19/17: Difference between revisions

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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 JI 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.