# Fourier Analysis of varying classical guitar bracings

I am doing a school project right now concerning studying the Fourier Analysis of a sound recording of a few different classical guitars. I am wondering what type of sounds would be the best to record. I'm recording just some basic pitches right now that I know have overtones on the guitar. I have a full audio recording studio at my school with digital software that I am using. My question is what would be the most ideal type of sound recordings to look at on the Fourier Transform? What should I physically play on the guitar and record to suit my needs? Any information would be appreciated and helpful!

This can be a rather complex process. If you want to infer something about the geometry and materials of the bracings and the quality of the tone produced you had better make sure you have all the guitars in the exact same set up in the lab and that the microphone or other device is mounted at the same location relative to the guitar.

The acoustic field emanating from the instrument not only depends on the bracing and strings but on the things like the size and shape of the sound hole. The hole, and body too, will create a spatially dependent lobe pattern for the sound. There will be peaks and dead spots in certain directions. The guitar does not emit sound equally in all directions. So if you don't mic them all identically you may conclude that a 50\$ Yamaha has "better" sound than a 5000\$ Ramirez.

The bracing will also affect the decay time of the notes produced and the time evolution of the frequency content of the notes. If that is your interest then I'd mic them all at boresight (i.e. mic pointing perpendicular to the plane of the sound hole opening) keeping in mind that mics may have directional properties as well. Then you capture sound for enough time to hear the attack, sustain, and decay (could be 60sec or more). When you FFT you don't just want to FFT the entire chunk of data but do a sliding window that is maybe a 10th of a second (or some other "intelligent" choice), and FFT each window. You will need to do some sig proc tricks to avoid or dampen artifacts on the data cutting etc. But this should give you an idea of the time evolution of the sound and that is really key to understanding the quality of an instrument.

Lastly, are you interested in the sound or the plate vibration? If you are interested in how the bracing affects the mechanical vibrations then you may not learn as much from the acoustic field (since there are other factors to consider like room temperature and humidity when the experiment is performed) as from measuring the vibrational modes of top of the guitar. This is a much more complicated experiment but you could do it with very small accelerometers or other probes attached to the top. This would likely damage the guitars in the process.

Lastly, if measuring the acoustic sound you want to make sure you attack the string the exact same way for each guitar. You could do it by hand, or set up a simple machine to do it for you but the frequency content of the sound will depend on, among other things, where along the length of the string you pluck it. So, again, if you pluck each guitar at a different place the experiment will not mean much.

• Most of the ideas are all totally spot on for recording a lot of things. I think the last para. is so important. By hand will negate any of the other parameters, so setting up a mechanical plucker is paramount. Not only the same spot on the string - not so easy with different scale guitars - but also the amount of attack (of the pick), otherwise the decay , and other factors, won't have the same meaning. +1. – Tim Sep 11 '19 at 10:28
• Just to add to your observation about consistent attack: plucking at the same location on guitars of differing scale lengths will mean plucking at distances from the bridges that are in the same ratio with respect the the individual scale lengths. – ex nihilo Sep 11 '19 at 13:22
• I am interested in the sound of the guitar. I really want to look at the quality of tone production that the different guitars produce. They each have tonal qualities that they are "supposed" to have from the certain type of bracing/soundboard construction so I am trying to see why this guitar has perhaps a bolder sound or a crispier sound than the traditional guitar. I do have my experiment set up as exactly as I can for each guitar every time and have kept everything as identical as possible in terms of procedure. Thank you so much for this it is most helpful! – Silvio-Antonio Zallo Sep 12 '19 at 13:50
• You may want to consider several types of experiments to help isolate different effects. Too much to discuss in comments. But I'd direct your attention to any book by Fletcher and Rossing. These guys have been leaders in musical acoustics and mechanics of instruments for decades. Some of their texts are advanced engineering level texts, but several and also written to explain things to musicians. – ggcg Sep 12 '19 at 14:16

There are basically three different vibrating structures in a guitar (or any other stringed instrument). The first is the strings themselves, and second is the body of the instrument, and the third is the air inside the instrument, which is affected by the volume of the guitar and the area of the sound hole.

If you simply record "notes played on the instrument" you are capturing the combined effect of all three systems at once.

Since two guitars will never have identical strings, it is a good idea to eliminate them from what you are measuring.

If you want to study the construction of the guitar body, I would damp the vibration of the strings completely, for example by inserting a cloth between the strings and the fingerboard. Don't remove the strings, because their tension will have an effect on how the guitar body vibrates.

Then, a standard technique to measure the response of the body is to excite it by tapping it. The obvious place to do that is at the bridge, which is where the vibrations of the strings get transferred into the body. You will probably also get some insight by tapping it at other places, for example in the center of the back.

The sound of a tap will quickly die away, but the interesting features would be any resonant peaks in the frequency spectrum, and the time it takes to decay, which measures you how resonant the guitar body is.

That measurement technique will be affected by the resonance of the air inside the guitar body, which has a significant effect on "colouring" the sound. You might want to repeat the experiment with the sound hole blocked, again using something like a cloth which will damp out the air vibrations in and out of the sound hole.

You probably won't have access to the facilities to do this, but the best way to completely eliminate the air response would be to test the guitar in a vacuum chamber. Then, you could be sure you really are measuring the effect of the mechanical design, and not something else. Of course you can't record the "sound" of a guitar in a vacuum, but you can attach transducers to the body to measure how it vibrates.

• I was worried about this problem seeing as I could not get identical guitars in the process without having to pay thousands of dollars. I was able to get two guitars with the same strings and soundboard material however. I really want to study how the sound comes out. I am getting a digital recording of some open strings and maybe I will do tapping next time on the bridge. I am interested in the construction but I don't think I have the resources to dig that deep into the guitar. I have a mute that can dampen the strings. I will try that next and see what it does for the data! Thank you! – Silvio-Antonio Zallo Sep 12 '19 at 13:56

If what you need to do is then compare the different Fourier transforms corresponding to the different guitars, I'd go with an open string. There you would clearly see the fundamental note and all further harmonics, with the strength of each one. If you play more than a note, you'll have overlapped information.

It occurs to me that you could record, say, a third, first each note separately, and then both notes so that you hear the interval, and analyze the corresponding Fourier transforms.

All this is a little vague, though, because I don't know what exactly what the objective of the subject is. Maybe if you explain some more, me or someone else could expand on the possibilities!

Hope this helps!