8/7: Difference between revisions

(25 intermediate revisions by 13 users not shown)

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~~

| Color name = r2, ru 2nd

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

~~| Cents = 231.17409~~

| Name = septimal supermajor second

| Sound = jid_8_7_pluck_adu_dr220.mp3

~~| Color name =~~

}}

In [[~~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]], 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¢.

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]].

== Approximation ==

== See also ==

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

* [[7/4]] – its [[octave complement]]

* [~~http:~~//~~en.wikipedia.org/wiki/Septimal_whole_tone Septimal whole tone - Wikipedia~~].

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

* [[7/6]] – its [[fourth complement]]

* [[Gallery of just intervals]]

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

[[Category:Second]]

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

[[Category:Supermajor second]]

~~[[Category:interval]]~~

[[Category:Over-7 intervals]]

~~[[Category:ratio~~]]

[[Category:second]]

[[Category:~~septimal]]~~

~~[[Category:superparticular]]~~

~~[[Category:whole_tone~~]]

@@ 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
+| Color name = r2, ru 2nd
-| Monzo = 3 0 0 -1
-| Cents = 231.17409
-| Name = septimal supermajor second
 | Sound = jid_8_7_pluck_adu_dr220.mp3
-| Color name =
 }}
+{{Wikipedia|Septimal whole tone}}
-In [[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]], 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¢.
+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]].
+== Approximation ==
+{{Interval edo approximation|8/7}}
 == See also ==
-* [[Gallery of Just Intervals]]
+* [[7/4]] – its [[octave complement]]
-* [http://en.wikipedia.org/wiki/Septimal_whole_tone Septimal whole tone - Wikipedia].
+* [[21/16]] – its [[fifth complement]]
+* [[7/6]] – its [[fourth complement]]
+* [[Gallery of just intervals]]
-[[Category:7-limit]]
+[[Category:Second]]
-[[Category:8/7]]
+[[Category:Supermajor second]]
-[[Category:interval]]
+[[Category:Over-7 intervals]]
-[[Category:ratio]]
-[[Category:second]]
-[[Category:septimal]]
-[[Category:superparticular]]
-[[Category:whole_tone]]