My journey for this project started about a year ago. I had picked up a ukulele as a new instrument to learn in my free time. I had a desire to do some kind novel project outside of work and decided I was going to find some new, unique way of recording the vibrations from a stringed instrument. If I could find some strange, non-traditional method, I might even be able to affect the dynamics of the string's vibrations to create a new sound. Transducers with highly non-linear responses, for example, would enable this.
This accelerometer project though, is a bit of a compromise and is effectively my third concept iteration on the target described above. Though I didn't realize it at the time of coming up with my first prototype of this iteration, I have since found that the idea is not original and has already been applied by several people. Most notably, I found that a few people at Analog Devices, who make several of these analog-output MEMS accelerometers, wrote a paper on the subject. Furthermore, this method is a very close cousin of contact piezo microphones that already exist on the market.
I want to talk briefly about the first two concepts because I do think they are interesting and I may want to revisit them someday.
Concept 1 : Optical Fiber Pickup
The idea behind this concept was to replace the strings with optical fiber and then feed them with spectrally narrow-ish-band (LED, not laser) light in CW mode. With notches then cut into the fiber somewhere between the bridge and the fretboard, I was hoping to be able to cause some of the light to exit TIR and transmit down towards the body of the ukulele. By then placing an array of 4 photo-diodes below the strings, I would have the option to either produce a poly-phonic output or a single analog output via a summing amplifier. If I could get the output beam to be sufficiently narrow/low-divergence, then string vibrations should create a proportional, variable irradiance incident upon the photodiode.
Some of the inherent limitations I ran into with this idea include:
- In the prototypes I made, I was unable to create the right type of notch that would cause enough of light to exit TIR in a controlled beam down towards the photodiodes.
- The notch making process I employed was very crude and purely experimental though. Maybe some real optical engineering and some iterative ray-tracing simulations could lead to an optimal notch shape that would allow enough out-coupling efficiency to exit to get a reasonable signal.
- In general, the available plastic optical fiber that I found is not rated for the string tensions required by the soprano ukulele. If the required frequency or required string length is reduced though, the required tension can decrease enough. The required tension increases with the square of the fundamental frequency and linearly with the length. Something like a bass guitar would be more apt for this.
Some other downsides include:
- Even the cheapest LED fiber-coupled transmitters I could find are both bulky and expensive.
- I was unable to figure out how to robustly constrain the transmitter end of the fiber mechanically. The aforementioned transmitter holds the fiber in place via a friction fit with a plastic lock nut. This was definitely not strong enough for the required string tensions.
- To prevent noise from the ambient light from destroying the signal or even saturating the sensor, optical filtering material would be needed to enclose the section of the bridge with the sensors. The most straightforward way would be to use some black material to block the entire spectrum, but a a cooler (and more expensive way) might be to use some kind of material that attenuates only the spectrum being transmitted through the fiber. For example, if a UV light source was used, then plexi-glass could be used since it acts as a longpass filter with a cutoff wavelength near the blue-light to UV-light transition zone.
Concept 2 : Capacitive Pickup
The idea here was to use metal strings sandwiched between two conductive plates. This would form a capacitive voltage divider via the capacitance from the upper plate to the string and the capacitance from the string to the lower plate. By feeding voltage divider with carrier signal (say, somewhere between 100kHz and 1MHz), I was hoping to create an amplitude-modulated waveform by plucking the string. If the string position changes relative to the two fixed plates, then the envelope of the carrier at the output of the voltage divider should as well. Demodulating this output (multiply by a reference carrier) would then allow you to recover the low-frequency audio signal. I was able to confirm that this works in PSPICE with some rudimentary simulations involving signal-controlled capacitor simulation blocks. This is fairly similar to the electric reed organs from the early 1930s that also use electro-static pickups to measure the position signal of vibrating metal reeds.
Some of the inherent limitations I ran into with this idea include:
- The effective capacitance between the plates and the string in the proof-of-concept that I built was somewhere between 100fF and 1pF. This is a huge problem because there are many stray capacitances in the system that far exceed this value. For example, on a breadboard, the capacitance between a two contacts in a signal row is about 5pF. All the extra parallel parasitic capacitance between ground and the live contact ends up destroying the dynamic range of the voltage divider.
- The plates and wires in my proof-of-concept very easily picked up 60Hz signal from the mains. There is probably a way to get around this via some sort of differential design, but I did not pursue it in earnest.
Concept 3 : Accelerometer Pickup
This is the final concept I landed on and is what this hackaday project page is based around. I wanted to simplify and implement something that I would have high confidence in. Since acoustic instruments have large chambers designed to resonate, sensing the accelerations of the outside surface of an acoustic instrument should provide a signal that is proportional to the forces/pressures imparted by the acoustic energy emitted by the strings. This is very unlike an electric guitar, which senses string velocity, and the above concepts 1 & 2, which sense string position. Piezo contact pickups sense the acoustic forces/pressures directly, but their frequency response is not very flat.
One might think then, that this concept fails the original targets/goals that I described at the start of this log; the accelerometer likely won't have any interesting non-linear effects that will fundamentally change the sound of the ukulele. However, there are two things which I hope will pan out into a more interesting study:
The first is that the analog MEMS accelerometers on the market typically output three channels corresponding to three orthogonal directions. Could the relative differences between the outputs of each of these channels encode something interesting worth hearing? Would it be possible to infer the two orthogonal polarization directions of a string vibrating in 3D and is there something interesting, audibly speaking, about the two different polarization states of a vibrating string?
The second is that various ways of mounting of the accelerometer to the instrument might induce different audible effects. For example, could introducing some strange material between the sensor and the body of the instrument create some interesting effects? Furthermore, could slower accelerations that aren't caused by the string's vibration (e.g. instrument movement during playing) create some interesting bass features?
Perhaps the two above items are wishful thinking. In the end though, I really just want to build something and put the design files on the internet.