81/70: Difference between revisions

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{{Infobox Interval

~~| Ratio = 81/70~~

| Name = septimal ultramajor second

~~| Monzo = -1 4 -1 -1~~

~~| Cents = 252.6804~~

| Name = ~~septimal semiaugmented second, <br>~~septimal ultramajor second

| Color name = rg2, rugu 2nd

~~| FJS name = M2<sub>35</sub>~~

| Sound = Ji-81-70-csound-foscil-220hz.mp3

}}

'''81/70''', the '''septimal ultramajor second''' is a [[7-limit]] [[interseptimal]] ratio of about 253 [[cent]]s. It is sharp of a major second [[9/8]] by a septimal quartertone [[36/35]], sharp of a supermajor second [[8/7]] by a syntonic comma [[81/80]], and flat of a subminor third [[7/6]] by a sensamagic comma [[245/243]].

~~'''81/70''', the '''septimal semiaugmented second''' or '''septimal ultramajor second'''~~ is ~~a [[7-limit]] [[interseptimal]] ratio~~ of ~~about 253 cents. It is sharp of a subminor~~ third [[7/6]] by a ~~sensamagic comma~~ [[~~245~~/~~243~~]]~~, and sharp of a major second~~ [[~~16/9~~]] by a ~~septimal quartertone~~ [[~~36/35~~]].

Notice it is also flat of the just minor third [[6/5]] by a subminor second [[28/27]]. For this fact it is useful in the [[sensamagic dominant chord]] where it functions as a dissonance yet to be resolved up to the minor third. The [[Canou family|canou temperament]] targets this progression and uses it as one of the generators.

It is ~~also sharp of a minor third [[6/5]] by a subminor second [[28/27]]. For this fact it is useful in the [[Canovian chord]] and provides the function of a voice leading up to the minor third.~~

== Approximation ==

It is near-perfectly approximated by [[19edo]] (4\19), with an error of 0.05 cents, and hence equally well done by the [[enneadecal]] temperament.

~~The interval is so~~ perfectly approximated by [[19edo~~|19-edo~~]], with an error of 0.05 cents~~. There are a number of edos that do this~~ equally well~~, [[171edo|171-edo]] to name one. The first edo that does this better than 19-edo with patent val is~~ [[~~660edo|660-edo~~]].

== See also ==

* [[140/81]] – its [[octave complement]]

* [[35/27]] – its [[fifth complement]]

* [[Gallery of just intervals]]

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

~~[[Category:Interval]]~~

~~[[Category:Ratio]]~~

[[Category:Second]]

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

[[Category:Supermajor second]]

[[Category:Interseptimal]]

[[Category:Interseptimal intervals]]

[[Category:Semifourth]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 81/70
+| Name = septimal ultramajor second
-| Monzo = -1 4 -1 -1
-| Cents = 252.6804
-| Name = septimal semiaugmented second, <br>septimal ultramajor second
 | Color name = rg2, rugu 2nd
-| FJS name = M2<sub>35</sub>
 | Sound = Ji-81-70-csound-foscil-220hz.mp3
 }}
+'''81/70''', the '''septimal ultramajor second''' is a [[7-limit]] [[interseptimal]] ratio of about 253 [[cent]]s. It is sharp of a major second [[9/8]] by a septimal quartertone [[36/35]], sharp of a supermajor second [[8/7]] by a syntonic comma [[81/80]], and flat of a subminor third [[7/6]] by a sensamagic comma [[245/243]].
-'''81/70''', the '''septimal semiaugmented second''' or '''septimal ultramajor second''' is a [[7-limit]] [[interseptimal]] ratio of about 253 cents. It is sharp of a subminor third [[7/6]] by a sensamagic comma [[245/243]], and sharp of a major second [[16/9]] by a septimal quartertone [[36/35]].
+Notice it is also flat of the just minor third [[6/5]] by a subminor second [[28/27]]. For this fact it is useful in the [[sensamagic dominant chord]] where it functions as a dissonance yet to be resolved up to the minor third. The [[Canou family|canou temperament]] targets this progression and uses it as one of the generators.
-It is also sharp of a minor third [[6/5]] by a subminor second [[28/27]]. For this fact it is useful in the [[Canovian chord]] and provides the function of a voice leading up to the minor third.
+== Approximation ==
+It is near-perfectly approximated by [[19edo]] (4\19), with an error of 0.05 cents, and hence equally well done by the [[enneadecal]] temperament.
-The interval is so perfectly approximated by [[19edo|19-edo]], with an error of 0.05 cents. There are a number of edos that do this equally well, [[171edo|171-edo]] to name one. The first edo that does this better than 19-edo with patent val is [[660edo|660-edo]].
 == See also ==
 * [[140/81]] – its [[octave complement]]
 * [[35/27]] – its [[fifth complement]]
 * [[Gallery of just intervals]]
-[[Category:7-limit]]
-[[Category:Interval]]
-[[Category:Ratio]]
 [[Category:Second]]
-[[Category:Whole tone]]
+[[Category:Supermajor second]]
-[[Category:Interseptimal]]
+[[Category:Interseptimal intervals]]
+[[Category:Semifourth]]