Music expresses that which cannot be said and on which it is impossible to be silent.
– Victor HugoCHAPTER AIMS: 1) Hearing – and dividing up – the Octave
2) Establishing the use of Major & Minor and other key changes
The Story So Far…
So far we’ve been dividing this Beethoven banquet into smaller courses, to make a more digestible feast. There’s plenty to go, all tasty, so don’t remove the napkin just yet.
This chapter, we’re only going to look at a nibble of music, a minute of our piece. But we’ll use it to touch on some fundamentals of harmonics, which will come in useful across the rest of the course.
The extract we’ll look at comes about a third of the way through the movement (6.22 on the “Whole Lot” widgit above).
6.22-7.34 Main Clip
If we turn to the very start of this clip, we hear one of harmonic’s most fundamental concepts: The Octave.
Musical notes are produced by matter vibrating at a particular frequency. If you double that frequency, you get the same note, only as a ‘higher’ version. That note, or rather that range of notes, is an known as an ‘octave’. You can keep doing that all the way up, or down, in pitch. Halving or doubling the wavelength of the note to create different higher and lower versions of that same note.
Let’s start with a single note:
We can then play the same note an octave higher. Here they both are:
The higher note played is exactly double the frequency of the lower note.
It’s like getting out of a lift at different floors of the same building. These are higher and lower versions of the same note. This makes more sense when you think the origin of our word ‘scale’ comes from the Italian for steps or a staircase. You play a scale upwards, you go upstairs, until you reach the next floor, or octave. When you look at a piano keyboard, you can see these octaves blocked out every eighth white note (or each 13th note if you count black and white).
Now listen again to the octave in action at the start of our Beethoven clip:
6.22-7.34 Main Clip
It’s a great demonstration of octaves. The strings travel twice between two octaves – up (0.01) – then down (0.03) – then up again (0.05) – and finally down (0.07) before finally coming to rest one octave higher (0.08).
However you look at it, these octave leaps say something very primal, and that’s because the Octave is such a fundemental unit of music, all music.
And that’s because the octave is fundamental to nature herself. The octave is a natural harmonic, the doubling or halving of frequencies. It is manifests itself the physical universe.
And how you divide up that octave is – unavoidable pun – key to the musical universe you create.
Take a piano keyboard: this in fact gives us a template for western music, be it classical jazz or pop. The keyboard initially divides the octave into twelve notes, or semi-tones. That counts every black and white note in the octave.
The major scale, familiar as “Do-Re-Mi”, further divides those twelve notes into a seven note scale. On the keyboard pictured, you play the white notes, but miss out the black ones. The eighth note therefore produces the term “Octave“.
Chinese music however traditionally uses what we term a pentatonic scale, ie one which divides the Octave into five notes. Even when played on a piano, the sound is reminiscent of the Orient:
Arabic music on the other hand can subdivide the Octave into as many as 24 notes, to create the more fluid harmonic texture we associate with music of the Middle East:
In other words: the Octave is a fact of physics. But how you divide up your octave is a man-made construct, that produces vastly different types of music.
Majors and Minors
After the majestic sweeping of octaves, Beethoven proceeds to employ a change of key, and he does it more than once. Here we have the first key:
6.34 Major Key
Do you notice how these three notes are a shorthand version of our ‘Ode to Joy’ theme? Now listen as Beethoven changes to a second, minor key:
6.40 Minor Key
Like they sound, these are different versions of the same key. First the major, and then the minor version.
Major and minor keys sound very different. We usually think of major keys are happy and vibrant. Minor keys are darkerHere is a D major chord:
And here is the minor version, a D minor chord.
The minor chord only has one note changed, the middle one. But this makes a huge difference to the overall effect of the sound.
There is a harmonic explanation for this. Major keys are harmonically stable, whereas minor keys are less harmonically secure. You can find the major triad of any note in overtones or resonances of that note. That means they occur naturally. So a major triad is something you’d expect to be able to communicate with any reasonably smart extra-terrestial creature.
Minor keys are however more of a hotch-potch, as anyone who’s had to learn all the different types of minor scale will attest. There is a strong degree of harmonic ambiguity to a minor key sound. It is that lack of stability which sounds sad or mournful to our ears.
The Harmonic Story
As we’ve said before, the harmonic movement of classical music so often defines the story of the piece. And, from the broadest viewpoint, that’s what happens here. We start in D minor, but finish in D major. They are very different keys (D minor is the relative minor of F major, which is a much more distant key to D major).
Let’s just hear that change. Our movement starts out in D minor:
Start in D minor
And then finishes – emphatically! – in D major:
End in D major!
If you keep switching between the two above clips, the difference should be clear.
And so, rather than returning to our ‘home’ key of D minor, we’ve instead finish this movement in D major. You can even think of this entire movement as a journey from minor to major, from doubt to triumph.
Listen to these three short clips from the music. Can you tell which are major and which minor?
But we’ve still not quite finished with our clip, as there is another key change to absorb…
Let’s just go over those changes:
6.34 Major Key
6.40 Minor Key
But now the key changes, with a lift upwards:
6.46 Key Change
Beethoven is using these key changes as a hinge, a gateway, as a way to lead us into a new section? Once again, harmonic motion is telling us something about the structure of the music. Like a chapter break, the key change sets us up for a renewed outpouring of our Ode to Joy theme.
Beethoven achieved a similar effect earlier on in the movement, changing key twice to achieve an ‘end of chapter’ effect:
3.03 Earlier Key Change
The key changes in the above clip occur at 0.09 and 0.16. They tell us immediately we are going somewhere new…
6.22-7.34 Main Clip
Let’s now remind ourselves of what we have covered, as we digest our short excerpt a final time:
- 0.00-0.12 Those octave leaps.
- 0.12-0.17 The theme begins, hesitantly in our first key…
- 0.17-0.23 The theme begins again, but this time in the minor key…
- 0.23-0.25 Now the big key change as the notes step up towards….
- 0.25-end …the full Ode To Joy Theme.
Now relax and enjoy the theme in it’s full unadulterated glory. It’s exactly what you want from a theme, simple and memorable, but at the same time with huge potential for adaptability and development.
That’s it for next. Next up, what should be by now a familiar choice: follow the Beethoven to the next course, with a historical look at the background to Beethoven’s composition of the ninth. Or else, begin the Wagner course.
- To follow further the history and science of harmonics, check out .
- For some gentle Beethoven piano music here is the famous second movement of the Pathetique sonata.
- This is the thrilling third movement of his Tempest Sonata. It’s not note perfect, but I can’t help thinking Beethoven would have approved of the rawness.
- For the more adventurous, try this third movement of his third last piano sonata (op 109). The movement takes the form of theme, followed by a number of scintillating variations.
- Then of course, there are Beethoven’s five piano concertos. Here is the slow movement of his fifth piano concerto, the ‘Emperor’, for more of Beethoven’s softer side.