Pajara: Difference between revisions

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<nowiki/>* In 11-limit CWE tuning, octave-reduced

There are two different mappings of the 11-limit. One is just called "pajara" and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. The other, called "pajarous" to avoid confusion, loses some accuracy and ~~there's little reason to use it unless you're using~~ 22edo, ~~which is~~ the ~~intersection~~ of ~~both systems~~.

There are two different mappings of the 11-limit. One is just called "pajara" and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. It is best tuned flat of 22edo. The other, called "pajarous" to avoid confusion, loses some accuracy for 3 and 5. It is best tuned sharp of 22edo, and has the advantage of being supported by all patent vals that support pajara save [[12edo]].

{| class="wikitable mw-collapsible mw-collapsed"

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== Tunings ==

As with [[archy]], there is a tradeoff in pajara between accuracy of 3 and accuracy of 7. Unlike tunings of archy which often hover around 710-712 cents, however, pajara is conventionally tuned flat of 22edo - this is because tunings sharp of about 710 cents lose a large degree of accuracy in 5/4 and especially 6/5. However, all EDOs that support pajara (except for 12edo) are from 22edo or sharper.

=== Tuning spectrum ===

{| class="wikitable center-all left-4"

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|

| 711.111

| ~~54e val~~

| Pajarous

|-

|

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|

| 712.500

| ~~32e val~~

| Pajarous

|-

| 25\42

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|

| 720.000

| ~~10e val~~, upper bound of 9-odd-limit diamond monotone

| Pajarous, upper bound of 9-odd-limit diamond monotone

|}

@@ Line 85: / Line 85: @@
 <nowiki/>* In 11-limit CWE tuning, octave-reduced
-There are two different mappings of the 11-limit. One is just called "pajara" and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. The other, called "pajarous" to avoid confusion, loses some accuracy and there's little reason to use it unless you're using 22edo, which is the intersection of both systems.
+There are two different mappings of the 11-limit. One is just called "pajara" and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. It is best tuned flat of 22edo. The other, called "pajarous" to avoid confusion, loses some accuracy for 3 and 5. It is best tuned sharp of 22edo, and has the advantage of being supported by all patent vals that support pajara save [[12edo]].
 {| class="wikitable mw-collapsible mw-collapsed"
@@ Line 302: / Line 302: @@
 == Tunings ==
+As with [[archy]], there is a tradeoff in pajara between accuracy of 3 and accuracy of 7. Unlike tunings of archy which often hover around 710-712 cents, however, pajara is conventionally tuned flat of 22edo - this is because tunings sharp of about 710 cents lose a large degree of accuracy in 5/4 and especially 6/5. However, all EDOs that support pajara (except for 12edo) are from 22edo or sharper.
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"
@@ Line 418: / Line 420: @@
 |
 | 711.111
-| 54e val
+| Pajarous
 |-
 |
@@ Line 428: / Line 430: @@
 |
 | 712.500
-| 32e val
+| Pajarous
 |-
 | 25\42
@@ Line 443: / Line 445: @@
 |
 | 720.000
-| 10e val, upper bound of 9-odd-limit diamond monotone
+| Pajarous, upper bound of 9-odd-limit diamond monotone
 |}