![]() ![]() Also shown are the two movable bridges, which simulate the nut and saddle of a guitar, the spring-loaded device used to press on the string at different positions, and the digital tuner used to measure sound frequencies. Our tabletop apparatus composed of a sonometer and a guitar fingerboard, with twenty metallic frets. Where X 0 is the (open) string length, or scale length, mentioned above and X i is the position of the i-th fret, asįigure 1. The frets are placed according to a precise mathematical relation: A “guitar outline” is also superimposed on this figure, to illustrate how our apparatus can simulate the functionality of a real guitar. ![]() These two bridges will simulate the “nut” and the “saddle” of a guitar, as shown in Figure 1. It is important to know the scale length of the fingerboard (or fretboard) being used, i.e., the correct string length for which the fingerboard was designed (usually between 640 - 660 mm for a classical guitar) and to set the distance between the two sonometer bridges accordingly. Figure 1 shows our experimental apparatus composed of the PASCO sonometer to which we added part of a classical guitar fingerboard, complete with twenty metallic frets, placed right under the steel string. ![]() Experimental Apparatus and the Intonation ProblemĪ conventional (monochord) sonometer, such as the PASCO WA-9613 or similar, can be used to simulate a (single string) guitar, with the addition of a fingerboard which can be easily obtained from a local luthier or through a music shop. In Section 3 we will outline a simple compensation procedure, which is very effective in correcting the intonation problem, as it will be shown in Section 4, which discusses our experimental results.Ģ. In the next section we will describe our experimental apparatus and the mathematical foundations of the intonation problem. In this paper we present a simplified approach to the problem, which is more suitable to be used as an in-class demonstration, or as a laboratory activity, to simulate how musical notes are produced on a guitar. In a recently published paper we described mathematical and physical models to be used for a more scientific approach to this problem, resulting in a complex “compensation” procedure which is very effective in improving the intonation of this type of instruments. It is then related to the correct placement of the “frets” on the “fingerboard” which enable the instrument to produce all the different notes, but it is further complicated by other subtle effects, which are usually dealt with in an empirical way by luthiers and guitar manufacturers. This problem is more complex than what might appear at first it obviously begins with the correct tuning of the “open” strings of the instrument to the desired notes, which can be easily accomplished with the help of a digital tuner. In particular, we will show in this paper how to simulate a guitar using a conventional sonometer, in relation to the problem of the instrument intonation, i.e., how to obtain correctly tuned notes on a guitar or similar string instruments. The physics principles involved in most musical instruments can be easily demonstrated with standard laboratory equipment and can become part of lecture or lab activities. Musical acoustics is an interesting sub-field of physics which is usually able to engage students in a dual perspective, by combining science and art together. The experimental procedures presented in this study can become a more structured laboratory activity to be used in general physics courses or acoustics classes. In particular, we use this modified apparatus in relation to the problem of the instrument intonation, i.e., how to obtain correctly tuned notes on these string instruments. In this paper we present a simple way to convert a conventional sonometer into a simulated fretted instrument, such as a guitar or similar, by adding a fingerboard to the sonometer. Keywords: Acoustics Musical Acoustics Guitar Sonometer Intonation Compensation Department of Physics, Loyola Marymount University, Los Angeles, USAĮmail: Februrevised Maaccepted March 9, 2012 ![]()
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