2.3.7 subgroup: Difference between revisions

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

'''Semaphore''' temperament tempers out the comma [[49/48]] = S7 in the 2.3.7 subgroup, which equates [[8/7]] with [[7/6]], creating a single neutral semifourth. Similarly to [[dicot]], semaphore can be regarded as an exotemperament that elides fundamental distinctions within the subgroup (from the perspective of a pentatonic framework, this is equivalent to erasing the major-minor distinction as dicot does), though the comma involved is half the size of dicot's [[25/24]].

The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 696.230c (though most other optimizations tune this a few cents flatter); a chart of mistunings of simple intervals is below.

|+ style="font-size: 105%;" | Semaphore (49/48)

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|}

'''Archy''' temperament tempers out the comma [[64/63]] = S8 in the 2.3.7 subgroup, which equates [[9/8]] with [[8/7]], and [[4/3]] with [[21/16]]. It serves as a septimal analogue of [[meantone]], favoring fifths sharp of just rather than flat.

The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 712.585c (though most other optimizations tune this a few cents flatter); a chart of mistunings of simple intervals is below.

|+ style="font-size: 105%;" | Archy (64/63)

|-

|}

'''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.

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.

|+ style="font-size: 105%;" | Gamelic (1029/1024)

|-