Keemun: Difference between revisions

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| Odd limit 2 = 13 | Mistuning 2 = 27.3 | Complexity 2 = 19

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'''Keemun''' is an [[extension]] of the [[hanson]] temperament, ~~and~~ [[tempering ~~out|tempers~~ out]] [[49/48]], [[56/55]], and [[100/99]] in the [[11-limit]]. This means it uses the same simple mappings for the 7th and 11th harmonics as [[orgone]]. Unfortunately, the optimal ~~tunings~~ for the 3rd and 5th harmonics is substantially flatter than that for the 7th & 11th ~~ones~~, requiring you to compromise one set for the other. ~~The edos~~ that support keemun in their patent ~~vals~~ are [[4edo]], [[15edo]], [[19edo]], and [[34edo]], with [[49edo|49d]] and [[64edo|64bde]] coming closer to balancing the errors equally.

'''Keemun''' is an [[extension]] of the [[hanson]] temperament. It identifies the hemitwelfth as [[7/4]][[~]][[12/7]] and the two-generator step as [[13/9]][[~]][[16/11]], [[tempering out]] [[49/48]], [[56/55]], [[91/90]] and [[100/99]] in the [[13-limit]]. This means it uses the same simple mappings for the [[7/1|7th]] and [[11/1|11th harmonics]] as [[orgone]]. Unfortunately, the optimal tuning for the [[3/1|3rd]] and [[5/1|5th harmonics]] is substantially flatter than that for the 7th & 11th, requiring you to compromise one set for the other. [[Edo]]s that [[support]] keemun in their [[patent val]]s are [[4edo]], [[15edo]], [[19edo]], and [[34edo]], with [[49edo|49d]] and [[64edo|64bde]] coming closer to balancing the errors equally.

This temperament was originally discovered by [[Dave Keenan]] and named by [[Herman Miller]] in 2006 after the {{w|Keemun|Chinese black tea}}<ref>~~Dave Keenan's original write-up:~~ [https://dkeenan.com/Music/ChainOfMinor3rds.htm ''11 note chain-of-minor-thirds scale'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13775 Yahoo! Tuning Group | ''Rich Holmes temperaments'']</ref>.

This temperament was originally discovered by [[Dave Keenan]] and named by [[Herman Miller]] in 2006 after the {{w|Keemun|Chinese black tea}}.<ref>[https://dkeenan.com/Music/ChainOfMinor3rds.htm ''11 note chain-of-minor-thirds scale''] by Dave Keenan</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13775 Yahoo! Tuning Group (archive) | ''Rich Holmes temperaments'']</ref>

See [[Kleismic family #Keemun]] for technical data. See [[Keemun extensions]] for a discussion on alternative 11- and 13-limit extensions.

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[[Category:Semaphoresmic clan]]

[[Category:Starling temperaments]]

[[Category:Keemic temperaments]]

[[Category:Listen]]

@@ Line 11: / Line 11: @@
 | Odd limit 2 = 13 | Mistuning 2 = 27.3 | Complexity 2 = 19
 }}
-'''Keemun''' is an [[extension]] of the [[hanson]] temperament, and [[tempering out|tempers out]] [[49/48]], [[56/55]], and [[100/99]] in the [[11-limit]]. This means it uses the same simple mappings for the 7th and 11th harmonics as [[orgone]]. Unfortunately, the optimal tunings for the 3rd and 5th harmonics is substantially flatter than that for the 7th & 11th ones, requiring you to compromise one set for the other. The edos that support keemun in their patent vals are [[4edo]], [[15edo]], [[19edo]], and [[34edo]], with [[49edo|49d]] and [[64edo|64bde]] coming closer to balancing the errors equally.
+'''Keemun''' is an [[extension]] of the [[hanson]] temperament. It identifies the hemitwelfth as [[7/4]][[~]][[12/7]] and the two-generator step as [[13/9]][[~]][[16/11]], [[tempering out]] [[49/48]], [[56/55]], [[91/90]] and [[100/99]] in the [[13-limit]]. This means it uses the same simple mappings for the [[7/1|7th]] and [[11/1|11th harmonics]] as [[orgone]]. Unfortunately, the optimal tuning for the [[3/1|3rd]] and [[5/1|5th harmonics]] is substantially flatter than that for the 7th & 11th, requiring you to compromise one set for the other. [[Edo]]s that [[support]] keemun in their [[patent val]]s are [[4edo]], [[15edo]], [[19edo]], and [[34edo]], with [[49edo|49d]] and [[64edo|64bde]] coming closer to balancing the errors equally.
-This temperament was originally discovered by [[Dave Keenan]] and named by [[Herman Miller]] in 2006 after the {{w|Keemun|Chinese black tea}}<ref>Dave Keenan's original write-up: [https://dkeenan.com/Music/ChainOfMinor3rds.htm ''11 note chain-of-minor-thirds scale'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13775 Yahoo! Tuning Group | ''Rich Holmes temperaments'']</ref>.
+This temperament was originally discovered by [[Dave Keenan]] and named by [[Herman Miller]] in 2006 after the {{w|Keemun|Chinese black tea}}.<ref>[https://dkeenan.com/Music/ChainOfMinor3rds.htm ''11 note chain-of-minor-thirds scale''] by Dave Keenan</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13775 Yahoo! Tuning Group (archive) | ''Rich Holmes temperaments'']</ref>
 See [[Kleismic family #Keemun]] for technical data. See [[Keemun extensions]] for a discussion on alternative 11- and 13-limit extensions.
@@ Line 223: / Line 223: @@
 [[Category:Semaphoresmic clan]]
 [[Category:Starling temperaments]]
+[[Category:Keemic temperaments]]
 [[Category:Listen]]

Keemun: Difference between revisions

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