True Temperament
Curved frets that solve local intonation problems
Notice how the fret curves differently for each string. Thicker bass strings need more compensation than thin treble strings.
Deviations from 12-Tone Equal Temperament Due to String Stretching
Equal temperament solves the global problem of tuning across keys. But there is a separate, mechanical problem: when you press a string down to a fret, you physically stretch it. This effect is desirable when we bend notes for expression, but it also insidiously raises the pitch of every fretted note above its ideal equal-temperament frequency. The result is that chords can sound slightly out of tune, especially higher up the neck where the stretch effect is more pronounced.
Fretting a string changes its tension and vibrating length, causing intonation issues that vary by string and fret position.
Why Fretting Raises Pitch
When you press a string down to a fret, you are forcing it to travel a longer path than when it sits at rest. The string must now travel down from the nut, to the fret, and back up to the bridge. This detour increases the total length of the string, stretching it.
The fundamental frequency of a vibrating string is determined by the equation:
When tension (T) increases due to stretching, the frequency goes up. This means the fretted note is slightly sharper than the ideal equal-temperament pitch. The effect is small but audible, especially in chords where multiple slightly-sharp notes compound the error.
The amount of stretch depends on several factors:
- Action height: Higher action means pressing the string down further, causing more stretch.
- String gauge: Thicker strings have a higher μ (mass per unit length), which affects how much the frequency changes with tension.
- Fret position: The geometry changes along the neck, so the stretch amount varies by fret.
- Scale length: Longer scale lengths mean higher base tension, which can make the stretch effect more or less pronounced depending on other factors.
The Solution: Per-String Fret Positioning
True Temperament frets are individually calculated for each string at each fret position. The result is the characteristic curved or "squiggly" appearance.
Each point on the fret is positioned to give the correct pitch for that specific string when fretted, accounting for its gauge, tension, and the geometry at that position.
Practical Benefits
Chords sound more in tune
All notes in a chord are properly in tune with each other, eliminating the need to "retune" certain strings to compensate for intonation issues, especially during recording.
Not just for one tuning
Since the compensation is based on physical string properties rather than specific notes, it works in any tuning.
Summary
- Fretting a string stretches it, raising its pitch slightly
- The amount of stretch varies by string gauge, action, and fret position
- Straight frets cannot compensate for per-string variations
- True Temperament frets are curved to provide optimal positioning for each string at each fret
- The result is improved intonation across the entire fretboard