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The Greek diacritics were introduced by Aristophanes of Byzantium, which became standard in the Middle Ages. My question is: Is the accent (tone) system of Ancient Greek which we are using now a result of linguistic reconstruction, or it is mainly based on historical references such as the descriptions of ancient grammarians or other sources? The characteristics of different tones might be described by natural language, but how about the position of these accents ? Are there fixed rules to accent words in ancient Greek ?
As for the last part of your question:
Ancient Greek indeed had some rules of accentuation, despite the fact that the position and type of it was not always possible to be determined on phonetic basis (as in e.g. Vedic Sanskrit and contrary to Latin).
Greek had some ground rules concerning accent placement, for example the stress was allowed to be placed only on one of the three last syllables, two syllables if the last vowel was long. There was a two-way accent contour constrast but only on long vowels.If the stressed vowel was long, an the following was short, then accent could be either rising or rising-falling. If the following vowel was also long, the the accent had to be rising. These are just some rules, and there some exceptions. The accentuation on finite verb forms was recessive, i.e. the stress went as far "left" as it could, so it was predictable. The accentuation of non finite verb forms and noun on the other hand was not predictable and lexically defined.
My question is: Is the accent (tone) system of Ancient Greek which we are using now a result of linguistic reconstruction, or it is mainly based on historical references such as the descriptions of ancient grammarians or other sources?