In the specifications article about the body that is ment as a simple introduction, I wrote that the body consists of a bundle of 18 wooden slats that are free to resonate and that these wood resonances give the tonal character. So, is this just a cosmetic gimmick, or is there more to it? How does it work?
The goal of the design of the body for this electric upright bass, is to get rid of the large surface and bulky volume of the body, but preserve the characteristic wood resonances that make up the timbre of the acoustic bass. As a designer I have chosen not to be free, but to commit myself to a translation of the acoustic upright bass to an electric bass. The upright bass is the source-reference and is already culturally defined. But this cultural definition is not objective, it is a ‘matter of taste’; instruments that are regarded high quality by expert musicians, are measured and compared to each other and to what is regarded low quality. The laboratory measurements on the instruments like material and shape measurements are objective, the opinions of expert musicians on the measured instruments are not. The starting point of the design is music, the endpoint is music, the part inbetween start and endpoint is my job as a designer and luthier: study of tradition, analysis, translation /design and production of a new instrument. When the instrument is finished – the endpoint for me - it is subjected to the cultural comparison.
Luckily, there is a ton of research available online, although it is mostly research on violins during past century that has layed the groundwork for current understanding of the tonal quality of upright basses. That doesn’t matter, I do not see any differences in the science and principles used between violins and upright basses.
Let’s start at the beginning. A question that is easily overlooked; ‘does it matter?’. Does it make sense to measure instruments, or does a professional player ‘automatically’ adjust the playing style to the instrument in order to change the tonal characteristics, so that an average instrument will sound statistically indistinguishable from an alleged ‘master grade’ instrument anyway? Is there really expertise to be gained, or is all this knowledge on ‘good’ instruments just as valid as the knowledge of a seasoned watcher of coin tosses who developed a ‘scientific method’ to predict the next toss?
The 1972 research paper Long-time-average-spectra applied to analysis of music by Erik Jansson and Johan Sundberg at the KTH Royal Institute of Technology in Stockholm may shed some light on this.
First of all, what amazes about this research is the impressive amount of work that went into it. Computers during these pioneering days of research, were no way near the capabilities we have now. To analyze the ‘long time sound’, a filterbank with 51 filters in parallel was used, where “The sampled output from every separate filter is quantized in steps of 1 dB and is added in a storage cell”. I wouldn’t be surprised if by the word ‘added’, they mean added mannually to the computer’s memory. Add to that, the software to analyse the filters’ data had to be tailored to the task. There was probably just one computer at the university.
Anyway, the research paper convincingly shows – among other things - that the resonant properties can be regarded as a fingerprint that can only very limited be altered by the playing style:
Nowadays, we have tools for spectrum analysis (free open source FFT like Audacity). You can simply select any digital sound recording, and this software tool will give you the long time average spectrum.
Note that the ‘fingerprint’ will be better when all notes (all frequencies, in KHz) are played with equal energy input; the graph then represents the energy output (in dB) of the instrument. To achieve this equal input researchers can use a hurdy gurdy-like ‘endless bow’.
Another important parameter for getting the spectrum shape is the resolution. In the research mentioned above that is from 1972, the spectrum analysis has a very low resolution of 51 filters. The shape is therefore not a good representation for the general features that were found in the years following this research when higher resolutions could be achieved. The current consensus on the shape of the long time average resonance spectrum of violin-like instruments looks something like this:
For now this graph may still look like just lot of spikes, but at the end of this article you will be able to read it.
A challenging way to look at graphs - any graph - is to imagine the line as the edge between two opposing 'forces'; there is something pushing the line up and something pushing the line down, the borderline where they meet, is the graph.
The spikes are where the measured value ‘volume’ is the least impeded, where the volume is allowed to spike. The spikes represent resonances. By definition, resonances occur where impedance is minimal.
These graphs are an abstract representation of resonances that occur in the instruments. The spike doesn't tell you what a resonance looks like, which is a pity because they form a hidden world of complex order we usually do not notice. I made a video to visually show resonance patterns that occur when you tap on a simple wooden plate.
The job of a luthier, in my case bass builder, is to tune the wooden plates towards specific resonance frequencies. These frequencies combined define the whole graph; the timbre of the instrument. The resonances are a response to the string that makes the body vibrate via the bridge. The combination of resonances of the body will determine if - for instance - the instrument sounds dark or bright.
More in general, the combination of resonances defines the sound; a metal plate sounds different from a wooden plate, they have different resonance spectrums. There are also differences between basses, the resonance spectrum plays a very important role in the sound quality of the instrument. Scientific research has identified several resonances that seem to be important for the sound quality of violin-like instruments. Next I will discuss the important partions of the resonance graph and their origin or funtion in defining the timbre. Be aware this is just a rough outline, there is much more to it, even a lifetime of study won't teach you enough.
The grey area is the lowest register which is rather broad. The area is flat; this is because the frequency is so low, that the elasticity of the body is so to say overruled by the mass dominated direct field.
A way to see this is to imagine trying to make the highest string (G) vibrate at the frequency of the low E string. The normal procedure to get a lower pitch while playing would be to lengthen the string, but that isn't possible here. The reason why you would want to lengthen the string is because the wavelength of the lower frequency is longer; the standing wave of the low E simply doesn’t fit in the G string (when tuned to G). This means the initial low E wave and the wave returning one from topnut and bridge cannot form a standing wave (= a resonance). The initial wave and the returning wave instead interfere to an average noise level, not a resonance.
Usually somewhere around 45-55Hz, the elasticity of the body starts to weigh in and the instrument starts to resonate. This is the first peak area in yellow, which for basses usually spans around 50-65Hz. It actually consists of two (or more) resonances that couple in phase.
Notice the body hardly resonates with the low E string frequency of 41Hz, which means the body hardly radiates sound at the 41Hz frequency. A miraculous feature of our brain is that it reconstructs, extrapolates the 41Hz base tone from the series of overtones (n x 41.2Hz => 82,4Hz 123.6Hz 164.8Hz 206Hz etc). This extrapolation is studied in the field of psycho acoustics, and lies beyond the scope of this article.
After the yellow bass area there are two spikes; blue and green. Influential researcher in violin family acoustics Carleen Hutchins related these two spikes to the cavity and the body resonance respectively; Erik Jansson called them P1 and P2. There is a lot of literature on the origin of these and other resonances and on the frequencies /volumes they apparently - or even ‘should’ - have. In the long time average spectrum analyses I did from bass recordings I found on the internet that I thought sounded good, the two spikes (blue and green) may differ a lot, and in honesty, sometimes there were no clear spikes to be found at all, while the recorded instrument itself sounded very good. I do not take the precise values of ‘good tone’ too seriously.
Right after the green spike there is the Dünnwald dip after Heinrich Dünnwald, this is a region of low volume – a negative V spike so to say, that is often, but not necessarilly present.
The last part is a wide bulge (orange arc), coined the bridgehill by Jim Woodhouse of the Cambridge University Engineering Department ( Bridgehill PDF), and later the bridge-body hill by Erik Jansson.
In the basses I measured, the top of this ‘hill’ lies around 500Hz-800Hz, which is somewehere in the 5th octave (= second octave above central C). It is in essence a flattened curve, a concept we are all familiar with since the Covid pandemic. A flattened curve is a potentially very strong resonance, if only it weren’t also very strongly damped. As the name bridgehill suggests, this strong damping has to do with the bridge.
In a conventional bridge, the upper part of the bridge has a rocking motion resonance, that hinges around the narrowest part of the bridge; this is the cause of the hill. On my bass, this narrow part of the bridge is formed by the two bridge-feet. The strings’ tension dampens the torsional resonance, which flattens the curve significantly.
On my bass the two bridge feet each rest on their own separate bar. This creates a tunable torsional resonance system consisting of the two bars, the bridge and the strings; the bridge has a sideways rocking motion, shifting the force between the two feet. The resonance frequency, the ‘top of the hill’ can be tuned by changing the distance between the bridgefeet and /or changing the mass of the bridge.
And to make it more complex, there is a second torsional resonance like this that is much lower in frequency, in acoustic basses this torsional spring system is formed by placing the bridge between the F-shaped openings. These openings weaken the top plate so the rocking motion becomes a very dominant path for the energy to dissipate.
This torsional resonance is far too low in frequency, it is also very strong and dominant. Actually it doesn’t even exist; the wood cannot hold the tension of the strings so if you build it like this, the top will very likely break, even while the topplate is already curved to make it stronger. A solution would be to make the topplate thicker, but that would also mean more mass that you need to set into motion, which leaves less energy for actual sound. Luckily there is a solution. In traditional lutherie there are two techniques to strengthen this part, without adding too much weight; the soundpost and the bassbar.
The soundpost is a bar that sits inside the bass body, clamped between top and backplate. If the soundpost were placed in the middle, centered under the bridge, there would be a minimum influence of the soundpost on the rocking motion (while it would give support). The more the soundpost is placed away from the center, the more this rocking frequency is altered. The tradition is to place the soundpost near the right bridgefoot (G-string side).
The bassbar is a long bar that is glued onto the inside the top plate, parallel to the length of the bass. The bar spreads the load and makes the topplate stiffer, which makes the resonant frequency higher (compare tuning a string, increasing the tension makes the string stiffer, so the resonant frequencies will be higher).
It gets more complex because the picture above is in 2d, which makes it look like the soundpost is in the same plane as the bridgefeet, which it isn’t. The real picture is like this:
The soundpost is the round stick that is clamped beween top and backplate. If the soundpost is placed directly under a bridge foot, it forces a node, which is somewhat comparable to the topnut or bridge-end of a string; if you pluck or bow a string closer to the bridge, you will excite relatively more high frequency resonances in the string; the string will sound brighter (or even harsh, when almost at the bridge). So placing the bridge that is essentially the driver of the topplate, directly on top of the soundpost, is not a good idea for efficiency and tone.
There are lots of paramaters to play with here. Although not quite true, a handy rule of thumb is that adding mass, has the same effect as removing stiffness. And of course it matters where you add or remove mass and stiffness.
The two resonant frequencies translated to my bass design:
The two bars of the top layer are clamped at the neck-side (red circles), and have an almost free end at the bottom at the tailpiece side. They can bend independently, which may result in torsional resonances. While one side moves up, the other may move down (this is not necessarily so, because there are many resonances acting on the system simultaniously, which could cause phases to align).
The role of the bridge-bodyhill in tone shaping can be compared to that of the singer’s formant that defines the timbre in a human voice.
Analytical research on the long time average frequency spectrum seems to suggests that you can simply take the pickup signal of an elecric bass guitar - say a Fender Jazz bass – and run it through a sophisticated graphic equalizer to get the sound of an acoustic upright bass. The catch is however, that you can spend energy only once…
For basses the effect of a resonating body – as opposed to a rigid and stiff body, is very obvious. Vibrating bodies consume energy, the louder they vibrate, the sooner the energy that is put in by plucking the string, runs out. Therefore, vibrant acoustic upright basses tend to have a much shorter lasting tone than stiff solidbody electric bass guitars.
The frequency spectrum itself also differs as the tone progresses in time. The low frequencies are dominant when the tone arises (‘boom’). When the tone settles, the higher frequencies become more apparent. As if the string’s tension squeezes the low frequencies with their big amplitudes out of the string.
This illustrates why simply adding a graphic equalizer set to the long time average resonance spectrum of an acoustic bass, to make a solidbody bass guitar sound like an acoustic upright bass, will not work. You need the energy distribution over tonal spectrum AND over time.
So far in a nutshell the analysis:
The long time average response shows that the body of a bass does not have a flat response, but instead resonates stronger at certain frequencies and weaker at others. The player has very limited influence on the resonance spectrum. There is a cultural consensus of what a (good) acoustic upright bass sounds like. Scientific research has identified several resonances that are important for the identification of violin-like instruments. It is my opinion – based on experience – that research on violins can be extrapolated to acoustic upright basses.
So the goal is a tuned resonating body, but the energy loss of the resonating body doesn’t need to be spent on setting air into motion. I also roughly know from analysis at which frequencies I want the body to resonate.
The conventional acoustic bass has all frequencies tuned into the voluminous body. If you want to lower a single frequency by shaving off some wood to make the plate more flexible and thinner, you may also change other frequencies unwillingly, and inevitably. It is like pulling on one node of a spider’s web, other nodes will move with it.
The idea of my body design, is to stack individual resonances, like when arranging a bouquet of flowers. It turned out to be a lot more complicated than just stacking resonators, but still this is basically the idea. The spectrum analyses above in the article are examples of so called Fourier transforms (after the French mathematician Jean-Baptiste Joseph Fourier (1768 –1830)). The Fourier transform is basically a mathematical method to analyse, to break down a complex waveform into its simplest building blocks; sinus waves. The analysis of a recorded sound will then give you a graph of the individual sinus frequencies and their loudness.
You might think that this was the main inspiration for this idea of stacking resonances, but the actual ‘Eureka’ came when I saw the viola d’amore. The viola d’amore is a violin-like instrument that has tunable sympathetic strings running through the neck. These strings are not played, but they will resonate sympathetically with strings that are played.
Because (the sympathetic) strings are very thin, they are not able to set a lot of air into motion by themselves; you can hardly hear them directly. That is why acoustic instruments often have large surfaced soundboards that couple easily with the strings vibration AND easily with air. Soundboxes are so to say mediators between string and air.
My very first experiment with sympathetic wooden resonators, back in januari 2002
Old model (2012-15) with 'resonator block'
Seen from the perspective I am interested in; since these sympathetic strings are themselves poor radiators of sound because of their small radiating surface compared to a soundbox, these strings are also poor ‘absorbers’ of sound coming from the speaker and amplifier. This is great news, because this means the small surface also significantly reduces feedback problems. The specific resonances I want the body to resonate with can be small surfaced wooden slats that do not need to couple with air. On the contrary even, easy coupling between wood and air should be avoided because it increases the chance of feedback problems.
So in origin, the idea-twist I made was to use a tunable wooden version of ‘sympathetic strings’ to get the sound of resonating wood in an electric upright bass. My first version of an electric upright bass with this idea was this bass with a ‘resonator block’, where the resonating layers are literally stacked on a soundpost-like extension of the bridge, which is very reminiscent of the bridge of a viola d’amore where the strings also rest on the bridge. I retracted the model for various reasons. As bassist Dave Swift (UK, Jools Holland), who tested this almost 9kg weighing bass put it; the sound is good, but it is too heavy and ‘too elaborate’, probably meaning it looks too complex. I agree.
The previous bass had a stiff and strong frame that held the resonator block. The body I have in the current design, does not have a constructional frame that holds resonators, the resonator is the construction. This makes the design a lot less ‘elaborate’ and it also provides a possibility to reduce the weight of the instrument.
By attaching the tailpiece to a aramid cable that runs through the body, all layers are driven. This cable, together with the carbon tubes that are clamped between the layers, are like a soundpost that connects top and back of an acoustic bass body. After stripping the skeleton and concentrating on the main idea of ‘stacking waves’, all pieces fell neatly into place.