136/135: Difference between revisions

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[[Optimal tuning]]s:

* [[Tp tuning|~~subgroup~~]] [[~~CEE~~]]: ~2 = ~~1200~~.~~000~~{{c}}, ~3/2 = ~~705~~.~~440~~{{c}}

* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.2838{{c}}, ~3/2 = 704.4600{{c}}

* [[Tp tuning|~~subgroup~~]] [[~~CTE~~]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.~~1088~~{{c}}

* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5286{{c}}

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: mapping generators: ~2, ~3, ~5

[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 704.~~1088~~{{c}}, ~5/4 = ~~387~~.~~8544~~{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.2838{{c}}, ~3/2 = 704.4600{{c}}, ~5/4 = 389.0228{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5286{{c}}, ~5/4 = 388.6162{{c}}

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

[[Badness]] (Sintel): 0.139

=== 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 out 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 for a good and more accurate tuning. Alternatively, if you do not care as much about prime 11, [[68edo]] makes for a great tuning.

[[Subgroup]]: 2.3.5.7.11.13.17

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: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 704.~~1088~~{{c}}, ~5/4 = ~~387~~.~~8544~~{{c}}, ~7/4, ~11/8, ~13/8

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.2838{{c}}, ~3/2 = 704.4600{{c}}, ~5/4 = 389.0228{{c}}, ~7/4 = 970.2512{{c}}, ~11/8 = 553.4578{{c}}, ~13/8 = 842.6669{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5286{{c}}, ~5/4 = 388.6162{{c}}, ~7/4 = 969.9161{{c}}, ~11/8 = 552.6614{{c}}, ~13/8 = 841.9647{{c}}

{{Optimal ET sequence|legend=1| 22, 27eg, 29g, 34d, 39dfg, 41g, 46, 58, 80, 104c, 114e, 126(f), 136ef, 148d, 167g, 216bdef }}*

{{Optimal ET sequence|legend=1| 22, 27eg, 29g, 34d, 39dfg, 41g, 46, 58, 80, 104c, 114e, 126(f), 136ef, 148d, 167g, 216bdef }} *

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

[[Badness]] (Sintel): 1.15

== Etymology ==

@@ Line 20: / Line 20: @@
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CEE]]: ~2 = 1200.000{{c}}, ~3/2 = 705.440{{c}}
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.2838{{c}}, ~3/2 = 704.4600{{c}}
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1088{{c}}
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5286{{c}}
 {{Optimal ET sequence|legend=1| 5, 12, 17, 46, 63, 143 }}
@@ Line 31: / Line 31: @@
 : mapping generators: ~2, ~3, ~5
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 704.1088{{c}}, ~5/4 = 387.8544{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.2838{{c}}, ~3/2 = 704.4600{{c}}, ~5/4 = 389.0228{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5286{{c}}, ~5/4 = 388.6162{{c}}
 {{Optimal ET sequence|legend=1| 10, 12, 22, 34, 80, 114, 194bc }}
+[[Badness]] (Sintel): 0.139
 === 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 out 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 for a good and more accurate tuning. Alternatively, if you do not care as much about prime 11, [[68edo]] makes for a great tuning.
 [[Subgroup]]: 2.3.5.7.11.13.17
@@ Line 57: / Line 61: @@
 : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 704.1088{{c}}, ~5/4 = 387.8544{{c}}, ~7/4, ~11/8, ~13/8
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.2838{{c}}, ~3/2 = 704.4600{{c}}, ~5/4 = 389.0228{{c}}, ~7/4 = 970.2512{{c}}, ~11/8 = 553.4578{{c}}, ~13/8 = 842.6669{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5286{{c}}, ~5/4 = 388.6162{{c}}, ~7/4 = 969.9161{{c}}, ~11/8 = 552.6614{{c}}, ~13/8 = 841.9647{{c}}
-{{Optimal ET sequence|legend=1| 22, 27eg, 29g, 34d, 39dfg, 41g, 46, 58, 80, 104c, 114e, 126(f), 136ef, 148d, 167g, 216bdef }}*
+{{Optimal ET sequence|legend=1| 22, 27eg, 29g, 34d, 39dfg, 41g, 46, 58, 80, 104c, 114e, 126(f), 136ef, 148d, 167g, 216bdef }} *
 <nowiki>*</nowiki> [[optimal patent val]]: [[177edo|177]]
+[[Badness]] (Sintel): 1.15
 == Etymology ==