2197/2187: Difference between revisions

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{{Infobox Interval

| Name = threedie

| Color name = s3o32, Satritho comma

| Color name = s3o32, satritho 2nd, Satritho comma

| Comma = yes

}}

The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. ~~Analogously~~ to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)3/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)3/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

It factors into simpler commas in the 2.3.5.13 subgroup as ([[325/324]])([[676/675]]), or can be expressed in the 2.3.7.13 subgroup as ([[169/168]])/([[729/728]]), i.e. S13/S27.

[[Category:Commas with unknown etymology]]

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 {{Infobox Interval
 | Name = threedie
-| Color name = s3o<sup>3</sup>2, Satritho comma
+| Color name = s3o<sup>3</sup>2, satritho 2nd,<br>Satritho comma
 | Comma = yes
 }}
-The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187.  Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.
+The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.
+It factors into simpler commas in the 2.3.5.13 subgroup as ([[325/324]])([[676/675]]), or can be expressed in the 2.3.7.13 subgroup as ([[169/168]])/([[729/728]]), i.e. S13/S27.
+[[Category:Commas with unknown etymology]]