What is the origin of the term perfect fifth and how does it relate to the length of a string and, specifically, the length of a guitar string.

I crudely measured my guitar string and found that the "perfect fifth" fret is about 1/4th the length of the entire string. At 1/2 length we hear from the octave up (fret 12).



Perfect fifths is a frequency ration of 1.5 (2:3), as compared the temperate 5th which is a frequency ration of 2^(7/12) = 1.4983. (Two to the power of 7 12th).

The perfect fifth happens exactly at one third of a string length. All harmonics of the string are related to integer fractions of the string length, which is the same as integer multiples of the fundamental frequency (open string). Temperate tuning splits the octave in 12 equal parts.

This is related to the difference of temperate tuning and harmonic tuning

  • Note: "tempered", not "temperate". – Caleb Hines Sep 25 '15 at 18:57

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