Marjory Kennedy was born in Perth to a well-known Scottish singer, David Kennedy and his second wife, Elizabeth Fraser. As a child she used to accompany her father on his tours in Scotland and abroad, playing the piano while he sang. Various of her siblings were also professional musicians, and three of them (Lizzie, Kate and James — soprano, contralto and baritone respectively) died in the fire that burnt down the Théâtre municipal of Nice, France, in 1881.
In 1887 she married her mother's younger cousin, the mathematician Alexander Yule Fraser. Marjory thus found herself a widow at the age of thirty-three, and with her two small children, David and Patuffa, to look after. She settled at 5 Mayfield Road in southern Edinburgh with her mother and two sisters and made her living as a music teacher and lecturer.
In the following years, she visited many of the islands to the west of Scotland, recording the traditional songs with a wax cylinder phonograph. She later arranged them for voice and piano, or sometimes for harp or clà rsach —an instrument her daughter Helen Patuffa played. The arrangements, with words translated to English by the Rev. Kenneth MacLeod, were published in her three-volume Songs of the Hebrides in the years 1909, 1917 and 1921. A fourth volume, From the Hebrides: Further Gleanings of Tale and Song, followed in 1925. One of the songs included in this collection eventually came to be widely known by the title "Eriskay Love Lilt".
For her contributions, Marjory was awarded with a CBE, together with an honorary degree of Doctor of Music from the University of Edinburgh, awarded in 1928. In 1930 she presented her archive of songs to the University Library, including her original wax cylinders of recordings. Marjory Kennedy-Fraser died in Edinburgh in the same year.
In order to preserve her original wax cylinder recordings, they were re-recorded on tape several decades later for the Sound Archives of the School of Scottish Studies. More recently, they have been digitized and are held in the collections at the University of Edinburgh.