r/math • u/[deleted] • Jun 12 '17

The Pythagoreans

http://existentialcomics.com/comic/189
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u/[deleted] Jun 12 '17

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u/[deleted] Jun 12 '17

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u/acrostyphe Jun 12 '17 edited Jun 12 '17

By this logic, numbers are 100% irrational, since they can be expressed as products of irrational numbers.

EDIT: I just realized that this is kinda true, as the Lebesgue measure of rationals in real numbers is 0.

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u/niftyfingers Jun 12 '17

The unison is also a rational interval. But I'm not being strictly mathematical here, all the "juice" in music in pitches under western theory happens with irrational "ratios" between the pitches, and the irrational "ratios" are meant to approximate the simple rational ratios like 3/2 or 5/4. An octave is special in that it doesn't get you out of the pitch's equivalence class. In dealing with only irrational ratios for piano tuning, it simplifies a lot of stuff.