 Second, consider an argument that frequencies cannot capture the relational structure among the pitches. This is loosely analogous to the argument that physicalism about color fails to capture the relational structure of the hues—for instance, that red is more similar to orange than either is to green. In the case of pitch, psychoacoustics experiments show that perceived pitch does not map straightforwardly onto frequency. Though each unique pitch corresponds to a unique frequency (or small frequency range), the relations among apparent pitches do not match those among frequencies. In particular, equivalent pitch intervals do not correspond to equal frequency intervals. For example, the effect upon perceived pitch of a 100 hertz change in frequency varies dramatically across the frequency range. It is dramatic at low frequency and barely detectable at high frequency. Similarly, doubling frequency does not make for equivalent pitch intervals. A 1000 hertz tone must be tripled in frequency to produce the same increase in pitch as that produced by quadrupling the frequency of a 2000 hertz tone. Apparent pitch is a complex function of frequency; it is neither linear nor logarithmic (see, e.g., Hartmann 1997, ch 12, Gelfand 2004, ch 12, Zwicker and Fastl 2006, ch 5). Pitch scales that capture the psychoacoustic data assign equal magnitudes, commonly measured in units called mels, to equal pitch intervals. The mel scale of pitch thus is an extensive or numerical pitch scale, in contrast to the intensive frequency scale for pitch. The former, but not the latter, preserves ratios among pitches.