If the text relates directly to the barbershop tradition, you could use:
dominanta septymowa charakterystyczna dla stylu rewelersów (which is a white lie, see the explanation below)

If you wish to be more precise, less understood -> dominanta septymowa w stylu "barbershop".

However, if only possible, I would leave it as "dominanta septymowa" and not go into any more details.

Why?

First and foremost, the cultural difference is too large. I wouldn't count on anyone apart from specialists to understand the difference between "dominant seventh" and "barbershop seventh". If you refer to "chór rewelersów", it is just the closest thing you can get to a barbershop quartet, but not the same, when we go down to technical details.

The most important part is that "chór rewelersów" in Poland has usually been a professional group trained in European classical music, therefore they sung in strictly tempered scale. "Barbershop seventh" is a chord derived from African-American tradition, and is untempered - the legendary "sweetness" of the chord is derived from equal proportions between the frequencies of the chord notes, which you cannot achieve if you strictly abide by the tempered scale. If not for this, it would be just "dominanta septymowa". Just a handful of experts here would understand the difference between the dominant seventh and the "angel's voice", so your translation this way or another would be at least slightly off the mark, unless you go into a lengthy explanation - which not many people would understand anyway, given that the male quartet a capella singing is not very popular in Poland.

The more precise academic version would be "czterodźwięk durowy z septymą zmniejszoną", but this is strictly technical (read as: sounds awkward) and most people educated in music would perfectly understand what you mean by "dominanta septymowa" and simultaneously you would avoid boring your readers to tears.

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Note added at 1 day14 hrs (2013-04-02 05:50:14 GMT) Post-grading
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Cieszę się, że mogłem pomóc - w razie czego chętnie znów pomogę, tyle że na ProZ wchodzę okazjonalnie i pewnie nie zawsze wyłapię pytania, ale są tu na pewno inni specjaliści, którzy przejmą pałeczkę. Pozdrawiam!