An interval is the distance in pitch between two notes measured using the diatonic scale. The size of an interval is expressed numerically and is an inclusive measurement; for example, C to G is a fifth, because going up the scale of C, counting C as one, the fifth note is a G, and so on. The quality of an interval is indicated by terms such as diminished, minor, perfect, major, and augmented.

 

The labels for size are ordinal numbers based on counting notes along a scale, taking the first note as "one" (rather than "zero"). Hence, the next note of the scale to either side of the reference note is labeled as a "second" away from it; a note two notes away is labeled as a "third" away; and the duplication of the reference note as the seventh note of a complete scale is labeled as the "octave."

 

Table of intervals
interval in semitones	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
interval	U	m2	M2	m3	M3	P4	d5	P5	m6	M6	m7	M7	P8	m9	M9	m10	M10

U = unison, P = perfect, M = major, m = minor, d = diminished

 

This taxonomy notoriously leads to some confusing arithmetic, e.g. "3rd + 3rd = 5th," and "3rd + 3rd + 3rd = 7th." Additional confusion can arise from the enharmonic equivalence of some intervals. Intervals wider than an octave are treated in the same way, e.g., a ninth like a second, a tenth like a third, etc.

 

In post-tonal theory, analysts usually jettison the traditional taxonomy altogether, labeling intervals according to the number of semitones (i.e., counting along a chromatic scale rather than a diatonic scale, and counting from zero rather than from one). See integer notation.

 

Types of interval

The somewhat hollow-sounding fourth, fifth, and octave of the scale are called perfect. They have what might be called a "purity" which distinguishes them from other intervals. The other intervals, as they are found in ascending the major scale from its tonic, or keynote, and all called major (major second, major third, major sixth, and major seventh). If any major interval is chromatically reduced by a semitone it becomes minor; if any perfect or minor interval is reduced it becomes diminished; if any perfect or minor interval is increased by a semitone it becomes augmented.

 

Enharmonic intervals are those which differ from each other in name but not in any other way. For example, C to G sharp (an augmented fifth) and C to A flat (a minor sixth) are enharmonic.

 

Compound intervals are those greater than an octave. For example, the interval between C and D, an octave and a tone higher, is called either a major ninth or a compound major second.

 

Inversion of intervals is the reversing of the relative position of the two notes defining them; for example, C to G inverted becomes G to C. A fifth when inverted becomes a fourth, a third becomes a sixth, and so on (i.e., the number-name of the new interval = 9 minus the number of the old interval). It will also be found that perfect intervals remain perfect (C to G is a perfect fifth; G to C a perfect fourth, etc,) major ones become minor, minor becomes major, augmented becomes diminished, and diminished becomes augmented.

 

Every interval is either concordant or discordant. The concordant ones comprise all perfect intervals and all major and minor thirds and sixths; the discordant ones comprise all augmented and diminished intervals and all seconds and sevenths. It follows from what has been said in this and the previous paragraphs that all concordant intervals when inverted remain concordant and all discordant intervals remain discordant.

 

Interval mnemonics

Recognizing and remembering intervals is made easier by singing snatches of familiar tunes that contain those intervals. The table below lists some well-known tunes at the beginning of which are the intervals listed alongside.

 

Interval	memorable tune
minor 2nd	"Jaws" (movie theme)
major 2nd	"Happy Birthday To You"
minor 3rd	"Greensleeves"
major 3rd	"Oh, When the Saints Go Marching"
perfect 4th	"Here Comes the Bride"
diminished 5th	"The Simpsons"
perfect 5th	"Twinkle, Twinkle, Little Star"
minor 6th	"The Entertainer" (3rd and 4th notes)
major 6th	"My Bonnie Lies Over the Ocean"
minor 7th	"Star Trek" (original TV closing theme)
major 7th	"Superman" (movie theme)
octave	"Somewhere Over the Rainbow"