2197/2187: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 2197/2187 | | Ratio = 2197/2187 | ||
| Monzo = 0 -7 0 0 0 3 | | Monzo = 0 -7 0 0 0 3 | ||
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}} | }} | ||
The '''threedie''', '''2197/2187''', is a 3.13 analog of the 2.5 [[128/125|diesis]]. 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]]. 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. | ||
[[Category:13-limit]] | [[Category:13-limit]] | ||
[[Category:Small commas]] | [[Category:Small commas]] | ||
Revision as of 14:44, 21 March 2022
| Interval information |
The threedie, 2197/2187, is a 3.13-subgroup analog of the 2.5-subgroup diesis. Measuring about 7.9 ¢, 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.