19/17: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

~~| Ratio = 19/17~~

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

~~| Cents = 192.55761~~

| Name = quasi-meantone

| Color name = 19o17u2, nosu 2nd

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}}

'''19/17''' is ~~the~~ interval ~~between~~ [[9/8]] and [[10/9]], two common sizes of whole tone. In [[meantone]] systems, the two are conflated into one interval, which ~~converges increasingly closely to a perfect~~ 19/17 ~~in successive steps of~~ the ~~golden~~ meantone ~~sequence~~. ~~Two~~ of them fall short of a perfect [[5/4]] by 1445/1444, or 1.1985 cents.

'''19/17''' is a [[19-limit]] [[just intonation]] interval intermediate in size to [[9/8]] and [[10/9]], two common sizes of whole tone. In [[meantone]] systems, the two are conflated into one interval, for which 19/17 is often a good rational approximation, depending on the exact meantone tuning. It is a particularly good rational approximation to the whole tone of quarter comma meantone, as two of them fall short of a perfect [[5/4]] by [[1445/1444]], or 1.1985 cents. 19/17 is also very close to the size of the whole tone in golden meantone, being only about a tenth of a cent off.

19/17 is the [[mediant]] of 9/8 and 10/9: (9 + 10)/(8 + 9) = 19/17.

== Approximation ==

== See also ==

* [[34/19]] its [[~~inverse interval~~]]

* [[15/14]] – its coordinated semi-meantone ((19/17)<sup>5</sup> × (15/14)<sup>2</sup> = (2/1) / ([[mercurial comma]]))

* [[34/19]] – its [[octave complement]]

* [[Gallery of just intervals]]

[[Category:~~19-limit~~]]

[[Category:Second]]

[[Category:~~Interval]]~~

[[Category:Whole tone]]

~~[[Category:Ratio]]~~

~~[[Category:Just interval~~]]

[[Category:Meantone]]

[[Category:~~Sound example~~]]

[[Category:Mercurial]]

[[Category:Taxicab-2 intervals]]

[[Category:~~todo:expand~~]]

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 {{Infobox Interval
-| Icon =
-| Ratio = 19/17
-| Monzo = 0 0 0 0 0 0 -1 1
-| Cents = 192.55761
 | Name = quasi-meantone
 | Color name = 19o17u2, nosu 2nd
@@ Line 9: / Line 5: @@
 }}
-'''19/17''' is the interval between [[9/8]] and [[10/9]], two common sizes of whole tone. In [[meantone]] systems, the two are conflated into one interval, which converges increasingly closely to a perfect 19/17 in successive steps of the golden meantone sequence. Two of them fall short of a perfect [[5/4]] by 1445/1444, or 1.1985 cents.
+'''19/17''' is a [[19-limit]] [[just intonation]] interval intermediate in size to [[9/8]] and [[10/9]], two common sizes of whole tone. In [[meantone]] systems, the two are conflated into one interval, for which 19/17 is often a good rational approximation, depending on the exact meantone tuning. It is a particularly good rational approximation to the whole tone of quarter comma meantone, as two of them fall short of a perfect [[5/4]] by [[1445/1444]], or 1.1985 cents. 19/17 is also very close to the size of the whole tone in golden meantone, being only about a tenth of a cent off.
+/17 is the [[mediant]] of 9/8 and 10/9: (9 + 10)/(8 + 9) = 19/17.
+== Approximation ==
+{{Interval edo approximation|19/17}}
 == See also ==
-* [[34/19]] its [[inverse interval]]
+* [[15/14]] – its coordinated semi-meantone ((19/17)<sup>5</sup> × (15/14)<sup>2</sup> = (2/1) / ([[mercurial comma]]))
+* [[34/19]] – its [[octave complement]]
 * [[Gallery of just intervals]]
-[[Category:19-limit]]
+[[Category:Second]]
-[[Category:Interval]]
+[[Category:Whole tone]]
-[[Category:Ratio]]
-[[Category:Just interval]]
 [[Category:Meantone]]
-[[Category:Sound example]]
+[[Category:Mercurial]]
+[[Category:Taxicab-2 intervals]]
-[[Category:todo:expand]]