Tetrachord scales on the guitar
Recently, while listening to a talk on standard guitar tuning, I was introduced to the concept of tetrachords as a way of navigating the guitar fretboard. This was a fascinating conceptual shift which motivated me to explore further the application of tetrachords to scales on the guitar neck. I had always wanted to expand my scale knowledge and this was a method that gels well with systems software thinking, being grounded in composability, abstraction and symmetry.
The goal of the text below is to derive 3-octave guitar scales from tetrachords. Tetrachords are 4-note scale fragments spanning a perfect fourth interval. Viewing the guitar fretboard through this lens appears to confer a number of advantages, including: Building scales from music theory fundamentals. Other methods for deriving scales start with learned patterns such as CAGED, 3NPS, etc. In cases such as CAGED, there is an organizing principle, namely the respective chord shapes, below we build directly on the scale definitions. All scale memorization is based around awareness of key anchor ports on the fretboard, the perfect intervals [1, 4, 5, 8]. Composability. 7-note scales are built out of pairs of tetrachords, of which only a handful are commonly needed. Tetrachord building blocks are snapped together to form scales like Lego or Tetris pieces. Scalability. Knowing 5 tetrachords gives 25 derived 7-note scales. Learning scales sub-linearly, O(sqrt(N)) with the number of scales. This advantage is tempered by the limited number of scales and modes that are contextually relevant. Minimizing rote memorization. It's not even necessary to remember that a major scale consists of the WWHWWWH intervals. Instead, only the (shorter) major tetrachord intervals WWH needs to be remembered and the fact that a major scale consists of two concatenated major tetrachords. The tetrachord names used below also assist here, acting as a mnemonic device for their associated scales. Range. The entire fretboard and guitar range can be covered with reusable patterns. Improvisation. Tetrachords can be used as an organizing principle for improvisation. Tetrachord intervals can imply [[1]](https://youtu.be/-3oo45vpQV4?t=844)[[2]](https://youtu.be/mQDEYda1-xQ?t=284) tendencies in melodic movement.
The derived scales below follow logically from tetrachord definitions. While some efficiency considerations are made, e.g. reducing position shifts with the left hand and awkward stretches, these scale patterns are not always optimal for playability. As an early intermediate-level guitar player, my own experience so far is that the win from tetrachordal thinking on the guitar is having a consistent and efficient method for understanding music theory on the fretboard.
All diagrams below are generated via a Python script, which provides an executable specification of the tetrachords and scales. The canonical version of this article lives in the tetrachords repository on GitHub.