19/17

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]\text{M2}^{19}_{17}[/math]
Special properties	reduced
Tenney height (log2 nd)	8.33539
Weil height (log2 max(n, d))	8.49586
Wilson height (sopfr(nd))	36
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.20442 bits
[sound info]
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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.

See also

• 15/14 – its coordinated semi-meantone ((19/17)⁵ × (15/14)² = (2/1) / (mercurial comma))
• 34/19 – its inverse interval
• Gallery of just intervals