Parimo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Aura (talk | contribs)
No edit summary
+infobox and some cleanup
Line 1: Line 1:
The '''parimo''' is a comma with a ratio of '''1771561/1771470''' and a monzo of {{Monzo|-1 -11 -1 0 6}}. It is an [[unnoticeable comma]] of the [[11-limit]] with a value of approximately 0.08893 [[cent|cents]]. It is significant in JI as the amount by which a stack of three [[243/242|rastmas]] falls short of a [[81/80|syntonic comma]]. Tempering it out leads to a form of '''parimic temperament''', which is like the metric microtemperaments in that the syntonic comma is split into three equal parts. However, in parimic temperament, the parts represent different intervals- one part represents the rastma, and two parts represent the [[121/120|biyatisma]].
{{Infobox Interval
| Icon =
| Ratio = 1771561/1771470
| Monzo = -1 -11 -1 0 6
| Cents = 0.08893
| Name = parimo
| Color name =
| FJS name =
| Sound =
}}
 
The '''parimo''' is a [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1771470''' = {{Monzo|-1 -11 -1 0 6}} and a value of approximately 0.09 [[cent|cents]]. It is the amount by which a stack of three [[243/242|rastmas]] falls short of a [[81/80|syntonic comma]]. Tempering it out leads to a form of '''parimic temperament''', which can be said to be the undecimal counterpart of the [[metric microtemperaments|metric temperament]] in that the syntonic comma is split into three equal parts in both systems. However, in parimic temperament, the parts represent different intervals one part represents the [[243/242|rastma]], and two represent the [[121/120|biyatisma]].  
 
== See also ==
* [[Unnoticeable comma]]


[[Category:11-limit]]
[[Category:11-limit]]
[[Category:Unnoticeable comma]]
[[Category:Unnoticeable comma]]

Revision as of 16:57, 10 October 2020

Interval information
Ratio 1771561/1771470
Factorization 2-1 × 3-11 × 5-1 × 116
Monzo [-1 -11 -1 0 6
Size in cents 0.0889308¢
Name parimo
FJS name [math]\displaystyle{ \text{ddd1}^{11,11,11,11,11,11}_{5} }[/math]
Special properties reduced
Tenney height (log2 nd) 41.5131
Weil height (log2 max(n, d)) 41.5132
Wilson height (sopfr(nd)) 106
Open this interval in xen-calc

The parimo is a 11-limit unnoticeable comma with a ratio of 1771561/1771470 = [-1 -11 -1 0 6 and a value of approximately 0.09 cents. It is the amount by which a stack of three rastmas falls short of a syntonic comma. Tempering it out leads to a form of parimic temperament, which can be said to be the undecimal counterpart of the metric temperament in that the syntonic comma is split into three equal parts in both systems. However, in parimic temperament, the parts represent different intervals – one part represents the rastma, and two represent the biyatisma.

See also