/info/intervals
 

Intervals

This page presents a summary of the definition of note intervals. This snippet of music theory is useful in MOZART when you use the command to change pitch by a named interval, and for constructing guitar chords.

 

 

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 - Gb
  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 - Db minor 2nd
  C - Eb minor 3rd
  C - Ab minor 6th
  C - Bb 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 - Dbb diminished 2nd
  C - Db minor 2nd
  C - D major 2nd
  C - D# augmented 2nd
  C - Ebb diminished 3rd
  C - Eb minor 3rd
  C - E major 3rd
  C - E# augmented 3rd
  C - Fb diminished 4th
  C - F perfect 4th
  C - F# augmented 4th
  C - Gb diminished 5th
  C - G perfect 5th
  C - G# augmented 5th
  C - Abb diminished 6th
  C - Ab minor 6th
  C - A major 6th
  C - A# augmented 6th
  C - Bbb diminished 7th
  C - Bb minor 7th
  C - B major 7th
  C - B# augmented 7th
  C - C'b diminished octave
  C - C' perfect octave
  C - C'# augmented octave

 

Doubly diminished and doubly augmented intervals also exist (eg C-Gbb  C-Gx) 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 Gb.are both retained for the note played with the same key on a piano.

 

 
 
 

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