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To my basic understanding: In ancient Greek they were primarily using tetra-chords and there was three main standard divisions of these tetra-chords called genus.

In the same era Pythagoras discovers the relationship between intervals and ratios, 3:2 for a perfect fifth is an example. I've also read that the ancient Greeks used Pythagoras findings to help tune the tetra-chords since they spann a perfect fourth. However it got me wondering:

A) Did the ancient Greeks use Pythagoras findings to create the tetra-chord in the first place or did they just use it for tuning later on?

B) If Pythagoras did not have anything to do with the creation of tetra-chords, then who did?

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I'm no expert on ancient Greek music, but Pythagoras did not invent the three tetrachord genera. It does appear that his mathematical work heavily influenced others who defined ancient music theory.

https://en.wikipedia.org/wiki/Musical_system_of_ancient_Greece

Pythagoras was born in the 6th century BCE, and he was the first to work out ratios of string lengths that produced certain tonal intervals such as the "perfect fifth." The systema teleion, from the 5th century BCE, discussed tetrachords as they were understood at that time. Historians do not agree on who invented Pythagorean tuning. Ptolemy and Boethius, both famous historians in their day, actually attribute the tuning to Eratosthenes, not Pythagorus. (See: https://en.wikipedia.org/wiki/Pythagorean_tuning)

But it was Archyta, a Pythagorean disciple from the 4th century BCE, who defined the diatonic, chromatic, and enharmonic genera as we know them today.

Also indebted to Pythagoras were philosophers Aristoxenus and Cleonides -- contemporaries of Plato and Aristotle -- who wrote the first treatises on harmonics in the centuries that followed.

More info here:

https://www.ancient.eu/Greek_Music/

It's hard to say for sure, but it seems very likely that the many music schools that popped up in the 6th and 5th centuries BCE began to formulate music theory, and it's quite possible tetrachords go back centuries before that.

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    If you have a four-stringed lyre in your hand, it's pretty natural to tune it 8 9 10 12 or something similar, for maximum consonance. So yes, I too am willing to bet that tetrachords go way back. – Scott Wallace May 9 '18 at 8:03
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    @Ringo I dont think you're time-line might be correct. To my understanding Pythagoras was born and spent most of his life in the 6th century BC, so that before systema teleion had been elaborated in its entirety. +1 Otherwise a great answer considering its very hard to find facts from a ancient time! – Daniella Zättarlund May 9 '18 at 18:30
  • Right, I think I got my centuries reversed because of the BCE thing. I'll amend my answer. – Ringo May 9 '18 at 18:54

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