Yesterday being the 30th of Av (and Rosh Chodesh Elul), prompted a question at shul: exactly when do we start saying Psalm 27—on the first day of Elul or the first day of Rosh Chodesh Elul? Most of my siddurim (including ArtScroll) have something ambiguous like "from the start of Elul". The Orthodox Union web site clearly states "beginning with the second day of Rosh Chodesh Elul . . ." On the other hand, Siddur Tehillat Hashem (Chabad) clearly states, "From the first day of Rosh Chodesh Elul . . .". (Just for the record, we included it.)
So is the tradition to have different traditions? What are the authorities for the two opinions?