Here's the definition by our brother in harmony Steve Morris:
| The barbershop 7th is used extensively outside of barbershop under other names. In music theory it is often called the
Harmonic 7th. It is also popular in blues or blues flavored music (where it is called the blue seventh.) It doesn't really work in
a tempered scale because the Harmonic 7th interval is essentially the minor 7th flatted almost a quarter tone which means it sits about half way between a major
6th and a minor 7th in a tempered scale. Which ever you pick you get dissonance and lack of resolution. It is generally approximated by adding a minor
seventh which makes it a dominant seventh or major-minor-seventh. Unlike the tempered versions of his chord a properly tuned Harmonic 7th has a very weak need to resolve; so much so that it is often used as the final resolving chord in place of the tonic. The Harmonic 7th is constructed by adding to the perfectly tuned major triad the lowest harmonic not already in the triad, in ratio notation: 4:5:6:7. That basically makes it the most consonant 4 note chord you can get. There is really no mystery about why the Harmonic 7th is so special. It is special in the same way that a major triad is itself special extended to 4 notes instead of 3. The only reason we all go gaga over it is that we never hear it in tempered scale music which is 95% of what we hear otherwise. Only in the just intonation of a cappella music or in string quartets or in the blues (which fixes the 7th by bending it on a guitar or harmonica) do you hear the true gelt Harmonic 7th the way God intended it. Another way of saying it is that a Harmonic 7th is simply what 4 singers with good ears will naturally sing when they are trying to make the closest harmony possible with 4 unique notes. Even though they are continually taking credit barbershoppers didn't invent it, they just re-discovered it. It is nice for us that they did but not particularly surprising. It would have been more surprising if they had missed it, sort of like if Columbus had missed America when he sailed West.
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