He begins the chapter with Rimsky-Korsakov's comment, after an evening in which Stravinsky and Rimsky-Korsakov's wife, Nadezhda, had played through the Schubert late C-major symphony in a piano four-hands arrangement. He said that before Schubert certain "bold and unexpected" modulations simply did not exist. For Rimsky-Korsakov, Schubert was the father of modern music. What kind of modulations was he referring to?
I want to just back up a bit and fill in a bit of background here. Music in the Western world, for a long time, was based on the individual melodic line. Most music in most places is still structured in this way. But in Western music going back eight or nine hundred years, the practice of combining independent melodic lines became the standard practice. In order that they blend in a pleasing way and not clash, certain methods or rules were adopted. This is where the idea of consonance and dissonance came from. Some notes clash, are dissonant, while others blend, are consonant. A good piece of music actually uses both these phenomena so as not to be bland and boring. But there were pretty strict rules for how dissonances were to be handled or resolved.
As we move into the 15th century, harmony begins to develop a life of its own as composers like DuFay developed techniques like fauxbourdon to harmonise melodic lines. (I know I am getting into esoteric knowledge when Blogger starts underlining words in red, even though I know they are spelled correctly!) Roughly from 1600, harmony became more and more structurally prominent and the idea of functionality came to the fore. Functional harmony was the common practice from around 1600 to around 1900, though just how it functioned changed enormously. Taruskin points out in passing that a good book on the use of harmony in the 19th century still has to be written!
The first stage of functional harmony focused on the idea of a tonic and a dominant. Pieces of music basically began in the tonic, the harmony built on the first note of the scale, or tonic. Then the music moved to the dominant harmony, that built on the fifth note of the scale. A couple of other chords or harmonies were used built on the fourth note of the scale, the subdominant (which prepared or led up to the dominant) and the sixth note of the scale (which was used to stand in for the tonic in a deceptive cadence), the submediant. Pop music to this very day rarely uses any harmonies other than these basic ones, though jazz certainly does. Closure is achieved by simply returning to the tonic after the dominant. This harmonic movement, from dominant to tonic, is called a cadence and all tonal music ends with one.
The tonic/dominant relationship was so powerful that it was soon extended in various ways. One was by using secondary dominants, that is, any harmony or chord can be preceded by its dominant. The whole harmonic space can also be organized by the circle of fifths:
As you move up by fifths, each key adds a sharp, while as you move down by fifths, each key adds a flat. This enabled modulation, the movement from one key to another, to be handled in a clear and organized way. A great deal of music, especially in the Baroque and Classical periods, is filled with harmonic sequences, which are passages that move through different harmonies in a specific pattern. The most common are ones that descend or ascend by fifths. Here is a good page on that. Sequences were used as a kind harmonic engine to drive the music forward.
By the time we get to Schubert and the early Romantic period, composers were looking for something different. Rather than driving forward, they wanted to pause, reflect and give the music an inwardness. What Schubert did was to exploit and normalize the use of sequences that moved by thirds rather than fifths: these are called mediant progressions. As Taruskin notes, third relations operate in Schubert on every structural level. Here is a harmonic reduction of a forty-bar passage from the Finale to the C-major symphony that provides an example. The chords marked "x" are flat submediants that have no functional role in harmonic structure up to this point. They alternate brusquely with the tonic and only work because of the common pitch, C, that unites them:
The flat submediant, a major third below the tonic, A flat major in the key of C, was the Romantic harmony par excellence and its use is largely credited to Schubert. That other harmony you see, the F# diminished chord, also has a mediant origin, it is two minor thirds above the tonic. Both these chords contain a C natural, which links them to the tonic.
This might be enough harmonic theory for one post, so let's listen to that Schubert symphony. This is the "Great" Symphony in C major (so-called because there is another, shorter, symphony by Schubert also in C major) with the Vienna Philharmonic conducted by John Eliot Gardiner:
Incidentally, in the first movement Schubert inserts a complete circle of major thirds within a circle of fifths!