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 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''', which enables the [[E-shaped chords]].
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'''.
 
== Commatic relations ==
In terms of commas, it is the difference between the following superparticular pairs:
 
* [[1225/1224]] and [[1275/1274]]
* [[2401/2400]] and [[2601/2600]]
* [[4914/4913]] and [[5832/5831]]
* [[Neuseisma|28561/28560]] and [[336141/336140]]
 
It factors into the following superparticular pair:
 
* [[37180/37179]] and [[Scintillisma|194481/194480]]


== Etymology ==
== Etymology ==

Revision as of 08:05, 27 November 2023

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 consisting of three 7/6s, one 26/17 and one 28/17 exceeds two octaves. By tempering it out is defined 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