8/7: Difference between revisions

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In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor 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 5edo's 240{{c}} step.

In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], most people think of it 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 5edo's 240{{c}} step.

A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].

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 {{Wikipedia|Septimal whole tone}}
-In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor 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 5edo's 240{{c}} step.
+In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], most people think of it 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 5edo's 240{{c}} step.
 A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].