Equal-tempered coordinate
d = s - s / 2^(n/12), where s is nominal scale length, n is fret number, and d is the distance from the nut witness point to that fret.
At fret 12, d = s/2. Adjacent slot spacing is the current cumulative coordinate minus the previous coordinate. Saddle compensation changes the practical string endpoint; it does not change the nominal fret formula.
Generate a coordinate table or plan per-string coordinates.
Scope of this reference
Define cumulative 12-TET fret coordinates, adjacent spacing, scale length, and compensation boundaries. Use Fret Position Formula Reference to make a repeatable decision for this named task, not to impose one specification on every instrument.
Practical example
For a 25.5-inch scale, fret 12 is 12.750 inches from the nut and fret 24 is 19.125 inches. These invariant checks verify the equal-tempered coordinates; practical saddle compensation changes the string endpoint, not the nominal fret-slot formula.
Record the conditions
For Fret Position Formula Reference, write down instrument type, tuning, installed strings, relevant hardware, climate when material, physical datum, unit, tool resolution, and the result before and after change. A result from this reference is comparable only when its method travels with the number.
Verification checklist
- For Fret Position Formula Reference, confirm the starting state and exact question.
- Repeat its critical measurements from the same reference.
- Compare its result with direct observation and applicable maker documentation.
- Change one reversible variable where the task permits.
- Retest the named symptom and preserve unresolved exceptions.
Related workflow
- fret position template — continue when that page answers the next unresolved measurement or decision.
- multiscale fretboard planner — continue when that page answers the next unresolved measurement or decision.
Limits
Fret Position Formula Reference cannot inspect hidden structure, material condition, service history, or player technique. Stop this reference workflow for electrical hazards, abnormal resistance, structural movement, conflicting readings, or unplanned material removal.