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March 20, 2012

More on Augmented Sixth Chords

Let's take a look at a few examples of augmented sixth chords in two piano sonatas of Beethoven:

music theory, augmented sixth example

music theory, augmented sixth example

music theory, augmented sixth example

Notice the raised fourth scale step and the sixth (which is already flat, because we're in minor) in the chord in the first example, first measure? Yep, an augmented sixth chord, in this case a German augmented sixth. Last time, we mentioned that there are usually chords in between a German augmented sixth and the dominant chord. You'll see this in both the first and second example. If you look back to the example in the previous entry of the German augmented sixth side-by-side with the dominant, you will see that the Eb and Ab of the augmented sixth go down by half-step to a G and D. Seems simple, right? But if you've learned about what's known as voice leading, you'll probably remember that this creates a parallel fifth, which is something that is to be avoided in 'proper' voice leading. That's why there are these extra chords in the first two examples. The second example from today is the textbook example: a German augmented sixth moves to what is known as a 'cadential six-four' chord before the dominant. The cadential six-four is a tonic chord in second inversion, that is, with the fifth in the bass. The 'six' refers to the interval between the bass and the third of the chord, and the 'four' refers to the interval between the bass and the root of the chord, both of which are above the fifth. Inserting a cadential six-four between the German augmented sixth and the dominant effectively removes the problem of the parallel fifth. You'll see in the first example that it doesn't necessarily have to be a cadential six-four chord that goes between the German augmented sixth and the dominant, but it often is.

The third example has a French augmented sixth. Again, you see the raised fourth scale step (since this example is in Eb, that's an A natural) and the flat six (Cb) in the second measure, which are the tell-tale signs of an augmented sixth chord. It's interesting to note that French and Italian augmented sixth chords can move directly to the dominant because they don't pose the same voice leading problem as German augmented sixth chords do.

Do you have a favorite example of an augmented sixth chord? Please do share on our facebook page!


March 1, 2012

Music Theory Chord Spotlight: Augmented Sixth Chords

Previously in this blog, you've been introduced to predominant chords, that is, chords that precede the dominant (an example of this is the supertonic, or ii). Augmented sixth chords also primarily have a predominant function, and are built upon the b6 scale degree (the sixth note in a natural minor scale). In addition to the b6, augmented sixth chords include another unique note, a raised scale step 4, that is, #4. So, in the key of C, an augmented sixth chord would include both an Ab (the b6) and an F# (the #4), and the interval between these two pitches is an augmented sixth, hence the chord's name.

There are three standard augmented sixth chords, and in English music theory terminology, these three chords were considered to have characteristics stereotypical to nationalities, and were given names to reflect that. Thus, we have the Italian, French, and German augmented sixth chords. It's interesting to note that these names only are used only in English, not in other languages' music theory terminology. Here they are:

music theory, augmented sixth chords

If we take a look at the relationship between an augmented sixth chord and a dominant chord, we can tell that there is a strong draw for it to lead to the dominant. Here is a German augmented sixth chord and a dominant chord in the key of C: you can see that the Ab goes down a half-step to the G, the F# goes up a half-step to the G, and the C and Eb eventually both move down a half-step to B and D, respectively. I say 'eventually' becuase there is usually another chord between a German augmented sixth chord and the dominant, but we'll cover that next week.

music theory, German augmented sixth

We'll also take a look at some examples next week to see how composers use these chords in practice, so stay tuned!


December 20, 2011

That Time of Year

It's that time of year again. You can say this at any point in the year and it will hold true, but right now, it really is that time of year. Let it suffice for us to bring you a music theory word of the week appropriate for that time of year: the French Overture. If you haven't yet caught a performance of Handel's Messiah, you can arm yourself with this knowledge: it begins with a French Overture (we're talking about the entire oratorio, not just the Hallelujah Chorus).

The French Overture is a specific type of overture common in baroque music. Overtures, as you may know, aren't just attempts to get to know someone or something better, they are what large scale musical compositions like operas and musicals and oratorios begin with. The French Overture has two trademark features: one is a preponderance of dotted rhythms, and the second is a two-part structure, with a slow first section followed by a faster, fugal section. An interesting performance practice feature of French Overtures is that quite often the dotted rhythms are performed as double-dotted rhythms. Here's what the first line of the overture to Handel's Messiah looks like:

music theory, Handel's Messiah

And here's what you might hear:

music theory, Handel's Messiah

Here's the subject of the fugue in the second section of the overture:

music theory, Handel's Messiah

These two sections are tied together harmonically as well. The first section ends with a half cadence in E minor, and the second section resolves this by bringing back material from the first section and ending with a perfect authentic cadence. Here's the last two measures of the first section:

music theory, Handel's Messiah

And here's the last two measures of the second section:

music theory, Handel's Messiah

Happy Holidays, everyone!


December 14, 2011

Music Theory and Popular Music

Have you ever wondered how the music theory you learn applies to popular music, like rock, today's top 40 hits, or heavy metal? Well, you need look no further than the current issue of Music Theory Online! Music Theory Online is an online academic journal, and provides a great forum for music theorists to discuss and present their scholarship. You may be wondering what 'professional' music theorists do: MTO is a good place to sample their work. Here's a couple highlights from the current issue, to whet your whistle:

1. Always one for new terminology, I'll direct your attention to Christopher Endrinal's proposal of the term interverse to replace the usual term bridge in popular songs. His argument is that bridges signify moving from one spot to another, but in rock music bridges aren't always about transitioning. His term places more emphasis on the musical material of the section itself. He also distinguishes interverses from the typical instrumental solo in rock songs, which he calls interludes. Interverses, however, have words too (hence the 'verse' part). Not only is there the interverse, but there are four types of interverses. You should check out his article for more information!

2. Brad Osborn discusses forms in what he terms 'post-millenial experimental rock.' On one level he shows us the connections between popularity and songs with recapitulatory structures (like a verse-chorus tune) versus songs which lie more on the fringe and feature through-composed forms. In traditional music theory, through-composed refers to pieces of music that do not feature large sections of material that is repeated. In art songs (like those by Schubert or Schumann), this means each stanza (or verse) has different music. In your studies you might also come across the German word for through-composed, which is 'durchkomponiert.' Osborn goes on to differentiate between through-composed styles of rock, linking math-metal bands with music generally structured on a series of diverse guitar licks, while post-rock bands he shows to base long pieces on a single motive.

It can be illuminating and helpful when learning music theory to consider what forms popular songs and rock music can take, and to practice 'analyzing' some of your favorite tunes and how they're put together. Both Endrinal's and Osborn's articles provide some interesting food for thought.


November 22, 2011

A Thanksgiving Theory Feast

Thursday is Thanksgiving here in the US, and nothing signifies time with family, friends, and food quite like music theory...Well, perhaps that's a stretch, but the similarities between the adjective 'hungry' and the homophonic Eastern European Country Hungary should be quite apparent, and, as Thanksgiving is foremost amongst holidays in regards to the foregoing adjective, let us in turn focus on the Eastern European country, and take a quick look at Hungarian composer György Ligeti's Musica Ricercata.

Ligeti composed Musica Ricercata, a set of 11 pieces for piano, in the early 1950s. If you've made it to the last few chapters in Theory in a Box, you will have encountered many different examples of how composers might compose or structure a piece of music. They might write it in a specific key to elicit a certain mood, they might rely on the chromatic scale (as in the example of Rimsky-Korsakov's Flight of the Bumble Bee), or, if you've been following our blog, you'd know that 20th century composers might have used the 12-tone method. While Ligeti does use modal melodies reminiscent of folk songs and even uses the 12-tone method for the last piece of Musica Ricercata, what is most unique is that each piece only has a set number of pitch classes in it. A pitch class refers to any note, regardless of octave, that shares the same name: so pitch class C would refer to all the Cs on a keyboard, and so on. In Musica Ricercata, Ligeti uses two pitch classes in the first piece, and for each successive piece adds one pitch class, so that by the final piece, all 12 pitch classes are used. To make this clearer, the first piece only contains the notes A and D, the second piece contains E-sharp, F-sharp, and G, the third contains C, E-flat, E-natural, and G, and so forth.

You might be wondering how does one write a piece that only has two or three notes in it. Rhythmic ingenuity helps out. In fact, the first piece is essentially only one pitch class, A (a D only makes its appearance at the very end), but Ligeti keeps it interesting by gradually increasing rhythmic activity and employing syncopation.

Other interesting features of Musica Ricercata are its use of key signatures and bitonality. While you know from the chapter on key signatures that flats and sharps do not mix in the key signature, Ligeti makes up new ones! In the fourth piece, the key signature consists of F-sharp and B-flat! This is mainly shorthand, however, as the piece is more or less in G minor and you remember that in minor keys it's common for the seventh scale degree to be raised, so in G minor you would have an F-sharp leading tone anyway (though not usually written into the key signature). It makes more sense when you know that only the pitches G, A, B-flat, F-sharp, and a brief disruptive G-sharp, occur in the fourth piece. This means there are no F-naturals to contend with, nor E-flats, making any E-flat in the key signature unnecessary for his purposes. You can hear Bitonality in the 10th piece. Bitonality means that two different keys are sounding simultaneously. In this instance, Ligeti wrote a line in D in the right hand, and a similar line in the left hand, but in F-sharp!

Let's look briefly at the title, too: Musica Ricercata. The second word refers to a form of music that was popular in the Renaissance and Baroque, that is, the Ricercare. Ricercares were pieces similar to fugues in that they used imitation and developed a given motif. The last piece in Musica Ricercata (the one that uses the tone-row), is a ricercare and is a tribute to the Italian Renaissance composer noted for his ricercares, Girolamo Frescobaldi.

So while you're piling on the potatos and turkey this Thursday, leave a little room by the cranberries to contemplate György Ligeti's Musica Ricercata, a veritable Thanksgiving feast for music theory!


October 27, 2011

Some Important Dates in Music Theory

The last entry on Arnold Schoenberg got me thinking about the 'timeline' of music theory. Schoenberg lived from 1874-1951, but you'll remember from earlier postings on musical modes that the concept of a theoretical underpinning for music dates back to ancient civilizations. Here are some important and interesting dates in the life of music theory: