MUSC 101 Music Fundamentals - Spring 2012

Unit 11 - Intervals

[Overview] [Syllabus]

Interval

When you play two notes either simultaneously or in succession, you're playing an interval. Intervals are classified according to their size and their quality. Size is the measure of how far apart the two notes are. Quality is an adjective that further describes the size. For example, a half step is called a minor second and a whole step is called a major second. The size is a second. The quality is major or minor.

Harmonic Intervals and Melodic Intervals

Intervals can appear in harmonic or melodic form. In harmonic form, the two notes are played simultaneously. In melodic form, the two notes notes are played in succession. Melodic intervals can be either ascending or descending.

Harmonic Interval
Melodic Interval Ascending
Melodic Interval Descending

Interval Size

Size is determined by counting the number of lines and spaces (or alphabet letters) spanning the two notes, including the beginning and end. For example, the size of the interval from C up to E is a third (CDE spans three letters, or three lines and spaces), D up to A is a fifth (DEFGA spans five lines and spaces), and E up to C is a sixth (EFGABC spans six alphabet letters), etc.

Size	Notation	Number of Lines and Spaces or Alphabet Letters Apart Counting Both the Beginning and End.
Unison		1
Second		2
Third		3
Fourth		4
Fifth		5
Sixth		6
Seventh		7
Octave		8
Ninth		9
Tenth		10

Question

What is the size of the interval from C to E?

Answer

It depends on whether it's an ascending interval or a descending interval. The interval C up to E is a third, but the interval C down to E is a sixth.

Notes	Notation	Size
C up to E		Third
C down to E		Sixth

When calculating interval sizes, accidentals are ignored. The intervals C-E and C-Eb are both thirds. They sound different because they contain a different number of half steps. The third from C-E contains four half steps. The third from C-Eb contains three half steps. The larger third is called the major third, the smaller third is called the minor third.

Name	Half Steps	Notation	Sound
Minor Third	3
Major Third	4

Interval Quality

Quality is used to distinguish intervals of the same size but with different numbers of half steps. The terms used for quality are:

• Major
• Minor
• Perfect
• Diminished
• Augmented

Interval Classification

Intervals are classified as perfect or imperfect. Unisons, fourths, fifths, and octaves are termed perfect intervals. Seconds, thirds, sixths, and sevenths are termed imperfect intervals.

Perfect Intervals

Perfect intervals are the unison, fourth, fifth, and octave. They occur naturally in the major scale between scale note 1 and scale notes 1, 4, 5, and 8.

Name	Notation in G Major	Notes in G Major Scale
Perfect Unison		1 - 1
Perfect Fourth		1 - 4
Perfect Fifth		1 - 5
Perfect Octave		1 - 8

Imperfect Intervals

Imperfect intervals are the seconds, thirds, sixths, and sevenths. They come in two forms, Major and Minor.

Major Intervals

Major seconds, thirds, sixths, and sevenths occur naturally in the ascending major scale between scale note 1 and scale notes 2, 3, 6, and 7.

Name	Notation in F Major	Scale Notes in F Major
Major Second		1 - 2
Major Third		1 - 3
Major Sixth		1 - 6
Major Seventh		1 - 7

Minor Intervals

Minor seconds, thirds, sixths, and sevenths occur naturally in the descending major scale between scale note 8 and scale notes 7, 6, 3, and 2.

Name	Notation in F Major	Scale Notes in F Major
Minor Second		8 - 7
Minor Third		8 - 6
Minor Sixth		8 - 3
Minor Seventh		8 - 2

Perfect intervals are never major or minor. Likewise, major and minor intervals are never perfect.

Consonance - Dissonance

Intervals can also be classified as Consonant and Dissonant.

Altered Intervals

If you expand or contract an interval by a half step you change its quality. The size may stay the same. The resulting quality depends on whether you alter a perfect interval or an imperfect (major or minor) interval.

Altered Perfect

When you alter a perfect interval by a half step it becomes either diminished or augmented. When a perfect interval is made one half step larger it becomes augmented. When a perfect interval is made one half step smaller it becomes diminished.

You can expand or contract the interval from either the top or bottom note.

Altered Imperfect

When you alter an imperfect interval by a half step it becomes either diminished, minor, major, or augmented as shown in the following diagram.

When a major interval is made one half step larger it becomes augmented. When a major interval is made one half step smaller it becomes minor. When a minor interval is made one half step larger it becomes major. When a minor interval is made one half step smaller it becomes diminished.

Altered Diminished / Augmented

An augmented interval made one half step larger becomes doubly augmented. A diminished interval made one half step smaller becomes doubly diminished.

Tritone

A tritone gets its name because it contains three whole steps WWW. The intervals of a diminished fifth and an augmented fourth are both tritones because they both contain six half steps.

B - F = WWW and F - B = WWW

Interval Naming Conventions

A common naming convention for intervals uses a combination of numbers and lower and upper case letters.

Upper Case

Perfect, Major, Augmented

Lower Case

minor, diminished

Size

numbers 1 to 13

Abbreviations

P, M, m, d, and A (note case)

Examples

P1, m2, M2, d3, m3, M3, A3, P4, A4, d5, P5, m6, M6, m7, M7, P8

Identifying Intervals

To fully identify an interval you need to know both its quality and size.

Valid qualities are:

• Perfect
• Major
• Minor
• Diminished
• Augmented
• Doubly Diminished
• Doubly Augmented

Valid sizes are:

• unison
• second
• third
• fourth
• fifth
• sixth
• seventh
• octave
• ninth
• tenth
• eleventh
• twelfth
• thirteenth

There are two methods you can use to identify intervals, the easy way and the hard way. If you know your Major scales, the easy way is really easy.

The Easy way - Identify intervals by their relation to note 1 of the major scale

In a major scale all ascending intervals are either perfect or major when compared with the first note of the scale.

Step 1. Construct the major scale that begins on the lower note of the interval.

Step 2. Determine if the upper note of the interval occurs naturally in that major scale. If it does, then unisons, 4ths, 5ths and 8ves are perfect, and 2nds, 3rds, 6ths, and 7ths are major.

Step 3. If the upper note of the interval does not belong to that major scale, determine how it differs from the interval of the same size that does occur in the major scale. Based on the half step difference from major scale interval, determine the quality according to this diagram.

The Hard way - Identifying intervals by counting half steps

1. Find the interval size by counting the lines and spaces between the two notes (including both notes).

2. Count the half steps contained in the interval, then use the table of intervals and then use the table of interval sizes to determine the quality.

Note: The Table of Intervals shown below lists only the most common names for an interval. Intervals that have the same number of half steps can have different names. For example an augmented fourth and a diminished fifth both have six half steps.

Table of Intervals

Half Steps	Label	Name	Notation	Sound
0	PU	Perfect Unison
1	m2	Minor Second
2	M2	Major Second
3	m3	Minor Third
4	M3	Major Third
5	P4	Perfect Fourth
6	A4, d5	Augmented Fourth, Diminished Fifth, Tritone
7	P5	Perfect Fifth
8	m6	Minor Sixth
9	M6	Major Sixth
10	m7	Minor Seventh
11	M7	Major Seventh
12	P8	Perfect Octave
13	m9	Minor Ninth
14	M9	Major Ninth
15	m10	Minor Tenth
16	M10	Major Tenth

Enharmonic Intervals

Intervals that sound the same (contain the same number of half steps) but have different names are called enharmonic intervals. For example a minor third, an augmented second, and a doubly diminished fourth are enharmonic intervals because they each contain three half steps. You can see the difference in music notation, but you cannot hear the difference.

Compound Intervals

Intervals larger than an octave are called compound intervals. Compound intervals are always formed from a simple interval with one of the notes raised or lowered an octave. For example a 9th is a second plus an octave and a 10th is a third plus an octave.

Minor 2nd
Minor 9th

Major 3rd
Major 10th

Listening

Click the Familiar Intervals link above to hear these intervals used in familiar tunes.

Other web sites with familiar song intervals

http://www.people.vcu.edu/~bhammel/theory/resources/macgamut_theory/songs_interval_recognize.html

http://en.wikipedia.org/wiki/Ear_training#Interval_recognition

http://audio.tutsplus.com/articles/general/boot-camp-for-your-ear-detecting-intervals-with-song-associations/

[Overview] [Syllabus]

Revised by John Ellinger, Spring 2012.