Abstract Rayleigh's theory for the effects of end-support motion on the modal frequencies of a vibrating string has been elaborated so as to incorporate some of the complex mechanical impedance conditions likely to operate at the pianoforte bass bridge. The notion has been put forward that the bass bridge, and the main vibrating portion of the soundboard, may be treated as independent mass systems mutually coupled and restrained by local compliances. Theoretical analysis of such dual mass combinations reveals double-peaked susceptance characteristics which may be predicted to impose progressive flattening in frequency of successive string modal vibrations within a specified range. The phenomenon may usefully serve to oppose a portion of the undesirable inharmonicity arising from finite string stiffness, thereby improving tonal performance, and it offers some rational justification for the adoption of “extended” bass bridges. The hypothesis has been tested on a short-stringed grand piano. Attachment of two suitable masses, one rigidly to the bass bridge and the other flexibly coupled to the soundboard, encourages a substantial subjective tonal improvement in the bass registers. The optimal size of these masses proved unexpectedly large; reasonable agreement can be reported between theoretically predicted and experimentally determined mass values. By taking account of the interaction of masses and compliances operating in association with the bass bridge, the hypothesis could partly explain the wide differences in tonal quality which may be encountered between various well-constructed pianos of comparable size.