E-shaped comma: Difference between revisions

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The '''E-shaped comma''' is a [[17-limit]] [[unnoticeable comma]] of measuring 0.055 [[cent]]s, with frequency ratio of 31213/31212. It is the amount by which a stack consisting of three [[7/6]]s, one [[26/17]] and one [[28/17]] exceeds two [[octave]]s. By tempering it out is defined the '''E-shaped temperament'''.
The '''E-shaped comma''' is a [[17-limit]] [[unnoticeable comma]] of measuring 0.055 [[cent]]s, with frequency ratio of 31213/31212. It is the amount by which a stack of two [[51/49]]'s falls short of [[13/12]]. Tempering it out defines the '''E-shaped temperament'''.


== Commatic relations ==
== Commatic relations ==
Line 13: Line 13:
* [[2401/2400]] and [[2601/2600]]
* [[2401/2400]] and [[2601/2600]]
* [[4914/4913]] and [[5832/5831]]
* [[4914/4913]] and [[5832/5831]]
* [[Neuseisma|28561/28560]] and [[336141/336140]]
* [[28561/28560]] and [[336141/336140]]


It factors into the following superparticular pair:  
It factors into the following superparticular pair:  
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[[Category:E-shaped]]
[[Category:E-shaped]]
[[Category:Commas referencing a famous use of a number]]

Latest revision as of 19:51, 8 July 2026

Interval information
Ratio 31213/31212
Factorization 2-2 × 3-3 × 74 × 13 × 17-2
Monzo [-2 -3 0 4 0 1 -2
Size in cents 0.05546605¢
Name E-shaped comma
Color name 17uu3oz42,
susuthoquadzo 2nd
FJS name [math]\displaystyle{ \text{m2}^{7,7,7,7,13}_{17,17} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 29.8597
Weil norm (log2 max(n, d)) 29.8597
Wilson norm (sopfr(nd)) 88
Comma size unnoticeable
S-expression S49/S51
Open this interval in xen-calc

The E-shaped comma is a 17-limit unnoticeable comma of measuring 0.055 cents, with frequency ratio of 31213/31212. It is the amount by which a stack of two 51/49's falls short of 13/12. Tempering it out defines the E-shaped temperament.

Commatic relations

In terms of commas, it is the difference between the following superparticular pairs:

It factors into the following superparticular pair:

Etymology

This comma was named by Xenllium in 2023. It came from its numerator of the lowest terms, 31213, which constructs an E-shape by square tiling. Its denominator, 31212 also constructs another form of E-shape.

See also