Saba was born in Tehran in 1902. His familiarity with music began when taking lesson of setar from his father and Tombak lessons from his aunt's maid. Saba completed his studies on Tombak under the supervision of the Tombak Master Haji Khan.
He learnt the principles of playing setar from Mirza Abdollah and continued and finished his studies with Gholam Hossein Darvish.
Before referring to the Violin, Saba studied Kamancheh under Hossein khan Esmaeil -zadeh. His first violin teacher was Hossein khan Hang Marin and in 1923 when Vaziri Higher School of Music was established he attended his violin classes. As it is quoted from Khaleghi, Vaziri must be known as the last violin instructor. Saba and Khaleghi were both the first students of Vaziri's music classes.
Saba is above all well known for his Violin and Setar despite he mastered many other instruments such as the Ney, the Tar, the Kamancheh and the Tombak.
He had a very personal way of playing the Setar, and his mastery of the instrument was so high that it became one of the major styles to be studied by Setar apprentices. His plectrums were careful, unique and perfect and his left and right plectrums on Setar were uncomparable. Saba enjoyed good relations with his contemporary poets and artists. He studied at the American School for a while till 1922 when he quited school for ever and spent all his energy in learning music. In his youth he worked in a carpenter workshop, a skill which would help him later in making musical instruments.
In 1927 Vaziri sent him to run the Conservatory of Rasht, in the borders of the Caspian Sea, where he managed to gather local melodies within three years. These collections influenced his later compositions and adaptations to the classical music. Some of these melodies were Zarde Malijeh, Koohestani, Deylaman, all of these in the mode of Dashty. He also introduced rythmical patterns such as 5/4, 7/4 into the Iranian classical music. Saba had also had a concise knowledge of the western classical music when studying the Violin. During his youth, he also went to Kamal -al -Molk school where he learnt painting. Saba in addition to loving Iranian classical literature, was familiar with the new literature. He had studied Nima and Hedayat's works and was intimate with Nima himself.
Saba was a perfect instructor, both in theory and performance. His studens became among the greatest masteros of Iranian classical music. Students such as Tehrani (Tombak), Tajvidi (violin), Payvar (santur), Kassae (Ney), Dehlavi (composer). He passed away in 1957 and was buried in Zahiroddole cemetry of Tehran.