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

 

...and so on.

 

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:

 

	C - G
	C - G
	C - G

 

but they are different kinds of 5ths.

 

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

 

Unisons, 4ths, 5ths and octaves (and the corresponding compound intervals) may be perfect.   Other intervals may be major or minor.

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 (raised by a semitone without changing the letter name) then the interval is said to be augmented.

If the upper note of a perfect or minor interval is flattened (lowered by a semitone without changing the letter name) 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 (for example C-G  C-G) 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 (also known as a tritone).  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 F and G.are both retained for the note played with the same key on a piano.