4:5:6:7 in Authentic Cadence

Somebody asked:
> I may be mistaken here, but I think that authentic cadences aren't
> terribly common in barbershop style.
>
> Gary,what is an "authentic cadence" ?

I started to answer that question with a series of dreadful textbookish
definitions, but the answer would almost certainly clearer by example.

In the key of C major, an authentic cadence is the chord progression from the
chord GBDF to CEG. In C minor, it would be GBDF to CEbG.

That is as opposed to a plagal cadence (for example) which in C major is FAC
to CEG, or FAbC to CEbG in C minor. Or as opposed to (probably) the most common
form of deceptive cadence: GBDF to ACE.

Obviously you can transpose those progressions into whatever key you'd like.

That progression (the authentic cadence) is extremely common in Western music
as a whole, but I seem to recall - again, perhaps incorrectly - that virtually
all chords in barbershop work are (dominant) seventh chords. In that case you
would not technically have an authentic cadence, since the tonic chord would be
a seventh chord. (That could be used as a fragment of a chain of secondary
dominants, but perhaps I ought not get into that.)


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> As you can see by this article, Rameau is the one who refused to use the
> 7th harmonic and proposed 9/5, locking musical theory into 5-limit.
> Maybe his influence is to blame for the current state of music.

By the way, Dave Hill, in his landmark lecture demo on JI from the early-mid
80s, also pointed out Rameau's rejection of 7:4 as a minor seventh. However, he
went on to suggest that dominant sevenths have increased and evolved in their
usage since Rameau's time. So, he went on to build the music on that tape with
4:5:6:7s.


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