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Knowing the mathematical ratio of the root to it's Major 7th is of course far less important than knowing what they sound like, being able to hear the difference between a minor/major/diminished/augmented 7th, and knowing what effect using each has in getting to where you want to be.

The focus on this in these articles is missing the forest so you can focus on a single tree.

A lot of the ratios have not been fixed in time either, or can't be fixed correctly across all instruments.. the article doesn't get into that.



There's a simple reason for 15/8 being the major 7th. It's the 15th harmonic. The 15th harmonic is not changing anytime soon!




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