8/7: Difference between revisions

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| Sound = jid_8_7_pluck_adu_dr220.mp3

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In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2¢. 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 ~~overtones in the~~ harmonic ~~series~~ 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¢. It's close in size to one step of 5edo = ~~240¢~~.

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}}.

~~Three~~ supermajor seconds is close to a perfect fifth. The difference is 1029/1024 (about 8.4¢), 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 ==

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* [[7/6]] – its [[fourth complement]]

* [[Gallery of just intervals]]

* [[8/7 equal-step tuning]]

[[Category:7-limit]]

~~[[Category:8/7]]~~

~~[[Category:Interval ratio]]~~

[[Category:Second]]

[[Category:Supermajor second]]

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 | Sound = jid_8_7_pluck_adu_dr220.mp3
 }}
-{{Wikipedia|Septimal whole tone }}
+{{Wikipedia|Septimal whole tone}}
-In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2¢. 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 overtones in the harmonic series 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¢. It's close in size to one step of 5edo = 240¢.
+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}}.
-Three supermajor seconds is close to a perfect fifth. The difference is 1029/1024 (about 8.4¢), 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 ==
@@ Line 19: / Line 19: @@
 * [[7/6]] – its [[fourth complement]]
 * [[Gallery of just intervals]]
+* [[8/7 equal-step tuning]]
 [[Category:7-limit]]
-[[Category:8/7]]
-[[Category:Interval ratio]]
 [[Category:Second]]
 [[Category:Supermajor second]]