Interval - Theory Music Reference

Interval

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:

third, sixth, and seventh intervals are called major or minor for their respective scales,
second interval is called minor if a half-step and major if a whole-step,
fourth, fifth, and octave intervals are called perfect for both scales, and
the terms augmented and diminished mean add or subtract another half-step respectively.

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.