<PAGE>   1



                                                                  Exhibit 10.34



                                TCI, Music, Inc.
                             67 Irving Place North
                            New York, New York 10003


                                                                   May 18, 1999


AT&T Broadband & Internet Services, Inc.
9197 South Peoria Street
Englewood, Colorado 80112

Attention: Madison E. Bond

Dear Mr. Bond:

         As an inducement to AT&T Broadband & Internet Services ("AT&T
Broadband") to enter into, and conditioned upon the execution and delivery by
it of, a revised affiliation agreement (the "MTV Agreement") with MTV Networks,
a division of Viacom International, Inc. ("MTVN"), replacing the existing
affiliation agreement between Tele-Communications, Inc. and MTVN and providing
for the distribution of MTVN's services on the AT&T Broadband cable television
systems, and subject to MTVN and TCI Music, Inc. ("TCIM") entering into an
agreement (the "Music.co Agreement") to form a joint venture to be named
"Music.co" to engage in the online music and music-related businesses,
including e-commerce, TCIM will enter into an agreement with AT&T Broadband
having the following terms:

EXCESS AMOUNT PAYMENT:              Upon the occurrence of the Triggering
                                    Event, TCIM shall become obligated to pay
                                    to AT&T Broadband an amount (the "Excess
                                    Amount") equal to ten percent


<PAGE>   2


AT&T Broadband & Internet Services, Inc.
May 18, 1999


                                    (10%) of the Excess Value, but in no event
                                    less than $15 million nor more than $30
                                    million.

TRIGGERING EVENT:                   The Triggering Event will be the first to
                                    occur of (x) the closing of an initial
                                    public offering (the "IPO") of Music.co's
                                    common stock (the "Shares") or (y) the
                                    second anniversary of the closing of the
                                    TCIM's contribution of certain assets of
                                    SonicNet and The Box to Music.co (the
                                    "Closing"); provided, however, that in the
                                    event the IPO has not occurred on or before
                                    the second anniversary of the Closing, AT&T
                                    Broadband will be entitled, by written
                                    notice to TCIM, to extend the Triggering
                                    Event until the date of the first to occur
                                    of (i) an IPO of the Music.co Shares or
                                    (ii) the fifth anniversary of the Closing.



EXCESS VALUE:                       The "Excess Value" will be an amount equal
                                    to the excess of the Share Value over the
                                    Base Amount. The "Share Value" shall be the
                                    Average Market Price or the Private Share
                                    Valuation (as defined in the Music.co
                                    Agreement), as applicable, of TCIM's Equity
                                    Interest in Music.co. TCIM's Equity
                                    Interest shall be a number of shares or
                                    partnership interests of TCIM equal to the
                                    amount of its aggregate partnership
                                    interest in Music.co acquired at the
                                    closing (the "Closing") of the transactions
                                    contemplated by the Music.co Agreement
                                    (converted into the equivalent number of
                                    shares in the event Music.co is then a
                                    corporation), together with all additional
                                    partnership interests, shares or other
                                    equity interests issued to it as a result
                                    of its making any Additional Contribution
                                    (as defined in the Music.co Agreement) at
                                    or following the Closing. The Average
                                    Market Price of TCIM's Equity Interest
                                    shall be equal to the average of the
                                    closing market prices of a share of
                                    Music.co common stock for thirty (30)
                                    trading days selected by AT&T Broadband out
                                    of the sixty (60) consecutive trading days
                                    immediately following Music.co's IPO. The
                                    Private Share Valuation of the Equity
                                    Interest shall be equal to the per share
                                    value of


                                       2
<PAGE>   3


AT&T Broadband & Internet Services, Inc.
May 18, 1999


                                    TCIM's shares or other equity interests as
                                    determined in accordance with the Music.co
                                    Agreement (including in connection with
                                    TCIM's exercise of its put right);
                                    provided, however, that in the event that
                                    (A) AT&T Broadband has deferred the
                                    occurrence of the Triggering Event, (B) the
                                    IPO does not occur prior to the fifth
                                    anniversary of the Closing and (C) TCIM has
                                    not exercised its "put" right, then the
                                    Private Share Valuation shall be determined
                                    by TCIM and AT&T Broadband in accordance
                                    with and based upon the provisions relating
                                    to such determination contained in the
                                    Music.co Agreement. The "Base Amount" shall
                                    equal the sum of (x) the lesser of (i) $175
                                    million and (ii) the value of TCIM's Equity
                                    Interest as determined pursuant to the
                                    Music.co Agreement for purpose of
                                    determining whether Music.co must issue to
                                    TCIM additional shares upon the IPO or the
                                    second anniversary of the Closing
                                    (regardless of when the IPO occurs) and (y)
                                    the amount of all Additional Contributions
                                    made by TCIM in accordance with the Music.co
                                    Agreement.

CONSIDERATION:                      TCIM may, at its election, pay the Excess
                                    Amount in cash in immediately available
                                    funds or by issuing to AT&T Broadband newly
                                    issued shares of Series A Common Stock of
                                    TCIM (with such shares valued at the
                                    average market price thereof over the 30
                                    trading days prior to the occurrence of the
                                    Triggering Event). The Excess Amount will
                                    be payable upon the 30th day following the
                                    date the per share value of the Shares is
                                    established as provided above.


REGISTRATION RIGHTS:                If TCIM issues shares of its Series A
                                    common stock to AT&T Broadband, TCIM will
                                    enter into a registration rights agreement
                                    with AT&T Broadband having terms and
                                    conditions which are customary under the
                                    circumstances and reasonably acceptable to
                                    the parties. Such registration rights
                                    agreement will provide AT&T Broadband with
                                    a single demand registration right and

                                       3


<PAGE>   4


AT&T Broadband & Internet Services, Inc.
May 18, 1999


                                    customary piggyback registration rights (in
                                    each case at TCIM's cost, other than
                                    underwriting commissions, selling expenses
                                    and costs of counsel for AT&T Broadband, if
                                    any), and shall include customary
                                    underwriter cut-backs and restrictions.

AFFILIATION AGREEMENT:              AT&T Broadband will negotiate in good faith
                                    to enter into an agreement with TCIM or a
                                    joint venture between TCIM and Music.co
                                    (the applicable of the foregoing being the
                                    "Music Provider") for AT&T Broadband to
                                    provide and enable the functionalities
                                    necessary to provide to AT&T digital
                                    subscribers an interactive music and
                                    music-related transaction/commerce channel
                                    to be developed by the Music Provider.


                                       4


<PAGE>   5


T&T Broadband & Internet Services, Inc.
May 18, 1999


         If the foregoing accurately signifies your understanding of our
agreement, please so signify by signing the enclosed copy of this letter where
indicated and returning it to the undersigned.

                                       Very truly yours,

                                       TCI Music, Inc.



                                       By:  /s/ David B. Koff
                                          -------------------------------------
                                          David B. Koff
                                          Vice President &
                                          Assistant Secretary

Agreed to and Accepted:


By:    /s/ Madison Bond
   -----------------------------------
Name:  Madison Bond
Title: Executive Vice President


                                       5