The Complete Idiot''s Guide to Music Theory

Interval
Combines
Ninth
Octave plus second
Tenth
Octave plus third
Eleventh
Octave plus fourth
Twelfth
Octave plus fifth
Thirteenth
Octave plus sixth
Fourteenth
Octave plus seventh
Compound intervals can have all the qualities of smaller intervals, which means
a compound interval can be (depending on the interval) major, minor, perfect,
augmented, or diminished.
Intervals and Half Steps
It might be easier for you to think of all these intervals in terms of half steps. To
that end, the following table shows how many half steps are between these
major and minor intervals.
Half Steps Between Intervals
Interval
Number of Half Steps
Perfect unison
0
Minor second
1
Major second
2
Minor third
3
Major third
4
Perfect fourth
5
Augmented fourth
6
Diminished fifth
6
Perfect fifth
7
Minor sixth
8
Major sixth
9
23
continues

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Part 1:
Tones
Half Steps Between Intervals
(continued)
Interval
Number of Half Steps
Minor seventh
10
Major seventh
11
Octave
12
Minor ninth
13
Major ninth
14
Minor tenth
15
Major tenth
16
Perfect eleventh
17
Augmented eleventh
18
Diminished twelfth
18
Perfect twelfth
19
Minor thirteenth
20
Major thirteenth
21
Minor fourteenth
22
Major fourteenth
23
24
What you’ve learned so far is traditional Western music notation—but it’s not the
only way to notate musical pitches. Some educators today use what is called the
Mod-12
system to teach notes and intervals. In this system, the intervals between
the 12 half steps in an octave are numbered, from 0 to 11. (If you count the
zero, that adds up to 12 intervals.)
For example, the interval we call unison has zero half steps between notes, and
is called “interval 0.” The interval we call a minor third has three half steps, and
is called “interval 3.”
The nice thing about using this system is that you don’t have to worry about
enharmonics. A diminished fifth and an augmented fourth both have six half
steps, and are both called “interval 6.”
You can also use the Mod-12 system to describe individual notes—based on their
interval from tonic. Tonic, of course, is note 0. The minor second degree is note 1,
and the major second degree is note 2. If you wanted to describe the tonic, the
major third degree, and the perfect fifth degree, you’d use the numbers 0, 4, and 7.
While many people like to use the Mod-12 system to teach intervals, I prefer the
old-fashioned method presented here in this chapter—for the sole reason that this
is what you’ll run into in the real world. When you’re playing in a concert band
or a jazz trio, you won’t hear other musicians say “play 4, 7, 11.” You 
will
hear
them say “play the major third, fifth, and major seventh.”
Still, if Mod-12 works for you, use it. It’s a perfectly acceptable way to learn the
12 tones we use in Western music—and it makes it a lot easier to deal with
enharmonic notes.
Note

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Chapter 2:
Intervals
And take special note of those intervals that are enharmonically identical—such
as the augmented fourth and the diminished fifth. What you call that particular
interval depends on which direction you’re heading, and which notation is the
easiest to read in a given piece of music.
The Least You Need to Know
◆
The smallest interval between any two notes is called a half step. Two half
steps equal one whole step.
◆
A sharp raises the value of a note by a half step. A flat lowers the value of a
note by a half step.
◆
The intervals between any two notes are described in terms of degree. For
example, the interval between the first and third notes is called a third.
◆
In a major scale, seconds, thirds, sixths, and sevenths are called major
intervals. You can create a minor interval by flattening these notes.
◆
In a major scale, fourths, fifths, and octaves are called perfect intervals.
When you flatten a perfect interval, you create a diminished interval;
when you sharpen a perfect interval, you create an augmented interval.
Exercises