Spectrographic analysis in lutherie is described. If you understand the harmonic nature of musical sound then you have everything you need to begin using audio spectroscopy in your lutherie investigations. A list of readily and inexpensively available components is provided, and three examples of the use of spectroscopy are presented. This is a reprint of an article that originally appeared in American Lutherie.
Last updated: September 11, 2018
[Originally published in American Lutherie #70, Summer 2002]
Copyright (c) 2001 by R.M. Mottola
Audio spectroscopy can be a useful tool in the design of stringed musical instruments. Differences in the structure and materials of sample instruments often result in differences in the tone of the instruments that are difficult to quantify. By showing differences in audio spectra over time, spectrograms can aid in the quantification of differences and help the designer understand the effect of structural changes.
This paper provides examples of spectrographic analyses performed as part of the development of an acoustic electric bass guitar. These examples give some idea of the types of analyses that can be made using audio spectrograms. The equipment used to make the analyses included a Personal Computer (PC) and readily and inexpensively available digital recording and spectrographic analysis software. The recording and analysis software are easy to use. The types of spectral analyses shown in the examples are readily available to any instrument maker with access to a PC.
Musical sounds are composed of a number of simultaneous tones. These tones are related in a harmonic series, with a fundamental (or first harmonic) at the pitch frequency, a second harmonic at double the frequency of the fundamental, a third harmonic at triple the frequency of the fundamental, etc. The characteristic sound of a sustained note played on an instrument capable of producing sustained notes, such as an organ, is the result of the relative intensities of the harmonics. Plucked string instruments are not capable of sustained notes. The volume of a note played on a guitar or other plucked instrument decays immediately following the initial attack. The characteristic sound of the decaying portion of a note played on a guitar is not only the result of the relative intensities of the harmonics that make up that note at any given instant, but also the way those relative intensities change over time, that is, while the note is decaying.
This is only the briefest summary of the harmonic nature of musical sounds. For more detailed information see either Music, Cognition, and Computerized Sound or The Physics of Musical Instruments. Both books have been favorably reviewed in previous editions of American Lutherie (#67 and #42, respectively).
An audio spectrogram is a display of changes in audio spectra over time. A spectrogram of a note played on a guitar will show not only the initial fundamental and its harmonics and their intensities, but it will also show how the intensities of the harmonics change while the note decays. A spectrogram provides a visual representation of the characteristic tone of an instrument. The ability to produce spectrograms can greatly enhance the ability of a designer and builder of instruments to understand what an instrument is doing harmonically. This in turn can aid in the design of instruments for specific sound characteristics. A typical spectrographic display is shown in figure 1. This is a one second (approximately) sample of an open A (A1, 55 Hz) played on a Fender Precision electric bass guitar.
There are two parts to the display. The top part above the line is an oscillographic representation of the sample. This is an amplitude over time display, and is probably the most familiar visual representation of sound. Although you can often get some idea of the fundamental frequency of the signal from such a representation, these are really most useful to visualize the envelope of the signal, or how the overall volume of the signal changes over time. As can be seen in the case of the electric bass, volume does not change much over time- there is a steady if slight decay. There is also an obvious low frequency vibrato at about 2 Hz, as can be seen by the slow rippling of the waveform.
The bottom part of the display is the spectrogram, which shows intensity at different frequencies over time. In this display, greyscale is used to denote amplitude at each frequency band, with white indicating zero amplitude (Note that halftone printing cannot show the subtle variations in grayscale seen in a black and white spectrographic display on a computer screen. Note further that most software provides for a color display.) Looking up any column indicates the relative intensities of the frequencies in the sample at a point in time. Looking at the display left to right shows how those intensities change over time. The harmonics can clearly be seen in the example- dark bands appear at 55 Hz (the fundamental), 110 Hz (2nd harmonic), 165 Hz (3rd harmonic), 220 Hz (4th harmonic), etc. It is apparent that the second harmonic is particularly strong. Also obvious from the spectrogram is that none of the lower harmonics decay very much over the course of the one second sample.
There are various dedicated pieces of hardware that can be used to perform spectral analysis, but these devices tend to be prohibitively expensive. For the purpose of analysis in the audio spectrum there are fortunately a number of excellent software packages which run on any standard PC equipped with a sound card.Most PCs built after about 1996 come with sound cards as standard features, and earlier models can be easily retrofitted. I made the experiments outlined here with a 1997 vintage bottom of the line Acer Aspire PC. If you already own a PC for other purposes the cost of materials for doing spectrographic analyses is minimal.
There are two basic steps to the analysis process- recording audio samples, and running spectrographic analysis on them. Thus two software packages are required- digital recording software and spectral analysis software.If you have outboard recording facilities that allow you to edit sample lengths and keep audio levels the same across samples, then only minimal digital recording facilities are needed. In fact the Sound Recorder program that comes with the Windows operating system is really all that is needed to convert the recordings into the .wav files needed for analysis. I don't have outboard recording equipment myself and so needed digital recording software that would provide basic editing, volume control, and VU meter function. The package I used for the examples is Total Recorder 3.0 by High Criteria Inc. A fully functional version can be downloaded free from their website at http://www.HighCriteria.com.
For spectrographic analysis the software I used is Spectrogram Ver 6.0 from Visualization Software LLC. This program was originally written by Richard Horne for his personal use in the analysis of bird songs, but it has grown to be an extremely versatile package.
The electric basses were recorded directly, plugged right in to the PC's sound card input jack. The upright bass was recorded in a living room using a standard vocal microphone (Shure SM 57).
There is a mystique surrounding the process of recording musical instruments, with visions of expensive recording studios and equipment dancing in the heads of folks who are not trained recording engineers. We amateurs can take heart in the fact that a number of the most notable experiments in violin acoustics were performed in an ordinary living room, as perusal of almost any issue of the Catgut Acoustical Society Journal will show. There are a number of easy-to-read books on the subject of home recording which can help demystify the process. Samples recorded in the same acoustic environment (i.e., the same room) and with the same equipment and technique will contain the same acoustic artifacts. Perfectly good recordings can be obtained in a quiet, reasonably well damped room (rugs, drapes, upholstery) with some care taken to diffuse the effects of parallel surfaces (furniture in corners, etc.).
The analysis examples presented will make more sense with a little background on what I was hoping to accomplish with this project. As mentioned I had performed this work in the context of the development of an acoustic electric bass guitar. Such instruments are a fairly common subclass of bass guitars, and generally have acoustic or semi-acoustic bodies, piezoelectric pickups, and onboard preamp circuitry. My "Mezzaluna" bass is typical of the type, which tend to sound more "acoustic-y" than solid body electric basses. It is a long-term goal of mine to produce such an instrument with a tone similar enough to that of an upright bass played pizzicato that it can serve as a reasonable substitute for that unwieldy instrument in the musical styles for which it is normally used.
The starting point in this effort was a listening comparison between the Fender Precision bass, considered by most to be the "standard" electric bass, and an upright bass. Although the differences are pretty obvious to the ear, my attempts at quantitative descriptions of those differences fell far short of what would be required as the basis of a re-engineering effort. The upright sounds a little more "bassy" and has less sustain, but that was about the extent of my description of the difference in tone. I hoped that comparison of spectrograms from the two instruments would show what was going on harmonically and quantify some of the perceived differences in tone.
Figure 2 shows a spectrogram for an upright bass prepared for comparison with that of the Fender bass shown in figure 1. Again, this is a one second sample of a note played on the open A string. By comparison the upright decays dramatically after about 0.1 seconds, particularly in the upper harmonics. The upper harmonics are also much weaker in the upright- harmonics above about 660 Hz decay dramatically following the initial attack, while there are noticeable harmonics up to about 1320 Hz in the Fender bass.
With more quantified information about the differences in the tone of these two instruments I could conduct some experiments with the aim of giving my own acoustic electric bass a voice more like that of the upright.
The first thing I looked at was strings. There is certainly a lot of marketing hype about strings, as the ads in any bass or guitar magazine will attest. My informal experience with strings is that, given similar construction and materials, they all sound pretty much the same, or at least similar enough so that it is not worth spending any time trying new brands. That being the case I generally use whatever brands are readily available at a decent price. In the evaluation of a previously built acoustic bass guitar I had wondered if that instrument would be improved by the addition of strings that were constructed more like those typically found on uprights (at least those used primarily for jazz). So my interest was piqued by an ad for flatwound bass guitar strings from company X which claimed that their strings were constructed more like upright jazz strings. The ad further enticed me by claiming that these strings had a more upright-like tone.
Fortunately I had built more than one instrument so it was easy to string one up with the brand X strings and another with a different brand of inexpensive flatwound bass strings from company Y. On a listening comparison they sounded pretty much the same.Since there is really no such thing as identical instruments (and since all my comparisons so far have been made of the open A strings) I next put the A strings from the two brands of strings on the same instrument. Now I had the two differently constructed A strings on the same bass, and they still both sounded pretty much the same. Figure 3 shows the spectrogram of the open A played on the brand X string, while figure 4 shows that for the brand Y string.
The spectrograms confirm what the ear didn't hear- the two samples are pretty much the same. The sample of the brand Y string does show a little more intensity in the frequencies above 1000 Hz in the first 0.1 second or so. The brand Y string also shows more damping in the 630 to 1000 Hz range. Although this was not a comprehensive analysis, there is enough information here to conclude that it would be difficult to make a case for the marketing claims of the brand X string based on the comparison of the spectrograms of these samples.
Another experiment I wanted to try involved mechanical damping of the strings. It is generally accepted that the first practical electric bass was invented in the early 1950's by Leo Fender, and produced by the company bearing his name (see Jim Roberts' excellent book How the Fender Bass Changed the World for more on the history of this instrument). It is not likely that an instrument which deviated greatly in tone from the upright would have gained acceptance, and it is clear that Mr. Fender made some attempt to attain upright-like tone in the early Precision basses by including a foam rubber "mute" inside the bridge cover of the instrument. Modern session bass players often will make use of an analog of such a mute when attempting to emulate the sound of an older electric bass. It was a simple experiment to see what effect such a mute would have on the sound of my bass.
A piece of soft foam rubber approximately 4" x 1.25" x 0.625" was positioned between the body and the strings approximately 4" from the bridge. The sound was distinctly more damped in tone than that of an unmodified instrument. Not quite upright tone, but a step in the right direction. The spectrogram (figure 5) showed that the mute did in fact alter the sound so it had some of the characteristics of that of the upright. The upper harmonics are well damped as is the case with the upright, but the damping curve is not the same. The second harmonic (110 Hz) is hardly damped in the upright but well damped in the muted electric bass.
Further experiments indicated that the damping quality imposed by the mute changes dramatically as the instrument is played in the higher positions, and results in a quite unusable tone anywhere above the second position. This, and the uncharacteristic damping even in the first position conspire to make this kind of mechanical muting of fairly limited utility.
A grand tradition among researchers is to claim that experiments that failed to achieve the desired results are still successes, because the results increase knowledge about the problem domain. Such claims can be made about the simple experiments outlined above. Although no useful modifications were made to my instruments as a result of these experiments, I did learn a little about how some modifications do (and do not) effect the tone of the instruments.
The examples presented should provide some idea of the utility of spectrographic analysis in the development of musical instruments. Rarely do changes made to the structure of an instrument yield a change in the sound of the instrument that can be considered obviously superior. It is often maddeningly difficult to ascertain just what changed in the tone after structural changes are made to the instrument. Audio spectroscopy can aid in the identification and quantification of subtle and not so subtle changes, and thus help the luthier to understand how mechanical changes to the instrument affect tone. The tools to do this are cheap, readily available, and within the technical reach of most instrument makers.