Augmented Sixth Chords (German)

Here's the second installment of the ultra-popular Augmented Sixth Chords series. If you missed the first installment (about Italian sixths), be sure to check it out before learning about the German sixth!

(Or as the Germans call it, the __(click)___.)

And, that's that!

The Major Scale

Half Steps and Whole Steps

In Western music, an octave is divided into 12 notes. The distance between each of these notes is called a half step. Two half steps make up a whole step.

When you play a C to a C on the piano using every key (black and white), you are playing a chromatic scale, made entirely up of half steps.

By varying the arrangement of whole steps and half steps, we are able to create different scales. In this post, we'll look at a very popular scale, the major scale.

The Major Scale

The major scale is made up of two tetrachords. (A tetrachord  is a set of four notes.) Each tetrachord follows the pattern "whole, whole, half." Next the two tetrachords are joined together by a whole step. So, the complete interval pattern of a major scale is "whole, whole, half, whole, whole, whole, half."

Major scale, on the staff.

This interval pattern (W, W, H, W, W, W, H) is true for all major scales. Note that, in major scales, the half steps occur between scale degree 3-4 and 7-8.

Tip: In the key of C, the major scale turns out to simply be every white key on the piano (C to C).

Creston Chunks: Measure 4

[This post is part of my Personal Practice Project: Creston Chunks.]

Paul Creston's Sonata for Eb Alto Saxophone and Piano is 123 measures of interesting stuff. With (almost) no single measure repeating itself anywhere in the piece, each measure has its own special stuff—something unique to study, analyze, and get under the fingers.

(Fortunately, there are a few motifs and harmonic ideas that show up with some frequency. For example, the piano accompaniment is comprised almost exclusively of seventh chords—primarily major-minor seventh chords.) 

With this "chunk" method, you become very well acquainted with each measure. It's almost as if each measure is its own little person with something unique to say.

Some have something interesting to say (m. 4), some have nothing to say (m. 35: a whole rest in both clefs), and some have a rather offensive message (m. 9: two sets of descending thirds, each a dissonant half step apart).

Meet measure 4 (and 5):

Essentially, measure 4 is an A7 chord. The 3rd (C#) and 7th (G) of the chord is maintained in the right hand, while the left hand covers the root (A) and the 5th (E).



In addition to featuring A7, the left hand hints at another chord. By moving a half step up from A and E, the left hand is playing Bb and Eb on beats 2 and 4. Combining these raised left hand pitches with the 3rd and 7th of the right hand, and by thinking enharmonically, we are able to derive another chord: Eb7.

So, in m. 4, both A7 and Eb7 appear. This is a great example of tritone substitution. A and Eb are separated by the interval of a tritone (an augmented 4th or a diminished 5th). The term tritone substitution refers to the fact that the two chords can easily substitute for one another. Why? Keep on reading!

When you have two dominant seventh chords whose roots are a tritone apart, something very cool happens: The 3rds and 7ths of their chords use the same pitches.

Let's look again at measure 4 to explore the tritone substitution. Thinking of A7, the 3rd of the chord is C# and the 7th is G. Now, thinking of Eb7 (beats 2 and 4, with Eb/D# being the root and Bb/A# being the 5th), Db (enharmonic to C#) is the 7th and G is the 3rd.

Put another way, the 3rd of the A7 is also the 7th of the Eb7, and the 7th of the A7 is also the 3rd of the Eb7.

This explains why the right hand is able to stay on the same notes despite the fact that two different chords are being created. Since the 3rd/7ths are shared between the two chords, it's up to the left hand to differentiate the chords by playing the root and 5th of the chords.

How exciting!

To summarize, measure 4 is pretty great. It exemplifies the tritone substitution beautifully (and it's quite fun to play).

Michael Cera: The Human Metronome

Lost and Found

I found my metronome today! This is huge news. Really. 

Blogworthy.

I thought it was hundreds of miles away, but my 'nome was actually less than a hundred inches away from my bed.

Good Time

Before this glorious day of 'nome's return, I had been relying on some alternative sources to find tempos and maintain good time. If you're ever without your trusty metronome and you need to keep good time, consider some of these options:

1. Internal sense of rhythm. (Knowing how long things take.)
   
   
   
   Meet George Michael.
   
   His sense of rhythm is as impeccable as his taste in flowery shirts.
   
   In the TV series Arrested Development, the undeniably cool George Michael (played by Michael Cera) is looking for a spot in his family's band when he highlights the importance of having a good internal metronome.
   
   
   
   
   
   "It's knowing how long things take." Brilliant.
   
   In a practice room, luxuries like iPods, Ghardetto's, George Michael, and external metronomes are permitted. However, in a performance setting, you must leave these items behind. On stage, all you're left with is your internal metronome.
   
   So, it makes sense to develop it. Devote some practice time toward working without a metronome. Re-introduce the metronome every so often to check and see how well your internal metronome fared. You can find some tips to help develop your own internal metronome at my post about Victor Wooten's grooviness.
   
   
2. A clock.
   
   A clock? Sure! A clock keeps steady time, doesn't it? It's exactly like a metronome. Except it's likely much larger than your 'nome, it hangs on the wall, doesn't necessarily make noise, and really only gives you one tempo. But other than that, it's a fine substitute for a 'nome.
   
   Bear with me now—we're about to get into some rather intense math:
   

   There are 60 seconds in a minute, and a clock's second hand ticks at every second. Sooo let me run some numbers here... 60 seconds per minute x 1 tick per second = 60 ticks per minute, or 60 beats per minute.

   If you're playing a lot of 60 BPM songs, you're in luck! Otherwise, subdivide eighth notes within the 60 BPM quarter notes to get 120 BPM, a common benchmark tempo. Of course all of these "calculations" are extremely simple and obvious, but the point is that in a no-metronome situation, you can use the clock to at least get a ballpark estimate of your desired tempo.
   
   
3. Your favorite songs.
   
   Think of some songs that you can easily hear in your mind just by thinking of them. Then, determine the tempos of these songs and devote the information to memory.
   
   This way, the next time you see a piece of music which calls for ~120 BPM, you can simply think of "Stars and Stripes Forever." (The recording I linked to is actually closer to 125 BPM, but the "march tempo" generally hovers around 120 BPM.)
   
   
   Or, you can think of Arrested Development's catchy theme song to approximate tempos around 175 BPM.
   

Those are just a few ways to help you keep the beat when you are away from your metronome. What are some methods you use to keep your time-keeping sharp?

Honing your internal metronome takes time, but it's well worth it. If you're successful, you could rival even the best time-keepers, like George Michael.

Here's a sample of his best work:

Augmented Sixth Chords (Italian)

The Italian sixth chord is the simplest type of augmented sixth chord, and I will stick to just this type for this post. I decided to post this entire lesson as a series of images. You can click each image to enlarge it.

One Man Band

The Film

I recently stumbled upon an animated short film by Pixar that I had never seen before, “One Man Band.” The short, like all of Pixar’s films, does a beautiful job of telling a simple story—a story which entertains but also teaches several musical/life lessons. (My sole, petty complaint is that I wish Pixar had hyphenated the title (One-Man Band). Other than that, superb little film.)

Here it is:

Pixar - One Man Band from Ricardo Pereira on Vimeo.

Synopsis

In the video, a street musician by the name of “Bass” is upstaged by a newcomer, “Treble,” at his usual busking spot. With only one audience member—a little peasant girl with only one coin to spare—the two musicians compete against each other in a musical duel, with hopes of winning the girl’s appreciation (coin).

As you may expect, the girl is not impressed. Instead, the showy duel completely disgusts the girl.

She is noticeably annoyed and disappointed as the musicians crescendo into the climax of their aggressive duel. In the next moment, the girl’s only coin is lost down the drain, and the musicians go silent.

In the final scene, the girl surprises Bass and Treble with her violin chops—an impressive cadenza which earns her a handsome sum of gold coins. 

Lessons Learned

The film is more than just a couple of dudes playing a ridiculous number of instruments at once. It’s rather parabolic, and it contains several important lessons about music (and life in general).

Here are a few:

1. Music not about competition. (Duet, not duel.)
   To be successful in a musical career, to some degree, may mean being better than the other one-man band. But if you focus too much on being better than another musician (“defeating” them), you start to bring hostility and antagonism into the mix—two things which have no place in music. Music is about harmony and cooperation. (Instead of a duel, Bass and Treble should have played a duet.)
   
2.  Music is not about money. (Money talks, but music says nicer things.)
   The “starving artist” stereotype supports this one. Musicians who wish to continue with music professionally are well aware that it’s not where the money’s at. Those who do keep at it do so because they love and appreciate music deeply. Music’s not about vying for the peasant girl’s gold coin. It’s about creating something beautiful, pure, and true.
3. Music is about connecting with other people. (Legato, not staccato.)
   It’s a force that should bring people closer together—not divide. A musician who plays with the goal of merely impressing the audience is thinking much too selfishly. The primary goal must be to connect with the listener. The music played by Bass and Treble was fast, loud, exciting, and technically impressive. But the men weren’t at all concerned with forging a connection with their listener, the peasant girl. As a result, the music fell flat; the characters were driven apart rather than drawn together (detached rather than connected). It is in the connections forged through music that music holds its greatest value.

Final Words ("Imagine")

This delightful 5-minute animation taught all of these lessons, without using even one word of dialogue. I credit this to Pixar’s imagination and creative genius but also to the fact that these lessons are profoundly fundamental.

So fundamental, in fact, that they’re easily applicable to every human being—musician or not: We’re not here on Earth to compete against one another, or to fight with each other, or to chase after trivial material goods. We’re here to come together and connect with our fellow human being—by living peacefully, being kind, and loving one another. (John Lennon used music to express these ideas beautifully.)

So, heed the lessons of "One Man Band"—make music for the sake of music itself, and not for the lesser purpose of winning a peasant girl's gold coin.