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.  


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.

Revision as of 17:16, 13 December 2021

Interval information
Ratio 19/17
Subgroup monzo 17.19 [-1 1
Size in cents 192.5576¢
Name quasi-meantone
Color name 19o17u2, nosu 2nd
FJS name [math]\displaystyle{ \text{M2}^{19}_{17} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.33539
Weil norm (log2 max(n, d)) 8.49586
Wilson norm (sopfr(nd)) 36

[sound info]
Open this interval in xen-calc

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.

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

See also