# Three-Notes-Per-String Patterns and Factorials

This lesson and the ones that come after it are about working out the possible orders in which you can play patterns involving 3, 4 or more notes per string. Before we get into that, let's look at an example of what I mean.

Here's a standard 3-notes-per-string ascending pattern for the Aeolian scale in A:

T------------------------------------------------7--8--10-------------------------------------- |--------------------------------------6--8--10------------------------------------------------ A-----------------------------5--7--9---------------------------------------------------------- |--------------------5--7--9------------------------------------------------------------------- B-----------5--7--8---------------------------------------------------------------------------- |--5--7--8-------------------------------------------------------------------------------------

We use patterns like this because they give us great advantages when using economy picking, but they can sound a bit monotonous. A good way to vary them is to vary the order you put your fingers down on each string. So, instead of playing 5-7-8 on the sixth string, let's play 7-8-5, and continue that pattern -- starting with the middle note, rising to the high note and then dropping to the low note -- throughout the pattern:

T------------------------------------------------8--10--7-------------------------------------- |--------------------------------------8--10--6------------------------------------------------ A-----------------------------7--9--5---------------------------------------------------------- |--------------------7--9--5------------------------------------------------------------------- B-----------7--8--5---------------------------------------------------------------------------- |--7--8--5-------------------------------------------------------------------------------------

How many more variations are there like this? Well, on each string you have three notes, so you have a choice of three possible notes to start from. Then there are two notes left, so the second note can be either of those; that gives 3x2 possibilities. The last note has to be the one that's left, so we don't have any more choices. So we'd expect to find 3x2x1=6 possible patterns like this, and so we do. Here they are for the sixth string; you can work out how to apply them to the pattern given, or to other three-note-per-string patterns you know:

|--5--7--8--| |--7--8--5--| |--7--5--8--| |--5--8--7--| |--8--5--7--| |--8--7--5--|

These patterns can, of course, be applied to the scale when it's descending as well. Working through them one by one, ascending the full scale through all positions each time, makes an excellent technical workout and provides flexibility for improvisation. It's also a very solid procedure for fully internalising a new scale shape once the basic CAGED positions have been learned.

The product 3x2x1 can be written as 3!, pronounced "three factorial". We'll meet larger factorial numbers in some subsequent lessons.