22/7: Difference between revisions

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== Approximation to π ==
== Approximation to π ==
It is the first non trivial convergent to the continued fraction of π. The next in the series is 333/106, a much more complex 53-limit interval. The difference between π and 22/7 is of only 0.697 cents.
It is the first non trivial convergent to the continued fraction of [[Acoustic pi|acoustic π]]. The next in the series is 333/106, a much more complex 53-limit interval. The difference between π and 22/7 is of only 0.697 cents.

Revision as of 21:43, 1 November 2025

Interval information
Ratio 22/7
Factorization 2 × 7-1 × 11
Monzo [1 0 0 -1 1
Size in cents 1982.492 ¢
Names undecimal minor thirteenth,
first pi approximant
FJS name [math]\displaystyle{ \text{P12}^{11}_{7} }[/math]
Tenney norm (log2 nd) 7.26679
Weil norm (log2 max(n, d)) 8.91886
Wilson norm (sopfr(nd)) 20
Open this interval in xen-calc

22/7 is a 11-limit interval one octave above 11/7.

Approximation to π

It is the first non trivial convergent to the continued fraction of acoustic π. The next in the series is 333/106, a much more complex 53-limit interval. The difference between π and 22/7 is of only 0.697 cents.