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Watch the Sixth's & Compound online guitar lesson by Jeff Beasley from Shred Ahead Blues Rock

The sixth interval is the product of the inversion of the common major and minor third. Inverting something simply means you're turning it upside down. For example in A the fourth string at the seventh fret is A and the third string at the sixth fret is C#. In this case the A is the root and the lower note whereas the C# is the harmony and the higher note. If we invert this interval of a major third by making the root A an octave higher on the the first string fifth fret and keep the C# where it is on the third string sixth fret we have a minor sixth distance of 8 frets. If we take a minor third we'll have the A note on the fourth string seventh fret and the note C on the fifth fret on the third string. Placing the A root on the octave A on the first string fifth fret and again keep the C on the third string fifth fret we have a major sixth or 9 frets.
Knowing the distances involved in the major scale will be of major importance in executing common passages using third or sixth intervals. The distances between the notes of the major scale are as follows: whole-whole-half-whole-whole-whole-half. This gives us seven different tones and an octave. Each tone if harmonized will produce a basic chord in that key. The chords in a major key are as follows: major, minor, minor, major, major, minor, diminished, major. This formula tells that the distance from a major one to a minor two is a whole step, the distance from a minor two to a minor three is a whole step, etc. Any note that is played that is not part of the major scale sequence can be considered a passing tone. If that passing tone is harmonized into a chord it can be called a passing chord. There are many types of passing chords but the most common is the diminished passing chord. The diminished chord a the equidistant quality allowing it to repeat itself every three frets. Diminished triads and fully diminished chords have this quality and offer the player the opportunity to move linearly on the fret board to increase or decrease tension in the listener.
Compound intervals are intervals or distances that are greater than an octave apart. If I replace the root on the minor sixth, first string fifth fret "A" with the sixth string fifth fret "A" I have the compound interval of 16 frets also known as a major tenth and If I do the same with the major sixth and have the distance of 15 frets or a minor tenth.