Meantone temperament

This article may be in need of reorganization to comply with Wikipedia's layout guidelines. Please help by editing the article to make improvements to the overall structure. (February 2021) (Learn how and when to remove this message)

Meantone temperaments are musical temperaments;^[1] that is, a variety of tuning systems constructed, similarly to Pythagorean tuning, as a sequence of equal fifths, both rising and descending, scaled to remain within the same octave. But rather than using perfect fifths, consisting of frequency ratios of value ${\displaystyle 3:2}$, these are tempered by a suitable factor that narrows them to ratios that are slightly less than ${\displaystyle 3:2}$, in order to bring the major or minor thirds closer to the just intonation ratio of ${\displaystyle 5:4}$ or ${\displaystyle 6:5}$, respectively. A regular temperament is one in which all the fifths are chosen to be of the same size .

Twelve-tone equal temperament (12 TET) is obtained by making all semitones the same size, with each equal to one-twelfth of an octave; i.e. with ratios ¹²√2  : 1. Relative to Pythagorean tuning, it narrows the perfect fifths by about 2 cents or ⁠1/ 12 ⁠th of a Pythagorean comma to give a frequency ratio of ${\displaystyle 2^{7/12}:1}$. This produces major thirds that are wide by about 13 cents, or ⁠1/ 8 ⁠th of a semitone. Twelve-tone equal temperament is almost exactly the same as ⁠1/ 11 ⁠ syntonic comma meantone tuning (1.955 cents vs. 1.95512).