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The initial part of a violin, viola, or cello bow in modern models is always octogonal, but the rest of the stick can be either of round section or octogonal-faceted.

Is it simply a different external design, a different school of bow-making, or something more?

Are there reasons to select one or the other in term of sound production or control?

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A few years ago I asked this exact question to the archetier who made my bow.

According to him, bow weight and flexibility are the things to have in mind when having a bow built. These are the things that make a difference in a bow.

Now about it being round or octagonal, it was a purely aesthetic decision. The bow can be heavier or lighter, jumpy or stiff, and still be either round or octagonal. This question is in the same league as "should my bow have silver ornaments or some cheaper metal?" and "how detailed should the mother-of-pearl engraving be?". Purely aesthetic.

ADDENDUM:

Sure enough, I called my archetier and he confirmed that it's an aesthetic question. There are factors to have in mind that differ when building the bow, but the way it works is all the same. Mind you this answer comes from a guy who makes bows for a living, whose father made bows for a living before him and etc. Plus half the orchestra I work at uses his bows, so I guess it's a pretty reliable source.

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I hear you but I doubt that the choice between round and octagonal is purely esthetic, and in any case it cannot be put on the same level than decorative elements. It may not affect the sound (I want to know more and I have not seen hard evidence in one way or the other) but it certainly affects the build process and the tools used and, as it affects the shape of the stick, it cannot be easily dismissed as aesthetic without more references. Do you now a bowmake that would be willing to answer us here ? – ogerard May 13 '11 at 20:34
    
It was my bowmaker the one who told me what I said. Here's to settle it: I'll call him on Monday and ask again. It won't be the definitive answer but atleast it'll be the answer of someone who makes bows for a living. – Allan K. May 13 '11 at 23:13
    
+1 Straight from the horse's mouth, as it were. – Rein Henrichs May 17 '11 at 23:42
    
+1 Thanks for checking and reporting. I appreciate it. – ogerard May 18 '11 at 7:00
    
I'm a bowmaker and I can confirm that while there is theoretically a difference in stiffness between an octagonal and a round bow, the difference is so slight that it is not perceptible or measurable. And the construction techniques are basically the same, since the normal procedure is to make a stick octagonal first even if it's going to be round when finished. – Scott Wallace Mar 13 at 20:27

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