Before the advent of Roman-numeral analysis, did musicians conceptualize applied/secondary chords as somehow moving towards their temporary tonics?
As discussed in Origin of Roman Numeral Analysis, Roman numerals weren't a widespread analytical tool until at least the 19th century.
With this in mind, imagine that you're a musician in 1770; you're accustomed to the figured bass tradition, so you see excerpts like the following relatively often:
Do you conceptualize this middle harmony in a way that somehow suggests a move (however brief) towards G?
Today, we would understand this as an applied (or secondary) chord to the dominant:
But since there was no Roman-numeral analytic tradition yet, this would be an anachronistic reading for our hypothetical 1770 musician.
Would they have understood this middle chord as in some way being related to G (and perhaps moving away from C), or would they have simply understood this as "first-inversion chord with a raised sixth"? In other words, was there some other functional understanding they had for this chord?
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Secondary dominants were common in Baroque music, since early days. There was also a different notion of leading tone: they could lead towards a tone by the common leading tone (raising the pitch) or by the supertonic (lowering the pitch).
Check out partimento materials and regole to gain insight of this thinking and how harmony/counterpoint were taught those days.
I think they'd have a pretty good idea of the leading-note function of that F?, and would therefore not have voiced the progression the way you did!
Remember, NOTES have tendencies. Not chords. Musicians knew 5 wanted to fall to 1, 4 to 3 etc. long before anyone felt it necessary to codify combinations of such active notes as named chords.
And remember, 'theory' doesn't tell a composer, particularly an innovative one, WHAT to write. It can help him (and others) codify what he DID write though.
From what I've read on the history of western harmony (there's a good Cambridge Press book about the subject), these were viewed as temporary key changes. These modulations were driven by chromatic voice leading. Lester's book, "Compositional Theory in the Eighteenth Century" had some examples of such progressions being termed (very short) key changes. Kirnberger (one of J.S.Bach's students) noted that these progressions connect larger structures. Rameau suggested that these are used to keep from having to close a phrase too quickly.
The earliest comments I've seen on "secondary dominants" (which were called applied or attendant chords) are in either York's or Shephard's harmony books around 1890. However, the concept was clearly known as discussed by Rameau and Kirnberger.
As an aside, earlier theorists seem to have considered these as actual key changes. Later theorists call them tonicizations or use terms like applied or attendant or secondary dominants (secondary because the secondary chords, not I, IV, or V, are made into temporary dominants.) Key change (AKA modulation) takes more time. Schoenberg suggests that not only does a key change take more time but the characteristic note (or notes) of a key must be "neutralized" before it's actually a modulation. (Moving from C to F needs the use of Bb other than in a C7 chord.)
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