One more example
| This interval includes three letter names (E,F,G)... |
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... so it must be some kind of a 3rd which belongs to the major family of intervals. |
| The bottom note is an E. |
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So that is the key signature we will use to determine which family member it is. |
As you can now see, this method of interval identification requires a fairly strong command of key signatures and scales. E major has four sharps (F#,C#,G#,D#).
Our next step is to see if the top note is a member of the E major scale. One of the sharps in the key of E is G# and the top note of our interval is G natural. Therefore, the interval is not major because it does not fit the major key rule.
So...is the interval larger or smaller than it would be if it did fit the rule? Normally, the top note would be a G# but now is a G natural which lowers the top note, making the interval smaller. Of the four forms a major interval can have (diminished, minor, major, augmented), the minor form is one half step smaller than the normal major interval so this interval would be a minor 3rd.
| What would it take to have a diminished interval? |
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If the top note is a Gb then the interval would be two half steps smaller than the normal major interval and would therefore be diminished. |
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Constructing Intervals:
The difficulty with this identification process is that you have to be familiar with the key signatures for each key. Identifying an interval is easier than constructing one from a given note. Here are the steps you can take using this method to construct an interval from a given note. 1) Count the appropriate number of letter names up or down from the given note. Remember to include the name of the note given to you. Place that note on the staff (without any accidentals). E.g. if it is down a third then you put the note three letter names below the top note (counting the top note). 2) Now look at the note on the bottom of the interval and assume it is the name of the key signature.
3) Now apply the rule discussed above. The rule is: if the top note is a member of the bottom note's major scale, then the interval is major or perfect. The interval is major or perfect with the number of letter names that separates them (e.g. P4, or M3). But this may not be the interval you want. If you need an augmented interval, you need a bigger distance between the notes. If you want a minor or diminished interval, you want less distance between the notes.
4)First ask, is the interval you have larger or smaller than the interval you want? If it is larger by 1/2 step, then the interval is augmented (for both the major and the perfect families) and you have to decrease its size by one half step. Remember, you can only change the note you added, not the original note. To make an interval smaller, you can do one of two things:
a) Lower the top note by using a flat (or natural if it is sharped).
b) Raise the bottom note by using a sharp (or natural if it is flatted).
If you are building an interval down, you would change the bottom note. If you are adding a note above the given note, you would change the top note.
If the interval is smaller by 1/2 step than the interval you want, then it is either minor (for major intervals) or diminished (for perfect intervals). If it is smaller by one whole step and the interval family is major, then the interval is diminished. If your interval is too small, then you would reverse the above process.
a) Raise the top note by using a sharp (or natural if it is flatted).
b) Lower the bottom note by using a flat (or natural if it is sharped).
In some rare instances, you may find that the interval is too large by a whole step. You would then have to use accidentals to lower or raise a note a whole step to get it to the desired size. You can actually double flat and double sharp an interval but it is rare.
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An Alternative Method for Identifying and Constructing Intervals
The major scale method is elegant but has a lot of knowledge overhead. A more brute force method is to merely count half steps between the two notes for identification or count half steps up or down from a given note to construct an interval. If this process is more appealing to you, use the list below to do your counting. This chart always assumes you have the right note name but are verifying the interval's flavor (perfect, minor, etc.).
| Interval | 1/2 Steps | | diminished 2nd | 0 | | minor 2nd | 1 | | major 2nd | 2 | | augmented 2nd | 3 | | diminished 3rd | 2 | | minor 3rd | 3 | | major 3rd | 4 | | augmented 3rd | 5 | | diminished 4th | 4 | | perfect 4th | 5 | | augmented 4th | 6 | | diminished 5th |
6 |
| perfect 5th |
7 |
| augmented 5th |
8 |
| diminished 6th |
7 |
| minor 6th |
8 |
| major 6th |
9 |
| augmented 6th |
10 |
| diminished 7th |
9 |
| minor 7th |
10 |
| major 7th |
11 |
| augmented 7th |
12 |
| diminished 8va |
11 |
| perfect 8va |
12 |
| augmented 8va |
13 |
After you have added the second note to make the interval the correct number of letter names apart, then count the number of half steps between them to see how much to raise or lower the new note to make the interval the correct size. Remember, you make an interval larger BYraising the top note or lowering the bottom note. And, conversely, you make an interval smaller by lowering the top note or raising the bottom note.
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Inverting Intervals
As you might expect, it is usually easier to identify smaller intervals than larger ones. For example, it is easier to count half steps in a third than in a sixth. By inverting an interval, you can turn a large interval into a smaller one for easier identification. To invert an interval, you take the bottom note of the interval and place it above the top note.
| For example, an interval made up of C4 and A4 is a sixth. |
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| By moving the C4 up to C5 the interval (now A4 and C5) becomes a third. |
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After counting half steps, you will see that the two intervals are not the same flavor. The sixth is a major interval and the third is a minor interval. The following rule can be used to help you quickly invert an interval: Subtract from nine and change the sign.
This is how the rule works: 1) Subtract the interval number from nine to find the number of the inverted interval.
2) Change the mode of the interval to the inverted equivalent: Diminished switches with Augmented; Minor switches with Major; and Perfect remains Perfect. The graphic to the right shows this inverting rule for both the major family of intervals (top) and the perfect family of intervals (bottom).
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Therefore, using the above example you would change the 6 to a 3 (after subtracting from 9) and the major mode becomes minor. You do not need to know what mode the sixth is before inverting it. You can invert it first to see what mode the third is (because it is easier) and then reverse the rule to discover that the sixth is major (the opposite of what the third is). What this all means is that if you have a large interval like a seventh which is more difficult to identify than a second, you can invert it to a second. Find its mode and then switch it back to a seventh. If the second proves to be minor, the seventh must be major, and likewise, if the second proves to be augmented then the seventh would be diminshed. This is just one more method you might use among the others outlined above to identify or construct intervals.
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