8/7: Difference between revisions

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{{Infobox Interval

~~| JI glyph = [[File:glyph_8_7.png|x48px]]~~

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

~~| Ratio = 8/7~~

~~| Monzo = 3 0 0 -1~~

~~| Cents = 231.17409~~

| Name = septimal whole tone, ~~<br>~~supermajor second, ~~<br>~~septimal major second

| Color name = r2, ru 2nd

~~| FJS name = M2<sub>7</sub>~~

| Sound = jid_8_7_pluck_adu_dr220.mp3

}}

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 '''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.

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

== Approximation ==

== See also ==

* [[7/4]] – its [[octave complement]]

* [[21/16]] – its [[fifth complement]]

* [[~~Gallery of Just Intervals~~]]

* [[7/6]] – its [[fourth complement]]

* [[~~Wikipedia:Septimal_whole_tone|Septimal whole tone - Wikipedia~~]]

* [[Gallery of just intervals]]

~~[[Category:7-limit]]~~

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

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

[[Category:Second]]

[[Category:~~Whole tone]]~~

[[Category:Supermajor second]]

~~[[Category:Superparticular~~]]

[[Category:Over-7 intervals]]

[[Category:Over-7]]

~~[[Category:Subharmonic~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph = [[File:glyph_8_7.png|x48px]]
+| Name = septimal whole tone, supermajor second, septimal major second, septimal supermajor second
-| Ratio = 8/7
-| Monzo = 3 0 0 -1
-| Cents = 231.17409
-| Name = septimal whole tone, <br>supermajor second, <br>septimal major second
 | Color name = r2, ru 2nd
-| FJS name = M2<sub>7</sub>
 | Sound = jid_8_7_pluck_adu_dr220.mp3
 }}
+{{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 '''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.
-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{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].
+== Approximation ==
+{{Interval edo approximation|8/7}}
 == See also ==
 * [[7/4]] – its [[octave complement]]
 * [[21/16]] – its [[fifth complement]]
-* [[Gallery of Just Intervals]]
+* [[7/6]] – its [[fourth complement]]
-* [[Wikipedia:Septimal_whole_tone|Septimal whole tone - Wikipedia]]
+* [[Gallery of just intervals]]
-[[Category:7-limit]]
-[[Category:8/7]]
-[[Category:Interval ratio]]
 [[Category:Second]]
-[[Category:Whole tone]]
+[[Category:Supermajor second]]
-[[Category:Superparticular]]
+[[Category:Over-7 intervals]]
-[[Category:Over-7]]
-[[Category:Subharmonic]]