The perfect fifth and the perfect fourth
Perfect Fifth
Perfect Fourth
On guitar, the perfect fifth is two frets up and three frets up when you cross to the next string, and seven frets up along one string. On guitar, the perfect fourth is the same fret and one fret up when you cross to the next string, and five frets up along one string.
The perfect fifth is shown above and the perfect fourth below, on the same pairs of strings. Play one shape and then the other, and you will hear that only the distance between the notes has changed.
Take a fifth, such as C up to G, and raise the C by an octave. Now the interval reads G up to C, which is a fourth. The two note names have not changed. What has changed is which one is underneath, and this is called inverting the interval.
Every interval has a partner like this. If you count the note names, the two numbers always add up to nine. If you count semitones, they add up to twelve. A fifth pairs with a fourth, a major third with a minor sixth, and a major second with a minor seventh. A major interval becomes minor when it is inverted, and a perfect interval stays perfect.
This is worth knowing because the neck asks you to do it all the time. A shape that will not fit on the strings you have left often fits once it is turned over, and the harmony stays the same.