is repeated until the windings are complete. 

*The calculations use a simple linear ratio for the lead-in and lead-out at each end, and a more involved formula that comes from working out fret positions for the bit in the middle. 

distance = scalelength * (1.0 - 2.0 ^ (turns / -12.0))

An Unexpected Turn Of Events

Smart people will already have realised that turning the winding motor 12 times to get a whole octave of windings does not result in 12 finished coils! The ratio of spring ID to former ID had been overlooked. The spring is wound on a 30mm former, but when released (and yes, this was a scary bit) it rapidly returns to the more relaxed state of 50mm diameter. It is the same length of wire in both cases so the larger relaxed diameter has less turns. To correctly compensate for this it needs to rotate (50/30) more turns than I first thought. 

After this, I settled for 4 lead-in turns, 4 lead-out turns and 26 fret turns based on 50mm ID. This equates to around 7 lead-in turns, 7 lead-out turns and around 44 fret turns when mapped to a 30mm former. The 26 fret turns allows some freedom in choosing the best 22 (plus a zero fret). 

After several rounds of debugging it was ready to run. Winding the spring took around 5 minutes and apart from a bit of congestion on the lead-in, it nailed it first time! The video clip speeds up the action into just over a minute.

Doing The Rounds

In between working on the Spring Winder, other parts of the Tubular Bass also needed to be made. The nut and bridge assemblies are both made from aluminium, mostly 15mm thick, but the nut and saddle are only 6mm. To anchor these, 47mm discs are turned on a lathe** and fitted inside the tube. The visible parts of the nut and bridge are bolted to these through slotted holes to allow a certain amount of height adjustment but keeping things sturdy and rigid. 

**I don't have a lathe so I laid a benchdrill on its side instead. Each part was rough cut into an octagon shape with an 8mm centre hole, then turned lathe-style. It doesn't have quite the same bearing system as a proper lathe so there is more judder and it doesn't give a great finish but it's good enough. Don't try this at home - it makes a lot of swarf!

The Steelworks

 An unexpected problem of this bass build was the complete lack of any useful edges or datum lines. Before any holes are drilled or cutouts are made, the tube needs to be marked out. This can't be done freehand, or with a ruler so I had to think outside the, um, tube. Fortunately a bit of spreadsheet magic enabled me to plot some graphs that I could wrap around the tube and use as cutting guides. Once in place it was time to fire up the angle grinder - not a tool I normally use when making guitars!

The guide allowed the two cutouts for the headstock to be made and marked the tuner holes for drilling too. 

Making holes in stainless with ordinary HSS drills is often less than successful, cobalt ones seem to fare much better. 

Fretwire?

Bashing fret wire into wood is quite satisfying. Bashing them into perspex as I have done on the last two builds is not great - it doesn't have the same give and one bash too hard could end up cracking the whole fboard. For the perspex fboards I had to make wider slots then rely on glue doing the rest. There has been one or two dislodged moments over the years, but on the whole they have lasted well. Cutting accurate slots on the stainless tube could have been an option, but I think it would look 'bitty'. Besides I had another daft idea that could only work on a tube...

Curly Wurly

Wouldn't it be great to use a specially wound spring fitted snugly on the tube to act as frets. It would start off with a wide coil spacing and reduces each turn. Between frets 12 and 13, the coil distance would be half that between coil 0 (the nut?) and 1. I drafted out a spec, supplied the equations and sent it off to a couple of spring companies for a quote. 

The coil winding fboard approach had a couple of side effects:

1. the frets won't be conventionally straight (perpendicular to the neck), they will be angled

Dingwall guitars make basses with fan frets. I've never played one, but apparently they combine good tone with playability. As long as the frets under each string are accurate to a single scale length, it doesn't matter that an adjacent string has a different scale length. Using a coil spring for the frets should be exactly the same. To capitalise on the thicker-strings-needing-a-longer-scale concept, so I'll need to ensure the spring is wound in the right direction!

2. the frets will also be on the back of the neck

Mmm, I suppose they will, but I'm going to do it anyway

Meanwhile, the spring company replies came back. One wanted £250 + VAT just to develop a spring with no guarantees of success, the other just wished me good luck...

The sensible option here would be to make the design more conventional, cut nice perpendicular slots and glue individual pre-radiused frets in. So I decided to make a purpose built spring winder instead*. Boing said Zebedee!

*To be honest I did try winding a spring manually first just to see how difficult it was. Stainless steel likes to fight back so this prompted the spring winder to be pretty chunky. As can be seen from the pic, manually winding a spring results in a very irregular string spacing which is no use at all.

Useful info gleaned from this exercise was the diameter of the former on which the spring is wound. Empirical equations exist, but this application is a way outside the normal wire-diameter-to-spring-diameter ratio. Two or three trial attempts showed that with a former of 30mm, a finished spring ID of approx 49mm was produced which was ideal.

Tubular Bass

Making a bass out of a length of exhaust pipe is tricky to imagine in detail. The compromise between fboard radius and a tube that I could hold and potentially reach the strings was a bit of inspired guesswork. I eventually settled on a 1.2m length of 50mm diameter stainless steel pipe to be the basis of this creation. It has a 1.5mm wall thickness and weighs around 4kg. 

To get an idea of how it would perform under stress (probably much better than I do 😮), a piece of 25mm x 50mm (1mm thick) 1m steel box section was tried. A couple of strings were fastened to it and it was tuned up. Under tension, the box section did not bend or warp any measurable amount, so the stainless tube is expected to shrug off the string tension easily without even breaking a sweat. 

Incorporating the tuners was the next hurdle. The tuners have to be fitted on the outside of the tube so they can be adjusted. That implies that the strings will need to be inside at that point to wrap around the peg part of the tuners. A cutout will be required for the strings to pass through, with enough finger space to allow strings to be changed. Fellow band-mates will tell you that I only change strings once every 20 years, but they exaggerate. It's probably more like 17 or 18...

Creating an opening for the strings that can be made with an angle grinder is one thing, but working out how everything will fit was seriously testing my sketching and trigonometry skills. It was time to go down the 3D CAD route just to try and visualise the thing as a whole. After a bit of mouse-clicking I chose a package called FreeCAD which uses the make-a-2D-shape-and-extrude-it concept (amongst others). After running through a tutorial I was ready to do some virtual work.

The headstock cutout developed into two matched cutouts allowing string access from above and below. The large holes are where the tuners will be fitted. I'm not modelling the tuners in 3D CAD! The tuners will need some sort of flat-curved washer system so that they can be clamped either side of the tube. 

A round aluminium disc will be mounted inside the tube by the tuner cutout. Another offset disc functioning as an adjustable nut is fastened to this and will stick out of the cutout by a few mm to support the strings. 

I then turned my attention to some dodgy 3D bridge scribbles I made earlier.  

The bridge also requires a cutout and inspiration came from the whistles in Steamboat Willie. The strings are not wrapped around anything at the bridge end, so it can be a smaller opening.

The bridge is also based on a set of aluminium discs. The bridge takes more string load than the nut so two static discs, followed by three other offset, er, shapes to create anchor points and a saddle area. 

What about the pickups?

The cutouts are mostly filled with aluminium and are physically positioned at the ends of the strings. Introducing a third cutout to house a pickup was considered, but would introduce an unnecessary weak point in the middle of the tube as well as making it look too conventional! Having a set of split P-bass pickups sitting in the middle of the tubular bass would give its purpose away too quickly.

A small piezo pickup designed to go under an acoustic saddle is going to be used to convert strings into signals. The piezo device is around 50mm x 1mm x 3mm and is unlikely to add anything significant to the weight of the instrument 😉.

Well, that's the theory. It remains to be seen how much of this is successful...

Goodwood or Good Wood

Last year I went to a Basschat event. We turn up at a school that's borrowed for the day and it gives a chance to exchange ideas and drool over exotica that is beyond normal means. It's much like going to a car show, where I need to see the orange Lamborghini and study it from different angles, talk about how VW is the sensible option and then buy some fluffy dice and go home.

During the 2019 Basschat meeting we had a great guest speaker (Pete Stroud) who took some time explaining why he made his own guitars, and the attention to detail that makes the difference between a good bass and a great one. He is a very unassuming and competent chap, and it was interesting to hear his reasoning for various design decisions. 

One thing that Pete was quite certain on was the influence of the wood on the sound. Although other parts like pickups also affect the sound, over the years he had noticed that whilst certain woods gave excellent tonal quality, others did not.

I have heard similar anecdotal evidence over the years and I believe that choice of wood definitely has an effect, but I'm not convinced it is the main factor to a solid body bass. Unfortunately that got me thinking - what would a bass sound like without the magic sonic benefits of wood? I couldn't quite imagine a completely non-wood instrument at the time and decided it required some further consideration.

Re-thinking the basic operation of a stringed instrument, it mostly boils down to providing a structure that can support both ends of a piece of stretched string so that it can be struck and resonate at a known frequency. The structure needs to be sufficiently rigid so it does not 'suck-out' particular frequencies, which is where the wood could add its sonic flavour. After that, the rest is just adding convenience, ergonomics and a bit of window-dressing.

In a cross-sectional view of a conventional guitar neck, a D-shaped back is typically mated to a larger radius curved f-board. Both the front and back surfaces are curved. Arguably guitars are easier to play with a smaller f-board radius and seem unnatural when it is too flat. 

Inspiration came from daydreaming about orange Lamborghinis again. Round tubing is used for various chassis members, spaceframes and exhausts for cars and bikes as it has a good strength to weight ratio. Lengths of stainless steel pipe are readily available and could be used as a basis for a string support system. The tubing inherently offers a generous f-board radius as standard and a rounded back that should fit the hand nicely. 

The downsides? All standard hardware (tuners, nut, frets, bridge & pickups) are designed to fit on a conventional guitar that is predominantly flat. Each of these items will have to be tailored to suit life on a tubular bass. This has the greatest possibility of a completely different sonic signature - it may sound awesome, or terrible, or just plain average. I need to find out if wood is good or steel is surreal!