Using Inharmonic Strings in Musical Instruments Kevin Hobby, 1 William A. Sethares, 2 and Zhenyu Zhang 2 1 Synchratron, 645 S. Englewood Ave., Evansville Indiana 47714 USA, synchratron@gmail.com 2 Department of Electrical and Computer Engineering, University of Wisconsin – Madison, WI sethares@wisc.edu and zzhang546@wisc.edu Abstract. Uniform strings have a harmonic sound; nonuniform strings have an inharmonic sound. This paper experiments with musical instruments based on nonuniform/inharmonic strings. Given a precise description of the string, its spec- trum can be calculated using standard techniques. Dissonance curves are used to motivate specific choices of spectrum. A particular inharmonic string consisting of three segments (two equal unwound segments surrounding a thicker wound portion) is used in the construction of the hyperpiano. A second experiment de- signs a string with overtones that lie on steps of the 10-tone equal tempered scale. The strings are sampled, and digital (software) versions of the instruments are made available along with a call for composers interested in writing for these new instruments. 1 Ideal and non-ideal Strings An ideal string vibrates in a periodic fashion and the overtones of the spectrum are located at exact multiples of the fundamental period, as required by the one-dimensional linear wave equation [6]. When the string deviates from uniformity, the overtones depart from the harmonic relationship and the sound becomes inharmonic. There is only one way to be uniform, but there are many ways to be nonuniform; there is only one way to be harmonic, but many ways to be inharmonic. In a “prepared piano,” weights and other objects are placed in contact with the string, giving it a nonuniform density and a sound that can be described as bell-like, metallic, or gong-like. Such preparations tend to lack detailed control. Our recent work [4] ex- plores one possible musical instrument and system, the hyperpiano, which is based on a particular inharmonic string consisting of three connected components. The design approach is illustrated in Fig. 1(a) where a nonuniform string is conceptualized as con- sisting of a sequence of connected segments, each of which is uniform. By carefully controlling the string segments, a large variety of inharmonic effects may be achieved. The invention of new musical instruments and ways to tune and play them has a long history [2], [12] and continues to the present, though modern approaches are often based on digital rather than analog sound production [11]. From an acoustical point of view, the idea of designing an instrument based on an inharmonic sound contrasts with the more common approach of beginning with an inharmonic vibrating element and trying to make it more harmonic.