14edo: Difference between revisions

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== Theory ==

=== Composition theory ===

14edo contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]].

=== Tuning 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.

@@ Line 9: / Line 9: @@
 == Theory ==
+=== Composition theory ===
+edo contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]].
+=== Tuning 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.