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                                                                     EXHIBIT 3.2

                           CERTIFICATE OF AMENDMENT
                                      TO
                         CERTIFICATE OF INCORPORATION
                                      OF
                                TCI MUSIC, INC.

   TCI Music, Inc., a corporation organized and existing under and by
virtue of the General Corporation Law of the State of Delaware, DOES HEREBY
CERTIFY:

   FIRST: That the Board of Directors of TCI Music, Inc., at a special
meeting of the directors on June 22, 1999, adopted resolutions setting forth
proposed amendments to the Certificate of Incorporation of said corporation. The
resolutions setting forth proposed amendments are as follows:

       RESOLVED, that proposed amendments to the Certificate of Incorporation of
   the corporation, (i) deleting in its entirety SECTION B of ARTICLE VIII --
   MEETINGS OF STOCKHOLDERS, (ii) amending and restating ARTICLE I -- NAME to
   read in its entirety as follows, and (iii) amending the first two paragraphs
   of ARTICLE IV -- CAPITALIZATION to read as follows, are recommended to the
   stockholders for approval as being in the best interests of the corporation:

                                   ARTICLE I

                                     NAME

        The name of the Corporation is Liberty Digital, Inc.


                                  ARTICLE IV

                               AUTHORIZED STOCK

        The total number of shares of capital stock which the Corporation shall
     have authority to issue is one billion seven hundred and fifty five million
     (1,755,000,000) shares, of which one billion seven hundred and fifty
     million (1,750,000,000) shares shall be common stock ("Common Stock") and
     five million (5,000,000) shares shall be preferred stock with a par value
     of $.01 per share ("Preferred Stock"). The Common Stock shall be a single
     class designated as Common Stock with a par value of $.01 per share and
     shall be issuable in series as provided in Section A of this Article IV. A
     description of the Common Stock and the Preferred Stock of the Corporation,
     and the relative rights, preferences and limitations thereof, or the method
     of fixing and establishing the same, are as


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     hereinafter in this Article IV set forth:

                                   SECTION A

                   SERIES A COMMON AND SERIES B COMMON STOCK

        One billion (1,000,000,000) shares of Common Stock shall be of a series
     designated as Series A Common Stock (the "Series A Common Stock") and seven
     hundred and fifty million (750,000,000) shares of Common Stock shall be of
     a series designated as Series B Common Stock (the "Series B Common Stock").
     Each share of the Series A Common Stock and each share of the Series B
     Common Stock shall, except as otherwise provided in this Section A, be
     identical in all respects and shall have equal rights and privileges.

   SECOND: That the stockholders of said corporation duly adopted the foregoing
resolutions at a meeting of the stockholders held September 8, 1999, which
meeting was called and held in accordance with the provisions of Section 222 of
the General Corporation Law of the State of Delaware.

   THIRD: That said amendments were duly adopted in accordance with the
provisions of Section 242 of the General Corporation Law of the State of
Delaware.

   IN WITNESS WHEREOF, TCI Music, Inc. has caused this certificate to be
executed by David B. Koff, its Vice President, on this 9th day of September,
1999.

                                       TCI MUSIC, INC.

                                       By: /s/  David B. Koff
                                           -------------------------------
                                            David B. Koff, Vice President


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