He was born in Tehran to Abul Qasim Khan Kamal ol-Saltaneh, son of Mohammad Jafar Khan Sadr ol-Hekma, son of Mahmud Khan Kashi Malak ol-Shoara Sadr ol-Shoara Saba ol-Shoara, son of Mohammad Hossain Khan Malak ol-Shoara. He studied several of Iranian and non Iranian musical instruments and became a Ostad in Radif, but selected violin and setar as his specific instruments. He was a student of Mirza Abdollah as well as Darvish Khan.
Saba is considered one of Iran's most influential figures in traditional and instrumental Persian music.
Saba perfected his tonbak skills with Haji-Khan Zarbi and received training on the santur from Ali Akbarshahy. In addition, he learned to play the kamanche under the guidance of Hossein Esmail-Zadeh. Later, when Alinaqi Vaziri established his School of Music, Saba enrolled to learn the theory of music and the art of playing the violin. He was also familiar with ney, Western flute, and tar.