Subject:Re: Why D and not F? Why 5-foot-8 and not 5-foot-10?From:"charles s. watson" <watson(at)INDIANA.EDU>Date:Tue, 8 Aug 1995 11:07:18 -0500I guess I was not clear at all. The convergence argument is statistically obvious (and correct)...why they converge on 293.66 Hz, rather than,say 298.3 or 292.1 (if in fact that is the case)? Chuck Watson On Tue, 8 Aug 1995, Daniel Levitin wrote: > >Dan Levitin's response does not answer Chuck Watson's question (in > >my understanding of it). Why "D" all over the continent rather than > >"F#"? Chuck's talking about the mean and Dan is talking about the > >variance about the mean. > > Why D and not F? Why 5-foot-8 and not 5-foot-10? > > Forgetting the airball chant for a moment (and ignoring the "height" > analogy, too) let's just assume that we measured the mean pitch of > everybody's speaking voice at a basketball game. Because the pitch of > a speaking voice pitch is a continuum, the distribution of these means > would approximate a normal distribution with some particular pitch as > the grand mean. There would be little variance with this large > sample. > > Whatever that mean speaking pitch was for the spectators at the > particular game we measured would represent the mean of some physical > property in humans (like height or weight). I see no reason a priori > to expect that this mean pitch would be different at different > basketball games. Of course, I'm assuming that a crowd in Boston is > just as representative a sample of Americans as a crowd in San > Francisco, insofar as the "speaking pitch" dimension is concerned, and > this admittedly is in potential conflict with Deutsch's findings of > regionalism in the tri-tone paradox. > > Would anybody in this group be surprised to find that the mean > speaking pitch of different samples of 10,000 spectators across the > U.S. is the same? My guess is that the pitch of the air ball chant is > correlated to this mean speaking pitch, and that in both cases we're > measuring a property of humans that is statistically stable and > normally distributed, just like measuring height, weight, or IQ. > > Similarly, to follow up on Hintzman's Height Hypothesis, would anybody > be surprised if the mean heights of spectators (sampled 10,000 at a > time) at different games around the US were the same? >

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