8/7: Difference between revisions
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In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to one step of 5edo = 240{{cent}}. | In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to one step of 5edo = 240{{cent}}. | ||
A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is 1029/1024 (about 8.4{{cent}}), which is tempered out in [[slendric]] and [[31edo]]. | A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{cent}}), which is tempered out in [[slendric]] and [[31edo]]. | ||
== See also == | == See also == | ||