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What I have been told is V6(over)4 to 5(over)3 means it's really I 6(over)4 to a root position dominant if I wasn't mistaken when taking notes? What is this, what does the 5(over)3 mean, why is this more useful than writing the chords flat out, and what purpose does this (I believe it's a part of the dominant function, so function?) serve?

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    wait I take back it being a function hahaha. It falls into a function according to my notes but it itself being a function is a very dumb thing to say Mar 13 '17 at 0:29
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You're talking about what is known as a cadential 6/4 chord, which is a very common embellishment of the V chord. The fifth scale degree is in the bass, but, at first, there's a sixth and a dissonant fourth above the bass which want to resolve to the normal fifth and third respectively (the fourth almost always literally resolves to the third, the sixth sometimes moves differently, like to a seventh above the bass).

You're right that, technically, this harmony has the notes of a I chord in second inversion, and some theorists and textbooks label it as a I6/4. However, most theorists these days prefer for the Roman numerals to indicate the chord's function more than simply its note content. The cadential 6/4 has no functional relationship to a I chord, which is tonic; it has dominant function because actually it's just a dissonant embellishment of the V chord. As such, most textbooks and theorists I know tend to prefer to label it as a V chord in order to show its function.

Whether this is the best possible choice is up for debate, but that's only a symbolism debate. Everyone agrees about the actual function of the chord. Often, composers of the Classical and Romantic periods treated the cadential 6/4 as the primary dissonance in the underlying harmonic structure of their music. For example, the unstable harmony that introduces and (at least theoretically) undergirds cadenzas in concertos is almost always a cadential 6/4. The trill signaling the end of the cadenza tends to mark the resolution of the sixth and the fourth to the fifth and the third above the fifth scale degree in the bass, which then leads to a PAC on I in most cases.

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  • so it's a PAC even if there are 2 different chords that fit the dominant function preceded by a subdominant and tonic? Mar 13 '17 at 3:31
  • leading to tonic + soprano landing on the root Mar 13 '17 at 3:32
  • Theorists (and pedants) like inventing names for things. If you think there is a difference in the musical effect of Perfect Cadence and a Perfect Authentic Cadence, then the terms might (or might not) have some meaning for you. But don't forget that the composers who wrote contemporary music in this style (Haydn, Mozart, Beethoven, etc) never read your 21st-century textbook. If you want to know how they thought about the chord progressions they used, read some 18th-century texts instead! (Hint: for Haydn at least, figured bass was still "contemporary music notation" - hence "6/4 5/3".)
    – user19146
    Mar 13 '17 at 4:38
  • @alephzero Sorry, where did I talk about a difference between a "Perfect Cadence" and a "Perfect Authentic Cadence"? Mar 13 '17 at 8:25
  • @FrankBadertscher Sorry, just saw your question. Generally, a cadence is what it is based on the last two harmonies of the phrase, regardless of how the penultimate harmony is approached. For example, it's a PAC whether the V–I is preceded by a subdominant or not. However, the cadential 6/4 harmony really isn't a separate thing from the V—it isn't two chords—it's just a V that's been embellished. Mar 13 '17 at 16:31

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