>Two non-internet friends are having an argument which the geniuses 
>on this list should be able to put to rest.  (I'm not a theory 
>guru.) Is there a name for for a major chord built on the flat 7th? 
>Example:  Bb D F in CM.  Thanks all.  Shel

The *name* of the chord is simply Bb Major (the respondent who called 
it something else misunderstood your question). In traditional theory 
its *function* is designated either VII (as opposed to viio, the 
diminished chord built on the unflatted seventh), or V of III if it 
behaves as a secondary dominant--but all of this only in the minor.

The frequent appearance of this chord in the major mode in pop music 
reflects the fact that most such music does not really fall into the 
traditional major or minor modes at all, but into the Dorian or 
Mixolydian, both of which have the seventh degree lowered and in 
which a major triad would be built on that note as a matter of course.

Traditional theory does allow for the borrowing of chords across 
modes, so you could still call it VII or V of III, with the unspoken 
understanding that either you are in Dorian or Mixolydian mode, or 
that (more conservatively) you have borrowed this chord (and the 
implied major III as well) from the minor.
-- 
Andrew Stiller
Kallisti Music Press

http://www.kallistimusic.com

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