For most of the common expressions, sayings, and idioms, finding where they originated exactly is nearly impossible. Usually what's provided is around the oldest time a phrase was recorded in a book, poem, or play. Sometimes, there will be an early printed use of a phrase in an old newspaper, which will often be quoted to give you an approximate age for the saying.
However, it should be noted that if a particular idiom is being used in a form of media, like a newspaper, then it's likely already a commonly known phrase, thus, it should be assumed that the phrase origins are probably from an older time.
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* I was worried Jake might get ill when we went on a trip to Hawaii, but after returning home a week later, he's still as fit as a fiddle.
* Jane's healthy diet, frequent exercising, and good overall hygiene all contribute to her being as fit like a fiddle.
Fiddles typically refer to stringed musical instruments, such as the violin. As with most
musical instruments, violens require frequent cleaning and maintainence to remain in
For example, violin strings must be replaced if they are broken, tiny pegs need to be kept tightened, and the bridge should be positioned properly for optimal sound output. Additionally, to prevent dust buildup, the violin needs to be cleaned every so often. This all contributes to the instrument's health; it keeps the instrument in a playable condition. One might even describe the violin as being healthy, or fit.
Thus, because musical tools are often kept in a state of good health, it would appear that a person's health began being directly compared with that of their instruments. A person could be in fit condition, just like their fiddle. I'm not entirely sure why the fiddle was chosen over other musical instruments; perhaps it has something to do with how common the instrument was at the time the phrase originated.
The modern version of this phrase is recorded in a book entitled English-men for my Money, written in the year 1616 by Haughton William. Towards the end of the book, it reads:
"This is excellent ynfayth, as fit as a fiddle."
Reference: archive.org contained the digital copy of the book containing the phrase in the quote above.