"Intervals" is the term for the distance from one note to another. It's important to be able to recognize intervals by sight and sound. Each interval sounds different and has a different function in harmony and melody. Even though there are specific names for each one, it's not too hard to learn the intervals if you base it off the major scale.
So in the major scale we numbered the notes one through eight. The distance of the first note to each note is the interval called a by that number: a second,a third, or a fourth etc... up to an octave (eighth).
Since these eight notes are from the major scale, they are called major intervals... usually.
C to E is a major third. C to A is a major sixth.
However, I said usually because a fourth and fifth are called a "perfect fourth" and a "perfect fifth", not a major fourth or major fifth.
There are also minor intervals, which are a half step below their respective major interval.
C to D is a major second, C to Db is a minor second.
C to B is a major seventh, C to Bb is a minor seventh.
However, a half step below a perfect fifth is an important interval called a "diminished fifth", also called a "tritone".
So minor intervals are a half step below a major interval. Also there are intervals that are a half step above a major interval and these are called augmented intervals.
C to D is a major second, C to D# is an augmented second.
C to G is a perfect fifth, C to G# is an augmented fifth.
Now all these examples are in the key of C, but intervals are from any note to any note UP OR DOWN in any key.
C to Eb is a minor third. D to F is a minor third. Ab down to F is also a minor third.
So a minor third is just the distance of two notes that are three half steps apart. This is the same for any interval. Here's another example:
C up to G is a perfect fifth; So is F up to C; so is F# down to B.
A perfect fifth is seven half steps away.
Note that if C up to A is a major sixth, C down to A is minor third. If you go up it's nine half steps, if you go down it's only three half steps.
Also note that intervals can be played one after another or simultaneously.
It is a lot of work to know every possible interval from any note to another. I encourage everyone to learn all 12 major scales while thinking about the notes in each scale numbered one through eight. Next, realize the minor and augmented intervals in between the notes in the major scale.
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