2.3.7 subgroup: Difference between revisions

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{{Main|Tour of regular temperaments#Clans defined by a 2.3.7 (za) comma}}

In the below tables, the generator of the temperament is highlighted in bold.

In the below tables, the generator of the temperament is highlighted in bold. Intervals in the tables reflect the 1.3.7.9.21 tonality diamond. It is structurally notable that they come in four triplets, each centered around one note of 5edo, consisting of a "minor", "middle", and "major" interval of each set.

==== Semaphore ====

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==== Gamelic ====

'''Gamelic''' temperament, better known as [[slendric]], tempers out the comma [[1029/1024]] = S7/S8 in the 2.3.7 subgroup, which splits the perfect fifth into three intervals of [[8/7]]. It is one of the most accurate temperaments of its simplicity.

'''Gamelic''' temperament, better known as [[slendric]], tempers out the comma [[1029/1024]] = S7/S8 in the 2.3.7 subgroup, which splits the perfect fifth into three intervals of [[8/7]]. It is one of the most accurate temperaments of its simplicity. While semaphore and archy equate each middle interval of each triplet with either the major or the minor, gamelic makes it a true "neutral" intermediate between them.

The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 699.126c, and therefore ~8/7 to 233.042c; a chart of mistunings of simple intervals is below.

@@ Line 29: / Line 29: @@
 {{Main|Tour of regular temperaments#Clans defined by a 2.3.7 (za) comma}}
-In the below tables, the generator of the temperament is highlighted in bold.
+In the below tables, the generator of the temperament is highlighted in bold. Intervals in the tables reflect the 1.3.7.9.21 tonality diamond. It is structurally notable that they come in four triplets, each centered around one note of 5edo, consisting of a "minor", "middle", and "major" interval of each set.
 ==== Semaphore ====
@@ Line 112: / Line 112: @@
 ==== Gamelic ====
-'''Gamelic''' temperament, better known as [[slendric]], tempers out the comma [[1029/1024]] = S7/S8 in the 2.3.7 subgroup, which splits the perfect fifth into three intervals of [[8/7]]. It is one of the most accurate temperaments of its simplicity.
+'''Gamelic''' temperament, better known as [[slendric]], tempers out the comma [[1029/1024]] = S7/S8 in the 2.3.7 subgroup, which splits the perfect fifth into three intervals of [[8/7]]. It is one of the most accurate temperaments of its simplicity. While semaphore and archy equate each middle interval of each triplet with either the major or the minor, gamelic makes it a true "neutral" intermediate between them.
 The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 699.126c, and therefore ~8/7 to 233.042c; a chart of mistunings of simple intervals is below.