Quartkeenlig: Difference between revisions

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

{{Infobox regtemp

| Title = Quartkeenlig

| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13

| Comma basis = [[15625/15552]], 117649/116640 (7-limit); <br>[[385/384]], [[6250/6237]], 67228/66825 (11-limit)

| Edo join 1 = 68 | Edo join 2 = 159

| Mapping = 1; 36 30 41 -35

| Generators = 33/32, 36/35

| Generators tuning = ~52.845

| Optimization method = CWE

| Pergen = (P8, P12/36)

| MOS scales = [[22L 1s]]

}}

Quartkeenlig is a rank-2 temperament with a generator of about 53 cents, which stands for 33/32 and 36/35 tempered together. Its name is taken from a portmanteau of the commas that constitute its basis. For technical data see: [[Kleismic family#Quartkeenlig]].

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

Quartkeeling is notable additionally because of its 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 stretching of 23edo. Threfore, much like [[bohpier]] can be considered to represent [[Bohlen-Pierce scale]] but with octaves, quartkeenlig similarly represents stretched 23edo but with conventional octaves.

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.

== Theory ==

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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 ===~~

Being a member of kleismic family, quartkeenlig supports the stacking of [[6/5]] to produce [[3/1]], and partitions 6/5 into 6 quartertone steps.

~~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: @@
-Quartkeenlig is a rank-2 temperament with a generator of about 53 cents, which stands for 33/32 and 36/35 tempered together.
+{{Infobox regtemp
+| Title = Quartkeenlig
+| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
+| Comma basis = [[15625/15552]], 117649/116640 (7-limit); <br>[[385/384]], [[6250/6237]], 67228/66825 (11-limit)
+| Edo join 1 = 68 | Edo join 2 = 159
+| Mapping = 1; 36 30 41 -35
+| Generators = 33/32, 36/35
+| Generators tuning = ~52.845
+| Optimization method = CWE
+| Pergen = (P8, P12/36)
+| MOS scales = [[22L 1s]]
+}}
+Quartkeenlig is a rank-2 temperament with a generator of about 53 cents, which stands for 33/32 and 36/35 tempered together. Its name is taken from a portmanteau of the commas that constitute its basis. For technical data see: [[Kleismic family#Quartkeenlig]].
-For technical data see: [[Kleismic family#Quartkeenlig]]
+Quartkeeling is notable additionally because of its 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 stretching of 23edo. Threfore, much like [[bohpier]] can be considered to represent [[Bohlen-Pierce scale]] but with octaves, quartkeenlig similarly represents stretched 23edo but with conventional octaves.
+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.
 == Theory ==
@@ Line 9: / Line 23: @@
 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 ===
+Being a member of kleismic family, quartkeenlig supports the stacking of [[6/5]] to produce [[3/1]], and partitions 6/5 into 6 quartertone steps.
-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]]