Tetracot: Difference between revisions
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'''Tetracot''', in this article, is the rank-2 [[regular temperament]] in the 2.3.5.11.13 [[subgroup]] [[generator|generated]] by a "sub-major" second of about 174–178{{cent}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four such generators make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]], resulting in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]]. This is in contrast to [[meantone]], where 10/9 is tuned sharper than or equal to just in order to be equated with [[9/8]]. | '''Tetracot''', in this article, is the rank-2 [[regular temperament]] in the 2.3.5.11.13 [[subgroup]] [[generator|generated]] by a "sub-major" second of about 174–178{{cent}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four such generators make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]], resulting in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]]. This is in contrast to [[meantone]], where 10/9 is tuned sharper than or equal to just in order to be equated with [[9/8]]. | ||
Tetracot has many [[extension]]s for the 7-, 11-, and 13-limit. See [[Tetracot | Tetracot has many [[extension]]s for the 7-, 11-, and 13-limit. See [[Tetracot extensions]]. Equal temperaments that support tetracot include {{EDOs| 27, 34, and 41 }}. | ||
See [[Tetracot family]] or [[No-sevens subgroup temperaments#Tetracot]] for more technical data. | See [[Tetracot family]] or [[No-sevens subgroup temperaments#Tetracot]] for more technical data. | ||