See attache Atholl Lineage from Burke's Peerage

The Murrays of Tullibardine descend from Malcolm de Moray whose son, Sir John, married the daughter of the Seneschal of Strathearn bringing them the lands of Abercairney (east of Crieff) around 1320. Another marriage by the family into the old Celtic aristocracy of Perthshire by Sir William brought further lands around Tullibardine and their place in Perthshire history.

The Murrays of Tullibardine

The exact linage after Walther or his brothers to the Murrays of Tullibardine is not clear. Burke’s Peerage says that Freskin’s grandson William Moray of Petty (William de Moravia) is the ‘probable’ ancestor of Sir Malcolm Murray, Sheriff of Perthshire.(1) Sir Malcom Murray’s son Sir William Murray succeeded his father and married Ada, daughter of Malaise, Seneschal of Strathern and thus acquired the lands of Tullibardine. http://clanmurray.org/history.html#burke

The Heraldry of the Murrays in Chapter 2 suggests that Malcolm was the second son of Walter Moray probably named after his maternal grandfather.

The earlier writers thought that Sir Malcolm Murray (No. 86) was a son of a John Moray, Sheriff of Perth, supposed to be a son of Hugh Moray of Duffus (No. 2, a), but there is no evidence to support this view, and as there were two, if not three, John Morays living at that time, this suggested origin has been abandoned.

(86) Sir Malcolm Murray or de Moravia died before 1289. He was witness to a charter granted by Malise, Earl of Strathearn, between 1251 and 1263. He was Sheriff of Perth about 1276, and is said to have married the daughter and heiress of Gilbert of Gask, with whom he got that property. He had two sons:

86(a) John Murray, who gave his lands of Culnacloich and Ruthtrelan in Strathbogie about 1284 and the lands of Aldie to his brother, William.

86(b) William (No. 87 below).

ARMS on Seal. Three stars, with a label of three points in chief (Laing's Seals). [Plate III., fig. 6.]