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 [[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. | ||
There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&50), '' | 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. | ||
== Temperament data == | == Temperament data == | ||
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<div style="line-height:1.6;">''' | <div style="line-height:1.6;">'''Splendecic temperament (10e&50)'''</div> | ||
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Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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<div style="line-height:1.6;">''' | <div style="line-height:1.6;">'''Prodecic temperament (10&50e)'''</div> | ||
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Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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<div style="line-height:1.6;">'''Intervals of | <div style="line-height:1.6;">'''Intervals of splendecic (10e&50)'''</div> | ||
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<div style="line-height:1.6;">'''Intervals of | <div style="line-height:1.6;">'''Intervals of prodecic (10&50e)'''</div> | ||
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== Scales == | == Scales == | ||
* [[Decic50]] - [[10L 40s]] scale | * [[Decic50]] - [[10L 40s]] scale | ||
[[Category:Cloudy clan]] | [[Category:Cloudy clan]] | ||