Here is the dividend fifths tuning pays that guitarists never collect: because every adjacent pair of courses sits exactly seven semitones apart, the fret relationship between any two-note interval and its fingering is a single subtraction. An interval of v semitones between a note on one course and a note on the next puts the upper finger at v − 7 frets relative to the lower one. One rule. The entire two-part harmony of Western music, filed under one number.
The offset table, computed
The table below is not typed from a method book — it is derived from the theory data this site runs on (each interval’s semitone count, minus the seven of the fifths pair), and CI recomputes it on every change:
| Interval | Size | Upper finger sits |
|---|---|---|
| Minor 3rd | 3 semitones | −4 frets |
| Major 3rd | 4 semitones | −3 frets |
| Perfect 4th | 5 semitones | −2 frets |
| Tritone | 6 semitones | −1 frets |
| Perfect 5th | 7 semitones | same fret |
| Minor 6th | 8 semitones | +1 frets |
| Major 6th | 9 semitones | +2 frets |
| Minor 7th | 10 semitones | +3 frets |
| Major 7th | 11 semitones | +4 frets |
| Octave | 12 semitones | +5 frets |
Read it with your hand: a perfect fifth is the open pair — zero offset, the tuning itself. A major third puts the upper finger three frets BEHIND the lower one; a major sixth, two frets ahead. Negative offsets feel backwards to guitar-trained hands for about a day, and then the symmetry takes over: unlike a guitar, whose B-string kink breaks every interval shape once per octave, these offsets hold on every pair, at every fret, in every key.
Scales, harmonized
Apply the offsets along a scale and you get the classic sound of fiddle-style harmony: whole scales in parallel thirds and sixths. The maps below are harmonized by the engine — scale degrees from the same data as the scale reference, each pair placed on adjacent courses at the lowest playable spot — and every pair is pitch-verified in CI. Notice how the third alternates major and minor as the scale demands; that alternation, automatic in the fingering, is diatonic harmony teaching itself.
G major in thirds
D major in thirds
G major in sixths
Practicing the maps
Play each map slowly, both notes exactly together — a lazy double stop rolls, and rolling is a choice, not an accident. Keep both fingers curled so neither touches the neighboring course it isn’t fretting, and check the pairs against the audio until your ear expects the alternation of major and minor. Then test the symmetry claim yourself: move the whole thirds map across one course pair and confirm the fingering survives, because on this instrument it genuinely does — the same experiment on a guitar is where interval shapes go to die.
Using them
Double stops are how one mandolin harmonizes itself: shadow a melody in thirds for instant bluegrass sweetness, drop to sixths when the tune sits high and you want the harmony below it, and add tremolo to a sustained pair for the string-section effect. Kickoffs, tags, and the last time through a fiddle tune are the traditional homes. For the full three- and four-course stacks these pairs grow into, the chord reference carries every quality — but most working mandolin harmony is exactly this page: two courses, one offset, played with conviction.