14edo: Difference between revisions

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== Theory ==

The character of 14edo does not well serve those seeking low-[[limit]] JI approaches, with the exception of [[Subgroup|5:7:9:11:17:19]] (which is quite well approximated, relative to other JI approximations of the low-numbered ~~EDOs~~). However, the [[ratio]]s 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage [[11-limit]] temperament where the [[comma]]s listed later in this page are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate ~~Ratios~~" column in the table.

The character of 14edo does not well serve those seeking low-[[limit]] JI approaches, with the exception of [[Subgroup|5:7:9:11:17:19]] (which is quite well approximated, relative to other JI approximations of the low-numbered edos). However, the [[ratio]]s 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage [[11-limit]] temperament where the [[comma]]s listed later in this page are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table.

14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a [[triad]]-rich 9-note [[~~MOS~~ scale]] of [[5L 4s]], wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.

14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a [[triad]]-rich 9-note [[mos scale]] of [[5L 4s]], wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.

=== Prime harmonics ===

=== Octave stretch ===

14edo benefits from [[octave stretch]] as harmonics 3, 7, and 11 are all tuned flat. [[22edt]] and [[36ed6]] are among the possible choices.

=== Subsets and supersets ===

Since 14 factors into primes as 2 × 7, 14edo contains [[2edo]] and [[7edo]] as subsets.

== Notation ==

@@ Line 9: / Line 9: @@
 {{EDO intro|14}}
 == Theory ==
-The character of 14edo does not well serve those seeking low-[[limit]] JI approaches, with the exception of [[Subgroup|5:7:9:11:17:19]] (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the [[ratio]]s 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage [[11-limit]] temperament where the [[comma]]s listed later in this page are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate Ratios" column in the table.
+The character of 14edo does not well serve those seeking low-[[limit]] JI approaches, with the exception of [[Subgroup|5:7:9:11:17:19]] (which is quite well approximated, relative to other JI approximations of the low-numbered edos). However, the [[ratio]]s 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage [[11-limit]] temperament where the [[comma]]s listed later in this page are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table.
-et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a [[triad]]-rich 9-note [[MOS scale]] of [[5L 4s]], wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.
+et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a [[triad]]-rich 9-note [[mos scale]] of [[5L 4s]], wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.
 === Prime harmonics ===
 {{Harmonics in equal|14}}
+=== Octave stretch ===
+edo benefits from [[octave stretch]] as harmonics 3, 7, and 11 are all tuned flat. [[22edt]] and [[36ed6]] are among the possible choices.
+=== Subsets and supersets ===
+Since 14 factors into primes as 2 × 7, 14edo contains [[2edo]] and [[7edo]] as subsets.
 == Notation ==