An example of a basic mathematical concept could be one such as could be described as 1,3 across the neck and back, and which could be represented as shown below:
We call this a mathematical pattern because it is based on positions related to a numbers system in regard to which frets are to be played and the inter-relationships between notes on strings and so forth. The 1,3 reference above can be used to represent both the logical fingering and the relative positions of the two frets on every string shown in the graphic. While this is ultimately NOT the numerical system we’ll be referring to in the mathematical pattern concepts discussion to follow it is an additional example of how numerical, or mathematical systems are a valid way of representing fingerboard patterns and related concepts. Certainly the visual aspect is also key to being able to understand and utilize any sequence conceptualized in this way, but numbers and numerical systems will be key as you will soon see
First Concept: Linear Up & Down
As we begin to deal with all this it’s crucial to realize that all patterns can be approached and practiced similarly. As we get the pattern going we practice it first with a simple concept we’ll call “Linear Up & Down.”
As you might suspect, the numbers represent the order in which the notes will be played. So this pattern is to be played as “Linear Up & Down” by following the number sequence 1, 2, 3, 4, 5… through 12 and then reverse by either thinking of 12, 11, 10… etc., or by reversing the numbers (as shown in the second graphic above) if that is easier to conceptualize. Either way, we are simply playing the notes of the pattern in ascending order and then in descending order. This simple concept is an ideal initial approach in order to get the pattern in your head AND to focus on playing it, as you should with ANY exercise, with consistent tempo, feel, volume, attack, technique, etc. The simpler the concept the better the opportunity to lay the groundwork for perfecting all aspects of the skills and techniques that lead to smooth, efficient playing.
Now that we understand the “Linear Up and down we can use it on any pattern. So, let’s do a different pattern, 1,2 across the neck and back:
If we number the note positions they will again be 1, 2, 3, 4, 5… through 12 as they ascend and then reverse descending. The positions of the notes on each string will have changed from 1,3 in the first pattern, to 1,2 in the second, but the “Linear Up and down remains the same. The two pattern sequences sound different, but much of the mental and physical aspects are the same in both. Cool huh?!?