response with 4 cards in major and long (6+) minor
The following guidances will apply for any natural non-canapé system of bidding, including but not limited to SAYC, Goren (4-card majors), Five Card Majors, Two Over One, and many Precision and ACOL variants.

The importance of finding any existing 8 card major fit, particularly a 4-4 fit in a major, and of identifying misfits promptly, underlie the requirement that a hand such as you describe must respond 1 Spade. Due to the weakness of your hand (6-9 points) you are only entitled to make one free-bid (ie non-forced and non-invited response) during the auction. The specific reasons for making this bid as 1 Spade instead of 2 Diamonds are the following:


To protect against partner having a hand that is 4-5 in the majors. Even if playing the Flannery Convention partner may have this shape but be outside the range allowed by the convention.
To maximize partner's opportunity to make his prepared 1 NT rebid with a balanced 15-17 HCP (when playing Weak Notrump) or a balanced 12-14 HCP (when playing a Strong Notrump).
To maximize partner's ability to make his prepared 2NT rebid with 18-19 HCP.
To keep the auction low until:
1) adequate combined partnership strength is revealed to enable playing safely at a higher level; and
2) A fit is revealed that makes it desirable to try for a game or slam contract. 


With a hand strength of 6-9 points (or 6-11 points if playing Two Over One) it is still incorrect to respond 2D over 1 Heart when holding 6 diamonds and only 3 spades. In such circumstance the correct response is 1 Notrump. It is absolutely imperative for bidding success and partnership harmony that proper discipline be exercised in the making of 2-over-1 responses to a suit opening. Such bids are immediately raising the level of the auction and, even more importantly, removing bidding room; they can only be engaged in successfully when the partnership is known to have adequate strength to do so safely.

Note that having made a 1 Spade response (to a 1 Heart opening) with a 6 to 9 point hand and 4-6 distribution in spades and diamonds, it is still incorrect to rebid 2D if partner rebids 2C. This bid again promises hand strength of 10+ points, by being a second free bid. In many systems this is stronger still by being an Artificial Fourth-Suit Forcing call. 

You have been asked for a preference by a partner who has declined to show additional strength; do so. The only acceptable calls at this point are:


Pass, showing a hand that distinctly prefers Clubs over Hearts, and cannot raise to 3 Clubs because it has only 6 or 7 points;
2 Hearts, showing a hand that prefers Hearts to Clubs, or has no preference;
2 Spades, showing a 6 card or longer spade suit and denying three card heart support;


If partner rebids 2 Hearts over your 1 Spade response, this is showing a minimum unbalanced hand with 6+ hearts and denying 4 spades. With your singleton the partnership has announced being in possession of about half the high card points in the deck, and has found a seven card major suit fit. Pass is the only call to even consider.

If partner rebids 1 Notrump over your one Spade response, then you are in territory usually governed by specific partnership agreements. Either or both of 2C and 2D will often be conventional bids inquiring further about Opener's major suit distribution and point range.  You do not have the mandated strength or major suit length to consider any of these. When not conventional they will typically show more strength (10+ points) than you possess, as again they are a second free-bid. As above, just Pass and be thankful of getting out of this mis-fit auction cheaply, Weak opponents might even enter the auction and give you the chance for getting a plus score from setting them.