
<PAGE>
 
                                                                    EXHIBIT 7(F)



                                TCI MUSIC, INC.
                      8101 East Prentice Avenue, Suite 500
                              Englewood, CO 80111



July 21, 1997



Board of Directors
The Box Worldwide, Inc.
c/o Communications Equity Associates
101 E. Kennedy Blvd., Suite 3300
Tampa, Florida  33602

Dear Sirs:

Reference is made to the Term Sheet attached hereto pursuant to which, subject
to the prior receipt of any required approvals of the Board of Directors of TCI
Music, Inc. ("TCIM") and The Box Worldwide, Inc. ("The Box") prior to July 22,
1997, we intend to merge The Box into a newly formed wholly owned subsidiary of
TCIM, with The Box as the surviving corporation, all as more fully described in
the Term Sheet.

The Term Sheet contemplates that the agreements contained therein will be
superseded by a definitive merger agreement and instruments which will contain
provisions incorporating and expanding upon the agreements set forth therein,
together with other provisions customary in the case of transactions of this
type, and such other provisions as are reasonable and appropriate in the context
of the transactions contemplated hereby.  Notwithstanding the foregoing, the
parties expressly acknowledge that the obligations of the parties pursuant to
the Term Sheet and this agreement, subject to the prior receipt of any such
required approvals of the Board of Directors of The Box and TCIM, will
constitute a binding agreement between them, subject to the terms and
preconditions set forth herein and in the Term Sheet, until such definitive
agreements are executed and delivered.  If such definitive agreements are not
executed and delivered, then, subject to the receipt of any such required
approvals of the Board of Directors of The Box and TCIM, the Term Sheet and this
agreement shall constitute such definitive agreements.

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Board of Directors
July 21, 1997
Page 2



If the foregoing is acceptable to you, please execute the copy of this agreement
in the space below, at which time this instrument will constitute a binding
agreement between us.

Very truly yours,

TCI MUSIC,  INC.



By: /s/ David Koff
    --------------
Name:
Title:  President


ACCEPTED AND AGREED
this 21st day of July, 1997

THE BOX WORLDWIDE, INC.



By: /s/ Alan McGlade
    ----------------
Name:  Alan McGlade
Title: President and CEO
<PAGE>
 
                                 Term Sheet

Parties
-------

SELLERS:  The Shareholders of The Box Worldwide, Inc. (the "Company").
BUYER:  TCI Music, Inc.

Transaction
-----------

The merger of the Company into a newly created, wholly owned subsidiary of the
Buyer with the Company as the surviving entity.

Securities Being Exchanged
--------------------------

25,668,448 shares of The Box Worldwide, Inc. Common Stock, $.001 par value per
share, such shares representing all the Company stock outstanding immediately
before the merger (after giving effect to conversion of the Company's
outstanding convertible preferred stock), less shares held by dissenting
minority shareholders ("Dissenting Shareholders") upon exercise of any appraisal
rights such shareholders may be entitled to under applicable state law.

Purchase Price
--------------

$1.50 per share ("Original Purchase Price")

Amount
------

$38,502,672

Instrument
----------

A convertible preferred stock ("New Preferred Stock") of Buyer

Number of Shares
----------------

The number of shares of New Preferred Stock to be issued will be determined by
dividing $38,502,672 (less the product of $1.50 times the number of shares of
the Company's common stock held by the Dissenting Shareholders) by three times
the average closing bid/ask price of TCI Music Series A Common Stock ("Common
Stock") for a period of 20 consecutive trading days ending on the third trading
day prior to the closing of the Transaction.  Cash will be paid in lieu of any
fractional shares of New Preferred Stock.  Each share of New Preferred Stock
will be convertible into three shares of Common Stock, as set forth in the
section below captioned "Optional Conversion".

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Dividend
--------

The holders of the New Preferred Stock will receive no dividends other than any
dividends on Common Stock (excluding stock dividends for which an anti-dilution
adjustment is made), which shall also be payable to holders of New Preferred
Stock on a fully converted basis.

Liquidation Preference
----------------------

In the event of liquidation, dissolution, or winding-up of the Buyer, the
holders of the New Preferred Stock will be entitled to receive in preference to
the holders of Common Stock an amount equal to the Original Purchase Price plus
the greater of (a) 3% or (b) CPI, with a 5% maximum in any year, compounded
annually.  Holders will have the right to convert up until the date of any
liquidation, dissolution or winding up.

A sale of all or substantially all of the Buyer's assets or any consolidation,
merger or other transaction or series of related transactions in which the
stockholders of the Buyer immediately prior to such transaction or transactions
do not retain at least 50% of the voting power of the Buyer shall be deemed to
be a liquidation or winding-up for purposes of the liquidation preference.

Optional Conversion
-------------------

The holders of the New Preferred Stock shall have the right, at any time from
the date of issuance at the option of such holder, to convert each share of New
Preferred Stock into three shares of Common Stock and thereafter as subject to
adjustment as provided below with respect to anti-dilution protection.  The
Buyer will use its best efforts to cause the shares of Common Stock issuable
upon conversion of the New Preferred Stock to be qualified for quotation on
NASDAQ, it being acknowledged that until the rights ("Rights") issued by Tele-
Communications, Inc. ("TCI") in connection with the Buyer's acquisition of DMX
Inc. shall have expired or been fully exercised, the shares of Common Stock
issuable upon conversion of New Preferred Stock may be required, for the purpose
of such qualification, to be treated as a class of securities separate from the
shares of Common Stock issued by the Buyer in its acquisition of DMX Inc.  The
shares of Common Stock issuable upon conversion of the New Preferred Stock will
not be entitled to any Rights, but otherwise will be identical to, and will be
of the same class and series as, the shares of Common Stock held by holders of
the Rights, both before and after the expiration or full exercise of the Rights.

Anti-dilution Protection
------------------------

If the Buyer issues or is deemed to issue shares of Common Stock (other than
shares issued or issuable to employees, officers or directors under plans or
arrangements approved by the Board 

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of Directors of the Buyer) at a purchase price per share less than the current
market price of shares of New Preferred Stock, the then current conversion price
of shares of New Preferred Stock shall be adjusted based upon a weighted average
anti-dilution adjustment. The conversion price of the New Preferred Stock shall
also be subject to customary adjustments for stock splits, dividends,
recapitalizations, subdivisions, combinations, reclassifications, etc.

Redemption
----------

The Buyer may redeem, with proper notice, the New Preferred Stock (i) at any
time after the closing sale price of the Common Stock (or, if the Common Stock
is not traded on a securities exchange or the NASDAQ NMS, the average of the
closing bid and asked prices) equals or exceeds, for a period of at least 30
consecutive trading days, 125% of the price used to establish the number of
shares of New Preferred Stock issuable to the Sellers or (ii) during the 30-day
period immediately following the fourth, sixth and eighth anniversary dates of
the issuance and shall be required to redeem the New Preferred Stock on the
tenth anniversary of the issuance, in each case at the Original Purchase Price
plus the greater of (a) 3% or (b) the CPI with a 5% maximum in any year,
compounded annually.

Voting Rights
-------------

Holders of the New Preferred Stock shall be entitled to attend all meetings of
the shareholders of the Buyer and shall be entitled to the number of votes for
each share held equal to the number of shares of Common Stock into which the
shares of New Preferred Stock are then convertible.  Holders of the New
Preferred Stock shall vote together as one class with holders of the Common
Stock.

Registration Rights
-------------------

The New Preferred Stock and the Common Stock underlying the New Preferred Stock
shall be registered pursuant to the combined registration statement/proxy
statement required to effect the Transaction.

Registration Expenses
---------------------

The Buyer shall pay all reasonable registration expenses in connection with the
above registration statement.

The Merger Agreement
--------------------

The parties agree to use their best efforts to negotiate in good faith a
definitive merger agreement.  If, after exhausting such efforts, the parties
fail within a reasonable period of time to execute and deliver a definitive
merger agreement, then this Term Sheet shall constitute such 

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definitive agreement. The merger agreement shall be prepared by counsel for the
Buyer, and shall contain, among other things, representations and warranties of
the Buyer and the Company, covenants of the Buyer and the Company and closing
conditions. The merger agreement (and this Term Sheet to the extent that it
shall be deemed to be the definitive merger agreement as provided for above)
shall be subject: (i) to the requisite approval of the shareholders of the Buyer
and the Company as required by applicable law; (ii) to a condition that the
Company may terminate the Transaction if the Company is presented with an
unsolicited offer for a transaction that is more favorable for the Company's
shareholders than the Transaction, provided that the Company gives the Buyer
reasonable notice of receipt of any unsolicited offer; (iii) to the parties
obtaining all approvals necessary to consummate the Transaction, including
expiration or termination of any applicable waiting period under the Hart-Scott-
Rodino Antitrust Improvements Act and any approvals or clearances required from
the U.S. Department of Justice, Federal Trade Commission, Securities and
Exchange Commission and Federal Communications Commission; (iv) to the Buyer
entering into the Contribution Agreement with TCI as will be revised on the
terms recently disclosed to the Company; and (v) the Transaction qualifying as a
tax-free reorganization under the Internal Revenue Code. In addition, the
respective obligations of the parties to consummate the Transaction shall be
subject to there being no material adverse change in the other parties'
financial condition, operations, assets, liabilities or business since the end
of the period covered by such party's most recent annual or quarterly report
under Section 13 or 15(d) of the Securities Exchange Act of 1934. Promptly after
execution of the letter agreement to which this Term Sheet is attached, the
Company shall obtain (and it will be a condition to effectiveness of the
obligations of the Buyer under the letter agreement and this Term Sheet that the
Company does obtain) an undertaking in form and substance reasonably
satisfactory to the Buyer from each director of the Company that he will cause
the shares of the Company's Common Stock that he beneficially owns to be voted
in favor of the Transaction pursuant to the terms of the definitive merger
agreement (including, if applicable this Term Sheet) so long as such definitive
merger agreement or such undertaking remains in effect and containing such other
provisions as are customarily included in voting agreements for similar
transactions.  If such undertakings are not obtained within 10 business days
after the date the letter agreement is executed by the Buyer and the Company,
the Buyer, at its election, may terminate the letter agreement and this Term
Sheet.  The letter agreement and this Term Sheet also may be terminated, at the
election of either the Buyer or the Company, if (i) the Company's Board of
Directors determines that its approval of the letter agreement and this Term
Sheet should be subject to receipt of an opinion of a financial advisor retained
by the Board of Directors or a committee thereof substantially to the effect
that the Transaction is fair to the shareholders of the Company from a financial
point of view (a "Fairness Opinion") and (ii) within 10 business days after the
date the letter agreement is executed by the Buyer and the Company, the Company
has not given the Buyer notice that a Fairness Opinion has been received.  If
the Company's Board of Directors elects not to make its approval of the letter
agreement and this Term Sheet subject to receipt of a Fairness Opinion, the
letter agreement and this Term Sheet will be binding on the Company immediately
upon such approval.  The Company and the Buyer shall bear their own expenses
(other than the registration expenses 

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referred to above) related to the Transaction, including legal expenses.

TCI Loan
--------

It will be a condition to the Company's obligations to complete the Transaction
that the Buyer shall have delivered to the Company a written commitment from TCI
to the Company that if the Buyer is not able to refinance the $40 million loan
currently owed by the Buyer to TCI before the scheduled maturity thereof, TCI
will extend the time for repayment of such loan to permit the Buyer to have a
reasonable period of time to obtain third-party financing sufficient to repay
the loan.

Digital Multiplex
-----------------

Buyer shall hire the Company on a contract basis on the date of signing the
letter agreement to which this Term Sheet is attached to develop a four channel
Digital Music Video Multiplex of Buyer which shall be distributed through TCI's
Digital Tier and the Headend In The Sky (HITS).  That contract may be terminated
at the Buyer's option if the Transaction is abandoned.


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