No, this is not about bourbon, though I enjoy a good mint julep.

There are again three tunings to discuss: the pure fifth of the harmonic series, the out-of-tune fifth that mars some poorly written music, and the equal tempered fifth.    Four tunings, or more, if we count older temperaments such as mean-tone.

The pure fifth of the harmonic series is very easy to hear, and variations from it also are readily apparent.   When a piano or organ tuner creates the temperament octave by ear, the tuner uses countable, audible beats, to create the slightly out of tune fifths that equal temperament requires. 

Then, the tuning of the pure fifth is that of the third harmonic and the tuning of the equal tempered fifth is two cents flatter.  The piano tuner who is building the temperament octave by ear, working from the C below middle C, seeks to detune, make narrower, the first fifth C-G so it sounds approximately a beat every two seconds.  The tuning is adjusted once four fifths have been tuned, by hearing the beats of the resulting major third, C-E.

The intonalism bad fifth is that between a lowered scale step and the raised scale step a fifth away.   It is 22 cents wider than it should be, and especially in choral music, results in what is called “comma drift”   The most common usage that gives this out of tune melodic fifth, and lowering of pitch,  is the apparently simple chord progression:  I IV ii V I.  If your chorus sings it four times, you will be a semitone flat.    Though the old theory books I’ve read don’t give this reason for it, they uniformly recommend that minor triad on the second scale step (ii) be used only in first inversion; this avoids the out of tune perfect fifth in the bass, and avoids the comma drift. 

Thomas Tallis, an organist, and a composer I don’t like, uses the ii in root position, and people wonder why they can’t sing the music without avoiding pitch drift!

In another post here I began a series of theory book example reviews, with the ii7 in root position criticized.