8/7: Difference between revisions

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{{Infobox Interval

| Name = septimal whole tone, supermajor second, septimal major second

| Name = septimal whole tone, supermajor second, septimal major second, septimal supermajor second

| Color name = r2, ru 2nd

| 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{{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 '''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{{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{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].

== Approximation ==

== See also ==

* [[7/4]] – its [[octave complement]]

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* [[7/6]] – its [[fourth complement]]

* [[Gallery of just intervals]]

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

[[Category:Second]]

[[Category:Supermajor second]]

[[Category:Over-7]]

[[Category:Over-7 intervals]]

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 {{Infobox Interval
-| Name = septimal whole tone, supermajor second, septimal major second
+| Name = septimal whole tone, supermajor second, septimal major second, septimal supermajor second
 | Color name = r2, ru 2nd
 | Sound = jid_8_7_pluck_adu_dr220.mp3
@@ Line 6: / Line 6: @@
 {{Wikipedia|Septimal whole tone}}
-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 '''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{{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{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].
+== Approximation ==
+{{Interval edo approximation|8/7}}
 == See also ==
 * [[7/4]] – its [[octave complement]]
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 * [[7/6]] – its [[fourth complement]]
 * [[Gallery of just intervals]]
-* [[8/7 equal-step tuning]]
 [[Category:Second]]
 [[Category:Supermajor second]]
-[[Category:Over-7]]
+[[Category:Over-7 intervals]]