I want to come at the question from a different angle: instead of defining what a key is first let's look at some music and try to describe what's going on melodically. In so doing perhaps we'll get a better understanding not only of what a key is but why they're very helpful descriptively.
Here's a transcription of the beginning of a traditional Thai piece called Javanese Suite. To hear a great performance of this by the ensemble Fong Naam click here.
If we had to describe the notes of this to someone (perhaps even to ourselves if we wanted to improvise our own embellishments) how might we start? Well we can see right away that there are a lot of repeating notes. Let's consider all the repeating notes as one note for the purposes of analysis (for example: there are 7 Ds in this musical passage: but for our purposes we'll just write down one D). Then let's put the notes in order from lowest to highest. Here's what we get:
We can now see that the entire passage is made up of only five different notes: G, B flat, C, D, and F. If we jumped in and improvised to this tune (which we can do with the YouTube link above) we should be safe if we stick to these notes. And by safe I mean that we won't be adding any "colors" to the piece that aren't already present.
[If you're so interested try playing along and adding some other notes like A, E, Fsharp and so on. They will objectively change the sonic nature of the tune. This is very different from saying that what is added would be 'good' or 'bad', because those judgments would depend upon a performing and listening community.]
So basically we can say that by knowing the notes that make up a piece we have a key to unlocking the door which might otherwise bar our entry.
And if we went through hundreds and even thousands of pieces we might start seeing patterns. And that is of course what has already happened for centuries and centuries. At this point we don't have to reinvent the wheel. There are handy names for the sets of notes we're going to encounter (and if there isn't there are still other ways to classify those sets, too!)
If we look at our five notes from above again we might recognize that they have a name: they form a G minor pentatonic scale. And this is the same group of notes as a B-flat major pentatonic scale:
Knowing what a pentatonic scale is and how to play one on your instrument(s) in any key would be crucial if you were going to play other music like this. For instance try playing along to Zhou Xuan's performance of Song of the Four Seasons. If you sing or play the melody you'll soon discover that it's from the F sharp major pentatonic scale. And if you had to transpose the song for some reason (like for certain instruments' tuning, or for a singer, etc) doing so shouldn't be too complicated if you know the pentatonic scale.
The former paragraph is getting at this main point: we might find hundreds of other tunes in G minor pentatonic, and the order of notes might be different melodically. It would be a severe pain if we couldn't recognize that:
D, F, D, G, D, C, B-flat
C, B-flat, C, D, C, B-flat, G
are both made up of the same group of notes. Knowing that they both are from the G minor pentatonic scale cuts down on what we have to categorize tremendously. See my post on permutations: it's obvious that we don't want to name every sequence of notes as they can become nearly infinite in number.
Now if you didn't play along with the recordings or if any of the above particulars are confusing don't be alarmed whatsoever! The main thing to take away from this post is this:
Knowing the notes that make up a piece of music is the key that allows us to enter into the music more fully. And being able to determine what pattern (if any) the notes are in is extremely important as it's less that we have to memorize.
This is why it's a good idea to learn many different kinds of scales: they allow us to categorize the music we encounter. And the more scales that we know the more able we'll be able to understand various styles of music.
To be sure there are some complicating factors that arise (e.g. a lot of music isn't in one single key or sometimes it's ambiguous as to what the key actually is or sometimes the sets of notes used don't correspond to any scale) but fundamentally the process is always the same: discern the notes and see if they fall into pre-established patterns.
More to come!
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