What is a “vertical scale” in a discussion of intonation contours?

Question

In Ladd, D. R., & Morton, R. (1997), the authors write:

It is customary to think of an intonation contour as having a linguistically distinctive shape or pattern and an independently variable pitch range. In a one-word English utterance, we may have any one of a handful of distinctive contour shapes— signalling that the contour is, for example, a question or a statement—and any of these shapes may be realized with more or less any pitch range or ‘‘vertical scale’’

Later, they clarify what they mean by "vertical scale":

But even in the case of pitch range effects that convey some kind of linguistic meaning, such as different degrees of emphasis, it still seems appropriate to distinguish them from the shape of the contour, and to treat them as orthogonal (as the ‘‘vertical scale’’ metaphor suggests).

But what am I to understand by "vertical scale", exactly? The f0 height with which an intonation contour is realized?

CITED 1. Ladd, D. R., & Morton, R. (1997). The perception of intonational emphasis: continuous or categorical? Journal of Phonetics.

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Answer 1

An 'intonation contour' graphs f0 vs time (and ignores power). The relation of avg f0 in an utterance, compared to the speakers avg f0 over a longer interval, gives information about emphasis or emotion. The relative changes in f0 during the utterance give information about syntax (question, etc). Since the relative changes are independent of avg f0, they may be considered as a separate graph, (orthogonal to the absolute f0 graph,) with the base and range 'normalized'. Only the normalized 'shape' of the contour affects syntax. 'Vertical scale' is meaningful only with the absolute graph -- with the relative contour it is arbitrary (normalized).