music theory

Fretboard Memorisation with Modular Arithmetic

2 months ago

The article introduces a method for memorizing the guitar fretboard using modular arithmetic modulo 12, assigning each note a numeric value from 0 to 11.
Traditional approaches require memorizing up to 144 positions (24 frets × 6 strings), which is effort-intensive and does not adapt to different tunings or instruments.
The proposed system requires memorizing only 12 key-value pairs (one per note) and uses a formula v ≡ r + f (mod 12), where v is the note value, r is the string's root value, and f is the fret number.
This system is tuning-agnostic and works for any number of strings or frets, even microtonal instruments with consistent intervals, but requires familiarity with modular arithmetic.
Drawbacks include the need for mental calculations modulo 12 and inapplicability to fretless instruments.