A constant concern in a cappella singing is the tendency for the pitch to go flat during the song. That doesn't mean flat like a stale beer, although it's about as appealing. It means the pitch becomes slightly lower than it should be. Why does this happen?
There are two main reasons. The first is the result of improper breathing. If you start a phrase with more breath pressure than you end the phrase, then your vocal chords have to change their tension to match the pressure. If they don't, then physics dictates that the pitch go down with the pressure. It is very hard to maintain this match, so don't even try. Instead, try to keep your breath pressure constant. This becomes particularly important near the end of phrases when you're running out of breath. Don't try to force it; it won't sound good. The section on breath control gives several techniques for maintaining a steady breath flow. Check it out.
The second main reason is tension. If your throat is tense, the steps up in pitch are held back a little, so you don't quite reach the proper pitch. When you then come back down, the step seems easy, and so you make the full interval step, but because you were starting too low, you also end up too low. The more often you try to make tense upward steps in pitch, the worse the song goes flat. Take a look at the section on relaxation to help you prevent this.
Another, less frequent reason, is the result of singing the wrong interval. We become very comfortable singing some common intervals and tend to sing those when another close, but uncommon interval is required. For example, most fourths and fifths that we sing are perfect fourths and perfect fifths, so an augmented fourth or diminished fifth can throw you off. You can read more about intervals below.
Swing easy at those high pitches.
You're not going to hit a home run just by relaxing, but that's the first step. Many of the techniques associated with breath control and voice quality will help you with your high range. Check out some of those topics.
Born Free, Twinkle Twinkle, and Over The Rainbow
Singing moves from one note to the next in amounts called intervals. The intervals have names like minor third, perfect fifth, and octave, but knowing the names isn't really that important. It's a good way to tell someone how big the interval should be, but here's another way, that helps you remember how the intervals sound.
The spacing between the four voice parts--bass, baritione, lead, and tenor--that make up each chord is measured in terms of these intervals.
Here's another video that shows the intervals on a keyboard. The interval between each pair of side-by-side keys on a piano is called a half step, half tone, or minor second, but when we sing a song, we usually don't use all the notes on the keyboard. Notice in the video, that playing the C scale uses only the white keys. These are the do-re-me-fa-so-la-ti-do notes that we're all familiar with. But notice that me-fa and ti-do use side-by-side white keys, so these are half steps, while all of the other pairs in the scale skip over a black key, and are called full steps or a major second. The reason for some being half steps and some being full steps has to do with harmonics, overtones, dissonance, consonance, and technical aspects of music theory, but basically it's because the set of notes sounds good together.
If you'd like to practice recognizing these intervals, the video below describes an online tool that you can use.