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Your puzzle is solving a nested analogy, where the goal is to find the word that fills in the final blank, based on the answer to the analogy in parentheses.

An example:

sky:blue::(bird:worm::cow:____):____

In this case, the answer to the part in parentheses is "grass", which makes the whole thing:

sky:blue::grass:____

So, the final answer is green.

Now, for the puzzle you must solve (which is not as straightforward as the example):

wing:horn::(toodle-oo:hour::oboe:____):____

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  • $\begingroup$ This is my first question on this site, so if anyone has any advice on formatting, difficulty, or the question itself, please let me know. Also, if it is too hard (I'm not really sure how difficult it will be for people on this site), just let me know, and I can provide more hints. $\endgroup$ – Bonhomme Jan 29 '17 at 4:17
  • $\begingroup$ No need to include a hint immediately. The premise is interesting, though. $\endgroup$ – greenturtle3141 Jan 29 '17 at 4:26
  • $\begingroup$ Okay, I've removed the hint for now, and I'll put it back later if necessary. $\endgroup$ – Bonhomme Jan 29 '17 at 4:38
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    $\begingroup$ @Bonhomme For future reference, people can see revision history $\endgroup$ – boboquack Jan 29 '17 at 4:45
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Also working from Gareth's partial answer of

wing:horn :: wood:____

I think he was on the right track of

another cross-language connection using the strong key of wing:horn = flugelhorn. Building on wood = Holz, there's a German stringed instrument called a scheitholz; Scheit translates into "log" (or "piece," "chip," etc). However, it's a little strange that this name would reverse the clue's word order (i.e. to log:wood rather than wood:log). Digging deeper, there's also a holztrompete that's admittedly pretty obscure, but has some nice coincidences: word order is maintained, and an English cognate makes up its second half, much like flugelhorn. More subjectively, the wiki page mentions oboes (seen in the original clue); even more subjectively, I play the trumpet.

As such, I'd guess the answer is

wing:horn :: wood:trumpet

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    $\begingroup$ Could very well be right. (I was just thinking the other day "hmm, I should revisit this one and do an exhaustive search for musical instruments whose German name begins with Holz". Looks like I should have done it :-).) $\endgroup$ – Gareth McCaughan Feb 8 '17 at 23:30
  • $\begingroup$ Admittedly, I had a different answer in mind, but this actually fits better than my answer, so I'm accepting it. $\endgroup$ – Bonhomme Aug 14 '18 at 15:31
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Partial answer

It's conjectured that

"toodle-oo" is a corruption of French "tout à l'heure".

Accordingly,

since "oboe" = "haut bois", the inner analogy must yield "wood".

So now we have

wing:horn :: wood:____

but I'm feeling dim and failing to see what that yields. Perhaps

it's another cross-language thing? E.g., I think a wing in German is a Flügel and there is a musical instrument called a flugelhorn; but wood in german is Holz and all that leads me to is that woodwind in German is Holzblas, which would yield an answer of "blow". But that's, well, not terribly convincing.

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  • $\begingroup$ You're right about the part in parentheses, but as you suspected, the final conjecture about Holzbas is not correct. Keep it up, you are very close! $\endgroup$ – Bonhomme Jan 29 '17 at 16:38
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Using Gareth answer we have

wing:horn :: wood:____

The relationship can be

wings have feathers made of keratin (horn)

Answer:

Cellulose (wood is made of cellulose)

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