Phaotic comma: Difference between revisions

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The '''phaotic comma''', or '''phaotisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a ratio of '''256000/255879''', and a size of approximately 0.82 [[cent]]s. It is significant in that it is the interval separating a stack of two [[81/80|meantone commas]] from [[40/39]]. Tempering it out thus splits 40/39 into two equal halves, each representing 81/80leads to a form of '''phaotic temperament'''.
The '''phaotic comma''', or '''phaotisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] (also 2.3.5.13 subgroup) comma with a ratio of '''256000/255879''', and a size of approximately 0.82 [[cent]]s. It is significant in that it is the interval separating a stack of two [[81/80|meantone commas]] from [[40/39]].  
 
== Temperaments ==
Tempering it out splits 40/39 into two equal halves, each representing 81/80. It leads to a form of '''phaotismic temperament''' in the full 13-limit and '''phaotic temperament''' in the 2.3.5.13 subgroup.
 
== See also ==
* [[Unnoticeable comma]]
 
[[Category:13-limit]]
[[Category:Unnoticeable comma]]
[[Category:Phaotismic]]

Revision as of 07:35, 23 April 2021

Interval information
Ratio 256000/255879
Factorization 211 × 3-9 × 53 × 13-1
Monzo [11 -9 3 0 0 -1
Size in cents 0.818472¢
Names phaotic comma,
phaotisma
FJS name [math]\displaystyle{ \text{A1}^{5,5,5}_{13} }[/math]
Special properties reduced
Tenney norm (log2 nd) 35.9309
Weil norm (log2 max(n, d)) 35.9316
Wilson norm (sopfr(nd)) 77
Open this interval in xen-calc

The phaotic comma, or phaotisma, is an unnoticeable 13-limit (also 2.3.5.13 subgroup) comma with a ratio of 256000/255879, and a size of approximately 0.82 cents. It is significant in that it is the interval separating a stack of two meantone commas from 40/39.

Temperaments

Tempering it out splits 40/39 into two equal halves, each representing 81/80. It leads to a form of phaotismic temperament in the full 13-limit and phaotic temperament in the 2.3.5.13 subgroup.

See also