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grouchymusicologist comments on A discarded review of 'Godel, Escher Bach: an Eternal Golden Braid' - Less Wrong

6 Post author: lukeprog 16 December 2011 05:51AM

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Comment author: grouchymusicologist 16 December 2011 02:43:36PM 4 points [-]

Complete traversals of a set of whole-tone-related keys are incredibly rare in music this early; I don't know of another example and would not be that surprised if one doesn't exist. You're right that such a piece seems easy in principle, but that's from a current viewpoint. So I think that Hofstadter may in part be implicitly relying on some knowledge of the early-eighteenth-century context when he stresses how unusual the piece is.

(There is actually also a technical reason why this loop is so strange -- it has to do with what music theorists call "crossing the enharmonic seam" -- but Hofstadter doesn't appear to be referring to that.)

Comment author: tingram 16 December 2011 03:33:25PM *  0 points [-]

It is a neat trick, and not something that happens often, but I would guess that's because it's not useful as anything other than a neat trick. I'm not seeing the eternal golden braid in it, is all.

Actually, if Bach had kept the pattern intact without "crossing the enharmonic seam" it wouldn't be much of a loop at all; the piece would end up in B# minor after six repetitions.

(edit: sp.)

Comment author: grouchymusicologist 16 December 2011 04:24:19PM 0 points [-]

Yeah, I'm in agreement with you and others that it isn't the most compelling example he could have chosen.

As to the enharmonic seam thing, that is indeed the point: you either have to cross the enharmonic seam by spelling two identical-sounding intervals differently (in this case, one of the major seconds has to be spelled as a diminished third) or else you have to deny the seeming aural fact of octave equivalence by spelling the return of C as B-sharp. Since composers are extremely reluctant to do the latter, they have no choice but to do the former -- a commonplace in the nineteenth century, a bit of a special trick in the mid-eighteenth.