Julia Divan

Banjo Build and Acoustic Analysis

I built this banjo for my Music Instrument Engineering class in my senior year at Tufts. The neck and body are made of walnut and red oak respectively. The drum is a synthetic bongo head I integrated into the design.

The class goal was to build an instrument, perform acoustic analysis on it, and compose a piece with it. My banjo's acoustics were compared to two other student-made instruments and a professionally made instrument. All acoustic analysis was done using LabVIEW.

Table of Contents

This was a semester-long project that has a lot of content, please use this table of contents to navigate to relevant sections.

Final Design

Final Design vs. CAD Rendering

What spectrums am I using and why?

Comparison to the Tenor Ukulele

Comparison to Another Student Built Banjo

Comparison to Professionally Made Banjo

Final Design

Before starting this project I had never done any woodworking of this sort. I was intimidated by the level of precision I would need for a project like this. However, I went in with a strong vision and plan and this ended up being my favorite thing I made at Tufts.

Final Design vs. CAD Rendering

Fabrication Process

Making the Neck

no sound - Made with Clipchamp (1).mp4

The part of this build I was most intimidated by was the neck. This was the most complicated cut of the build. I spent a long time deciding what order to do the cuts in. Having already made CAD drawings of the neck was helpful because I was able to print them out to scale and use them as a guide when doing my initial cuts.

Walnut wood blank with my engineering drawings.

Neck after using the angle jig on the table saw.

The order of the cuts I was something I thought about a lot as I wanted to optimize the process. I decided to do them in this order:

Cut the Tenon joint at the base of the neck
- I had to make my own jig for the table saw to make the tenon joint safely.
Cut the side profile on the bandsaw.
Use the angle jig to cut the angles of the neck on the table saw
Use the bandsaw to cut out the headstock shape.
Use the spoke shave to do the majority of shaping and rounding on the neck.
File and rasp the fine details.

Close-up of spokeshaving (this is so satisfying to do)

Final Banjo Neck

While I was definitely very intimidated by this part of the build it ended up being my favorite part. It was so much fun. I loved seeing the shape emerge. I was able to tailor the dimensions of the neck to my hands and it feels perfect when I am playing it.

Making the Body

What is actually in the banjo body?

The body of the banjo comprises of 3 red oak layers. The layers are held together by walnut dowels and glue. There is a 7 1/4” bongo head embedded in the top layer that acts as the resonating body. I originally planned to CNC out both the top and bottom layer but decided it would be easier to do it by hand instead. I did end up CNCing the sun design on the back of the body. I also had to CNC out supports for the bongo head.

CAD renderings showing the different layers of the body.

The eight pieces make up the middle layer of the body.

I began by cutting 8 octagon pieces out using the miter saw set at a 22.5-degree angle. I then glued the pieces together and tied a tourniquet around it to make sure all the pieces were flush when drying. This is the middle layer of the body.

For the top and bottom layers, I cut the outer octagon using the bandsaw. For the top layer, I cut out the circle for the bongo head using the jigsaw and then fit it to the bongo head using a spindle sander to accommodate the slight angle on the bongo head.

Jigsaw-ing out the inner circle for the bongo head.

The three layers of the body are glued together and aligned with 10 dowels. I used the drill press to put holes in the body and neck for the dowels. My strategy was to always have 2 dowels in at a time to keep everything aligned. It was important that the neck was very flush to the body when drilling to ensure there were no gaps.

For the sun design on the back of the body I used the X-Carve CNC Router. I designed it in Onshape and created the gcode using the VCarve software.

Body of the banjo on the drill press.

Once I had all of the holes drilled and everything installed on the inside of the body I glued everything together.

Timelapse of the gluing and dowel setting process.

The Brass Tailpiece

I was unable to find a tailpiece that would fit onto my banjo body so I cut one out of some scrap brass using the waterjet. I then polished and bent it to the correct angle. I found that the holes for my strings were too sharp (I had a string snap at the tailpiece while tuning).

To correct for this I put heat shrink around the strings to prevent them getting cut. This has worked and I am able to keep it in tune well now.

Finishing Touches

To finish the banjo I sanded to 330 sandpaper and finished with Tried and True Polymerized Linseed Oil and Beeswax. I applied on coat following the recommendations on the can. I applied one coat.

Timelapse of me finishing the banjo.

Acoustic Analysis

Once my banjo was built I compared it to 2 other student-made instruments, a tenor banjo and another mountain banjo. For all of our sound collection data we used LabView to record and analyze the sound data.

What spectrums am I using and why?

We collected data using JTFA (Joint Time Frequency Analysis) and a Power Spectrum.

The JTFA we used is a Short Time Fourier Transform (STFT) which essentially breaks the signal into short sections and performs a Fourier Transform on each section. This allows for a time-localized frequency analysis and creates a spectrogram. A spectrogram plots time on the x-axis, frequency on the y-axis, and uses color to show the intensity.

This is useful because it gives a dynamic view of how the sound and frequencies of a signal evolve over time.

The power spectrum shows how the energy in the signal is distributed throughout the frequency range. Unlike the JTFA, it does not account for when these frequencies occur in time. This is done by doing a Fourier Transform on the entire signal to decompose it into it's constituent frequencies.

This is useful because it shows what frequencies in the signal have the most energy.

Comparison to the Tenor Ukulele

Goals of this Analysis:

Generate power spectrums and JTFA spectrums for 2 of the same notes on my banjo and on my partner's tenor ukulele.
Compare the generated spectrums of our 2 instruments.

The biggest difference in these spectrograms is the volume of the instrument. When comparing the spectrograms of the banjo to those of the uke there is noticeably more activity on the banjo spectrogram. This leads me to believe that the banjo has a louder and more sustained sound than the ukulele.

The power spectrums for these instruments are very similar when the same note is played.

Comparison to Another Student Built Banjo

Our question: How does the difference in drum materials affect the sound of our instruments? Is this difference consistent even when the bridge placement is varied?

Our hypothesis: Adrien’s banjo has a tighter drum. This will make it sound louder regardless of where the bridge is placed.

Experimentation and Results

We both took multiple JTFA and power spectrum measurements of the same notes at different bridge locations and compared them to each other.

Our hypothesis was correct. Regardless of where the bridge is placed, it is clear in these JTFA spectrums that the banjo with the tighter drum has more power. The standard bridge location has the most power for both of our banjos.

The placement in the middle of the drum is the quietest location for both of our banjos. This may have to do with where the nodes on the drumhead are.

Comparison to Professionally Made Banjo

Neither my partner nor I had access to professionally made versions of our instruments. I decided to find a JTFA spectrum online for a banjo and found a spectrum for the G4 string in this study, Acoustics of the banjo: measurements and sound synthesis. I rescaled the axes to directly compare the two.

These spectrums are similar in that they both have the highest concentrations at ~500 Hz. The biggest difference between these graphs is that the professional banjo seems to have a stronger sound for a longer amount of time. With my banjo the frequency being picked up dwindles significantly after 0.5 seconds. The traditional banjo has a strong frequency at ~500 Hz for the full 1.5 seconds.

Spectrogram of my banjo playing a G4.

Spectrogram of professionally made banjo playing a G4.

Why do I think these spectrums look so different?

Different drum material
- My banjo drum is a synthetic bongo head drum. The traditional banjo head is also synthetic but is not the exact same material.
Different drum diameter
- My drum is 7.25” in diameter whereas theirs is 11”. The larger diameter = larger resonating body = louder.
Resonator vs no resonator
- Their banjo has a resonator on the back which makes it significantly louder and therefore makes the notes last longer.
Different strings
- I have nylon strings on my banjo which are known to have a mellower, softer tone. The measured banjo has metal strings which tend to have a sharper sound.

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