In this world, especially in Jazz music scene, it is very difficult to play with good groove on automatic backing track generators. They very likely play with less swing. As you have heard in the famous song "It Don't Mean a Thing If It Ain't Got That Swing", jazz music without swing feel does not impress much to audience.
In my analysis, the beats of good groove are multi-layered by two parameters: the length of the notes, and a classification as on-beat, off-beat; and should be played with what I call "drift". This "drift" is not a denominational terminology. Almost every note in Jazz is played earlier/later than its location where it should be played if it is written in a music sheet.
It is very important to a good rhythm section to configure the bassist and the drummer with proper drifts; otherwise their rhythm limits the possibility of improvisation of the lead players who play on the band.
And another parameter is what I call "riding". Riding indicates the direction of alignment in a melody. Assume there are several measures here, and a series of notes. When the begining of these notes are aligned at the begining of the measures, the melody is configured in head-aligned-riding; when the ending of these notes are aligned at the ending of the measures, the melody is configured in bottom-aligned-riding.
Generally, melodies which are played in high latitudes tent to be head-aligned-riding while melodies which are played in low latitude tent to be bottom-aligned-riding; therefore I sometime refer the bottom-aligned-riding as equatorial rhythm.
For further information, please see my description "Introduction of Drift and Riding - Important Parameters for Generating Good Groove".
This application is being written for the proof of the theory, now.
This application can run on Pulsar. This consists a submodule which is called "quasijazzer-band" which includes some patch files and sound fonts, etc.