Mirkwai comma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Expand the temperaments section; +categories
Clarify
Line 8: Line 8:
| Sound =  
| Sound =  
}}
}}
The '''mirkwai comma''' ('''16875/16807''') is a [[7-limit]] [[small comma]] measuring about 6.99033 [[cent]]s.  
The '''mirkwai comma''' ('''16875/16807''') is a [[7-limit]] [[small comma]] measuring about 6.99 [[cent]]s.  


== Temperaments ==
== Temperaments ==
Tempering this comma out leads to the rank-3 [[mirkwai family]] of temperaments, in which the main rank-3 temperament is like [[canopus]] but with another dimension for twos. It is tempered out in rank-2 temperaments such as [[miracle]], [[octoid]], [[semisept]], [[grendel]], [[kwai]], [[pluto]], and [[mirkat]]. See [[Mirkwai clan]] for a collection of rank-2 temperaments where it is tempered out.
Tempering this comma out alone in the 7-limit leads to the rank-3 [[mirkwai family]] of temperaments, in which the main rank-3 temperament [[mirkwai]] is like [[canopus]] but with another dimension for twos. It is tempered out in rank-2 temperaments such as [[miracle]], [[octoid]], [[semisept]], [[grendel]], [[kwai]], [[pluto]], and [[mirkat]]. See [[mirkwai clan]] for a collection of rank-2 temperaments where it is tempered out.


== See also ==
== See also ==

Revision as of 13:52, 22 October 2022

Interval information
Ratio 16875/16807
Factorization 33 × 54 × 7-5
Monzo [0 3 4 -5
Size in cents 6.990326¢
Name mirkwai comma
FJS name [math]\displaystyle{ \text{dddd}{-4}^{5,5,5,5}_{7,7,7,7,7} }[/math]
Special properties reduced
Tenney height (log2 nd) 28.0794
Weil height (log2 max(n, d)) 28.0852
Wilson height (sopfr(nd)) 64
Open this interval in xen-calc

The mirkwai comma (16875/16807) is a 7-limit small comma measuring about 6.99 cents.

Temperaments

Tempering this comma out alone in the 7-limit leads to the rank-3 mirkwai family of temperaments, in which the main rank-3 temperament mirkwai is like canopus but with another dimension for twos. It is tempered out in rank-2 temperaments such as miracle, octoid, semisept, grendel, kwai, pluto, and mirkat. See mirkwai clan for a collection of rank-2 temperaments where it is tempered out.

See also