Editing Logarithmic scale (section)

== Logarithmic units ==
A '''logarithmic unit''' is a [[Units of measurement|unit]] that can be used to express a quantity ([[Physical quantity|physical]] or mathematical) on a logarithmic scale, that is, as being proportional to the value of a [[logarithm]] function applied to the ratio of the quantity and a reference quantity of the same type. The choice of unit generally indicates the type of quantity and the base of the logarithm. 

=== Examples ===
Examples of logarithmic units include [[units of information]] and [[information entropy]] ([[nat (unit)|nat]], [[shannon (unit)|shannon]], [[ban (information)|ban]]) and of [[signal level]] ([[decibel]], bel, [[neper]]).  [[Frequency level]]s or logarithmic frequency quantities have various units are used in electronics ([[Decade (log scale)|decade]], [[octave (electronics)|octave]]) and for music pitch [[Interval (music)|interval]]s ([[octave]], [[semitone]], [[Cent (music)|cent]], etc.).  Other logarithmic scale units include the [[Richter magnitude scale]] point.

In addition, several industrial measures are logarithmic, such as standard values for [[Logarithmic_resistor_ladder|resistors]], the [[American wire gauge]], the [[Birmingham gauge]] used for wire and needles, and so on.

=== Units of information ===
* [[bit]], [[byte]]
* [[hartley (unit)|hartley]]
* [[nat (unit)|nat]]
* [[shannon (unit)|shannon]]

=== Units of level or level difference ===
{{further|Level (logarithmic quantity)}}
* [[bel (unit)|bel]], [[decibel]]
* [[neper]]

==== Units of frequency level ====
* [[Decade (log scale)|decade]], [[One-third octave|decidecade]], [[savart]]
* [[octave]], [[Whole tone|tone]], [[semitone]], [[Cent (music)|cent]]

=== Table of examples ===

{| class="wikitable"
|-
! Unit
! Base of logarithm
! Underlying quantity
! Interpretation
|-
| [[bit]]
| {{math|2}}
| number of possible messages
| [[Quantities of information|quantity of information]]
|-
| [[byte]]
| {{math|2<sup>8</sup> {{=}} 256}}
| number of possible messages
| [[Quantities of information|quantity of information]]
|-
| [[decibel]]
| {{math|10<sup>(1/10)</sup> ≈ 1.259}}
| any [[Power, root-power, and field quantities|power quantity]] ([[sound power]], for example)
| [[sound power level]] (for example)
|-
| [[decibel]]
| {{math|10<sup>(1/20)</sup> ≈ 1.122}}
| any [[Power, root-power, and field quantities|root-power quantity]] ([[sound pressure]], for example)
| [[sound pressure level]] (for example)
|-
| [[semitone]]
| {{math|2<sup>(1/12)</sup> ≈ 1.059}}
| [[frequency]] of [[sound]]
| [[pitch interval]]
|}

The two definitions of a decibel are equivalent, because a ratio of [[Power, root-power, and field quantities|power quantities]] is equal to the square of the corresponding ratio of [[Power, root-power, and field quantities|root-power quantities]].{{citation needed|reason=The two definitions of the logarithmic unit or of the quantity are not equivalent.  The same numeric value is obtained in a linear system with a constant impedance and the choice of units, but they are inherently different units despite having the same name.|date=December 2019}}<ref>[https://repository.oceanbestpractices.org/bitstream/handle/11329/2340/A-Century-of-Sonar.pdf?sequence=1 Ainslie, M. A. (2015). A Century of Sonar: Planetary Oceanography, Underwater Noise Monitoring, and the Terminology of Underwater Sound.]</ref>