Quartkeenlig: Difference between revisions

(3 intermediate revisions by 2 users not shown)

Line 1:

~~#REDIRECT [[Kleismic family #~~Quartkeenlig]]

Quartkeenlig is a rank-2 temperament with a generator of about 53 cents, which stands for 33/32 and 36/35 tempered together.

[[Category:~~Temperaments~~]]

For technical data see: [[Kleismic family#Quartkeenlig]]

== Theory ==

EDOs which support quartkeenlig: {{EDOs|68, 91, 159}}.

The simplest mos of quartkeenlig is [[22L 1s]].

The fifth in the standard sense constitutes 13 steps, and it is close to the [[7edo]] fifth. In 91edo, it is exactly the 7edo fifth. However it should be noted that from a regular temperament theory perspective it is not mapped to [[3/2]]. In order to reach just 3/2, one would need to stack 36 generators.

=== Relationship to 23edo and octave stretching ===

If 23 steps of pure [[TE tuning]] quartkeenlig in the 11-limit are considered without octave equivalence, the resulting scale would have an octave of 1215.62 cents, which is almost exactly the octave recommended for harmonic [[23edo and octave stretching|stretching of 23edo]].

Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals. In addition, such a system would be fourthless like stretched 23edo, as [[4/3]] occurs nearly halfway between the 9th and 10th steps

[[Category:Quartkeenlig| ]]

[[Category:Rank-2 temperaments]]

[[Category:Kleismic family]]

@@ Line 1: / Line 1: @@
-#REDIRECT [[Kleismic family #Quartkeenlig]]
+Quartkeenlig is a rank-2 temperament with a generator of about 53 cents, which stands for 33/32 and 36/35 tempered together.
-[[Category:Temperaments]]
+For technical data see: [[Kleismic family#Quartkeenlig]]
+== Theory ==
+EDOs which support quartkeenlig: {{EDOs|68, 91, 159}}.
+The simplest mos of quartkeenlig is [[22L 1s]].
+The fifth in the standard sense constitutes 13 steps, and it is close to the [[7edo]] fifth. In 91edo, it is exactly the 7edo fifth. However it should be noted that from a regular temperament theory perspective it is not mapped to [[3/2]]. In order to reach just 3/2, one would need to stack 36 generators.
+=== Relationship to 23edo and octave stretching ===
+If 23 steps of pure [[TE tuning]] quartkeenlig in the 11-limit are considered without octave equivalence, the resulting scale would have an octave of 1215.62 cents, which is almost exactly the octave recommended for harmonic [[23edo and octave stretching|stretching of 23edo]].
+Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals. In addition, such a system would be fourthless like stretched 23edo, as [[4/3]] occurs nearly halfway between the 9th and 10th steps
+[[Category:Quartkeenlig| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
 [[Category:Kleismic family]]