What is Cent (music)?

Information about Cent (music)

The cent is a logarithmic unit of measure used for musical intervals. Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes.

1200 cents are equal to one octave — a frequency ratio of 2:1 — and an equally tempered semitone (the interval between two adjacent piano keys) is equal to 100 cents. This means that a cent is precisely equal to 21/1200, the 1200th root of 2, which is approximately 1.0005777895.

If you know the frequencies a and b of two notes, the number of cents measuring the interval between them may be calculated by the following formula (similar to the definition of decibel both formally as well as in its purpose to linearize a physical unit which is exponential but perceived logarithmically by humans):



Likewise, if you know a note b and the number n of cents in the interval, then the other note a may be calculated by:



To compare different tuning systems, convert the various interval sizes into cents. For example, in just intonation the major third is represented by the frequency ratio 5:4. Applying the formula at the top shows this to be about 386 cents. The equivalent interval on the equal-tempered piano would be 400 cents. The difference, 14 cents, is about a seventh of a half step, easily audible. The just noticeable difference for this unit is about 6 cents.

A. J. Ellis based the measure on the acoustic logarithms semitone system developed by de Prony, on Bosanquet's suggestion, and introduced it in his edition of Hermann von Helmholtz's On the Sensations of Tone. It has since become the standard way of measuring intervals in equal temperament systems or for comparison with equal temperament systems.

Sound Files

The following .ogg files play various cents intervals. In each case the first note played is middle C. The next note a C which is sharper by the assigned cents value. Finally the interval is played.

The file plays middle C, followed by a tone 1 cent sharper than C, followed by both tones together.
Problems listening to the file? See media help


The file plays middle C, followed by a tone 6 cents sharper than C, followed by both tones together.
Problems listening to the file? See media help


The file plays middle C, followed by a tone 10 cents sharper than C, followed by both tones together.
Problems listening to the file? See media help

References

See also

External links

logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself.

Presentation of data on a logarithmic scale can be helpful when the data covers a large range of values – the logarithm reduces this to a more
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In music theory, the term interval describes the difference in pitch between two notes. Although frequently used in connection with intervals, the term "distance" does not adequately describe the physics and subjective effects of two interacting frequencies.
..... Read more.
In music, there are two common meanings for tuning:
  • Tuning practice, the act of tuning an instrument or voice.
  • Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical basis.

..... Read more.
Perfect octave
Inverse unison
Name
Other names -
Abbreviation P8
Size
Semitones 12
Interval class 0
Just interval 2:1
Cents
Equal temperament 1200
Just intonation 1200 In music, an octave
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An equal temperament is a musical temperament. It is a system of tuning in which every pair of adjacent notes has an identical frequency ratio. Equal temperaments are often intended to approximate some form of just intonation.
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semitone
Inverse major seventh; diminished octave
Name
Other names minor second
or diatonic semitone;
augmented unison
or chromatic semitone
Abbreviation m2; aug1
Size
Semitones 1
Interval class 1

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The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power) relative to a specified or implied reference level.
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In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series.
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In psychophysics, a just noticeable difference, customarily abbreviated with lowercase letters as jnd, is the smallest difference in a specified modality of sensory input that is detectable by a human being.
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Alexander John Ellis (or Alexander Sharpe) (14 June, 1814 - 28 October, 1890) was an English philologist and music theorist. He is noted for translating and extensively annotating Hermann Helmholtz's On the Sensations of Tone
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Robert Holford Macdowall Bosanquet (31 July 1841–7 August 1912) was an English scientist and music theorist, and brother of Admiral Sir Day Bosanquet, and philosopher Bernard Bosanquet.

Bosanquet was the son of Rev. R. W. Bosanquet of Rock Hall, Alnwick, Northumberland.
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An equal temperament is a musical temperament. It is a system of tuning in which every pair of adjacent notes has an identical frequency ratio. Equal temperaments are often intended to approximate some form of just intonation.
..... Read more.
Do or C is the first note of the fixed-Do solfege.

In Western music, the expression "middle C" refers to the note "C" (or "Do" in fixed-Do solfege) located exactly between the two staves of the grand staff, quoted as C4 in scientific pitch
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Do or C is the first note of the fixed-Do solfege.

In Western music, the expression "middle C" refers to the note "C" (or "Do" in fixed-Do solfege) located exactly between the two staves of the grand staff, quoted as C4 in scientific pitch
..... Read more.
Do or C is the first note of the fixed-Do solfege.

In Western music, the expression "middle C" refers to the note "C" (or "Do" in fixed-Do solfege) located exactly between the two staves of the grand staff, quoted as C4 in scientific pitch
..... Read more.
Alexander John Ellis (or Alexander Sharpe) (14 June, 1814 - 28 October, 1890) was an English philologist and music theorist. He is noted for translating and extensively annotating Hermann Helmholtz's On the Sensations of Tone
..... Read more.
In music theory, the term interval describes the difference in pitch between two notes. Although frequently used in connection with intervals, the term "distance" does not adequately describe the physics and subjective effects of two interacting frequencies.
..... Read more.
In music, there are two common meanings for tuning:
  • Tuning practice, the act of tuning an instrument or voice.
  • Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical basis.

..... Read more.