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9f56eef1 | 1 years ago (raw) | root | parent | reply | flag 
 @b4c50e1b 

Starting from ignorance on my part except for making junk guitars for a couple of years, it amuses me how simple things quickly are made complicated. I put only 4 marks on my fretboards ... halfway (Octave), 2/3 (perfect 5th), 3/4 (perfect 4th). The 4th mark equates to minor 3rd ... where the 3rd fret on a fretted guitar would be.

Thus the dreaded tritone sits happily between the perfect 4th and perfect 5th.
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John Carlos Baez | 1 years ago (raw) | root | parent | reply | flag 
 @8a3ca29f - things get really complicated!  In the Pythagorean scale here we get two different notes: the augmented 4th which is a bit lower than the tritone, and the diminished 5th which is a bit higher.  The augmented 4th is 

1024/729 ≈ 1.404664

the tritone is

√2 ≈ 1.414214

and the diminished 5th

729/512 ≈ 1.423828

I sure don't claim I can hear the difference!   But if two were played simultaneously they would sound out of tune.