The Russian Musical Society (RMS) was an organisation founded in 1859 by the Grand Duchess Elena Pavlovna (a German-born aunt of Tsar Alexander II) and her protégé, pianist and composer Anton Rubenstein, with the intent of raising the standard of music in the country and disseminating musical education.
The RMS's formal successors were the St. Petersburg Conservatory, which opened (also under the auspices of Anton Rubenstein), in September 1862, and the Moscow Conservatory, founded by Nikolay Rubinstein in September 1866.

Sources

Brown, David, Tchaikovsky: The Early Years, 1840-1874 (New York: W.W. Norton & Company, Inc., 1978)
Poznansky, Alexander, Tchaikovsky: The Quest for the Inner Man (New York: Schirmer Books, 1991)
Struttle, Wilson, Tchaikovsky, His Music and Times (Speldhurst, Kent, United Kingdom: Midas Books, 1979)
Warrack, John, Tchaikovsky (New York: Charles Scribner's Sons, 1973)