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Section 1

Naming Intervals

Intervals are named according to the number of scale notes they include. That’s equivalent to saying that they are named for the number of staff lines and spaces they include, or the number of letter names.

For instance, the interval from C to G covers five
lines and spaces or five letters, counting its starting and ending notes: C (D, E, F) G, so it’s called a fifth. Similarly, D to F is a third: D, (E), F. D to F♯ is also
a third, but a different kind. E to F covers only two letters, so it’s a second. C to the same C is a type of unison, since it includes only one letter, and so is
C to C♯ or C to C♭.

Movie 5.1 shows the basic intervals in harmonic form.

Major And Minor Intervals

Each type of interval can have different qualities, which are determined by counting half steps. The quality of seconds, thirds, sixths, and sevenths can be major Major A term used to describe the quality of an interval, scale
or chord.

Seconds, thirds, sixths and sevenths can be either major
or minor. The major form of the interval is one half step larger than its minor form.

In a scale, if the third formed between the first note and the third note of a scale contains 4 half steps, the scale is major. If the third contains three half steps, the scale is minor.

Likewise, if the bottom third of a triad contains
4 half steps, the chord is major. or minor Minor A term used to describe the quality of an interval, scale
or chord.

Seconds, thirds, sixths and sevenths can be either major
or minor. The minor form of the interval is one half step smaller than its major form.

In a scale, if the third formed between the first note and the third note of a scale contains 3 half steps, the scale is minor. If the third contains four half steps, the scale is major.

Likewise, if the bottom third of a triad is minor
(contains 3 half steps) the chord is minor. . A major third, such as C-E, includes four half steps and is a half step larger than a minor third like D-F, which has only three half steps.

Movie 5.2  Major and minor intervals

A major interval is one half step larger than the minor interval
of the same name.

Movie 5.1  Naming intervals

Intervals are named according to the number of scale notes they include.

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Be careful — when counting half steps, we are not counting the notes, but rather the spaces between them.

Perfect Intervals

Unisons, fifths, fourths, and octaves cannot be called major or minor; they have one basic quality, which is perfect Perfect The term used to describe a unison, octave, fifth or fourth that is neither augmented (larger by a half step) or diminished (smaller by a half step). . A perfect fifth, for example, has seven half steps; a perfect fourth has five half steps.

Figure 5.1  Counting letter names and half steps to determine interval and quality.

Movie 5.3  Perfect intervals

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Augmented And Diminished Intervals

If a major or perfect interval is enlarged by one half step, it’s augmented Augmented A term used to describe an interval or a chord that has the following qualities:

• An augmented interval is enlarged one half step beyond major or perfect.

• An augmented triad is built by stacking two major thirds, which produces an augmented fifth between its outer notes. . If a minor or perfect interval is reduced one half step,
it’s diminished Diminished A term used to describe an interval or a chord with the following qualities:

• A diminished interval is one half step smaller than minor or perfect.

• A diminished triad is built by stacking two minor thirds which produces a diminished fifth between its outer notes. .

For example, F to A♯ is a third (it includes three letter names) but it has five half steps, one half step larger than major, so it’s an augmented third. B to F (going upward) is spelled as a fifth, B (C, D, E,) F, but it has only six half steps, so it’s a diminished fifth.
D rising to F♭ is a third that is one half step smaller than minor, so it’s a diminished third.

Augmented and diminished intervals are identified with the signs “+” and “°.”

Movie 5.4  Augmenting and diminishing the perfect and major/minor intervals

Suggested Practica Musica Activities 5.1

• Interval Types: Practice recognizing intervals (quality provided).
• Comparing Interval Qualities: Compare interval qualities between intervals of the same name.
• Identify Perfect Intervals: Distinguish between perfect fourths, fifths and octaves.

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Review 5.1

4. Unisons, octaves, fifths and fourths have one
basic quality called perfect. C-G is a perfect fifth.

5. If an interval is a half step larger than major or perfect, it’s augmented. If it’s a half step smaller than minor or perfect, it’s diminished. C♯-E♭ is
a diminished third and C-E♯ is an augmented
third. C-G♯ is an augmented fifth; C-G♭ is a diminished fifth.

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Section 2

Identifying Intervals

To identify an interval you must do two things: first get the numeric name of the interval by counting the number of letter names it covers, and then count the half steps in it to determine its quality. This chart of the most common intervals will help (Figure 5.2). Notice that two possible answers are given for each size in half steps. An augmented
second and a minor third, for example, both have three half steps.

You may find it helpful at first to look
at or imagine the piano keyboard when identifying an interval. Movie 5.5 shows how to distinguish between two intervals that both have eight half steps – one is a type of fifth and the other a type of sixth.

Movie 5.5  Counting half steps and
letter names on the keyboard to identify
an interval.

The intervals C to G sharp and C to A flat each contain 8 half steps but have different names. C to G sharp covers five letter names and is
a type of fifth, whereas C to A flat is a type
of sixth.

Figure 5.2  Interval Chart

For each number of half steps, there are at least two possible interval names.

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Beyond Augmented And Diminished

In theory, intervals can even be doubly or triply augmented or diminished but you won’t often see such oddities. If you did encounter an interval such as A♭ rising to D♯, however, you could analyze it this way: it includes four letter names (A, B, C, D), so it’s a fourth, and it has seven half steps, which is one greater than an augmented fourth. Therefore it’s a doubly-augmented fourth.

Identifying Intervals Quickly

One aid to interval identification is to memorize the qualities of the “natural intervals,” which are the intervals as they appear in
the C major scale, with no sharps or flats. Then you can use them as standards with which to compare intervals that do have sharps
or flats.

For example, all natural fifths or fourths on the staff are perfect, except those between B and F. So if you see a non-natural fifth like C-G♯ you remember that the natural fifth C-G is perfect, and since this one’s upper note is raised a half step it must be one half step larger than perfect. So C-G♯ is an augmented fifth. Similarly, all natural thirds are either major or minor.

It’s very important to memorize the qualities of the natural thirds and fifths. When you see B ascending to D you will know instantly that B-D is a minor third, containing three half steps. So if you encounter instead a B♭-D you’ll know that since the B is now lowered a half step the interval has gotten larger than its natural version and therefore it must be a major third.

Movie 5.6  Learn the qualities of the natural thirds, fourths and fifths to help you quickly identify any third, fourth or fifth.

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Figure 5.3  Identical modifiers leave the quality unchanged.

Figure 5.4  The quality of an interval, when added to a perfect interval, remains unchanged.

Movie 5.7  Interval arithmetic

Suggested Practica Musica Activities 5.2

• Hearing Intervals: Practice recognizing intervals
by ear.

• Interval Playing: Practice finding intervals on the
keyboard (enharmonics provided).

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Inverting Intervals

If you reverse the notes of an interval you obtain its inversion Inversion The rearrangement of the notes of an interval or chord. The interval C-E,
for example, is the inversion of E-C; e.g. a third inverted becomes a sixth.
A chord is inverted if any note other than its root is in the bass.

Melodic inversion is a transformation technique used by composers to develop a melodic idea. Inversion changes the direction of each interval in the melody. A rising third becomes
a descending third, for instance.
A tonal inversion, which is most common, never leaves the original key and, as a result, some intervals are a half step larger or smaller than the original. A real inversion maintains the exact intervals and soon leaves the original key. .
For example, C rising to E is a major third; its inversion is E rising
to C, a minor sixth. Knowing the principle of inversion is handy for quick recognition, because inversion reverses an interval’s quality.
Major intervals become minor upon inversion; diminished intervals become augmented. Perfect intervals, however, remain perfect.
As for the number of the interval, it’s always 9 minus the old number:
a sixth, for example, will invert to a third (9 minus 6 equals 3).

So if you see the note C with a B above it, you can use the inversion principle to quickly identify the interval as a major seventh: if the
B were below the C it would be a minor second away (that’s easier
to count out than a seventh), and a minor second inverts to a major seventh (minor inverts to major; 9 minus 2 equals 7).

So far we have been looking at intervals within a single octave. These are known as simple intervals Simple Intervals An interval spanning an octave or less. Intervals greater than an octave are compound intervals. . If you add an octave to an interval its quality is unchanged. Such intervals are known as compound intervals Compound Intervals An interval plus an octave. Adding an octave to a simple interval leaves its quality unchanged. There are names for many compound intervals less than two octaves: a second plus an octave can be called a ninth, a third plus an octave a tenth, a fourth plus an octave an eleventh, then come the twelfth and the thirteenth. After the thirteenth we usually name the interval by its simple form. . There are names for many compound intervals less
than two octaves: a second plus an octave can be called
a ninth, a third plus an octave a tenth, a fourth plus an octave an eleventh, then come the twelfth and the thirteenth. After the thirteenth we usually name the interval by its simple form.

Movie 5.8  Inverting a major, minor, augmented
or diminished interval reverses the interval’s
quality.

Movie 5.9  Compound intervals. Adding an octave to an
interval has no effect on the interval’s quality.

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More About Enharmonic Equivalents

You can easily make a mistake in identifying or writing intervals if you don’t distinguish between notes that are enharmonic equivalents such as F♯ and G♭ or E and F♭
(see Chapter 1).

A second, the difference between any two adjacent scale steps, will always be spelled with two adjacent letter names. F to G♭ is a second, as are F to G and F to G♯. However, F to F♯ is not a second but a kind of unison, since it involves only one letter name — even though the F♯ is played on the same piano key
as the G♭.

What matters for naming an interval is not how it sounds,
but how it’s written on the staff. Similarly, a third such as
C to E is not at all the same thing as C to F♭, though the two use the same piano keys and have the same number of half steps. C to F♭ would actually be called a kind of fourth — in this case a diminished fourth — because it includes four letter names: C, D, E, F, and yet has one half step less than an
ordinary perfect fourth like C-F.

Suggested Practica Musica Activities 5.3

• Inverting Intervals: Name the inversion of the displayed
interval.

• Interval Spelling: Practice building all of the common
intervals beginning on any pitch.

Figure 5.5  Enharmonic equivalents sound the same
but have different names.

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Review 5.2

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Section 3

Consonance and Dissonance

Movie 5.10  Consonant intervals

Movie 5.11  Dissonant intervals

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Figure 5.6  The augmented fourth, known as the tritone, contains three whole steps.

Movie 5.12  The consonance of the fourth is variable.

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Review 5.3