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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.

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