26/25

Interval information

Ratio	26/25
Factorization	2 × 5-2 × 13
Monzo	[1 0 -2 0 0 1⟩
Size in cents	67.90023¢
Name	large tridecimal third tone
Color name	3ogg2, thogugu 2nd
FJS name	[math]\displaystyle{ \text{d2}^{13}_{5,5} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	9.3443
Weil norm (log2 max(n, d))	9.40088
Wilson norm (sopfr(nd))	25
Comma size	medium
[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 26/25, the large tridecimal third tone appears as the difference between the 26th and 25th harmonics. Thus it makes the difference between 13/8 and 25/16 (a stack of two 5/4's). If it is treated as a comma, then 5/4 and 13/10 both collapse to a Neogothic-flavored major third in between them representing half of 13/8. It measures about 67.9¢.

Approximation

26/25 is very well approximated in 53edo as 3\53 (+0.024 ¢), and in 28edt as 1\28edt (+0.027 ¢). Its equal multiplication - 1ed26/25 - is effectively the same thing as 28edt.

Edo approximations for 26/25 (67.90 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
16	1\16	75.00	+7.10	+9.47
17	1\17	70.59	+2.69	+3.81
18	1\18	66.67	-1.23	-1.85
19	1\19	63.16	-4.74	-7.51
34	2\34	70.59	+2.69	+7.62
35	2\35	68.57	+0.67	+1.96
36	2\36	66.67	-1.23	-3.70
37	2\37	64.86	-3.04	-9.36
52	3\52	69.23	+1.33	+5.77
53	3\53	67.92	+0.02	+0.11
54	3\54	66.67	-1.23	-5.55
69	4\69	69.57	+1.66	+9.57
70	4\70	68.57	+0.67	+3.92
71	4\71	67.61	-0.29	-1.74
72	4\72	66.67	-1.23	-7.40

See also

• 25/13 - its octave complement
• 27/26 - the small tridecimal third tone
• Gallery of just intervals
• List of superparticular intervals