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Modulation describes the transit between keys. A modulation is a combination of three factors: the “harmonic distance” traveled – the time spent in travel – the time spent in arrival
To demonstrate this, let’s compare two modulations, one by Muzio Clementi and one by J. S. Bach
In both cases, the harmonic distance is the same: The music travels from the key of the tonic to that of the dominant—neighboring keys on the circle of fifths, and thus closely related.
In the Clementi, the travel time is extremely short: The move from the tonic to dominant key happens in a few seconds.
Compared to the time spent getting there, the time spent in arrival is considerably longer: Clementi dwells in the new key, cadencing there repeatedly.
The Clementi is analogous to an easy trip to a nearby house: You’ve brought a put luck dinner and settle in for a long, comfortable evening.
The same journey is much more elaborate and extended in the Bach:
The opening measures establish the home key.
The initial move away from the key is reinforced by a change in texture: The figuration of the opening bars is interrupted by several rising scales.
This first move away was provisional. The progression returns to the tonic, but more insecurely, and the push away is strengthened. With significant effort and heightened complexity, Bach’s Prelude reaches the same goal as the Clementi: An arrival on the dominant.
However, after such pain-staking effort, there is a shock upon arrival: The music abruptly departs!
The Bach modulation might be described as a visit to your in-laws at Thanksgiving: It should be an easy trip but you forget something you have to go back for--and then get lost. When you finally arrive, your in-law makes an unwelcome remark and you throw everyone back in the car, headed somewhere else for the holidays.
Thus, although the two modulations cover the same harmonic distance—from tonic to dominant—they differ greatly in structural import and expressive impact because of their different proportions of time spent in travel and the time spent in arrival.
One way of measuring the time spent in arrival is the number of cadences in the new key. For instance, Mozart’s Piano Sonata in C-Major begins by establishing the home key.
The music then modulates to the dominant, where there is a marvelously inventive series of cadences — eight in all!
Later in the movement, Mozart revisits the dominant key. However, this time, there is only one cadence — and then the music packs its bags and leaves.
The greater the number of cadences, the greater the structural significance of a modulation.
Conventional harmony textbooks typically provide MapQuests between keys, describing the most common paths and smoothest chord connections. While this information is certainly apt, it is secondary to the musical significance of a modulation. When you are listening to a modulation, try to ask three crucial questions: How far am I going? How long is it taking? How much time do I spend when I get there?