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Your guideline for Earth objects that may be in existence in Eorzea is did this exist by the 18th century? The race naming conventions based in Earth cultures make repeated reference to this time period, and while the technology and cultural development isn't a 1:1 analogy, it's a good frame of reference to go by.
So, in order:
• Guitar-like instruments have been around for a very long time, and instruments known as "[adjective] guitars" were recorded in the 11th century. They were known simply as "guitar" by the 14th.
• The violin was invented in the same time period as the cello (16th century), and we have cellos, so it's safe to assume we have violins (and violas) too.
• Harpsichord were the predecessors of the fortepiano (which in turn was the predecessor of the modern piano), and harpsichords exist in XIV (they're a housing item). The invention of the fortepiano was made at the beginning of the 18th century, which is the very tail end of time period XIV draws its inspiration from. If the fortepiano exists, it's probably considered by the people of Eorzea to be a very modern instrument - and things like upright pianos almost certainly haven't been invented yet.
• "Edo-era Japan" is the keyword for Doman culture in XIV, so look at when the specific instruments you're thinking of were invented. If it was during (or before) the Edo period, it probably exists. If it was after, it probably doesn't.
So, in order:
• Guitar-like instruments have been around for a very long time, and instruments known as "[adjective] guitars" were recorded in the 11th century. They were known simply as "guitar" by the 14th.
• The violin was invented in the same time period as the cello (16th century), and we have cellos, so it's safe to assume we have violins (and violas) too.
• Harpsichord were the predecessors of the fortepiano (which in turn was the predecessor of the modern piano), and harpsichords exist in XIV (they're a housing item). The invention of the fortepiano was made at the beginning of the 18th century, which is the very tail end of time period XIV draws its inspiration from. If the fortepiano exists, it's probably considered by the people of Eorzea to be a very modern instrument - and things like upright pianos almost certainly haven't been invented yet.
• "Edo-era Japan" is the keyword for Doman culture in XIV, so look at when the specific instruments you're thinking of were invented. If it was during (or before) the Edo period, it probably exists. If it was after, it probably doesn't.