Level (logarithmic quantity)
In the International System of Quantities, the level of a quantity is the logarithm of the ratio of the value of that quantity to a reference value of the same quantity. Examples are the various types of sound level: sound power level (literally, the level of the sound power, abbreviated SWL), sound exposure level (SEL), sound pressure level (SPL) and particle velocity level (SVL).
Level of a quantity Q, denoted LQ, is defined by
where
Level of a field quantity, denoted LF, is defined by
where
For the level of a field quantity, the base of the logarithm is r = e.
A root-power quantity is a field quantity. The Level of a root-power quantity, denoted LF, is therefore
where
For the level of a root-power quantity, the base of the logarithm is r = e.
Level of a power quantity, denoted LP, is defined by
where
For the level of a power quantity, the base of the logarithm is r = e2.
The neper, bel, and decibel (one tenth of a bel) are units of level that are often applied to such quantities as power, intensity, or gain. The neper, bel, and decibel are defined by
If F is a root-power quantity:
If P is a power quantity:
If the power quantity P is equal to F2, and if the reference value of the power quantity, P0, is equal to F02, the levels LF and LP are equal.
The octave is a unit of level (specifically "frequency level", for r = 2) though that concept is seldom seen outside of the standard. A semitone is one twelfth of an octave.
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