# decibels

### Definition

Decibels provide a logarithmic unit of measurement for amplitude ratios. Decibels are to amplitude as cents are to frequency. Increasing an amplitude by 10 decibels is equivalent to multiplying the amplitude by 10.

The following formula converts an amplitude ratio into decibels:

decibels = 10 × log10(ratio)

The following formula converts a pitch interval in decibels to an amplitude ratio:

ratio = 10(decibels/10)

### Examples

Jeffrey Hass of the Indiana University Center for Electronic and Computer Music places the just-noticable difference for amplitudes at ”between 0.2 and 0.4 dB”.

The following table is extracted from hyperphysics.phy-astr.gsu.edu and from www.soundadvice.info. The latter includes decibel ranges for many individual musical instruments. The reference point of this table (0 dB) is the threshold of hearing.

 Decibels Ratio 0 Threshold of Hearing 40 Single instrument playing ppp 100 Full orchestra playing fff 120 Threshold of Pain

In frequency-spectrum graphs the value 0 dB typically signifies the largest amplitude in the graph; all other amplitudes are plotted as negative values.

The difference between two adjacent dynamics (e.g. mp and mf) played by a single instrument falls typically in the range from 4 to 6 decibels.

 © Charles Ames Page created: 2014-03-04 Last updated: 2015-04-14