Great question. Perhaps you've seen this entry from our Fact Sheet:
Sour and Sweet Cherry
"All sour cherries are self-fruitful, such as Montmorency, North Star, Balaton, Meteor, English Morello, Early Richmond, Hansen Bush Cherry and Nanking. Most sweet cherries are self-unfruitful(self-incompatible, SI) and require cross pollination with another variety as the pollen source.
Some varieties, e.g. Bing, Lambert, Royal Ann/Napoleon, are also cross-unfruitful and cannot be depended upon to provide pollen for each other. Index, Lapins, Skeena, Sweetheart, WhiteGold, Sonata, Stella, Symphony, Sunburst, and BlackGold are self-fruitful (SF) sweet cherries that can serve as “universal” pollen sources for many self-unfruitful sweet cherry varieties (Stella does not work for Bing in some areas).
Their use as “universal” pollinators should also take bloom timing into consideration as follows. Early-bloom: SI – Somerset; SF – Lapins and Skeena. Early- to early-mid-bloom: SI – Kristin, Chelan, and Black Republican; SF – Sweetheart and WhiteGold. Mid- to late-mid-bloom: SI – Royalton, Summit, Ranier, Royal Ann / Napoleon, Bing, Burlat, Van, Regina, Lambert, Sam, and Windsor; SF – Sonata, Stella, Symphony, and Sunburst. Late-bloom: SI – Gold and Hudson; SF – BlackGold. Move bees into orchards on the first day of bloom."
It does appear that Montmorency and Black Tartarian will cross, but they don't reliably bloom at the same time (M is late and BT is early).