Pear-shaped, flame-shaped

Satie's Trois Morceaux en forme de poire (1903 (with the opening movement, a 7th Gnossienne, dating to 1891 as a part of the incidental music to the play Le Fils des étoiles)), for piano, four hands, is a favorite piece with a favorite title.  But I've always found that title an awkward fit for the music, too comic, too awkward, silly even.  (Satie could do comic, awkward, and yes, silly, but that doesn't describe these pieces, even granting that the Trois Morceaux  is actually a suite framing its titular Three Pieces with two movements in advance and two following for a total of seven movements.) But I think it's likely that I've been fundamentally misunderstanding this.  How would you describe, in a single word, the shape of a (European) pear?  There's a perfectly good, if mostly forgotten, word for that shape: spelled either pyriform or piriform. (There is ambiguity about the etymology here, the former suggests a Latin root, pirum for pear, but the latter of which comes from the Greek πῦρ, flame.)  The image of a flame immediately suggests a character altogether different from that which we now associate with a pear-like form: a body in which most weight has drooped or dropped to its bottom, or even a event or action which has gone badly wrong. Gone South = Gone pear-shaped. But these pieces don't do that at all.  Could Satie have been referring more to the lithe and pyric pear, tapering in and up to the top, rather than the amply-bottomed, bulbous, pear, tapering out and down to the bottom? The progression of the three pieces at the center of this suite —   Lentement / En Leve / Brutal  (slowly/rising/brutal) — certainly suggest more of a flame than a bottom-heavy fruit.  A bit of research into pear history also tells us that the present premiership of the apple among orchard fruits is relatively recent and Satie would have come of age within the closing era of the regency of the pear, then thought more elegant and, as now, more delicate than its Rosaceae family cousin. The title of the Trois Morceaux en forme de poire  is aspirational not deprecating.