Intervals

The smallest possible interval in the Western system is the half-step, which is defined as being the distance from one note to its nearest neighbor.  If you look at a piano keyboard, any two adjacent keys (regardless of color) are a half-step apart.  By the same token, any two half-steps together will yield a whole step. 

The musical alphabet, in its simplest form, uses seven letters: A B C D E F G.  These letters repeat through the entire pitch space (so a note higher than G would be A).  The intervals between all of these notes are whole steps, except for B-C and E-F, where we find half-steps.

To determine the distance (the interval) between two notes, we count (starting on the first note) to the second, and the resulting number is the interval (or distance) between the two pitches. 

Here are some examples:

3.11  Calculate the interval from A to D

The distance from A to D is calculated by performing the following:

A	B	C	D	E	F	G
1	2	3	4	5	6	7

Count from A to D (inclusive), and you will get the number 4.  Therefore, the interval between A and D is 4, or a "fourth."

3.12  Calculate the interval from C to G

To determine the distance between C and G, start counting on C until you reach G, and that will be the answer:

A	B	C	D	E	F	G
		1	2	3	4	5

The answer is, then, a fifth (5) from C to G.

3.13  Calculate the interval from F to E

Remember that the alphabet repeats, so you must either "wrap around" (from G back to A) or reorient your counting like below:

F	G	A	B	C	D	E
1	2	3	4	5	6	7

The answer is, then, a seventh (7) from F to E.

NOTE: The distance between two notes is the same whether you are reckoning it as moving up or down: the distance from C up to G is 5, the distance from G down to C is 5.

3.2 Compound (Large) Intervals

Any interval larger than an octave (8) is considered a "compound interval" because it uses more than the normal eight notes.  Compound intervals are simply intervals greater than an octave, as the examples below illustrate:

3.21  Determine the interval from middle C to treble E, as designated below:

 

There are several ways to solve this problem:

a) Count (using a table like the ones above):

C	D	E	F	G	A	B	C	D	E
1	2	3	4	5	6	7	8	9	10

The correct answer, then, is a tenth, (10).

b) Count, using the staff:

 

The correct answer, using this method, is again, a tenth.

c) Use math

If you are clever, you may already know that the distance from C to E is a third (3), and also that there are seven notes in the musical scale.  You could simply add 3 + 7 to reach 10, which is correct.

Regardless of the method you choose, you will be required to know all of the compound intervals to the double octave (fifteenth).

3.3  Interval Quality

The above exercises are simple ways to determine the distance between two notes.  Unfortunately, they are limited in terms of their accuracy.  Consider, for example the following example:

 

Here we see two different intervals on a piano keyboard, a third from C-E and from A-C.  If we play each interval and listen carefully, we can tell that there is a subtle difference between the twothey are not of equal size!

We can prove this by counting the number of half steps between the notes.  In this case, we find there is an unequal number of whole and half steps in this case:

 

It is plain to see that the C-E third is slightly larger than the A-C third.  They are both thirds, that is plain to see, yet they are thirds of differing size.  This is what we mean by the quality of the interval. 

We will delay a more in-depth discussion of interval quality, as it is easier to understand this phenomenon once we have mastered major and minor scales.

For now, remember that intervals have a numeric value that describes their size (quantity) and a quality that describes the number of half steps and whole steps in a more exact manner.

We'll cover the aspects of quality a little more thorougly in the next section on scales.