Intervals

The interval between two notes is their distance apart on a major or minor scale.  For historical reasons, the notes at both ends are counted, so that the names of the intervals are as tabulated below:

	C - C	unison		C – C'	octave
	C – D	2nd		C – D'	9th
	C – E	3rd		C – E'	10th
	C – F	4th		C – F'	11th
	C – G	5th		C – G'	12th
	C – A	6th		C – A'	13th
	C – B	7th		C – B'	14th

Because the notes at both ends are counted adding intervals requires care: for example two octaves make a 15th.  An octave and a 2nd is a 9th.

Intervals greater than an octave are compound intervals.  For the most part we'll concentrate on simple intervals here – much of what is said of them applies equally to the corresponding compound intervals.

The numerical value of an interval can always be found simply from the counting the letters in the note names.  for example the following intervals are all 5ths but they are different kinds of 5ths.

	C – G
	C – G
	C – G

 

Interval quality naming conventions have a long history. Most classically trained musicians know the conventions, but it takes a bit of effort to learn for the first time. There are two classes of intervals: perfect and imperfect.

 

Perfect intervals are the set of intervals, which were determined to be consonant up though the 15th(?) century. This set of intervals includes unisons (1), fourths (4), fifths (5), and the octave (8) plus their compound counterparts

 

Imperfect intervals are intervals which are not as pure as the perfect intervals. They fall into two groups depending on their accepted consonance/dissonance quality:

 

consonant imperfect intervals:

Major/minor third, Major/minor sixth.

dissonant imperfect intervals:

Major/minor second, Major/minor seventh.

To distinguish different intervals with the same letter names, they are classified as perfect, major, minor, augmented and diminished.  

The intervals from the tonic to other notes on a major scale are all either perfect or major.  Again taking the scale of C major as a prototype we have:

	C - C	perfect	unison
	C – D	major	2nd
	C – E	major	3rd
	C – F	perfect	4th
	C – G	perfect	5th
	C – A	major	6th
	C – B	major	7th
	C – C'	perfect	octave

For each major interval there is a minor interval, which can be found by flattening the upper note by a semitone but preserving the letter names of the notes.  Thus the minor intervals from C are

	C – D	minor	2nd
	C – E	minor	3rd
	C – A	minor	6th
	C – B	minor	7th

If the upper note of a perfect or major interval is sharpened then the interval is said to be augmented. If the upper note of a perfect or minor interval is flattened then the interval is said to be diminished.

Thus the names of intervals from the note C can be tabulated as:

	C - C	perfect	unison
	C – C	augmented	unison
	C – D	diminished	2nd
	C – D	minor	2nd
	C – D	major	2nd
	C – D	augmented	2nd
	C – E	diminished	3rd
	C – E	minor	3rd
	C – E	major	3rd
	C – E	augmented	3rd
	C – F	diminished	4th
	C – F	perfect	4th
	C – F	augmented	4th
	C – G	diminished	5th
	C – G	perfect	5th
	C – G	augmented	5th
	C – A	diminished	6th
	C – A	minor	6th
	C – A	major	6th
	C – A	augmented	6th
	C – B	diminished	7th
	C – B	minor	7th
	C – B	major	7th
	C – B	augmented	7th
	C – C'	diminished	octave
	C – C'	perfect	octave
	C – C'	augmented	octave

Doubly diminished and doubly augmented intervals also exist (eg C-G  C-G(double sharp)) but are rare.

Note that some intervals are enharmonically equivalent to each other – for example an augmented 4th and a diminished 5th are both 6 semitone intervals. In music composed for an equally tempered scale where all semitone intervals are identical, they therefore sound the same.  But nevertheless it is still customary to retain the proper names of the intervals, just as the names Fand G.are both retained for the note played with the same key on a piano.
 

How to recognise intervals by ear.

Minor 2nd	-"Something's Coming" (Bernstein, West Side Story)	-Joy To The World
Major 2nd	-"I've Got You Under My Skin" (C. Porter) -Happy Birthday	-Yesterday (Beatles)
Minor 3rd	-Greensleeves	-"I'm Leaving on a Jet Plane" -Hey Jude -Frosty The Snowman
Major 3rd	-"Michael Row the Boat Ashore" -Oh When The Saints (Go Marching In)	-"Summertime"
Perfect 4th	-"Here Comes the Bride" (Wagner) -"Auld Lang Syne"	-Hallelujah (Handel)
Augmented 4th (D5th)	-"Maria" (Bernstein) -"The Simpsons"  (1st and 3rd)
Perfect 5th	-Twinkle Twinkle Little Star -"God Rest Ye Merry Gentlemen"	-Theme from Swan Lake (Tchaikovsky) -"Flintstones"
Minor 6th		-Theme from Love Story (Mancini?)
Major 6th	-"My Bonnie Lies over the Ocean"
Minor 7th	-"Somewhere" (West Side Story)
Major 7th	-"Somewhere Over the Rainbow" –(1st and 3rd)
Octave	-"Somewhere Over the Rainbow"