2.3.7.11 subgroup: Difference between revisions

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=== Rank-2 temperaments ===

~~{{Main|Tour~~ of ~~regular temperaments#Temperaments defined~~ by an 11-~~limit~~ comma}}

[[Supra]], which extends [[archy]], provides a simple yet high-damage approximation to the subgroup. It is generated by a perfect fifth, tuned a little sharp so that two make [[8/7]][[~]][[9/8]] and six make [[16/11]], tempering out [[64/63]] and [[99/98]]. Alternatively, [[suhajira]] can be considered an extension of archy that adds neutral intervals, with the perfect fifth split into two neutral third generators, each representing [[11/9]]~[[27/22]], thus tempering out 64/63 and [[243/242]].

~~{{Todo|inline=1|expand}}~~

[[Skwares]] takes the 11/9~27/22 neutral third, adds an octave to it and splits it in halves for ~[[11/7]], tempering out 99/98 and 243/242.

[[Radon]], which adds prime 11 to [[slendric]] by tempering out [[896/891]], provides a more complex entry, well represented by 41edo and 46edo. A similar temperament at this level is [[hemif]], which tempers out 243/242 and 896/891 and can be tuned to 58edo. In both cases, the diatonic major third represents [[14/11]].

On the high-accuracy side, [[gary]] is an important temperament that finds 7 and 11 far into the [[chain of fifths]].

=== Rank-3 temperaments ===

[[Parapyth]] equates [[28/27]] with [[33/32]] and uses this interval as a spacer added to the chain of fifths to finds intervals of 7 and 11.

[[Symbiotian]], which makes 33/32 and 28/27 sum to the [[Pythagorean apotome]], is an efficient high-accuracy counterpart of parapyth.

[[Olympian]] equates 33/32 with a stack of two 64/63's. It is very accurate yet still easy to notate on the staff, using the septimal comma as spacer added to the chain of fifths to finds intervals of 7 and 11.

[[Category:Just intonation subgroups|#]]

@@ Line 24: / Line 24: @@
 === Rank-2 temperaments ===
-{{Main|Tour of regular temperaments#Temperaments defined by an 11-limit comma}}
+[[Supra]], which extends [[archy]], provides a simple yet high-damage approximation to the subgroup. It is generated by a perfect fifth, tuned a little sharp so that two make [[8/7]][[~]][[9/8]] and six make [[16/11]], tempering out [[64/63]] and [[99/98]]. Alternatively, [[suhajira]] can be considered an extension of archy that adds neutral intervals, with the perfect fifth split into two neutral third generators, each representing [[11/9]]~[[27/22]], thus tempering out 64/63 and [[243/242]].
-{{Todo|inline=1|expand}}
+[[Skwares]] takes the 11/9~27/22 neutral third, adds an octave to it and splits it in halves for ~[[11/7]], tempering out 99/98 and 243/242.
+[[Radon]], which adds prime 11 to [[slendric]] by tempering out [[896/891]], provides a more complex entry, well represented by 41edo and 46edo. A similar temperament at this level is [[hemif]], which tempers out 243/242 and 896/891 and can be tuned to 58edo. In both cases, the diatonic major third represents [[14/11]].
+On the high-accuracy side, [[gary]] is an important temperament that finds 7 and 11 far into the [[chain of fifths]].
+=== Rank-3 temperaments ===
+[[Parapyth]] equates [[28/27]] with [[33/32]] and uses this interval as a spacer added to the chain of fifths to finds intervals of 7 and 11.
+[[Symbiotian]], which makes 33/32 and 28/27 sum to the [[Pythagorean apotome]], is an efficient high-accuracy counterpart of parapyth.
+[[Olympian]] equates 33/32 with a stack of two 64/63's. It is very accurate yet still easy to notate on the staff, using the septimal comma as spacer added to the chain of fifths to finds intervals of 7 and 11.
 [[Category:Just intonation subgroups|#]]