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.

Cadences

In connection with harmony and form I have several times mentioned the cadence. Lots of people know what I am talking about, but others might not so let me talk about the cadence a bit. It is a very useful exercise to reexamine the fundamentals of music from time to time. Composition in the Classical Era had, if not unbreakable rules, then certainly procedures that were followed without fail. One of these is that each piece and significant section of a piece had to end with a cadence. In fact, the cadence defined the parts of the piece. For an overview and some examples, have a look at the Wikipedia article on the cadence.

Cadences come in varying strengths. The strongest, called a Perfect Authentic Cadence is required to end a piece--or even a significant section of a piece--in the Classical Era. Even after many years as a performer I was surprised to hear this stated so firmly by a theorist and even more surprised to discover he was correct. It is simply not the case that composers often used cadences to end pieces in the Classical Era--no, pieces HAD to have a solid cadence at the end.

A cadence is more than mere punctuation. Every sentence in prose writing normally ends with a period, but in music phrases may end in various ways, sometimes with, sometimes without a cadence. Also, cadences come in varying degrees of strength from ones that are very solid indeed, to ones that are deceptive, leading not to the home chord or tonic, but to some other chord. In those cases the cadence does not close off the music, but leads it on. Cadences in some form or another have been used ever since mentioned by Guido of Arezzo around 1026. We can see how cadences work in just one phrase of a piece by Haydn. Here is the opening of his Piano Sonata in E flat major:

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Here are the first nine measures of the piece. The first phrase ends on the first beat of the ninth measure, which is also the beginning of the next phrase. Now look at the smaller sections. The first two measures begin and end with an E flat chord, but there is no cadence. The next three measures move to a B flat chord, known as the dominant and with some faster moving ideas, end up, in measure six, on a new chord: C minor. Measure eight ends with two separated chords, an F minor followed by a B flat with an added 7th (the A flat note). These two chords, followed by the E flat chord that is the first beat of measure nine, create a Perfect Authentic Cadence which is the dominant (B flat, prepared by the F minor chord) followed by the tonic (E flat) both in their strongest form. In microcosm, this is how classical harmony works. No matter what the first chord might be, until we have the full cadence of measure 8 to 9, we have not defined a tonality. Here is a performance of the piece so you can hear how this works:

The full cadence, ending the first phrase and defining the tonality, occurs at the 20 to 22 second mark. What happens in measure six, at the 14 second mark, shows the subtlety of the system. Here, where we might expect an E flat chord, we get instead a C minor chord. C minor is closely related to E flat, but still different. Going to C minor expands and opens out the phrase. These sorts of things: presenting a tonality, but delaying confirmation, expanding to closely related areas and finally confirming the tonality--all these are typical harmonic devices and they all depend on either using a cadence in a strong or weak form, or on delaying the cadence. Not only a single phrase, as here, but entire movements several minutes long, are constructed with these same devices.

If you learn to listen for cadences, it will clarify the musical form for you.