Uniform strings have a harmonic sound; non-uniform strings have an inharmonic sound. Given a precise description of a non-uniform string, its inharmonic spectrum can be calculated using standard techniques. This paper addresses the inverse problem: given a desired/specified spectrum, how can string parameters be chosen so as to achieve that specification? The design method casts the inverse problem in an optimization framework that can be solved using iterative techniques, and experiments show that viable solutions are often possible despite the multi-modal character of the cost function. Three properties of inharmonic strings are studied: their behavior under changes in tension, changes in density, and changes in length. These are important to the use of the inharmonic strings in musical instruments where it is often desirable that a set of strings has consistent timbre (spectrum) over many different pitches. Several different strings are designed: one that has partials derived from the golden ratio φ, one with overtones that beat with each other, and a family of strings designed for performance in n-tone equal temperament. An Online Supplement for this article contains details of these string designs for all n from 7 to 20 and can be accessed at http://dx.doi.org/10.1080/17459737.2018.1491649. Several of the strings have been constructed, and the predicted frequencies of the overtones are verified by direct measurement.

均匀的琴弦发出和声；不均匀的琴弦会发出不和谐的声音。给定不均匀弦的精确描述，可以使用标准技术来计算其不谐谱。本文解决了一个反问题：给定所需/指定的频谱，如何选择字符串参数以达到该规格？该设计方法将逆问题置于可使用迭代技术解决的优化框架中，并且实验表明，尽管成本函数具有多峰特性，但可行的解决方案仍然是可行的。研究了非谐波琴弦的三个特性：它们在张力变化，密度变化和长度变化下的行为。这些对于在乐器中使用非谐波弦非常重要，在这种情况下，通常希望一组弦在许多不同的音高上具有一致的音色（频谱）。设计了几种不同的弦：一种具有从黄金分割率得出的偏音的弦φ，其泛音相互跳动，以及一串旨在以n音相等的气质演奏的弦。本文的在线增补包含从7到20的所有n的这些字符串设计的详细信息，可以从http://dx.doi.org/10.1080/17459737.2018.1491649访问。已经构造了几个琴弦，并且通过直接测量来验证泛音的预测频率。