[MUSIC] In the last lecture we learned a shortcut for determining key signatures of sharp major keys G through C sharp major. The final sharp in the key signature is the last note of the scale. So if you've memorized F, C, G, D, A, E and B and you have of course you can easily go from key signature to key and from key to key signature. A major, a half step down is G sharp, therefore the sharps are F, C and G and so on. Flats are a little trickier. First you must remember the order of flats in a key signature, B, E, A, D, G, C, F. We'll be using it to figure out key signatures in keys. Here's a nice flat scale, E flat major. We can see that there are three flats, B, E, and A flat. So this is the key signature. Notice that the tonic E flat is the second to last flat, that's a shortcut you can use then. In major keys with flats, the second to last flat is the tonic, or Do when we use moveable Do. Four flats, B, E, A, D, the tonic is A flat, the second to last flat. Two flats B flat and E flat, the tonic is B flat, the second to last flat. But what about one flat, B flat? There's no second to last flat. You just need to know this one. The major key with one flat is F major. Figuring out flat keys is easy in both directions. What is the major key with five flats? The flats are B, E, A, D and G flat. The second to last flat is D flat, so D flat major. What is the key signature of A flat major? Go through the order of flats until you get to A flat and then go one more. So B flat, E flat, A flat, plus D flat, four flats, A flat is the second to last flat. Now you try one. What major key has six flats B, E, A, D, G, and C flat? The second to last flat is G flat, so the key is G flat major. Here are all the major keys with their key signatures, the sharp keys are on the right, the flat keys are on the left. But down there at the bottom, there's a bit of a traffic jam, as three sharp keys overlap with three flat keys. For each of these, the sound of the notes is exactly the same, at least when played on an equal-tempered instrument, like a piano. F sharp and G flat major sound exactly the same, for example. This circle of keys is called more formally the Circle of Fifths. Because the root of every key is exactly a perfect fifth higher than the previous key for the sharp keys, and exactly a perfect fifth lower than the previous key for the flat keys. In this lecture, we learned the shortcut for figuring out the key signatures of flat major keys and sharp major keys. For sharp major keys, the first note of the scale is a half step above the last sharp in the key signature. So A major, first half step below A is G sharp, so the sharps are F sharp, C sharp, and G sharp. For the flat keys, the first note of the scale is the second to last flat. So for D flat major, the flats are B flat, E flat, A flat, D flat plus one, G flat. We also learned about the Circle of Fifths, which looks like a clock face in which every hour is a major key. Three keys at 5 o'clock, 6 o'clock and 7 o'clock on the clock, can be spelled with both sharps and flats. In the next lecture we'll start talking about the key signatures of minor keys. [MUSIC]