An *interval* is the difference between two things – objects, points, states, or even sounds.

We can measure different intervals using different tools:

- A ruler measures intervals of
*length*or*space.* - A clock measures intervals of
*time.* - A musical interval measures the difference between two
*pitches*– it is the distance between sounds.

These tools often provide various levels of measurement, some more precise than others. Let’s look at different degrees of precision in measurement.

**Measuring Distance Using a Ruler**

A ruler has numbers, which give an approximate idea of length in inches.

But what if I am measuring an object that falls between the numbers, such as the pencil illustrated below?

This pencil is bigger than 5 but not quite 6. So, exactly how long is it? I can’t tell with this ruler – it only provides a *general* idea of length, not an *exact* length.

To give an exact length, or to allow you to measure with greater *precision*, rulers also have lines in between the numbers. Now I can see that the pencil is *exactly *5 ¼ inches long.

**Measuring Time Using a Clock**

Similar to a ruler, a clock provides a means of measuring time. The numbers, which tell us the hour, give us a general idea of the time. From the picture below, I know that it is sometime during the 3 o’clock hour.

But, has it just turned 3:00 or is it almost 4:00? If I have an appointment at 4:15 do I have plenty of time to get there or do I need to hurry? I can’t tell with this clock. I need greater precision.

This clock is much better! It has a minute hand, which provides greater *precision* when measuring time. Thanks to this clock, I now know that it is *exactly *3:05, which means I can relax and have a cup of tea before going to my 4:15 appointment!

**Measuring Pitch Using Musical Intervals**

Like the ruler and clock, musical intervals measure differences in pitch to a *general* degree as well as a more *precise* degree. Again like the other measurement tools, musical intervals measure the general degree using numbers.

Unlike the other tools, which refer to the numbers by saying one, two, or three (example – *one* o’clock, or *two* inches), musical intervals refer to numbers by saying second, third, or fourth. Musical intervals do not have a first or an eighth – instead, these are special intervals called *unison* and *octave* respectively.