The Complete Idiot''s Guide to Music Theory

Note
The lowest note of
an interval, chord, or
scale, is called the 
root.
Definition
The basic intervals, starting on C.
Interestingly, when you examine the frequencies of two notes, as discussed in the
previous chapter, you find that the second note in an octave is an exact multiple
of the first note. For example, the A above middle C has a frequency of 440Hz;
the A an octave above that has a frequency twice that, 880Hz. For this reason
two notes with the same name have the same sound, even if they’re pitched an
octave or more higher or lower.
Note

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Chapter 2:
Intervals
21
Major and Minor Intervals
When you describe intervals by degree, you still have to deal with those pitches
that fall above or below the basic notes—the sharps and flats, or the black keys
on a keyboard.
When measuring by degrees, you see that the second, third, sixth, and seventh
notes can be easily flattened. When you flatten one of these notes, you create
what is called a 
minor
interval. The natural state of these intervals (in a major
scale) is called a 
major 
interval.
Here’s what these four intervals look like, with C as the root, in both major and
minor forms.
Major and minor intervals, starting on C.
Perfect Intervals
Certain intervals don’t have separate major or minor states (although they can
still be flattened or sharpened). These intervals—fourths, fifths, and octaves—
exist in one form only, called a 
perfect 
interval. You can’t lower these intervals to
make them minor or raise them to make them major; there’s no such thing as a
minor fifth or a major octave. The intervals, because of their acoustical proper-
ties, are perfect as-is.
Remember, in this chapter
we’re dealing with inter-
vals within a major scale.
Minor scales (described in
Chapter 3) have different
“natural” intervals between
degrees of the scale.
Note
Why is a perfect interval so perfect? It all has to do with frequencies, and with
ratios between frequencies. In a nutshell, perfect intervals sound so closely related
because their frequencies are closely related. 
For example, a perfect octave has a ratio of 2:1 between the two frequencies—
the octave is twice the frequency of the starting pitch (which is called the 
funda-
mental
). If the fundamental is 440Hz, the octave above is twice that frequency,
or 880Hz. Similarly, a perfect fifth has a ratio of 3:2, and a perfect fourth has a
ratio of 4:3. Other intervals have more complex ratios, which makes them less
perfect. For example, a perfect third has a ratio of 5:4, not quite as simple—or
as perfect. 
Put into a series, each increasingly complex interval ratio forms what is called a
harmonic series,
and the intervals (in order) are called 
harmonics.
But don’t get
hung up on all the math; what’s important is that you know what the perfect inter-
vals are, not the math behind them.
Note

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