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Piano Power: Intervals
Part 1
By Richard Prokop, Greenacres Press, Inc.
(more articles from this author)
2000-11-14
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Definition: An interval defines the space between two notes in terms of size and quality. Size is indicated by a numeric designation such as 2nd, 3rd, 4th, 5th. Quality is specified by use of the terms perfect, major, minor, diminished or augmented.

The Size of an Interval
In the example below, the size of an interval is determined by counting the number of letter names between and including two given notes. The first interval formed by two F's is a unison or prime (indicated by the letter "p"). The last interval formed by an F and the F eight steps above it is called an octave (indicated by the symbol "8va"). The intervals in between range from a 2nd to a 7th.

Below are intervals of a 9th, 10th, 11th, 12th, that exceed the space of an octave.

Using Major Scales to Determine Perfect and Major Intervals
Rule: Within any major scale, the intervals 1-4, 1-5, 1-8 are Perfect intervals, (written as P4, P5 and P8va, respectively). The intervals 1-2, 1-3, 1-6, 1-7 are Major intervals, (written as M2, M3, M6, M7 respectively). Considering our knowledge of the C major scale (see the example below), and using the rule above, we can immediately determine the following:

* C-F is a Perfect 4th
* C-G is a Perfect 5th
* C-C is an octave
* C-D is a Major 2nd
* C-E is a Major 3rd
* C-A is a Major 6th
* C-B is a Major 7th

Knowing the notes of all the major scales provides us with a great foundation for the study of intervals. As you will see, there is no need to memorize the number of whole and half steps in a given interval in order to identify it.

The Quality of an Interval
Fourths, Fifths and Octaves have three basic quality types. From smaller to larger they are: diminished (D), perfect (P), augmented (A). A diminished interval is a half step smaller than a perfect interval. An augmented interval is a half step larger than a perfect interval.

The example below demonstrates the P5 (C-G) in the middle, flanked by the D5 (C-Gb) on the left, and the A5 (C-G#) on the right. The difference in the size of the intervals is achieved by lowering or raising the top note (G) by increments of 1/2 step.

The next example below demonstrates the P5 (C-G) in the middle, flanked by the D5 (C#-G) on the left, and the A5 (Cb-G) on the right. The difference in the size of the intervals is achieved by lowering or raising the bottom note (C) by increments of 1/2 step.

Seconds, Thirds and Sixths have four basic quality types. From smaller to larger they are: diminished (D), minor (m), major (M), augmented (A). A diminished interval is a half step smaller than a minor interval. A minor interval is a half-step smaller than a major interval. An augmented interval is a half step larger than a major interval.

The example below demonstrates the D6 (C-Abb) on the extreme left, followed by the m6 (C-Ab) and the M6 (C-A). On the extreme right is the A6 (C-A#). The difference in the size of the intervals is achieved by lowering or raising the top note (A) by increments of 1/2 step.

The next example below demonstrates the D6 (Cx-A, where x' indicates a double sharp) on the extreme left, followed by the m6 (C#-A) and the M6 (C-A). On the extreme right is the A6 (Cb-A). The difference in the size of the intervals is achieved by lowering or raising the bottom note (A) by increments of 1/2 step.

Identifying Intervals
Hopefully, you have been studying the notes of the twelve major scales from the previous articles. Now, you can put that knowledge to use when identifying intervals. Here's how it works:

You are asked to identify an interval:
"What interval is G-E?"

Initially you respond:
"Yikes! I don't know. "

But you recover quickly and think:
"I know that the G major scale contains the notes G-A-B-C-D-E-F#-G. Additionally, G-E is 1-6 of the G scale. I learned from the rule in today's article that steps 1-6 of any major scale is a M6. Therefore G-E is a Major 6th (M6)!"

See, that wasn't bad! Try some more.

What interval is A-Eb?

* Well, A-E is 1-5 of the A major scale.
* Our rule states that 1-5 of any major scale is a Perfect 5th (P5). Therefore, A-E is a P5.
* We also learned that if a Perfect 5th is made 1/2 step smaller, it becomes a Diminished 5th.
* If we make a A-E 1/2 step smaller by flatting the E, we have a Diminished 5th (D5).
* Therefore, A-Eb is a Diminished 5th (D5).

What interval is Gb-Ebb?

* The Gb major scale is: Gb, Ab, Bb, Cb, Db, Eb, F, Gb.
* Gb-Eb is 1-6. By definition, 1-6 of any major scale is a Major 6th (M6).
* Gb-Ebb is a 1/2 step smaller than Gb-Eb.
* By definition, a Minor 6th (m6) is a 1/2 step smaller than a Major 6th (M6).
* Therefore, Gb-Ebb is a minor 6th (m6).

What interval is F#-D?

* To make things easier let's pretend that the given interval is F-D.
* F-D is 1-6 of the F major scale, therefore it is a Major 6th (M6).
* F#-D is 1/2 step smaller.
* By definition, a Minor 6th (m6) is a 1/2 step smaller than a Major 6th (M6).
* Therefore, F#-D is a minor 6th (m6).

Here's another complicated one.

What interval is D#-C?

* Pretend that the given interval is D-C.
* The D major scale is: D-E-F#-G-A-B-C#-D
* By definition, 1-7 of a major scale is a Major 7th. Therefore, D-C# is a Major 7th (M7).
* By definition, a Minor 7th (m7) is a 1/2 step smaller than a Major 7th (M7).
* Therefore, D-C is a Minor 7th (m7).
* By definition, a Diminished 7th (d7) is a 1/2 step smaller than a Minor 7th (m7).
* Therefore, D#-C is a Diminished 7th (D7).

Here are some more intervals for you to identify. Remember to use your knowledge of the major scales as demonstrated above:


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