Exploring Music's Complexities

Introduction to Intervals

Melodic and Harmonic Intervals


Understanding intervals begins with an understanding of scales. Benjamin Hollis defines a scale as a group of pitches (scale degrees) arranged in either ascending or descending order. These pitches span an octave (1). In Western music a major scale (heptatonic scale) consists of seven different pitches. There are half steps between the third and fourth and seventh and eighth scale degrees; whole steps exist between all other steps. This means there are 12 divisions or semitones in scales. For a comprehensive description of the pentatonic scale refer to  reference 2.

Scale of C


Simply put, a chord is a matter of sounding together three or more notes of any scale.  The particular scale from which the chord is constructed is referred to as the related scale of that chord.  There are many different chordsSome sound dissonant, meaning not harmonious. Some are two-note chords, others are more than three notes and some chords can be “broken” (3).

A two note and broken chord



Music theory defines an interval as the difference between two pitches (5). Two note chords are called intervals. In Western music an interval is named according to its number and quality of a diatonic scale.  A diatonic scale is built on the intervals made by natural notes (i.e. neither flat nor sharp) and based on seven whole steps of perfect fifths: C – G – D – A – E – B – F.  An interval’s name is further qualified using the terms perfect, major, minor, augmented and diminished.  For example, a perfect, major, minor, augmented, or diminished and number by unison, second, third, fourth, etc.


Sonic Ratio Frequencies

Put another way, an interval is the ratio between two sonic frequencies.  As explained by the Physics Classroom:  “Certain sound waves when played (and heard) simultaneously will produce a particularly pleasant sensation when heard, are said to be consonant. Such sound waves form the basis of intervals in music. For example, any two sounds whose frequencies make a 2:1 ratio is said to be separated by an octave and result in a particularly pleasing sensation when heard. That is, two sound waves sound good when played together if one sound has twice the frequency of the other. Similarly, two sounds with a frequency ratio of 5:4 are said to be separated by an interval of a third. such sound waves also sound good when played together. Examples of other sound wave intervals and their respective frequency ratios are listed in the table below.

Interval Frequency Ratio Examples
Octave 2:1 512 Hz and 256 Hz
Third 5:4 320 Hz and 256 Hz
Fourth 4:3 342 Hz and 256 Hz
Fifth 3:2 384 Hz and 256 Hz  “ (4)

Be advised!  Intervals are everywhere.



  1.  Hollis, Benjamin.  The Method Behind the Music.  https://method-behind-the-music.com/theory/scalesandkeys.
  2. How to Play the Pentatonic scale.  https://beginnerguitarhq.com/pentatonic-scale/
  3. https://www.thoughtco.com/chord-definition-2701891
  4. Prout, Ebenezer (1903), “I-Introduction”,Harmony, Its Theory And Practise (30th edition, revised and largely rewritten ed.), London: Augener; Boston: Boston Music Co., p. 1, ISBN 978-0781207836
  5. The Physics Classroom» Physics Tutorial » Sound Waves and Music » Pitch and Frequency


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  1. Esoteric History of Music | Wonder of Sound Music Notes
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