Decic: Difference between revisions

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'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[~~15/14 equal-step tuning|~~linus ~~temperaments~~]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.

'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[linus]] temperaments. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.

There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&50), ''splendecic'' (10e&50) and ''prodecic'' (10&50e). They share the comma list of the [[No-elevens subgroup temperaments|no-elevens subgroups]], tempering out 105/104, 170/169, 196/195 and 289/288. Decic adds 385/384, splendecic adds 4375/4376, and prodecic adds 441/440 to the 11-limit comma list.

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* [[Decic50]] - [[10L 40s]] scale

[[Category:~~Temperaments]]~~

[[Category:Decic| ]]

~~[[Category:Cloudy clan~~]]

[[Category:Rank-2 temperaments]]

[[Category:Marvel temperaments]]

[[Category:~~Decic|~~ ]]~~~~

[[Category:Cloudy clan]]

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-'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[15/14 equal-step tuning|linus temperaments]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.
+'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[linus]] temperaments. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.
 There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&amp;50), ''splendecic'' (10e&amp;50) and ''prodecic'' (10&amp;50e). They share the comma list of the [[No-elevens subgroup temperaments|no-elevens subgroups]], tempering out 105/104, 170/169, 196/195 and 289/288. Decic adds 385/384, splendecic adds 4375/4376, and prodecic adds 441/440 to the 11-limit comma list.
@@ Line 529: / Line 529: @@
 * [[Decic50]] - [[10L 40s]] scale
-[[Category:Temperaments]]
+[[Category:Decic| ]] <!-- main article -->
-[[Category:Cloudy clan]]
 [[Category:Rank-2 temperaments]]
 [[Category:Marvel temperaments]]
-[[Category:Decic| ]]<!-- main article -->
+[[Category:Cloudy clan]]