Knowing how to hear and sing the seven notes or degrees of the scale is a much easier and more reliable way to sight-sing from a score than
interval-by-interval. You can't get "off" because you're always working relative to the tonic note, not the previous note. It works with all
music that has obvious tonality, or sense of the key, which almost all music does.
There are two phases of learning to sight-read music this way. First, you learn what the notes of the scale sound like in the context of the key, by number, 1 to 7. (You can also use do, re, mi etc. instead of the numbers but that adds an unnecessary complication.) Second, you learn to match the numbers with the actual scale note letters in the common keys. For example in the key of C, E is 3, G is 5 etc. If you are in the key of F, E is note 7, G is note 2 etc. This is something that comes over time. You can speed up the process by deliberately learning the notes (and key signatures) of the common keys. Start with C major first. Go on to G, D, and F; then later the remaining keys.
The web-based apps are below; but if you want to download either of the apps to your computer, right click on "Download" and select "Save target as" (or similar option in your browser). Flash Player is needed to run the app on your computer outside of your web browser.
The applet below helps you with both of those two phases. As the tune plays, hear what each note number sounds like relative to the tonic note (note 1). While you are learning the scale note numbers, don't pay any attention to what the actual notes are as absolutes (C, D etc.). After you have gotten a feel for the numbers, you can start to associate them with the letters in each key. It will be different for each different key. That is why you should learn to hear the scale numbers first. When it comes time to learn what they actually are in each key you will need to know the notes of the treble clef: the lines from the bottom up are E, G, B, D, F and the spaces are F, A, C and E.
Here is another applet that can help with those two learning stages. This one is a little more interactive. Look at the