Interval (music)

In music theory, an interval is the difference in pitch between two notes.

When speaking of notes in the chromatic scale, it is normal to use names such as "major third", "perfect fifth" and "augmented fourth". When speaking of other scales, however, or when talking about two pitches without the context of a scale, such names are often meaningless. Some such intervals have names of their own.

It is also possible to measure the size of the interval between any two notes by using the logarithmic measure of cents. 1200 cents are equal to an octave, and an equally tempered semitone is equal to 100 cents.

Table of contents 1 Basic intervals: whole tone and semitone 2 Intervals in the chromatic scale 2.1 Compound intervals 2.2 Concordant and discordant intervals 2.3 Modifying intervals 3 Other intervals

Basic intervals: whole tone and semitone A semitone, (also called half tone or half step), is the smallest interval in Western musical tuning. It corresponds to the the difference between two adjacent keys on a piano, or between two frets on a guitar.

In terms of pitch, it is equal to a frequency ratio of 2^1/12 in equal temperament, 256/243 in Pythagorean tuning, (3/2)^1/7 in perfect fifth tuning, and various rational numbers, such as 16/15, in just intonation.

A whole tone (also called tone or whole step) is equal to two semitones in equal temparament, where it is 2^1/6. It is 9/8 in Pythagorean tuning, (9/4)^1/7 in fifth tuning, and either 9/8 or 10/9 in just intonation, depending on the note in the scale.

Intervals in the chromatic scale Intervals are named after the number of notes they span in the diatonic scale. The names are inclusive of the two notes being considered; for example the interval between a C and a G is a fifth (C,D,E,F,G is a distance of 5 notes). In addition to the number of tones between notes, the nature of the interval can also be described. In a major scale, intervals starting from the tonic can be perfect or major. A Unison is the interval between a note and itself (meaning normally just one note heard.)

Fig 1. Intervals in the C major scale

In minor scales the minor interval is introduced:

Fig 2. Intervals in the C minor melodic scale

Fig 3. Intervals in the C minor harmonic scale

Compound intervals

When an interval exceeds an octave, it is called a compound interval. For example, a note a 10th above the tonic in a major scale is known as a 'compound major third.'

Concordant and discordant intervals

Concordant intervals usually sound "right". Discordant intervals jar, and can sound as if one of the notes wants to move up or down (called a resolution; this is the basis of suspensions.) Concordant intervals include all perfect intervals (4ths, 5ths, 8ves) and a few imperfect intervals, namely major and minor 3rds and 6ths; all other intervals are called discordant intervals, including 2nds, 7ths, and augmented or diminished notes.

Modifying intervals

It is possible to modify intervals. Naming follows these rules:

• If the bottom note of a perfect or major interval is lowered a semitone (or the top note is raised), the interval has been augmented.
• If the bottom note of a perfect or minor interval is raised a semitone (or the top note is lowered), the interval becomes diminished.
• If the bottom note of a minor interval is lowered a semitone, the interval becomes major.
• If the bottom note of a major interval is raised a semitone, the interval becomes minor.

Modified intervals often have more than one name. For example, a minor 7th can also be written as an augmented 6th. These are called enharmonic intervals. Typically names with 'minor' or 'major' in them are preferred, so the more correct way to write the interval given in the example is 'minor 7th.' The primary exception to this being in the case of a diminished 7th, which has a specific function within a full diminished 7th chord.

The interval of augmentation and diminishment is a semitone only in modern equal temperament, where a semitone is exactly half a tone. More generally it is a tone less a semitone. An interval is augmented by changing one its semitones into a tone. Also this means that an augmented 6th is not generally equal to a minor 7th. This is only true in modern music.

Other intervals There are also a number of intervals not found in the chromatic scale which have names of their own. These intervals describe small discrepencies between notes tuned according to just intonation:

• A Pythagorean comma is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the frequency ratio 531441:524288, and is equal to 23.46 cents
• A syntonic comma is the difference between four justly tuned perfect fifths and two octaves plus a major third. It is expressed by the ratio 81:80, and is equal to 21.51 cents
• Diesis is generally used to mean the difference between three justly tuned major thirds and one octave. It is expressed by the ratio 128:125, and is equal to 41.06 cents. However, it has been used to mean other small intervals: see diesis for details
• A schisma[?] is the difference between five octaves and eight justly tuned fifths plus one justly tuned major third. It is expressed by the ratio 32805:32768, and is equal to 1.95 cents. It is also the difference between the Pythagorean and a syntonic commas.

A number of cultures around the world who do not use the chromatic scale have their own names for intervals found in their music.

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For the mathematical use of the word "interval", see interval (mathematics).