The goal of this article is to share with fellow guitarists a simple way of finding any harmonic interval all over the fretboard. This method allows you to quickly build intervals, such as thirds, sixths, tenths, etc., from any note on any string.
First, lets go through some basics:
Interval is a distance between two notes measured by number of semitones, or half-steps. On the guitar, one fret represents a semitone. Twelve frets make an octave. Some intervals extend above the octave. Those are called compound intervals. For example: the major 3rd (normally 4 frets), when placed an octave higher, becomes the major 10th (4+12=16 frets). The exact number of semitones (frets) is called the interval quality. This is what gives an interval its full name and sound.
The following table explains the simple / compound interval relationship and the number of frets for each interval.
Now we’re going to apply this table of intervals to a guitar neck. Let’s look at basic guitar tuning in terms of intervals. The string pairs (that is, each string in coupled with the next higher string) 6/5, 5/4, 4/3 and 2/1 make Perfect 4th (5 frets). 3/2 string pair makes Major 3rd (4 frets). You already know this if you can manually tune your guitar.
So, the interval between Low E and High E would be 5+5+5+4+5=24 frets (two octaves).
Using this knowledge we can easily find the interval between any two notes on any two strings at the same fret. Fig.1 explains this graphically:
1st fret F-to-F : 5+5+5+4+5=24 frets (2 octaves)
4th fret G#-to-F# : 5+5=10 frets (Minor 7th)
5th fret E-to-A : 5frets (Perfect 4th)
8th fret F-to-G : 5+5+4=14 frets (Major 9th)
10th fret F-to-D : 4+5=9 frets (Major 6th)
In each of the above examples, we moved vertically through the string pairs, adding string pair intervals along the way. Let’s call it the “vertical movement.” We were able to build many types of intervals. But there are still many other types of intervals. How do we get those?
To be able to build all interval types we have to move horizontally as well as vertically. The horizontal movement is simple: we move right to add frets; we move left to subtract frets. It is possible to add or subtract one, two or three frets. More than three frets would get the left hand ‘overstretched’. Fig.2 explains the “horizontal movement” graphically:
1st fret F-to-A : 5+5+5+1=16 frets (Major 10th)
4th fret G#-to-G# : 5+5+2=12 frets (Octave)
5th fret E-to-F# : 5-3=2 frets (Major 2nd)
8th fret F-to- F# : 5+5+4-1=13 frets (Minor 9th)
10th fret F-to-E : 4+5+2=11 frets (Major 7th)
In these examples we moved vertically through the string pairs then horizontally along a single string. Note that in some examples we moved left to add frets, in other examples we moved right to subtract frets.
So, now every possible interval is within our reach. It is not even necessary to know the note names, just pick first note and find the second one counting the right number of frets. We can always go to the table of intervals for reference.
I believe that this simple method can be useful in many ways: building chord shapes, analyzing scale ‘boxes’ for ‘double stops’, harmonizing scales and runs, and much more.
Happy guitar playing.