8/7: Difference between revisions

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{| ~~class~~=~~"wikitable"~~

{{Infobox Interval

|-

| 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

~~| | JI glyph for 8/7~~

}}

|}

'''~~8/7~~'''

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.

|3 ~~0 0 -1>~~

~~231~~,~~17409 cents~~

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]]

* [[7/6]] – its [[fourth complement]]

* [[Gallery of just intervals]]

[[~~File:jid_8_7_pluck_adu_dr220.mp3]] [[:File~~:~~jid_8_7_pluck_adu_dr220.mp3|sound sample~~]]

[[Category:Second]]

[[Category:Supermajor second]]

In [[Just_intonation|Just Intonation]], 8/7 is the "septimal supermajor second" of approximately 231.2¢. Although it falls between the familiar major second and minor third of [[12edo|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|superparticular]] ratio. In [[7-limit|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|7/4]]) and octave. It differs from the Pythagorean major~~ second ~~of [[9/8|9/8]~~] ~~by [[64/63|64/63~~]~~], a microtone of about 27.3¢.~~

[[Category:Over-7 intervals]]

~~See the Wikipedia article for [http://en.wikipedia.org/wiki/Septimal_whole_tone Septimal whole tone].~~

~~See also: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~ [[Category:7-~~limit]]~~

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

~~[[Category:interval]]~~

~~[[Category:ratio]]~~

~~[[Category:second]]~~

~~[[Category:septimal]]~~

~~[[Category:superparticular]]~~

~~[[Category:whole_tone~~]]

@@ Line 1: / Line 1: @@
-{| class="wikitable"
+{{Infobox Interval
-|-
+| Name = septimal whole tone, supermajor second, septimal major second, septimal supermajor second
-| | [[File:glyph_8_7.png|alt=glyph 8 7.png|122x111px|glyph 8 7.png]]
+| Color name = r2, ru 2nd
-|-
+| Sound = jid_8_7_pluck_adu_dr220.mp3
-| | JI glyph for 8/7
+}}
-|}
+{{Wikipedia|Septimal whole tone}}
-'''8/7'''
+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.
-|3 0 0 -1&gt;
-,17409 cents
+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]]
+* [[7/6]] – its [[fourth complement]]
+* [[Gallery of just intervals]]
-[[File:jid_8_7_pluck_adu_dr220.mp3]] [[:File:jid_8_7_pluck_adu_dr220.mp3|sound sample]]
+[[Category:Second]]
+[[Category:Supermajor second]]
-In [[Just_intonation|Just Intonation]], 8/7 is the "septimal supermajor second" of approximately 231.2¢. Although it falls between the familiar major second and minor third of [[12edo|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|superparticular]] ratio. In [[7-limit|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|7/4]]) and octave. It differs from the Pythagorean major second of [[9/8|9/8]] by [[64/63|64/63]], a microtone of about 27.3¢.
+[[Category:Over-7 intervals]]
-See the Wikipedia article for [http://en.wikipedia.org/wiki/Septimal_whole_tone Septimal whole tone].
-See also: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:7-limit]]
-[[Category:8/7]]
-[[Category:interval]]
-[[Category:ratio]]
-[[Category:second]]
-[[Category:septimal]]
-[[Category:superparticular]]
-[[Category:whole_tone]]