When a chords tones are stacked in thirds, the chord is said to be in "tertian order". In other words, if you have a C
major13 chord (which contains all the notes of a C major scale: C, D, E, F, G, A, B and C) and the order of the notes
from low to high is C, E, G, B, D, F and A, that C major13 chord is in tertian order. This chord is pictured below.
Similarly, if you order the notes of a C minor11(b13) chord C, Eb, G, Bb, D, F and Ab, that chord is in tertian order.
This chord is pictured next to the major13 chord below.

Since there are only 6 strings on the guitar (well, on the standard guitar) there is no way to play a complete 13 chord
of any kind. However, if we arpeggiate the chord tones, we can convey the sound of a tertian sonority. Below is the
tertian arpeggio for a C major13 chord. The most efficient way to play this is most likely by sweeping it. The symbols
above the notes represent picking directions. The symbol that looks like a "V" represents an upstroke while the
symbol that looks a little like a staple represents a down stroke. The two up-strokes in a row might be awkward for
some. If it is, just pull-off from the last note of the arpeggio to the first note and pick the rest of the exercise as
notated.
By flatting all the E's, A's and B's in the major version, you have the tertian arpeggio for a natural minor scale, the
complete chord being a C minor11(b13). The technique is the same as the major version.
Now that you've got the basic major and minor tertian sonorities down, let's apply it to the other 5 modes of the major
scale. Since you already know the major and minor patterns, altering them to convey the sound of another mode
should be easy. For example, to change the major (Ionian) arpeggio to the Mixolydian tertian arpeggio, just flat the 4th
note of the major arpeggio (the 7th note in the major scale). If you want to change the minor tertian arpeggio to the
Dorian arpeggio, simply sharp the 6th note in the arpeggio (the 13th note in the scale). Below is a sequence that goes
through all 7 modes diatonically starting and ending with the C major tertian arpeggio.