Courses:PHYS341/2021/Project12

fig.1: The flexatone.

Flexatone

The flexatone is a percussion instrument (an idiophone of indefinite pitch) that is famous for it's comedic glissando sound.

This page is an introduction to the instrument that is the flexatone, as well a report of my investigation into a playing individual notes with a flexatone.

Introduction

fig2: Instructions on how to play the Flex-a-tone correctly, by the Playatone Company.

History

The flexatone is a rather modern instrument. Although we do not have any record of who exactly invented the flexatone, the flexatone was first patented in 1922 in the Britain, then in 1924, Playatone Co. patented the ‘Flex-a-tone’ in the USA, which marketed it as an instrument that would “make Jazz jazzier” (fig.2). Sporting an extremely unique sound texture, it is most often used as a comedic effect in movies rather than in a more musical or orchestral setting, as it is harder to produce a particular specific pitch. However, there are pieces that call specifically for flexatones, such as Arnold Schoenberg's Variations for Ochesctsra, Op.31 (1926-1928) or Fugue for Percussion by Lou Harrison (1941) .

Structure

fig.3: An example of how to hold the flexatone.

The flexatone has a small flexible metal sheet fastened at the top to a wire frame which ends in a handle. On either side of the metal sheet, wooden mallets are attached by thin strips of metal at the bottom of the metal sheet. The metal sheet is most often made of aluminium and is curved downwards from where it is attached to the frame and is bent away from the main part of the sheet (fig.1).

Playing the Flexatone

The most common technique when playing the flexatone is a tremolo. This is achieved by holding the handle in one hand while placing the thumb on the end of the metal sheet, and shaking the entire instrument up and down (fig.3). By pushing down on the sheet with the thumb and creating a curvature in the metal sheet, it is possible to raise the pitch. It is very hard to produce a singular particular pitch since the difference in thumb pressure that would lead to different pitches are very subtle.

Other ways of producing sound on a flexatone include blocking the wooden beaters and striking the metal sheet with a different beater or bowing it, much like the musical saw.

The Physics

fig.4: A man playing a musical saw in front of a statue of a man playing a musical saw.

The full acoustical physics of a flexatone are extremely complicated. Here is a rather basic version, heavily based on the physics of an instrument that relies on the same physical principles, the musical saw.

The musical saw is, like you would imagine, a saw, that was used as an instrument in folk music for many centuries. Traditionally they would be normal saws with teeth, but modern musical saws are teeth-less and made specifically for the sake of playing. The saw's handle is often clamped between the knees or feet with the player sitting down, while the other end (often fitted with a handle) is used to bend the saw into a S-curve. Then the saw is bowed with any bow of a string instrument to create a sound (fig.4)

Metal sheets, much like other metal plates are a two-dimensional vibrating systems, which can be either free, fixed, or hinged at any of their four sides. They possess modes (the areas that are act as nodes at depending how the plane is bound) that are often illustrated with sand placed on the sheet which gathers at the nodes, creating a visible pattern. Also, unlike with strings, the tension within the system comes from the internal strength of the metal itself, rather than from an external force.

The flexatone is a rectangular metal plate that is free at one end and fixed at one end, however the bending of the sheet creates new areas that are bound, which act like a fixed end. By curving the metal sheet, it will vary the tension on the sheet, and creates areas of stress. These areas of stress will reflect the waves that are coming at it from an area of lower tension. This creates a confined vibrational pattern. Similar to the musical saw, the metal sheet portion of the flexatone is able to vibrate freely despite the dampening by the hand and the fastened end, thanks to this internal reflection of the transverse waves that arises when the curvature of the sheet exceeds a critical value.

The musical saw is often played using a bow like string instruments and with the same principles as the strings in a string instrument acting upon it, which will drive the oscillations in the metal sheet. Although it is most definitely possible to bow a flexatone, most commonly it utilizes the mallets that are attached to it, which means that the sound that is produced is closer to a noise rather than a musical note, as it dies out relatively fast.

Investigation

It is often seen to not be able to play a specific notes on the flexatone in a way that will allow the percussionist to play the same note at any given time. This is mostly due to the metal sheet's extreme sensitivity to pressure and the limitations of human control over such subtle changes of pressure. As a percussionist in high school, I have come across a piece of music that had notes that the composer had wanted the flexatone to play. No matter how hard I tried, I failed to be able to play the notes that were written. This has sparked my interest as to whether it is possible to create a method for more accurately being able to play certain notes and therefore a recognizable tune on the flexatone.

With the method of changing the pitch being a rather simple motion of applying pressure on to the end of the metal sheet in a single direction, I initially thought that I would be able to figure out an equation or a way to calculate the distance between the handle and the metal sheet, through some sort of calculation, and would then proceed to prove my calculations to be correct or incorrect by testing it out on an actual flexatone.

fig.5: My device to measure the distance between the handle and the metal sheet.

Unfortunately, as I had researched for a couple of months on the mechanics and physics behind the flexatone, I ran into a couple of obstacles:

1. There is not as much research done specifically on the acoustics of the flexatone. Although the books and articles that had to do with the physics of percussive instruments always included the physics behind metal plates, they were most always the bells, gong, or cymbals.The flexatone would barely every be mentioned, and on the rare occasion that it did, it was more of a brief mentioning of it's construction and would not delve any deeper. They just never used the flexatone as a case that they should study.
2. As an Asian Languages and Culture major, the materials that I was able to find that explained the physics of these idiophones were hard to comprehend. They would most always include complex equations that involved more letters than numbers. I honestly did try to make sense of the principles, yet as I kept trying, it was apparent that calculating the exact distance before testing out my calculations would be way too complicated and advanced for that to be accomplished.

Therefore I decided to change my approach. I decided to create some sort of device (that is rather poorly made) that the flexatone will be able to be placed on top of, which will be able to provide a more concrete visual aid to see the distance between the handle and the metal sheet when producing a specific pitch. This in turn would provide specific distances that would need to achieved to roughly be able to repeatedly replay the same pitch with the flexatone.

fig.6: A spectrum graph of a recording of the flexatone at the distance of 12cm. (Focus on the device)

fig.7: A spectrum graph of a recording of the flexatone at the distance of 12cm. (Focus on the graph)

I attached a ruler perpendicularly to a piece of wood that I would then be able to attach the flexatone to (fig.5). As can be seen in Figure 5, the handle was my 0 value, and when in it's resting position the metal sheet measured to be 12 cm from the handle. Before beginning, I bent the wooden mallets that are on the flexatone farther out, so that they would not accidentally touch the metal sheet and cause extra sound. After securing the flexatone to my device, I used my finger to lower the metal sheet 1 mm at a time and struck the metal sheet on the outside with a plastic mallet. While doing so, I recorded the sound at each millimeter using Audacity (fig.6 and fig.7). From these spectrum graphs I was able to pick out the most frequency with the largest amplitude. Continuing this process for every millimeter, I then had a list of the average frequencies produced at each millimeter. With this list, I then compared it to a list of the frequencies of each note for an equal-tempered scale (A4=440Hz) and found the distances that had the closest frequencies to them:

Distance in cm (Handle = 0)	Average Frequency Produced (Hz)	Equivalent Pitch	Frequency of the pitch in the equal-tempered scale (Hz)
12.0	1235	D#6/Eb6	1244.51
11.5	1300	E6	1318.51
11.1	1399	F6	1396.91
10.7	1466	F#6/Gb6	1479.98
10.3	1577	G6	1567.98
10.0	1650	G#6/Ab6	1661.22
9.8	1758	A6	1760.00
9.3	1868	A#6/Bb6	1864.66
8.9	1963	B6	1975.53
8.7	2058	C7	2093.00
8.5	2174	C#7/Db7	2217.46
8.3	2386	D7	2349.32
8.2	2494	D#7/Eb7	2489.02
7.7	2606	E7	2637.02

With the distances for each note figured out, I tried to see if this would allow me to play a melody with separate distinct notes.

So, here is my attempt at playing "Hot Cross Buns" on the flexatone: