The oldest of the double-mallet grips, the traditional grip, probably came about soon after the xylophone with the modern keyboard layout (instead of the older longitudinal trapezoid layout of e.g. Polish xylophone virtuoso Joseph Gusikov (1806 – 1837)) found its way into the orchestras around 1900. Very little, if any, documentation existed of the grip until German percussionist Peter Sadlo (1962 -) in 1994 completed his dissertation Die Kunst des Schlagens which describes and analyzes the traditional grip among others. The following year in August, American marimbist Nancy Zeltsman (1958 -) had the article Traditional Four-Mallet Grip published in the magazine Percussive Notes. In 2003, Peter Sadlo released his book Hauptsache Mallets which to some extent is a summary of certain parts of his dissertation, and that features a detailed description of the traditional grip together with also the Burton, the Musser and the Stevens grip. In the same year Zeltsman’s book Four-Mallet Marimba Playing came out that contains a comprehensive description of the traditional grip and its use.
The traditional grip is the only cross-grip that has the secondary, outer mallet, below the primary, inner mallet. There seems to be two versions of the grip where one, represented by Zeltsman, always has the thumb on top of the inner mallet, and another, which Sadlo represents, that lets the thumb grip the mallet shaft from the side at small intervals. The first version is the one used by Theodor Milkov in this YouTube video: http://www.youtube.com/watch?v=X4Xm9He1uaY. The second version is mentioned in the Gary Burton (1943 -) video The 4 Mallet (Burton) Grip at http://www.vicfirth.com/education/keyboard/burton.php.
Among famous musicians that used or are using the traditional grip are for example Adrian Rollini (1903 – 1956) and Keiko Abe (1937 -).
Below are two images of my right hand demonstrating the traditional grip at the interval of a fourth on an instrument with 48 mm center to center between the naturals and with mallets that are 435 mm long and mallet shafts of 8 mm in diameter.