The most important thing to realize about an interval is that it is not a note, meaning, an interval is not a sound. An interval is the distance in pitch between two sounds. More specifically, an interval is the name given to the sensation in the human brain as the brain perceives the difference in pitch between two notes.
Now, think carefully about that. It is as if you were trying to explain to someone about another measurement we use, an inch. An inch is used to measure "space". But an inch itself is not a "point in space". An inch is the name we give to the DISTANCE between two points in space.
An Interval is the name we give to the DISTANCE in PITCH between two notes.
The next most important thing to realize is that each interval has a particular feeling associated with it, a particular emotional content.
Play the 3rd string, 2nd fret. Then play the 3rd string 5th fret. Those notes are 3 frets apart. Listen to the effect of playing one, then the other. Now do this:
Play the 3rd string, 2nd fret. Then play the 3rd string 6th fret. Those notes are 4 frets apart. Listen to the effect of playing one, then the other.
The first one is called a MINOR THIRD. It has a sad, dark quality. The second one is called a MAJOR THIRD. It has a brighter, happier quality.
When we play an interval by playing one note, and then the second one, that is called a melodic interval, because, like a melody, the notes come one at a time.
If we play the two notes together, so they blend their sound, that is called playing a harmonic interval. On the guitar, we can't do that by playing the notes on the same string, so we have to do the second one on a different string. That is easy, since, unlike the piano which has only one key for every note, the guitar can play the same note in a few different places.
So, we will repeat the above example by playing the second note on a different string.
First, the MINOR THIRD:
Play the 3rd string, 2nd fret with the 2nd finger. Let it ring. Play the 2nd string 1st fret with the 1st finger. Let it ring.
That is a HARMONIC MINOR THIRD. It is what makes an Aminor chord a minor chord. It is dark and sad. Curiously, most people prefer this sound to the MAJOR THIRD. Does this mean we like being sad?
Now, the MAJOR THIRD:
Play the 3rd string, 2nd fret with the 2nd finger. Let it ring. Play the 2nd string 2nd fret with the 3RD finger. Let it ring.
That is a HARMONIC MAJOR THIRD. It is what makes an A Major chord a major chord. It is brighter and happier than a minor chord.
Composers use the emotional content of intervals in their melodies and harmonies (chords) to convey emotion. As a melody is being played, it is the distance in pitch between the notes as they are played one after another, that contains and conveys the emotion of the melody.
Along with what I have already said, you should know that every Interval has two names: a number name and a type name.
Interval Numer Name
Intervals might be 2nds, 3rds, 4ths, 5ths, 6ths, or 7ths.The number name comes from the number of letters that make up the distance between the notes. So, if I play the note A, and then the note D, that is a 4th, because there are 4 letters between them, A-B-C-D. The guitar is tuned in 4ths, each string being 4 letters away from the next, except between the 3rd and 2nd. That is a third, the notes being G and B ( G-A-B, a 3rd).
Interval Type Names
The type name is much more complicated. Types of Intervals are Major, Minor, Diminished, Augmented and Perfect. The reasons for the type name are rather complex, and beyond the scope of this discussion, but further study on your part will make it clear to you.
However, even with what I have presented here, you have a lot of material to think about as you go about your practicing and playing.