It's the circle of 5ths

It's always amazing when you have a breakthrough moment with a student. This happened for me yesterday afternoon while giving a piano lesson to my newest student - an adult who recently completed her Grade 8 practical exam. We were working through some theory when she asked what seemed like a very basic question. How do you know what sharps to write in what order in the key signatures? This was strange I thought. Here's a student who has played pieces of quite a high level yet she's not sure about how the keys work. Tentatively, I asked her if she knew about the circle of fifths? No. The circle of 4ths for flats? No again. So I got a big piece of paper and a pencil and we did some basic maths to show the pattern of how sharp and flat keys work. Once you understand it, it's really very simple but no-one had ever explained this to her before. For instance everything about sharp key signatures moves in fifths. C major has no sharps or flats. If we want to find the major key with one sharp in the key signature we go up a fifth from C - to G. G has 1 sharp - F sharp. If we want to find the major key with two sharps we go up a fifth from G - to D. And then to our F sharp we add a second sharp up a fifth from F - C sharp. So, D major has two sharps F sharp and C sharp. And so it keeps going. Flats work on the same pattern except everything is in 4ths. The look on her face when this clicked was absolutely stunning. She couldn't believe it was so easy. How could she not have realised this before? This encounter emphasised a few things to me. Never assume what a student may or may not know. Always check what might seem even the most basic knowledge. Also, encourage students to ask questions. The learning environment has to be one that encourages them to communicate with you without feeling like they are "stupid". And, as the teacher, I have to listen carefully for even the tiniest cues that might indicate there is a gap in knowledge somewhere that needs to be filled. That lesson made my day.