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

~~| FJS name = M21917~~

| Sound = jid_19_17_pluck_adu_dr220.mp3

}}

'''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~~.

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

== Approximation ==

== See also ==

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

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

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

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

* [[Gallery of just intervals]]

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

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

[[Category:Second]]

[[Category:Whole tone]]

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

[[Category:Meantone]]

~~[[Category:Listen]]~~

[[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
-| FJS name = M2<sup>19</sup><sub>17</sub>
 | Sound = jid_19_17_pluck_adu_dr220.mp3
 }}
-'''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.
+/17 is the [[mediant]] of 9/8 and 10/9: (9 + 10)/(8 + 9) = 19/17.
+== Approximation ==
+{{Interval edo approximation|19/17}}
 == See also ==
+* [[15/14]] – its coordinated semi-meantone ((19/17)<sup>5</sup> × (15/14)<sup>2</sup> = (2/1) / ([[mercurial comma]]))
-* [[15/14]] – its coordinated semi-meantone ((19/17)^5 * (15/14)^2 = (2/1) / ([[mercurial comma]]))
+* [[34/19]] – its [[octave complement]]
-* [[34/19]] – its [[inverse interval]]
 * [[Gallery of just intervals]]
-[[Category:19-limit]]
-[[Category:Interval ratio]]
 [[Category:Second]]
 [[Category:Whole tone]]
-[[Category:Just interval]]
 [[Category:Meantone]]
-[[Category:Listen]]
 [[Category:Mercurial]]
+[[Category:Taxicab-2 intervals]]
-[[Category:todo:expand]]