Stretch tuning

Sometimes, peals of bells are tuned with stretch, so that the nominals of the trebles are sharper than the musical scale would require by a quarter or a third of a semitone. Stretch tuning was common in peals of bells produced before the true-harmonic revolution in the late 1890s. Paul Taylor re-introduced the practice at the Taylor bellfoundry from the early 1950s and it continued until the late 1980s.

Virtual pitch theory, that the strike pitch or note of a bell is generated inside our ears or brain, provides a good explanation for this practice. The work I did for my PhD allowed quantification of the degree to which strike notes of bells are shifted by other partials, and the results agree well with stretch encountered in practice.

As an introduction, here is a demonstration taken from my 2019 talk on bell acoustics showing how the strike pitch of a bell changes when other partials change.

Here is an article examining the effect in detail, using the research results to predict the stretch tuning in a number of peals of bells.