Hemimean clan: Difference between revisions

Line 988:

: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Undetrita (5-limit)]].''

~~The undetrita temperament (111 & 118)~~ tempers out the hemimean comma (3136/3125) and [[scheme comma]] (14348907/14336000) in the 7-limit~~; 3025/3024, 3388/3375~~, and ~~8019/8000 in~~ the ~~11-limit~~. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It ~~is also related~~ to ~~the~~ [[~~Subgroup temperaments #No~~-sevens subgroup|twentcufo ~~temperament~~]], ~~which is~~ no-~~sevens~~ version of 111 & 118.

Undetrita tempers out the hemimean comma (3136/3125) and [[scheme comma]] (14348907/14336000) in the 7-limit, and may be described as the 111 & 118 temperament. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It tempers out 3025/3024, 3388/3375, and 8019/8000 in the 11-limit, which relates itself to [[no-sevens subgroup temperaments #Twentcufo|twentcufo]], the no-7's version of 111 & 118.

[[Subgroup]]: 2.3.5.7

Line 995:

: mapping generators: ~2, ~448/405

[[Optimal tuning]] ([[~~POTE~~]]): ~2 = ~~1\1~~, ~448/405 = 172.~~917~~

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.8545{{c}}, ~448/405 = 172.8961{{c}}

: error map: {{val| -0.146 -0.098 +0.859 -0.458 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~448/405 = 172.9143{{c}}

: error map: {{val| 0.000 +0.102 +1.115 -0.255 }}

[[Badness]]: 0.~~114188~~

[[Badness]] (Sintel): 2.89

=== 11-limit ===

Line 1,009:

Line 1,014:

Optimal ~~tuning (POTE)~~: ~2 = ~~1\1~~, ~400/363 = 172.~~912~~

Optimal tunings:

* WE: ~2 = 1200.0112{{c}}, ~400/363 = 172.9138{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~400/363 = 172.9123{{c}}

Badness: 0.~~043883~~

Badness (Sintel): 1.45

==== 13-limit ====

Line 1,022:

Line 1,029:

Optimal ~~tuning (POTE)~~: ~2 = ~~1\1~~, ~72/65 = 172.~~930~~

Optimal tunings:

* WE: ~2 = 1199.7099{{c}}, ~72/65 = 172.8882{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 172.9265{{c}}

Badness: 0.~~038771~~

Badness (Sintel): 1.60

==== Undetritoid ====

Line 1,035:

Line 1,044:

Optimal ~~tuning (POTE)~~: ~2 = ~~1\1~~, ~400/363 = 172.~~933~~

Optimal tunings:

* WE: ~2 = 1199.8901{{c}}, ~400/363 = 172.9167{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~400/363 = 172.9310{{c}}

Badness: 0.~~042744~~

Badness (Sintel): 1.77

= Subgroup extensions =

@@ Line 988: / Line 988: @@
 : ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Undetrita (5-limit)]].''
-The undetrita temperament (111 & 118) tempers out the hemimean comma (3136/3125) and [[scheme comma]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It is also related to the [[Subgroup temperaments #No-sevens subgroup|twentcufo temperament]], which is no-sevens version of 111 & 118.
+Undetrita tempers out the hemimean comma (3136/3125) and [[scheme comma]] (14348907/14336000) in the 7-limit, and may be described as the 111 & 118 temperament. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It tempers out 3025/3024, 3388/3375, and 8019/8000 in the 11-limit, which relates itself to [[no-sevens subgroup temperaments #Twentcufo|twentcufo]], the no-7's version of 111 & 118.
 [[Subgroup]]: 2.3.5.7
@@ Line 995: / Line 995: @@
 {{Mapping|legend=1| 1 0 -2 -8 | 0 11 30 75 }}
+: mapping generators: ~2, ~448/405
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~448/405 = 172.917
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.8545{{c}}, ~448/405 = 172.8961{{c}}
+: error map: {{val| -0.146 -0.098 +0.859 -0.458 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~448/405 = 172.9143{{c}}
+: error map: {{val| 0.000 +0.102 +1.115 -0.255 }}
-{{Optimal ET sequence|legend=1| 111, 118, 229, 347, 576c }}
+{{Optimal ET sequence|legend=0| 111, 118, 229, 347, 576c }}
-[[Badness]]: 0.114188
+[[Badness]] (Sintel): 2.89
 === 11-limit ===
@@ Line 1,009: / Line 1,014: @@
 {{Mapping|legend=0| 1 0 -2 -8 0 | 0 11 30 75 24 }}
-Optimal tuning (POTE): ~2 = 1\1, ~400/363 = 172.912
+Optimal tunings:
+* WE: ~2 = 1200.0112{{c}}, ~400/363 = 172.9138{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~400/363 = 172.9123{{c}}
-{{Optimal ET sequence|legend=1| 111, 118, 229, 347 }}
+{{Optimal ET sequence|legend=0| 111, 118, 229, 347 }}
-Badness: 0.043883
+Badness (Sintel): 1.45
 ==== 13-limit ====
@@ Line 1,022: / Line 1,029: @@
 {{Mapping|legend=0| 1 0 -2 -8 0 5 | 0 11 30 75 24 -9 }}
-Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 172.930
+Optimal tunings:
+* WE: ~2 = 1199.7099{{c}}, ~72/65 = 172.8882{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 172.9265{{c}}
-{{Optimal ET sequence|legend=1| 111, 229f }}
+{{Optimal ET sequence|legend=0| 111, 229f }}
-Badness: 0.038771
+Badness (Sintel): 1.60
 ==== Undetritoid ====
@@ Line 1,035: / Line 1,044: @@
 {{Mapping|legend=0| 1 0 -2 -8 0 -11 | 0 11 30 75 24 102 }}
-Optimal tuning (POTE): ~2 = 1\1, ~400/363 = 172.933
+Optimal tunings:
+* WE: ~2 = 1199.8901{{c}}, ~400/363 = 172.9167{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~400/363 = 172.9310{{c}}
-{{Optimal ET sequence|legend=1| 111, 229 }}
+{{Optimal ET sequence|legend=0| 111, 229 }}
-Badness: 0.042744
+Badness (Sintel): 1.77
 = Subgroup extensions =

Hemimean clan: Difference between revisions

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