<PAGE>
                                                                     EXHIBIT 4.1

--------------------------------------------------------------------------------





                                HISTORIC TW INC.,
                    TIME WARNER ENTERTAINMENT COMPANY, L.P.,
                           TIME WARNER NY CABLE INC.,
                           WARNER COMMUNICATIONS INC.,
               AMERICAN TELEVISION AND COMMUNICATIONS CORPORATION
                                       and
                             TIME WARNER CABLE INC.


                                       TO


                              THE BANK OF NEW YORK,



                                     TRUSTEE,

--------------------------------------------------------------------------------

                          Ninth Supplemental Indenture
                          Dated as of November 1, 2004

--------------------------------------------------------------------------------




<PAGE>
                                                                  EXECUTION COPY


                  NINTH SUPPLEMENTAL INDENTURE dated as of November 1, 2004
among HISTORIC TW INC. (f/k/a "Time Warner Inc."), a corporation duly organized
and existing under the laws of the State of Delaware ("HTW"), TIME WARNER
ENTERTAINMENT COMPANY, L.P., a Delaware limited partnership ("TWE" or the
"Issuer"), TIME WARNER NY CABLE INC., a Delaware limited liability company
("TWNY"), TIME WARNER CABLE INC., a corporation duly organized and existing
under the laws of the State of Delaware ("TWC"), each of the other partners of
the Issuer signatories hereto (the "TW Partners"), and THE BANK OF NEW YORK, a
banking corporation duly organized and existing under the laws of the State of
New York, as Trustee (the "Trustee").

                                    RECITALS

                  HTW, TWE, the TW Partners and the Trustee have executed and
delivered an Indenture dated as of April 30, 1992, as amended by the First
Supplemental Indenture dated as of June 30, 1992, the Second Supplemental
Indenture dated as of December 9, 1992, the Third Supplemental Indenture dated
as of October 12, 1993, the Fourth Supplemental Indenture dated as of March 29,
1994, the Fifth Supplemental Indenture dated as of December 28, 1994, the Sixth
Supplemental Indenture dated as of September 29, 1997, the Seventh Supplemental
Indenture dated as of December 29, 1997, and the Eighth Supplemental Indenture
dated as of December 9, 2003 (the "Indenture"), providing for the issuance from
time to time of unsecured debentures, notes or other evidences of indebtedness
(the "Securities"), to be issued in one or more series as provided in the
Indenture and the guaranties of the Securities by the TW Partners (the "TW
Partner Guaranties").

                  HTW, TWE, TWC and each of the TW Partners have duly authorized
the execution and delivery of this Ninth Supplemental Indenture to provide for
the elimination of the forbearance on the part of the Trustee and the Holders
from assertion of any liability in respect of the outstanding obligations under
the Securities against TWNY, a general partner of TWE, subject to the terms and
conditions described herein.

                  This Ninth Supplemental Indenture is being executed pursuant
to, and in accordance with, Section 901 of the Indenture, and consent of the
Holders is not required to effect this Ninth Supplemental Indenture.

                  All things necessary to make this Ninth Supplemental Indenture
a valid and binding agreement of HTW, TWE, TWC, TWNY and the TW Partners have
been done.

                  NOW, THEREFORE, WITNESSETH:

                  For and in consideration of the premises and other good and
valuable consideration, the sufficiency and receipt of which are hereby
acknowledged, and the purchase of the Securities by the Holders thereof, it is
mutually agreed, for the equal and proportionate benefit of all Holders of the
Securities, as follows:


                                       2


<PAGE>
                                   ARTICLE ONE
                       INCORPORATION OF PREVIOUS DOCUMENTS

                  SECTION 101. Incorporation of Previous Documents.

                  This Ninth Supplemental Indenture is a supplemental indenture
within the meaning of the Indenture and shall be read together therewith, and
shall have the same effect as though all the provisions thereof and hereof were
contained in one instrument. Unless otherwise expressly provided, the provisions
of the Indenture are incorporated herein by reference.

                  SECTION 102. Definitions.

                  Unless otherwise provided herein, the terms used herein shall
have the meanings ascribed to such terms in the Indenture.


                  SECTION 103. Governing Law.

                  This Ninth Supplemental Indenture, the Indenture and the
Securities shall be governed by and construed in accordance with the laws of the
State of New York.

                                   ARTICLE TWO
                                PARTNER LIABILITY

                  The amendments and agreements provided for in this Article Two
shall become effective (the "Effective Time") upon the later of execution and
delivery of this Ninth Supplemental Indenture by each of the parties hereto, and
November 2, 2004.

                  TWNY (or any successor in interest thereto that is and remains
a general partner of the Issuer) (the "TWE General Partner") hereby irrevocably
agrees, from and after the Effective Time and for so long as it is a general
partner of the Issuer, to waive the benefit of Section 202 of the First
Supplemental Indenture and Sections 503, 508 or 804(d) of the Indenture, in each
case solely with respect to any liability it may have in respect of the
Securities as a general partner of the Issuer under the Delaware Revised Uniform
Limited Partnership Act (6 Del. C. Section 17-403) (as the same is in effect on
the date hereof, and as the same may be revised, replaced or supplemented from
time to time, the "DRULPA"). Notwithstanding anything in the Indenture to the
contrary, including, without limitation, anything in Section 202 of the First
Supplemental Indenture or in Sections 503, 508 or 804(d) of the Indenture, after
the Effective Time, any forbearance undertaken by the Trustee and the Holders in
respect of assertion of liability for obligations under and relating to the
Securities against the TWE General Partner is hereby rescinded and shall be of
no further force or effect, with the consequence of such rescission and waiver
being that the TWE General Partner shall be deemed to have such liability in
respect of the Securities as a general partner would otherwise have pursuant to
the relevant provisions of the DRULPA in the absence of any agreement of
forbearance or non-recourse on the part of the Trustee or the Holders.

                  After the Effective Time, notwithstanding anything in the
DRULPA to the contrary, the TWE General Partner agrees, for the benefit of the
Trustee and the Holders, to waive any provision of the DRULPA that would purport
to limit the TWE General Partner's


                                       3
<PAGE>

liability in respect of the Securities to those obligations incurred by the
Issuer after the TWE General Partner became a general partner of the Issuer and
agrees that any liability it may incur as a general partner of TWE in respect of
the Securities shall be as if the Securities were issued after it became a
general partner of TWE. Except as provided in the immediately preceding
sentence, nothing in this Ninth Supplemental Indenture shall be deemed to create
or impart (i) any liability on the TWE General Partner except as expressly
provided in the DRULPA in the absence of an agreement on the part of a claimant
to forbear against the assertion of liability or (ii) any obligation on the part
of the TWE General Partner to remain a general partner of the Issuer or to
continue to assume any liability in respect of the Securities in the event it
ceases to be a general partner, except as may be imposed by the express
provisions of the DRULPA. Nothing in this Ninth Supplemental Indenture shall be
deemed to create, impart, amend or modify any liability on the part of any
Person other than the TWE General Partner.


                                  ARTICLE THREE
                  ADDITION OF TWNY AS A PARTY TO THE INDENTURE

                  By execution of this Ninth Supplemental Indenture, TWNY agrees
that it shall be a party to, and shall be subject to, bound by and entitled to
the benefits of, the Indenture, as supplemented by this Ninth Supplemental
Indenture, until such time, if any, as TWNY shall cease to be a general partner
of the Issuer.

                  This instrument may be executed in any number of counterparts,
each of which so executed shall be deemed to be an original, but all such
counterparts shall together constitute one and the same instrument.


                  The Trustee makes no representations as to the validity or
sufficiency of this Ninth Supplemental Indenture. The recitals and statements
herein are those of HTW and its affiliates party hereto, and not of the Trustee,
except as to the satisfaction of the Trustee with the form hereof.

                                     * * * *



                                       4
<PAGE>


                  IN WITNESS WHEREOF, the parties hereto have caused this Ninth
Supplemental Indenture to be duly executed by their respective officers or
agents, and their respective seals to be hereunto affixed and attested, all as
of the day and year first above written.


                                    HISTORIC TW INC.


                                       By
                                          /s/ Raymond G. Murphy
                                          ----------------------------------
                                          Name:  Raymond G. Murphy
                                          Title: Vice President & Treasurer



                                    TIME WARNER ENTERTAINMENT COMPANY, L.P.

                                       By
                                          /s/ Raymond G. Murphy
                                          ----------------------------------
                                          Name:  Raymond G. Murphy
                                          Title: Senior Vice President & Asst.
                                                 Treasurer


                                    TIME WARNER NY CABLE INC.

                                       By
                                          /s/ Raymond G. Murphy
                                          ----------------------------------
                                          Name:  Raymond G. Murphy
                                          Title: Vice President & Asst.
                                                 Treasurer


                                    WARNER COMMUNICATIONS INC.

                                       By
                                          /s/ Raymond G. Murphy
                                          ----------------------------------
                                          Name:  Raymond G. Murphy
                                          Title: Vice President & Treasurer


                                       5


<PAGE>
                                 AMERICAN TELEVISION AND COMMUNICATIONS
                                   CORPORATION


                                    By
                                       /s/ Raymond G. Murphy
                                       ----------------------------------
                                       Name:  Raymond G. Murphy
                                       Title: Vice President & Treasurer


                                 TIME WARNER CABLE INC.

                                    By
                                       /s/ Raymond G. Murphy
                                       ----------------------------------
                                       Name:  Raymond G. Murphy
                                       Title: Vice President & Asst. Treasurer


                                 THE BANK OF NEW YORK,
                                   as Trustee
                                    By
                                       /s/ Geovanni Barris
                                       ----------------------------------
                                       Name:  Geovanni Barris
                                       Title: Vice President, Corporate
                                              Trust Administration


                                       6