Dominant (temperament): Difference between revisions

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However, it is not very accurate for the same reason that 12edo is inaccurate in the 7-limit, as either 5/4 or 7/4 must be tuned very sharply (with 5/4 reaching over 462 cents in the best tuning of 7/4, and likewise 7/4 reaching over 1006 cents in the best tuning of 5/4). Thus, the "best tuning" is a compromise between the two, tuning 3/2 basically just.

Other possible tunings include [[17edo]] (17c ~~val), [[29edo]] (29cd~~ val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].

The most obvious extension to the 11 and 13-limit is treating the major and minor thirds as [[14/11]] and [[13/11]] as well as 5/4 and 6/5, tempering out [[56/55]] and [[66/65]]. This favors even sharper fifths on the edge of the [[gentle region]]. 29edo tunes this about as well as possible, albeit using the second best approximation of most harmonics.

Other possible tunings include [[17edo]] (17c val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].

Dominant was known as ''dominant seventh'' in 2003, but the ''seventh'' part was dropped shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10437.html Yahoo! Tuning Group | ''The meantone family'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10864.html#10870 Yahoo! Tuning Group | ''names and definitions: meantone'']</ref>.

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 However, it is not very accurate for the same reason that 12edo is inaccurate in the 7-limit, as either 5/4 or 7/4 must be tuned very sharply (with 5/4 reaching over 462 cents in the best tuning of 7/4, and likewise 7/4 reaching over 1006 cents in the best tuning of 5/4). Thus, the "best tuning" is a compromise between the two, tuning 3/2 basically just.
-Other possible tunings include [[17edo]] (17c val), [[29edo]] (29cd val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].
+The most obvious extension to the 11 and 13-limit is treating the major and minor thirds as [[14/11]] and [[13/11]] as well as 5/4 and 6/5, tempering out [[56/55]] and [[66/65]]. This favors even sharper fifths on the edge of the [[gentle region]]. 29edo tunes this about as well as possible, albeit using the second best approximation of most harmonics.
+Other possible tunings include [[17edo]] (17c val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].
 Dominant was known as ''dominant seventh'' in 2003, but the ''seventh'' part was dropped shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10437.html Yahoo! Tuning Group | ''The meantone family'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10864.html#10870 Yahoo! Tuning Group | ''names and definitions: meantone'']</ref>.
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