In the basic article on music intervals, we discussed what an interval is and how they relate to scales. We just called those intervals by their general scale degree name such as 2nds or 3rds or 7ths. Now we will talk about more specific intervals and different types of them.
Different intervals will have different modifiers. The modifiers will further describe the intervals. Before when we just called them by their scale degree distances, it was like calling a particular building a barn. Now we're going to talk about whether it is a blue barn or a red barn. We do this by measuring the intervals in half steps.
Because these new music intervals will have a static, definite distance, we can apply these to any key or scale, or just arbitrary notes for that matter. As I said earlier, different intervals will get different modifiers. We will group some of these music intervals together. Unisons, 4ths, 5ths, and Octaves will be in one group, and 2nds, 3rds, 6ths, and 7ths, will be in the other group. Let's start with the first group.
Unisons
A "perfect" unison is exactly 0 half steps.
C -> C is a perfect unison. It is the exact same note.
Our next modifier is "diminished". When you diminish an interval, you make it smaller by one half step. So 0 - 1 = -1.
A -> Ab is a diminished unison.
"Augmented" is the opposite. When you augment an interval, you make it bigger by one half step.
D -> D# is an augmented unison.
So perfect, diminished, and augmented are the only modifiers for the first group. Again, they can be applied to unisons, 4ths, 5ths, and octaves.
Fourths
A perfect 4th is 5 half steps.
D -> G
A -> D
A diminished 4th is 4 half steps.
D -> Gb
A -> Db
An augmented 4th is 6 half steps.
D -> G#
A -> D#
Fifths
A perfect 5th is 7 half steps.
G -> D
D -> A
A diminished 5th is 6 half steps.
G -> Db
D -> Ab
An augmented 5th is 8 half steps.
G -> D#
D -> A#
Octaves
A perfect octave is 12 half steps.
G -> G
D -> D
A diminished octave is 11 half steps.
G -> Gb
D -> Db
An augmented octave is 13 half steps.
G -> G#
D -> D#
That's it for the first group of music intervals. The modifiers for the next group are major, minor, diminished and augmented.
2nds
A major 2nd is 2 half steps.
D -> E
E -> F#
A minor 2nd is 1 half step.
D -> Eb
E -> F
3rds
A major 3rd is 4 half steps.
D -> F#
A -> C#
A minor 3rd is 3 half steps.
A -> C
D -> F
6ths
A major 6th is 9 half steps.
B -> G#
D -> B
A minor 6th is 8 half steps.
B -> G
D -> Bb
7ths
A major 7th is 11 half steps.
D -> C#
F -> E
A minor 7th is 10 half steps.
D -> C
F -> Eb
Now it gets tricky when we use diminished and augmented on the second group of intervals. Just remember that diminish means decrease by 1 half step and augment means increase by 1 half step.
2nds
A diminished 2nd is a minor 2nd decreased by 1. A minor 2nd is 1 half step, so a diminished 2nd is 0 half step. While it may be the exact same note, we still have to call it by the next letter name because it is an interval of a 2nd, not a unison.
So D-> Ebb is a diminished 2nd.B -> Cb is a diminished 2nd.
An augmented 2nd is a major second increased by 1 half step, so it is 3 half steps.
So A -> B# is an augmented 2nd.F -> G# is an augmented 2nd.
Remember, even though this is the same note as a minor 3rd, we have to go with the 2nd's letter name.
3rds
A diminished 3rd is a minor 3 decreased by 1 half step, so it is 2 half steps.
D -> Fb
G# -> Bb
An augmented 3rd is a major 3rd increased by 1 half step.
G -> B#
F -> A#
6ths
A diminished 6th is a minor 6th decreased by 1 half step.
E -> Cb
F -> Dbb
An augmented 6th is a major 6th increased by 1 half step.
Ab -> F#
Eb -> C#
7ths
A diminished 7th is a minor 7th decreased by 1 half step.
A -> Gb
G -> Fb
An augmented 7th is a major 7th increased by 1 half step.
C - B#
Gb -> F#
This is the same as a perfect octave, but remember we have to call it by the 7th's name.
This has been one tricky and long lesson just for music intervals, but if you keep practicing with these and use them more and more, it all will make perfect sense before too long. Just remember to use the letter name of the scale degree (2, 3, 5, etc) and flat it or sharp it until it is the right distance.
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Hope this helps! Practice hard and let me know if you have any questions!