In one of my guitar classes, I had a student mentioned that she never thought she’d have to learn algebra to learn music. Algebra you ask? No .. we weren’t learning algebra. We may have been applying a little geometry to our musical education. We definitely were learning how to count (at least from one to twelve). We counted backwards and forwards. Maybe we added or subtracted notes. Yet, algebra is not something that we were using.
You see, there is a certain amount of math involved in music theory. A student of the banjo, guitar and mandolin must understand numbers to truly have an understanding of the fingerboard. Not all musicians understand music theory and yet, they are great players. However, the student who manages to understand the numerical relationships of notes, will have an easier time creating and playing melody lines and lead riffs.
When comparing the banjo, guitar and mandolin, you will find certain numerical similarities, as well as some differences. The guitar, for instance, is tuned to fourths. This means that the note adjacent to another note you play on the next string is the forth note of the root note’s scale. Confused? Well, it is simpler than it sounds. The mandolin is tuned to fifths. The banjo? It is a little more complex regarding scale structure. I do not mean to confuse you further but on the banjo and in one instance, the guitar, the pattern of notes shift. It will be the shifts that alter a simple box relationship and make playing a scale a little more difficult.
Geometry & Music?
What about Geometry? Boxes, circles, angles and rectangles also exist on the banjo, guitar and mandolin. If you study the fingerboard of each of these instruments, you will discover relationships between many of the notes. It is these geometrical relationships that open up the fingerboard for a student.
So when you go to see your music instructor, if they do not know the relationships of the notes on the fingerboard, then they probably can’t help to clearly explain the instrument to you. A good instructor will not only know how to play the instrument but will be able to provide a fingerboard map to a student, which will guide you towards better lead play.