§ 424. Institute of arts and sciences. Real property which may hereafter be acquired within a city having a population of one million or more by a corporation, organized exclusively as an institute of arts and sciences for the general purposes of the encouragement of the study of and the advancement of knowledge in the arts and sciences within such city on which a building has been constructed as an academy of music which is maintained and operated by such corporation as such and to otherwise further the purposes for which such corporation was organized, shall be exempt from taxation including the buildings thereon as provided for corporations in section four hundred twenty-a of this article although a portion thereof is leased or otherwise used for the public performances of opera or concerts, lectures, graduation exercises or for such other non-commercial uses for the purposes of income, if such income is necessary for and is actually applied to the maintenance and support of such academy of music.