136/135: Difference between revisions

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~~See also: [[Srutal archagall]] for the rank-2 temperament tempering out {[[256/255|S16]], [[289/288|S17]]}.~~

=== Diatic ===

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{{Optimal ET sequence|legend=1| 10, 12, 22, 34, 80, 114, 194bc }}

~~See also: [[Srutal archagall]] for the rank-2 temperament tempering out {[[256/255|S16]], [[289/288|S17]]}.~~

=== Diatismic ===

The only edo tuning that has less than 25% [[relative error]] for all primes in the [[17-limit]] tempering [[136/135]] is [[46edo]], which also tunes 20/17 with less than 25% relative error and 51/40 even more accurately. If you allow 7/4 to be sharper than 25% then [[80edo]] makes a good and more accurate tuning that extends to the [[23-limit]]. Alternatively, if you don't care (as much) about prime 11, [[68edo]] makes a great tuning in the no-11's [[19-limit]] and no-11's no-29's [[31-limit]].

The only edo tuning that has less than 25% [[relative error]] for all primes in the [[17-limit]] tempering 136/135 is [[46edo]], which also tunes 20/17 with less than 25% relative error and 51/40 even more accurately. If you allow 7/4 to be sharper than 25% then [[80edo]] makes a good and more accurate tuning that extends to the [[23-limit]]. Alternatively, if you don't care (as much) about prime 11, [[68edo]] makes a great tuning in the no-11's [[19-limit]] and no-11's no-29's [[31-limit]].

[[Subgroup]]: 2.3.5.7.11.13.17

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<nowiki>*</nowiki> [[optimal patent val]]: [[177edo|177]]

=== Srutal archagall ===

[[Srutal archagall]] is an efficient rank-2 temperament tempering out both [[256/255|S16]] and [[289/288|S17]], which is equivalently described as [[charic]] [[semitonic]] due to the fact that {S16 × S17 , [[24576/24565|S16/S17]]} = {[[256/255|S16]], [[289/288|S17]]}

== Etymology ==

@@ Line 19: / Line 19: @@
 {{Optimal ET sequence|legend=1| 5, 12, 17, 46, 63, 143 }}
-See also: [[Srutal archagall]] for the rank-2 temperament tempering out {[[256/255|S16]], [[289/288|S17]]}.
 === Diatic ===
@@ Line 32: / Line 30: @@
 {{Optimal ET sequence|legend=1| 10, 12, 22, 34, 80, 114, 194bc }}
-See also: [[Srutal archagall]] for the rank-2 temperament tempering out {[[256/255|S16]], [[289/288|S17]]}.
 === Diatismic ===
-The only edo tuning that has less than 25% [[relative error]] for all primes in the [[17-limit]] tempering [[136/135]] is [[46edo]], which also tunes 20/17 with less than 25% relative error and 51/40 even more accurately. If you allow 7/4 to be sharper than 25% then [[80edo]] makes a good and more accurate tuning that extends to the [[23-limit]]. Alternatively, if you don't care (as much) about prime 11, [[68edo]] makes a great tuning in the no-11's [[19-limit]] and no-11's no-29's [[31-limit]].
+The only edo tuning that has less than 25% [[relative error]] for all primes in the [[17-limit]] tempering 136/135 is [[46edo]], which also tunes 20/17 with less than 25% relative error and 51/40 even more accurately. If you allow 7/4 to be sharper than 25% then [[80edo]] makes a good and more accurate tuning that extends to the [[23-limit]]. Alternatively, if you don't care (as much) about prime 11, [[68edo]] makes a great tuning in the no-11's [[19-limit]] and no-11's no-29's [[31-limit]].
 [[Subgroup]]: 2.3.5.7.11.13.17
@@ Line 62: / Line 58: @@
 <nowiki>*</nowiki> [[optimal patent val]]: [[177edo|177]]
+=== Srutal archagall ===
+[[Srutal archagall]] is an efficient rank-2 temperament tempering out both [[256/255|S16]] and [[289/288|S17]], which is equivalently described as [[charic]] [[semitonic]] due to the fact that {S16 × S17 , [[24576/24565|S16/S17]]} = {[[256/255|S16]], [[289/288|S17]]}
 == Etymology ==