Assuming that subjects compared the residue pitches of the complex tones in the test trials, we estimated how much the relative contribution of the mistuned harmonic to the residue pitch (its weight) would need to change in order to produce the observed effect on d′. We assumed that d′ is a linear function of the difference in residue pitch (estimated F0), as Plack and Carlyon (1995) reported d′ for F0 discrimination to be roughly a linear function of F0 difference; a given proportional change in estimated F0, therefore, corresponds approximately to the same proportional change in d′. A linear relationship between frequency and d′ was also reported for pure tone frequency discrimination (Jesteadt and Sims 1975; Turner and Nelson 1982). The calculation of residue pitch for the present stimuli was based on Goldstein’s (1973) model, which assumes that the pitch of a harmonic complex tone can be estimated from the frequencies of the individual harmonics and that the weight of each harmonic is inversely proportional to the variance of the frequency estimate of that harmonic. Specifically, we used Eq. 6 of Gockel et al. (2007), which is based on Goldstein’s model and that specifies the change in the estimated F0 expressed as a proportion of the F0, i.e., the change in the residue pitch of a complex tone, that results from mistuning a single harmonic as:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{\overline{\varDelta F0}}{\mathrm{F}0}=\frac{P_j{j}^2}{\sigma_j^2}/\sum_{k=1}^N\frac{k^2}{\sigma_k^2} $$\end{document}ΔF0¯F0=Pjj2σj2/∑k=1Nk2σk2where P j is the frequency shift of harmonic j (with j = 3 or j = 4 here) as a proportion of the nominal frequency of the harmonic, N is the overall number of components that contribute to the F0 estimate, k is harmonic number, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sigma}_k^2 $$\end{document}σk2 is the variance associated with the frequency estimate of harmonic k. By changing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sigma}_j^2 $$\end{document}σj2 relative to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sigma}_k^2 $$\end{document}σk2 (for k ≠ j), the weight of the mistuned harmonic relative to the weights of the other harmonics is changed. Comparison of different values for N and relative weights showed that the change in estimated F0 produced by the frequency shift is roughly proportional to the weight of the shifted harmonic. In other words, a reduction in the weight of the mistuned harmonic by a factor of 2 reduces the pitch shift by roughly 50 %. Therefore, the effect of context on d′ that was observed here corresponds to a similar sized effect of context on the actual weights.