In much of tonal music, two-part density is written in parallel thirds and sixths. This tends to be too commercial sounding for most jazz writers and is usually avoided. It can still be used to good effect in the correct situation.
The example below, written by Eric Richards, is a perfect example of how to use 3rds and 6ths. It fits the Latin style very well and could have easily dominated the chart. In the interest of variety the composer does not let this happen. It is but a brief four measures long - out of a total of 272 measures.
The example below is of two-part density using parallel fourths, also called quartal harmony (see HARMONY - QUARTAL). It is also an example of planing (see COMPOSITIONAL TECHNIQUES - PLANING).
Below, Michael Abene has written an interesting mix between unison and two-part density, and between parallel and contrary motion. Another interesting item in this example is the doubling of trumpets and soprano saxophones. The trumpets definitely dominate but the added soprano saxophone gives it a smoother, less piercing, and relaxed sound quality. Writing unison trumpets and soprano saxophones can cause serious intonation problems if not written in a comfortable register and played by experienced musicians. Notice the planing of P4 intervals in the last two measures.