Syntonic–kleismic equivalence continuum: Difference between revisions

Line 122:

[[Badness]] (Sintel): 32.4

== Meso ==

This temperament, which can be described as 7c & 12c or 19 & 64, was first named by {{u|Jerdle}} in [[User:Jerdle/The Ocean]] page. It is generated by a [[19edo]]/[[flattone]]-like fifth, but finds 5/4 at -15 generators (a double-diminished fourth) rather than a major third. It is of very high badness, and probably not that practical, but perhaps the 19-note [[mos]] could be used for some kind of 19edo [[well temperament]]. Only two [[patent val]]s [[support]] this temperament ([[19edo]] and [[64edo]]), but additionally, the [[dual-fifth]] systems [[83edo]] and [[102edo]] support this temperament with their second-best fifths (83b and 102b), and those are probably the best tunings. Note that octave-stretching significantly reduces the error on all odd harmonics.

[[Subgroup]]: 2.3.5

[[Comma list]]: 71744535/67108864

: mapping generators: ~2, ~3

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1202.4029{{c}}, ~3/2 = 696.0426{{c}}

: [[error map]]: {{val| +2.403 -3.510 -0.521 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 694.5477{{c}}

: error map: {{val| 0.000 -7.407 -4.530 }}

[[Badness]] (Sintel): 18.8

== Hogzilla ==

Line 330:

Line 350:

[[Badness]] (Sintel): 7.45

~~== Meso ==~~

This temperament, which can be described as 7c & 12c or 19 & 64, was first named by {{u|Jerdle}} in [[User:Jerdle/The Ocean]] page. It is generated by a [[19edo]]/[[flattone]]-like fifth, but finds 5/4 at -15 generators (a double-diminished fourth) rather than a major third. It is of very high badness, and probably not that practical, but perhaps the 19-note [[mos]] could be used for some kind of 19edo [[well temperament]]. Only two [[patent val]]s [[support]] this temperament ([[19edo]] and [[64edo]]), but additionally, the [[dual-fifth]] systems [[83edo]] and [[102edo]] support this temperament with their second-best fifths (83b and 102b), and those are probably the best tunings. Note that octave-stretching significantly reduces the error on all odd harmonics.

~~[[Subgroup]]: 2.3.5~~

~~[[Comma list]]: 71744535/67108864~~

~~{{Mapping|legend=1| 1 0 26 | 0 1 -15 }}~~

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

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1202.4029{{c}}, ~3/2 = 696.0426{{c}}

~~: [[error map]]: {{val| +2.403 -3.510 -0.521 }}~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 694.5477{{c}}

~~: error map: {{val| 0.000 -7.407 -4.530 }}~~

~~{{Optimal ET sequence|legend=1| 7c, 12c, 19 }}~~

~~[[Badness]] (Sintel): 18.8~~

[[Category:19edo]]

[[Category:Equivalence continua]]

@@ Line 122: / Line 122: @@
 [[Badness]] (Sintel): 32.4
+== Meso ==
+This temperament, which can be described as 7c & 12c or 19 & 64, was first named by {{u|Jerdle}} in [[User:Jerdle/The Ocean]] page. It is generated by a [[19edo]]/[[flattone]]-like fifth, but finds 5/4 at -15 generators (a double-diminished fourth) rather than a major third. It is of very high badness, and probably not that practical, but perhaps the 19-note [[mos]] could be used for some kind of 19edo [[well temperament]]. Only two [[patent val]]s [[support]] this temperament ([[19edo]] and [[64edo]]), but additionally, the [[dual-fifth]] systems [[83edo]] and [[102edo]] support this temperament with their second-best fifths (83b and 102b), and those are probably the best tunings. Note that octave-stretching significantly reduces the error on all odd harmonics.
+[[Subgroup]]: 2.3.5
+[[Comma list]]: 71744535/67108864
+{{Mapping|legend=1| 1 0 26 | 0 1 -15 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1202.4029{{c}}, ~3/2 = 696.0426{{c}}
+: [[error map]]: {{val| +2.403 -3.510 -0.521 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 694.5477{{c}}
+: error map: {{val| 0.000 -7.407 -4.530 }}
+{{Optimal ET sequence|legend=1| 7c, 12c, 19 }}
+[[Badness]] (Sintel): 18.8
 == Hogzilla ==
@@ Line 330: / Line 350: @@
 [[Badness]] (Sintel): 7.45
-== Meso ==
-This temperament, which can be described as 7c & 12c or 19 & 64, was first named by {{u|Jerdle}} in [[User:Jerdle/The Ocean]] page. It is generated by a [[19edo]]/[[flattone]]-like fifth, but finds 5/4 at -15 generators (a double-diminished fourth) rather than a major third. It is of very high badness, and probably not that practical, but perhaps the 19-note [[mos]] could be used for some kind of 19edo [[well temperament]]. Only two [[patent val]]s [[support]] this temperament ([[19edo]] and [[64edo]]), but additionally, the [[dual-fifth]] systems [[83edo]] and [[102edo]] support this temperament with their second-best fifths (83b and 102b), and those are probably the best tunings. Note that octave-stretching significantly reduces the error on all odd harmonics.
-[[Subgroup]]: 2.3.5
-[[Comma list]]: 71744535/67108864
-{{Mapping|legend=1| 1 0 26 | 0 1 -15 }}
-: mapping generators: ~2, ~3
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1202.4029{{c}}, ~3/2 = 696.0426{{c}}
-: [[error map]]: {{val| +2.403 -3.510 -0.521 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 694.5477{{c}}
-: error map: {{val| 0.000 -7.407 -4.530 }}
-{{Optimal ET sequence|legend=1| 7c, 12c, 19 }}
-[[Badness]] (Sintel): 18.8
 [[Category:19edo]]
 [[Category:Equivalence continua]]

Syntonic–kleismic equivalence continuum: Difference between revisions

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