www.alphadictionary.com

I was trying to translate "quarter note" in music to Russian, and I ended up having to do it by way of the word
crotchet
.

It made me wonder if there is any relationship between the following:
crotchet
crotchety
and of course, the infamous word "crotch".

Well, I do not know if any derive from any of the others...
...it might be the case that a crotch also refers to a hook shape, so really in that sense, I would think that an eighth note sort of fits that spec a little better, but 1/8 note has a different formal name. I guess I could envision hook relating to somebody's crotch 8-0 {male, that is , or at least one would most likely think "male", 8-| }

Otherwise, I cannot see any overt rationale.

Yep, they're all hooked together.

Courtesy of etymonline.com:

crotch
1530s, original meaning "pitchfork," from O.N.Fr. croche "shepherd's crook," var. of croc "hook" (see crochet); meaning "region where the body forks" is 1590s.

Ok, good. At least "region where the body forks/'hooks", in a way" makes more sense than my lurid interpretation.
Thanks.

By the way, why would a quarter-note in Russian have anything to do with crochet? Wouldn't it just be some form of chetvyortaya chast'?

Correct. However, upon lookup to find the Russian term in my dictionar[y/ies], the ones I used had neither an entry for "quarter note" per se, nor a melded entry like "~ note/quarter ~" under "quarter/note".

I knew the Russian word for "one-quarter" and I knew the Russian word for "note". But I have learned that is not always sufficient to know for translation; there can often be a totally different term. In fact, many times if I try to merge such words together, the famous phrase I get back is "Н-у-у, можно сквзать, но никогда не говорят в [России/Минске/Ялте...]. So after awhile I QUIT making simple assumptions about concatenating English terms together and thinking it would be correct.

Consequently, I had to look in my music book to find a synonym, if any, for "quarter note"...and there it was, "crotchet". So I looked up crotchet in my English-Russian dictionary, and at that point, I could see the translation you indicated.

Now I see my mistake. It's crotchet, not crochet. Conferring with a musician of my acquaintance I learned that crotchet is a British term for the quarter note. The term probably formed prior to our generally recognized notational system, so it's quite odd nowadays, at least to American ears.