The phenomenon that I call "going away and coming home" is present in all Western music. (It may be true of other culture's music but I cannot speak to that with any authority.) Going away and coming home is operating on all levels, micro and macro.
"Home" refers to the feeling of being settled. It might be compared to the period at the end of a sentence. "Away" refers to being unsettled, the feeling that more is to come, like a comma in a sentence. The interplay of home and away creates the feeling of movement, the feeling that the music is pulling you forward, its "dynamic" quality. It also gives music its structure.
You are probably already aware that our music is tonal (with very few exceptions), that is to say, it is based on a scale. A scale is a subset of all available tones, and a scale has specific relationships of the tones to each other.
The scale itself is a perfect illustration of home and away. Play the first note of a major scale. (I'll call the notes of the scale 1, 2, 3, etc.) Then play 1 to 2. As you listen, does the 2 have more energy to move forward, or does it want to fall back to 1? I think you'll find it's the latter. Then play 1-2-3 and ask the same thing. You'll probably agree that 3 has more forward momentum than 2, but not enough; it, too, wants to fall backward to 2 and then 1. Now play 1-2-3-4. It's starting to feel like it finally has some forward momentum, but 4 also very easily can just relax back to 3. Now play 1-2-3-4-5. I think you'll hear immediately that with 5 we have really gotten somewhere; it feels like you have reached the crest of a hill. The note 5 really doesn't want to fall back but has a drive to go forward. As you play 1-2-3-4-5-6, the pull to go forward is stronger still, and when you play 7, the urge to go to 8 is extremely strong. (The 7th note of the scale is sometimes called the "leading tone" for this reason.) If we call the notes 1 and 8 "home" (which they must be, since they begin and end the scale), the note 5 is as "far away" as you can go before you are returning home again. Although the scale appears to be linear when you look at it, musically it is more of a circle. The tones 1 and 5 are are opposite poles of the circle. (For more about the scale itself, see my post "The Cosmic Mystery of the Musical Scale.")
It makes sense that if the scale (micro level) embodies home and away, then everything built on the scale will also have home and away.
As you might have guessed, the importance of the tones 1 (I) and 5 (V) are everywhere in our music, and specifically, the chords built on I and V. If you take the simplest of songs, let's say "London Bridge is Falling Down," you will see it is harmonized with just two chords, I and V. This is because every piece of music, no matter how short or simple, must have home (I) and away (V). Having only "home" would be boring indeed, and having only "away" would be almost impossible since, without home, away cannot even be recognized as being away and would be quite disorienting.
While everything other than 1(I) is away, 5 (V) is the most away. The chords of II, III, IV etc. are also away, but the strongest feeling of away is V. You'll find that almost all our music ends with the V and then the I chord. (The remaining ones end with IV to I, which is also a 5 to 1 relationship, but the other direction in the scale and in the circle of fifths; see my explanation in earlier posts.)
On the macro level, sections of music exhibit home-away-home as well. A tremendous amount of our music is based on the A-B-A form. The A section functions as home, where you start, the B as away, and then A as the return to home. Songs have one or more verses (section A), then usually the chorus, or "bridge" (section B), and then end with the verse (A). The simplest classical pieces will probably be A-B-A, and the B section is either different in its thematic material, or it is in a different key, or both. Going to another key is definitely felt as "going away" and the return to the original key has the satisfying feeling of coming home. Larger musical works such as sonatas, symphonies, etc. are all based on some variant of A-B-A. There are some exceptions, of course, but composers (and we listeners) have found this so satisfying that we just don't seem to be able to abandon it. When you consider that a piece of music unfolds over time (as opposed to a painting where you see everything at once), it is imperative that the music have a structure, or architecture, that can be discerned by the listener. A-B-A does the trick.
I find it endlessly fascinating that, regardless of the complexity of a given piece of music, the going away and coming home is always operating, always pulling us forward. You can study all sorts of complex "music theory" in books or classes, but if you understand "going away and coming home," you'll understand a great deal about music.
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