Valinorsmic clan: Difference between revisions

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== Valinor ==

''Valinor'' is the 2.5.7.11 temperament defined by tempering out 176/175. When extending to prime 13, two strong extensions are considerable: ''valimar'' and ''valarin''; these intersect in [[tridecimal didacus]].

''Valinor'' is the 2.5.7.11 temperament defined by tempering out 176/175. When extending to prime 13, two strong extensions are considerable: ''valimar'' and ''valarin''; these intersect in [[Hemimean clan #tridecimal didacus|tridecimal didacus]].

[[Subgroup]]: 2.5.7.11

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=== Valimar ===

This extension to the no-threes 13-limit is motivated by extending the valinorsmic chain of 5/4s, where two form 11/7, so that four form 16/13. This logic is supported by rank-2s such as tridecimal didacus and the 13-limit [[magus]]/[[amigo]] extensions, as well as [[winston]] and [[valentino]]. This is also natural considering [[S-expression]]s, noting that 176/175 = S8/S10 is (nontrivially) equivalent to (S11*S12)/(S14*S15), and this extension tempers out S11/S14 = [[1573/1568]], and S12/S15 = [[3584/3575]]. It remains well-tuned in ETs with optimal valinorsmic 5/4s (such as [[37edo|37]], [[40edo|40]], and [[43edo|43]]).

This extension to the no-threes 13-limit is motivated by extending the valinorsmic chain of 5/4s, where two form 11/7, so that four form 16/13. This logic is supported by rank-2s such as tridecimal didacus and the 13-limit [[magus]]/[[amigo]] extensions, as well as [[Orwell extensions|winston]] and [[Valentine extensions|valentino]]. This is also natural considering [[S-expression]]s, noting that 176/175 = S8/S10 is (nontrivially) equivalent to (S11*S12)/(S14*S15), and this extension tempers out S11/S14 = [[1573/1568]], and S12/S15 = [[3584/3575]]. It remains well-tuned in ETs with optimal valinorsmic 5/4s (such as [[37edo|37]], [[40edo|40]], and [[43edo|43]]).

[[Subgroup]]: 2.5.7.11.13

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=== Valarin ===

This extension equates two, ideally slightly flattened, [[8/7]]s to [[13/10]], which is also natural given valinorsmic's tuning tendency towards sharpening [[7/4]]. This extension is supported by rank-2 temperaments including tridecimal didacus, [[tridecimal orwell]], [[lupercalia]] (an extension of [[valentine]]), and [[llywelyn]].

This extension equates two, ideally slightly flattened, [[8/7]]s to [[13/10]], which is also natural given valinorsmic's tuning tendency towards sharpening [[7/4]]. This extension is supported by rank-2 temperaments including tridecimal didacus, [[Orwell extensions|tridecimal orwell]], [[Valentine extensions|lupercalia]] (an extension of [[valentine]]), and [[llywelyn]].

[[Subgroup]]: 2.5.7.11.13

@@ Line 5: / Line 5: @@
 == Valinor ==
-''Valinor'' is the 2.5.7.11 temperament defined by tempering out 176/175. When extending to prime 13, two strong extensions are considerable: ''valimar'' and ''valarin''; these intersect in [[tridecimal didacus]].
+''Valinor'' is the 2.5.7.11 temperament defined by tempering out 176/175. When extending to prime 13, two strong extensions are considerable: ''valimar'' and ''valarin''; these intersect in [[Hemimean clan #tridecimal didacus|tridecimal didacus]].
 [[Subgroup]]: 2.5.7.11
@@ Line 25: / Line 25: @@
 === Valimar ===
-This extension to the no-threes 13-limit is motivated by extending the valinorsmic chain of 5/4s, where two form 11/7, so that four form 16/13. This logic is supported by rank-2s such as tridecimal didacus and the 13-limit [[magus]]/[[amigo]] extensions, as well as [[winston]] and [[valentino]]. This is also natural considering [[S-expression]]s, noting that 176/175 = S8/S10 is (nontrivially) equivalent to (S11*S12)/(S14*S15), and this extension tempers out S11/S14 = [[1573/1568]], and S12/S15 = [[3584/3575]]. It remains well-tuned in ETs with optimal valinorsmic 5/4s (such as [[37edo|37]], [[40edo|40]], and [[43edo|43]]).
+This extension to the no-threes 13-limit is motivated by extending the valinorsmic chain of 5/4s, where two form 11/7, so that four form 16/13. This logic is supported by rank-2s such as tridecimal didacus and the 13-limit [[magus]]/[[amigo]] extensions, as well as [[Orwell extensions|winston]] and [[Valentine extensions|valentino]]. This is also natural considering [[S-expression]]s, noting that 176/175 = S8/S10 is (nontrivially) equivalent to (S11*S12)/(S14*S15), and this extension tempers out S11/S14 = [[1573/1568]], and S12/S15 = [[3584/3575]]. It remains well-tuned in ETs with optimal valinorsmic 5/4s (such as [[37edo|37]], [[40edo|40]], and [[43edo|43]]).
 [[Subgroup]]: 2.5.7.11.13
@@ Line 45: / Line 45: @@
 === Valarin ===
-This extension equates two, ideally slightly flattened, [[8/7]]s to [[13/10]], which is also natural given valinorsmic's tuning tendency towards sharpening [[7/4]]. This extension is supported by rank-2 temperaments including tridecimal didacus, [[tridecimal orwell]], [[lupercalia]] (an extension of [[valentine]]), and [[llywelyn]].
+This extension equates two, ideally slightly flattened, [[8/7]]s to [[13/10]], which is also natural given valinorsmic's tuning tendency towards sharpening [[7/4]]. This extension is supported by rank-2 temperaments including tridecimal didacus, [[Orwell extensions|tridecimal orwell]], [[Valentine extensions|lupercalia]] (an extension of [[valentine]]), and [[llywelyn]].
 [[Subgroup]]: 2.5.7.11.13