For questions related to microtonal tuning systems, or systems that use intervals smaller than a half step.
Microtonality is the usage of musical intervals that are smaller than the standard semitone of 12-Tone Equal Temperament.
In tuning theory, the 2:1 perfect octave is split into 1200 subdivisions known as cents. One cent is exactly equal to a frequency ratio of 2^(1200):1, or the 1200th root of two to one. As such, the 12-TET semitone is exactly 100 cents.
Tuning systems in practice do not use the cent as their smallest interval, since an interval one cent wide is difficult for a human to distinguish from a perfect unison under most conditions. However, the cent as a basis of measurement is incredibly useful in comparing and discussing microtonal music. For example, in many Just Intonation tuning systems, the 3:2 perfect fifth is about 1.955 cents sharper than its 12-TET counterpart.
Some microtonal systems of music are based around dividing the octave into a different number of equidistant intervals. These kinds of systems are generally known as Equally Divided Octave temperaments. 12-TET just so happens to be 12-EDO, but theoretically there are an infinite number of other systems. 17-EDO, for example, is considered to be under the umbrella of microtonal music because its semitones are significantly smaller than 100 cents. 24-EDO has its smallest intervals set at exactly 50 cents, meaning that it actually contains all of the normal 12-TET intervals within it while also creating the quarter-step interval that splits the half-step into two.
Microtonality is based around a rejection of the limitations of the widely standardized 12-TET system, and often flies in the face of what conventional music accepts as normal. The area outside of the standard notes of the piano has great potential for exploitation, but remains largely unexplored compared to the ubiquitous 12 semitones in most commercially available music.