Monday, June 4, 2012

The Deceptive Cadence

The idea of a deceptive cadence reveals some interesting things about harmony in general. There are certainly some things about harmony that are derived from the natural order of things. The strong relationship between dominant and tonic parallels the simple frequency relationship between the two notes. The octave from C to C is a simple 2 to 1 relationship while the 5th is the next simplest at 3:2. If you are a guitarist you know that if you touch the string at the 12th fret, dividing it in two, you get a harmonic one octave higher. If you touch the string at the 7th fret, dividing it in 3rds, you get an octave plus a 5th, demonstrating the relationship. So, harmony begins with these simple relationships and for a long time music tended to alternate between tonic and dominant harmony, chords built on the first note of the scale and the fifth note of the scale. Here is the scale of C. As you can see, the fifth note of the scale is G.

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After much use of the chord built on the fifth note, followed by the chord built on the first note, V to I in the symbols we use for harmonic analysis, the usage became not 'natural', but conventional. All meaning, whether in language or music, depends on the use of shared conventions. So the standard 'cadence' or harmonic formula indicating what is the tonic, became this:

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In the simplest form, a major chord built on the fifth note (GBD), is followed by the tonic (CEG). This was soon strengthened by making the dominant (the chord built on G) dissonant by adding a note a 7th above the root (F). This creates a dissonant interval, the tritone between F and B, which resolves to the sixth, E to C. Tension - resolution is the basic principle of harmony. This V7 - I formula became conventional, that is, expected. But as soon as you have an expected convention, creativity allows you to violate the convention. All humor, for example, is about setting up an expectation and then defeating it. There is a nice example from television. In the first episode of Buffy the Vampire Slayer a couple break into a high school after dark. He is a leather-clad bad boy and she is a petite blond. The obvious convention, from dozens of horror movies, is that the blond girl is going to be the victim. But what happens is the roles are reversed: she turns into a vampire and attacks the bad boy.

We have the defeat of expectations in harmony as well. In fact, all advanced harmony depends on it. The simplest defeat of expectations is to replace the tonic in a standard cadence with another chord: the one built on the sixth note of the scale. This creates a deceptive cadence.

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Instead of the firm movement confirming the tonic, this has a 'suspended' feeling, avoiding the tonic. J. S. Bach, as the master of harmony, managed to make this a lot more intense by using an altered deceptive cadence, moving to a Neapolitan, then finally the V - I. This is found in his Toccata in F, BWV 540. Here is the harmony by itself:

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To describe what is going on here, I have to introduce the notion of 'inversion', described by Rameau in his book on harmony published in 1722, just a few years after Bach wrote his toccata. A triad has three notes: CEG. But any one of the three can be found in the bass, giving a different 'color' to the chord. If the root is in the bass, it is 'root-position', if the third, it is a '6' chord and if the fifth, it is a 6/4 chord (these numbers just describe the intervals above the bass). So the 'root' of the chord and the 'bass' of the chord can be different things. A seventh chord, that is, a triad with another note, the seventh, added, gives us a whole different set of inversions. If the root is in the bass, it is a 7th chord, if the third is in the bass, it is a 6/5 chord, if the fifth is in the bass it is a 4/3 chord and if the 7th is in the bass, it is a 4/2 chord. This last is the most dissonant version. So if you look back at Bach's progression, you see the dominant 7th goes deceptively to the sixth chord, but in the most dissonant inversion and with a 7th! Then this chord pretends it is an ordinary dominant and resolves to Eb. But Eb is far away from D minor. The chord built on the note just one semitone above the tonic is called the "Neapolitan Sixth" and it is a very colorful harmony, indeed. From there, Bach can easily move to the regular dominant seventh and then the tonic. Let's have a listen to the whole toccata:

The passage I have been talking about is between 3:57 and 4:10 in the recording. At the beginning of the piece Bach has long, long pedal in the bass on the tonic, followed by another on the dominant.

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