5041/5040

Interval information

Ratio	5041/5040
Subgroup monzo	2.3.5.7.71 [-4 -2 -1 -1 2⟩
Size in cents	0.3434647¢
Names	third brown pair comma, 19th highly compositema
Color name	71oorg1
FJS name	[math]\displaystyle{ \text{P1}^{71,71}_{5,7} }[/math]
Special properties	square superparticular, reduced
Tenney height (log2 nd)	24.5987
Weil height (log2 max(n, d))	24.599
Wilson height (sopfr(nd))	168
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.2002 bits
Comma size	unnoticeable
S-expression	S71
Open this interval in xen-calc

5041/5040, the third brown pair comma, or the 19th highly compositema is a 71-limit superparticular interval measuring about 343 millicents.

Theory

5041/5040 represents the difference between 72/71 and 71/70; therefore tempering this comma out splits their product, 36/35, in two; as 36/35 is the ratio of 6/5 to 7/6, tempering out this comma also splits 7/5 in two, by equating 84/71 to 71/60. It is also the answer to the Brocard's problem question of n! + 1 = m^2, to which there's only three known so far - 25/24, 121/120, and this.

References

• Wikipedia Contributors, Brocard's problem.