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]\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 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.

Approximation

Edo approximations for 19/17 (192.56 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
6	1\6	200.00	+7.44	+3.72
12	2\12	200.00	+7.44	+7.44
13	2\13	184.62	-7.94	-8.60
19	3\19	189.47	-3.08	-4.88
25	4\25	192.00	-0.56	-1.16
31	5\31	193.55	+0.99	+2.56
37	6\37	194.59	+2.04	+6.28
38	6\38	189.47	-3.08	-9.77
44	7\44	190.91	-1.65	-6.04
50	8\50	192.00	-0.56	-2.32
56	9\56	192.86	+0.30	+1.40
62	10\62	193.55	+0.99	+5.12
68	11\68	194.12	+1.56	+8.84
69	11\69	191.30	-1.25	-7.21
75	12\75	192.00	-0.56	-3.49

See also

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