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. 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]]~~. However, ~~pajarous~~ equates [[12/11]] with [[10/9]], and the only tuning equating [[11/10]] with both is 22edo.

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. However, it equates [[12/11]] with [[10/9]], and the only tuning equating [[11/10]] with both is 22edo.

{| 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~~.

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.

=== Tuning spectrum ===

Line 420:

|

| 711.111

| ~~Pajarous~~

| 54e val

|-

|

Line 430:

|

| 712.500

| ~~Pajarous~~

| 32e val

|-

| 25\42

Line 445:

|

| 720.000

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

| 10e val, 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. 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]]. However, pajarous equates [[12/11]] with [[10/9]], and the only tuning equating [[11/10]] with both is 22edo.
+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. However, it equates [[12/11]] with [[10/9]], and the only tuning equating [[11/10]] with both is 22edo.
 {| 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.
+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.
 === Tuning spectrum ===
@@ Line 420: / Line 420: @@
 |
 | 711.111
-| Pajarous
+| 54e val
 |-
 |
@@ Line 430: / Line 430: @@
 |
 | 712.500
-| Pajarous
+| 32e val
 |-
 | 25\42
@@ Line 445: / Line 445: @@
 |
 | 720.000
-| Pajarous, upper bound of 9-odd-limit diamond monotone
+| 10e val, upper bound of 9-odd-limit diamond monotone
 |}