19/17: Difference between revisions

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~~'''19/17'''~~

{{Infobox Interval

|~~0 0 0 0 0 0~~ -~~1 1>~~

| Name = quasi-meantone

| Color name = 19o17u2, nosu 2nd

| Sound = jid_19_17_pluck_adu_dr220.mp3

}}

~~192~~.~~5576~~ 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.

[[~~File~~:~~jid_19_17_pluck_adu_dr220~~.~~mp3~~]] [[:~~File:jid_19_17_pluck_adu_dr220.mp3|sound sample~~]] [[Category:~~19-limit~~]]

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

[[Category:~~just_interval~~]]

== Approximation ==

[[Category:~~sound_example~~]]

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

== See also ==

* [[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:Second]]

[[Category:Whole tone]]

[[Category:Meantone]]

[[Category:Mercurial]]

[[Category:Taxicab-2 intervals]]

@@ Line 1: / Line 1: @@
-'''19/17'''
+{{Infobox Interval
-|0 0 0 0 0 0 -1 1&gt;
+| Name = quasi-meantone
+| Color name = 19o17u2, nosu 2nd
+| Sound = jid_19_17_pluck_adu_dr220.mp3
+}}
-.5576 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.
-[[File:jid_19_17_pluck_adu_dr220.mp3]] [[:File:jid_19_17_pluck_adu_dr220.mp3|sound sample]]      [[Category:19-limit]]
+/17 is the [[mediant]] of 9/8 and 10/9: (9 + 10)/(8 + 9) = 19/17.
-[[Category:just_interval]]
+== Approximation ==
-[[Category:sound_example]]
+{{Interval edo approximation|19/17}}
-[[Category:todo:expand]]
+== See also ==
+* [[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:Second]]
+[[Category:Whole tone]]
+[[Category:Meantone]]
+[[Category:Mercurial]]
+[[Category:Taxicab-2 intervals]]