INTERVALS

OVERVIEW

An interval is the relationship between two notes. It is one of the simplest, yet most profound, foundations of music. To name intervals in Western culture, reference is made to major and minor scales and the order in which notes appear within those scales.

In other musical cultures, intervals are not directly linked to scales and can even be represented with images that evoke their character¹.

MAJOR INTERVALS

The easiest way – though not the most scientifically precise – to start understanding intervals is to consider the major scale. The note on which the scale is built is called the root. The relationship between the root and any note of the scale is called an interval. The interval’s name depends on the note’s position in the scale. For example, the interval between the root and the third note of a major scale is called a major third.

• C – D → major second

• C – E → major third

• C – A → major sixth

• C – B → major seventh

MINOR INTERVALS

Similarly, we can consider the Phrygian minor scale (different from the natural minor by a flattened second) and compare the root with each note. The interval between the root and the third note of the minor scale is called a minor third.

• C – D♭ → minor second

• C – E♭ → minor third

• C – A♭ → minor sixth

• C – B♭ → minor seventh

PERFECT INTERVALS

Combining major and minor intervals covers 8 of the 12 semitones of a common Western instrument octave. Three remaining notes are common to both major and minor scales and are called perfect intervals: the fourth, fifth, and octave.

• C – F → perfect fourth

• C – G → perfect fifth

• C – C’ → octave

TRITONE

The tritone completes the 12 semitones of the octave. It has a dissonant character, often used to create tension before resolving to the tonic.

ALL INTERVALS IN THE EQUAL-TEMPERED SCALE

Semitones	Harmonic Ratio	Name	Actual Frequency (Hz)
0	1/1	C (root)	261.63
+1	16/15	D♭	279.07
+2	9/8	D	294.33
+3	6/5	E♭	313.96
+4	5/4	E	327.04
+5	4/3	F	348.84
+6	7/5	F#	366.28
+7	3/2	G	392.45
+8	8/5	A♭	418.61
+9	5/3	A	436.05
+10	16/9	B♭	465.12
+11	15/8	B	490.56
+12	2/1	C’	523.26

A UNIVERSAL VIEW

For a Western musician, referring to these scales is the fastest way to identify intervals, especially when using instruments divided into semitones. However, each interval has its own timbre and physical-scientific significance independent of scale numbering. Western scales simply order notes by pitch, which does not always reflect interval consonance. For example, ordering intervals by consonance would place the octave and fifth first.

DESCENDING INTERVALS

Intervals are usually thought of ascending, e.g., a fifth is assumed above the root. For beginners, it’s easier to consider only ascending intervals. If imagining one below the root, you can think “a fifth one octave lower” instead of “a descending fourth”². Descending intervals are useful in counterpoint, inversion, and solo construction, though their perception is often more logical-mathematical than psychoacoustic.

NOTES

• What is called a “fifth” in Western music is called 徵 (Zhi) in Chinese music.

• Books like The Complete Musician by S. Laitz, though traditional, suggest finding descending intervals by converting them into ascending equivalents (p. 37). For example, a descending seventh is treated as an ascending minor second, then lowered an octave.