Guitar Fretboard Navigation: Cross-String Movement Formulas
Master practical techniques for finding notes and intervals across guitar strings using mathematical relationships
š Part 2 of 2: This builds on the theoretical foundation from Part 1: Why Strings Are Tuned This Way. Start there if you want to understand the "why" behind these techniques.
š” The Guitar Secret: Finding Notes Across Strings
The basic idea: When you move up the fretboard on one string, you can find that same note by moving back on the next string.
šÆ How it works:
- ā¢ Guitar strings are tuned 5 frets apart (except G to B which is 4 frets)
- ā¢ If you go up 2 frets on the low E string, the same note is 3 frets back on the A string
- ā¢ If you go up 3 frets, the same note is 2 frets back
- ā¢ They always add up to 5 (or 4 for G to B)
It works for going from higher to lower notes too. If you go down 2 frets on the high E string, the same note is 3 frets away (but forward rather than back).
Why this helps:
This shows us two possible paths to find the same note. It's just another way of thinking about the fretboard.
Example: A to C
Two paths to the same note C: 8th fret E string OR 3rd fret A string
š¢ Maths and More Examples
You don't have to understand the maths. Looking at the diagrams will be enough for most to understand this concept. Just look at how many frets away the note is on the same string from the note you want to start from and figure out the other puzzle piece that adds up to 5 (4 for G and B string pair). You'll see 2s pair with 3s, 1s pair with 4s and so on.
š„ The Two Formulas
Here are the two simple formulas that let you find any note on any adjacent string pair:
Moving to Higher Notes
C = M - SCross-string position = Movement - String interval
Moving to Lower Notes
C = M + SCross-string position = Movement + String interval
Where: C = Cross-string fret position, M = Movement along string (in frets), S = String tuning interval (5 or 4 frets)
š Key Insight
The same note is always found in a predictable relative position on adjacent strings:
Higher String (thinner):
Same note is found BACK
Back = -S
Lower String (thicker):
Same note is found FORWARD
Forward = +S
š Moving to Higher Notes (Ascending)
When moving UP to a higher note on a thinner string, you typically move BACK on the fretboard.
Ascending Formula
C = M - SMove back = negative = minus sign
Example: Minor 3rd Up (E to A Strings)
Movement (M): A to C = +3 semitones (minor 3rd up)
Calculation: C = M - S = 3 - 5 = -2
Result: Move back 2 frets: 5th - 2 = 3rd fret A string ā
Compare: Same-string C on 8th fret vs cross-string on 3rd fret
Example: Major 3rd Up (G to B Strings)
Movement (M): C to E = +4 semitones (major 3rd up)
Calculation: C = M - S = 4 - 4 = 0
Result: Same fret: 5th fret B string ā
Compare: Same-string E on 9th fret vs cross-string on 5th fret
More Examples:
Major 3rd up (+4 frets): C = 4 - 5 = -1 ā move back 1 fret
Perfect 5th up (+7 frets): C = 7 - 5 = +2 ā move forward 2 frets
š Moving to Lower Notes (Descending)
When moving DOWN to a lower note on a thicker string, you typically move FORWARD on the fretboard.
Descending Formula
C = M + SMove forward = positive = plus sign
Example: Whole Step Down (A to E Strings)
Movement (M): D to C = -2 semitones (whole step down)
Calculation: C = M + S = (-2) + 5 = +3
Result: Move forward 3 frets: 5th + 3 = 8th fret E string ā
Compare: Same-string C on 3rd fret vs cross-string on 8th fret
Example: Minor 3rd Down (B to G Strings)
Movement (M): G to E = -3 semitones (minor 3rd down)
Calculation: C = M + S = (-3) + 4 = +1
Result: Move forward 1 fret: 8th + 1 = 9th fret G string ā
Compare: Same-string E on 5th fret vs cross-string on 9th fret
More Examples:
Whole step down (-2 frets): C = -2 + 5 = +3 ā move forward 3 frets
Perfect 4th down (-5 frets): C = -5 + 5 = 0 ā same fret
High E to B string (-2 frets): C = -2 + 5 = +3 ā move forward 3 frets on the B string
This works for any note - go down 2 frets on high E, same note is 3 frets forward on B string!
š§ Memory Aid
Move Forward = +S ā¢ Move Back = -S
The same note is found back on higher strings, forward on lower strings
Where:
- M = Movement along current string (+ascending, -descending)
- C = Cross-string movement (+forward, -backward)
- S = String tuning interval (5 or 4 frets)
šø Practical Applications
šµ Power Chords (Perfect 5th)
E-A strings: 7 - 5 = +2 ā 2 frets forward
A-D strings: 7 - 5 = +2 ā 2 frets forward
G-B strings: 7 - 4 = +3 ā 3 frets forward
Classic power chord shape!
šµ Major 3rds
E-A strings: 4 - 5 = -1 ā 1 fret back
A-D strings: 4 - 5 = -1 ā 1 fret back
G-B strings: 4 - 4 = 0 ā Same fret
Essential for major chord shapes!
šµ Octaves
E-A strings: 12 - 5 = +7 ā 7 frets forward
A-D strings: 12 - 5 = +7 ā 7 frets forward
G-B strings: 12 - 4 = +8 ā 8 frets forward
Perfect for melodic doubling!
šµ Perfect 4th
E-A strings: 5 - 5 = 0 ā Same fret
A-D strings: 5 - 5 = 0 ā Same fret
G-B strings: 5 - 4 = +1 ā 1 fret forward
Great for sus4 chords!
šÆ Visual Examples: Different String Pairs
A-D String Pair: Cross-String Relationship
A-D String Formula (5-Fret Interval):
Movement along string (M): C to E = +4 frets (ascending)
String interval (S): A to D = 5 frets
Cross-string movement (C): C = M - S = 4 - 5 = -1
Result: Move 1 fret back: 3rd - 1 = 2nd fret D string ā
G-B String Pair: Cross-String Relationship (4-Fret Interval)
G-B String Formula (4-Fret Interval):
Movement along string (M): C to E = +4 frets (ascending)
String interval (S): G to B = 4 frets
Cross-string movement (C): C = M - S = 4 - 4 = 0
Result: E is on the same 5th fret B string ā
Descending: A to E Strings
Descending: D to C = -2 frets (descending)
Formula: C = M + S = -2 + 5 = +3
Result: 5 + 3 = 8th fret E ā
Descending: B to G Strings
Descending: F to E = -1 fret (descending)
String interval: B to G = 4 frets
Formula: C = M + S = -1 + 4 = +3
Result: 6 + 3 = 9th fret G ā