Memorizing the fretboard typically requires learning up to 144 positions on a 24-fret guitar, a process that fails when switching tunings. The author proposes a system based on modulo 12 arithmetic, treating the chromatic scale as a cyclic group where notes A through G# map to values 0 through 11. The open A-string directly reflects this mapping: fret 12 returns to A (12 ≡ 0 mod 12). For any string, the note value v at fret f is v ≡ r + f (mod 12), where r is the string's root value (e.g., E = 7). This reduces memorization to just 12 key-value pairs.

Advantages include tuning-agnostic application across any number of strings or frets, and adaptability to microtonal systems with consistent intervals. The method requires only knowing each string's tuning. Drawbacks involve the prerequisite of modular arithmetic fluency and rapid mental calculation modulo 12, plus inapplicability to fretless instruments. The author credits Oscar Levin's *Discrete Mathematics – An Open Introduction* for the modular arithmetic foundation.

While likely not historically novel, this approach offers a mathematically rigorous alternative to rote memorization, directly linking fret positions to semitone intervals from the string's root note.