Major intervals have four possible qualities: Major, Augmented, Minor, Diminished.
In an earlier lesson we practiced these qualities using the 2nd. Let's see what this looks like with the interval of a 3rd.
To review Seconds see Unisons and Seconds.
Remember: a key signature is just a short hand for all the accidentals in a key. The easiest way to know if a note is part of a scale is to have your key signatures memorized.
To review Major Key Signatures see Major Key Signatures.
The bottom note is an A. Notice how the top note, C♯, is a note in the A major scale. In other words, there is a C♯ in the key signature for the key of A. Therefore, this is a Major 3rd (M3). Don't forget that the C♯ in the key signature applies to all the Cs that follow it. (A major 3rd is also the distance of two whole-steps, or 4 half-steps.)
Notice how the top note, C𝄪, is a half-step higher than the note in the A major scale, C♯. In other words, there is a C♯ in the key signature for the key of A and C𝄪 is one half-step higher. Therefore, this is an Augmented 3rd (A3). (An augmented 3rd is the distance of 5 half-steps.)
Notice how the top note, C, is a half-step lower than the note in the A major scale, C♯. In other words, there is a C♯ in the key signature for the key of A and C natural is one half-step lower. Therefore, this is a minor 3rd (m3). (A minor 3rd is the distance of 3 half-steps.)
Notice how the top note, C♭, is a whole-step lower than the note in the A major scale, C♯. In other words, there is a C♯ in the key signature for the key of A and C♭ is one whole-step lower. Therefore, this is a diminished 3rd (d3). (A diminished 3rd is the distance of a whole-step or 2 half-steps.)
Sometimes the bottom note is not a normal key. For instance, what should you do if the bottom note is an Fb? There is no key of Fb. Below are two suggestions.
The best way to deal with a bottom note that is not a normal key is to ajust the accidentals. You do this by temporarily adding a sharp or flat to both notes to move it to a normal key. A sharp will cancel out a flat and a flat will cancel out a sharp. So, for instance, if the bottom note is an Fb, we can add a sharp to both notes. This will move the bottom note up to an F, which is a standard key, and we can now determine the quality using the normal method.
In the example below we see an interval of a 3rd with an F flat for the bottom note and an A double-flat for the top note. By adding a sharp to each note, we raise the pitch of both notes by one-half step to an F natural and A♭. It is now possible to use the key signature of F to easily see that this is a minor 3rd. (The key of F does not have an A♭ in the key signature, so the top note is one half-step lower than the note in the key. Therefore it is minor.)
Another method is to count the half-steps. The number of half-step is given in the examples above. This is not recommended because it can be difficult to count all the half-steps in larger intervals such as the 7th. Adjusting the accidentals is an easier method once you have your key signatures memorized.