Intervals

One of the most fundamental concepts in music theory is the idea of intervals. An interval is the distance between two pitches. They are usually expressed as a letter followed by a number. The number is an indication of the number of lines and spaces in the staff that the interval encompasses, and the letter is an indication of the quality – that is, the exact number of half steps between the two notes.

So, how can you figure out what note is a given interval above or below a given note? This is one foolproof method:

First, put a note on the line or space that the number in the interval says to.  Do this by counting from the letter of the note you’re given up to until you reach the number the interval says. For example, if you are looking for a major 3rd  above A, count A as 1, B as 2, and C as 3. C is a third above A. If you go above G, then start back at A. If you’re descending, then just count backwards. For example, if you are looking for a perfect 4th below E, then count E as 1, D as 2, C as 3, and B as 4. If you go below A, then continue at G.

Second, find the number of half steps between the starting and ending pitch. Draw a piano from C to C. All of the intervals between white keys are either major or perfect intervals above C. D is the second key above C, which means that it is also two half steps above C. It’s also the second note of C Major, so therefore it is a major second. Likewise, E is the fourth key above C, so it’s four half steps. It’s the third note of C major, so it’s a major third. Using this method, you can determine the distances between major intervals easily. Remember that the fourth and fifth intervals are perfect rather than major, as well as the octave and unison.

So, what do you do if the interval isn’t major or perfect? You just need to add or subtract half steps. If you are looking for an augmented interval, simply add one half step to whatever number you got earlier in this step. Minor intervals also always subtract one half step. Diminished intervals, however, change depending on whether you start with a perfect or a major interval. For perfect intervals, a diminished interval subtracts one half step, but for major intervals, it subtracts TWO half steps.

The last step to notating the interval is to count the number of half steps up from the starting pitch. A major 3rd above A is going to be four half steps above A. So, count up from A, but for this step, DON’T count A. The ending pitch is either C# or Db. In step 1, we found the answer is going to be some form of C, so the answer is C#.

Next time, I’ll give more examples of this process to guide you through it and make you feel even more comfortable.