Separation in pitch between two notes, or the two notes sounded together; sometimes called a dyad. It is a fundamental component of scales and chords

The basic method for describing intervals is ordinate to the degrees of the diatonic scale.

Press any adjacent label button to hear what the interval sounds like.


The general method for describing intervals results from analyzing difference between the major and minor scales.

Here are the written forms of these scales with C as tonic for comparison:
Press button to hear scale:
For further illustration the piano keyboard provides consistent interval distance through all half-steps

 This comparison ultimately leads to this generally accepted convention for describing intervals:

Extending this nomenclature across octaves using C as prime reveals more generally:


Intervals may also be called by more than one name, which helps in generally describing melodic and harmonic relationships concerning scale_degrees and modes.  Here is a table showing common and alternate (not exhaustive) interval names:

Halfsteps Common name Alternate name
0 unison  diminished second
1 minor second augmented first
2 major second diminished third
3 minor third augmented second
4 major third diminished fourth
5 perfect fourth augmented third
6 diminished fifth augmented fourth
7 perfect fifth diminished sixth
8 minor sixth augmented fifth
9 major sixth diminished seventh
10 minor seventh augmented sixth
11 major seventh diminished octave
12 octave diminished ninth
13 minor ninth augmented octave
14 major ninth diminished tenth
15 minor tenth augmented ninth
16 major tenth diminished eleventh
17 perfect eleventh augmented tenth
18 diminished twelfth augmented eleventh
19 perfect twelfth diminished thirteenth
20 minor thirteenth augmented twelfth
21 major thirteenth diminished fourteenth
22 minor fourteenth augmented thirteenth
23 major fourteenth diminished fifteenth
24 perfect fifteenth augmented fourteenth

When comparing notes for intervals generally we are considering the sustain portion of the sound made by the instrument, as in this example image of a note waveform which we might observe on some scope:

Assuming indefinite sustain (without decay), we merely add the waves together to arrive at the combined waveform of the interval.  In this next example we show (a) fundamental, (b) wave representing its perfect fourth, (c) summative waveform, and (d) observed beat-frequency waveform:

The significance of the beat-frequency becomes more apparent when comparing dissonant notes.  The next image shows combined (summative) wave for a minor-second interval with its beat-wave highlighted:

This highlighted wave may be heard as a sort of pulse, and may frequently be used as a key factor in rates of vibrato, tremolo, or as a fundamental component underlying the rhythm of the musical work.