2200/2197: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = Petrma
| Name = petrma
| Color name = 3u<sup>3</sup>1oyy-2, trithu-aloyoyo negative 2nd
| Comma = yes
| Comma = yes
}} The Petrma, 2200/2197, is tempered out by several edos, most notably [[50edo]].
}}  
The '''petrma''', '''2200/2197''', is a [[13-limit]] [[comma]] measuring about 2.4{{cent}}. It often arises as the difference between other commas: ([[169/168]])/([[275/273]]), ([[352/351]])/([[676/675]]), ([[847/845]])/([[1001/1000]]), ([[625/624]])/([[4225/4224]]), and ([[729/728]])/([[123201/123200]]). It factors into ([[1575/1573]])([[10648/10647]]).
 
Tempering out this comma in the 13-limit leads to the rank-5 '''petrmic temperament''', and enables [[petrmic chords]]. It is tempered out by several edos, most notably [[50edo]].
 
[[Category:Petrmic]]
[[Category:Commas named after composers]]
[[Category:Commas named after music theorists]]
 
{{todo|add etymology|research|comment=is it named after Petr Pařízek?}}

Latest revision as of 03:13, 4 November 2024

Interval information
Ratio 2200/2197
Factorization 23 × 52 × 11 × 13-3
Monzo [3 0 2 0 1 -3
Size in cents 2.362385¢
Name petrma
Color name 3u31oyy-2, trithu-aloyoyo negative 2nd
FJS name [math]\displaystyle{ \text{dd}{-2}^{5,5,11}_{13,13,13} }[/math]
Special properties reduced
Tenney height (log2 nd) 22.2046
Weil height (log2 max(n, d)) 22.2066
Wilson height (sopfr(nd)) 66
Comma size unnoticeable
Open this interval in xen-calc

The petrma, 2200/2197, is a 13-limit comma measuring about 2.4 ¢. It often arises as the difference between other commas: (169/168)/(275/273), (352/351)/(676/675), (847/845)/(1001/1000), (625/624)/(4225/4224), and (729/728)/(123201/123200). It factors into (1575/1573)(10648/10647).

Tempering out this comma in the 13-limit leads to the rank-5 petrmic temperament, and enables petrmic chords. It is tempered out by several edos, most notably 50edo.