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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* 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]

[[Optimal ~~GPV~~ sequence]]s:

[[Optimal ET sequence]]s:

* 7-limit: {{~~Vals~~| 10, 30b, 40, 50, 60, 110d, 170cdd }}

* 7-limit: {{Optimal ET sequence| 10, 30b, 40, 50, 60, 110d, 170cdd }}

* 11 and 13-limit: {{~~Vals~~| 10, 30be, 40, 50 }}

* 11 and 13-limit: {{Optimal ET sequence| 10, 30be, 40, 50 }}

* 17-limit: {{~~Vals~~| 10, 30beg, 40, 50 }}

* 17-limit: {{Optimal ET sequence| 10, 30beg, 40, 50 }}

[[Badness]]:

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* 17-limit: 0.025064

</div></div>

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* 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]

[[Optimal ~~GPV~~ sequence]]s:

[[Optimal ET sequence]]s:

* 11 and 13-limit: {{~~Vals~~| 10e, 30bee, 40e, 50, 60e, 110de }}

* 11 and 13-limit: {{Optimal ET sequence| 10e, 30bee, 40e, 50, 60e, 110de }}

* 17-limit: {{~~Vals~~| 10e, 30beeg, 40e, 50, 60e, 110deg }}

* 17-limit: {{Optimal ET sequence| 10e, 30beeg, 40e, 50, 60e, 110deg }}

[[Badness]]:

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* 17-limit: 0.026050

</div></div>

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* 11, 13, 15, and 17-odd-limit: ~3/2 = [700.00000, 702.85714]

[[Optimal ~~GPV~~ sequence]]s:

[[Optimal ET sequence]]s:

* 11, 13, and 17-limit: {{~~Vals~~| 10, 40ee, 50e, 60e }}

* 11, 13, and 17-limit: {{Optimal ET sequence| 10, 40ee, 50e, 60e }}

[[Badness]]:

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<nowiki>*</nowiki> in 17-limit POTE tuning

</div></div>

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<nowiki>*</nowiki> in 17-limit POTE tuning

</div></div>

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

[[Category:Decic| ]]

[[Category:Rank-2 temperaments]]

[[Category:Marvel temperaments]]

[[Category:Cloudy clan]]

~~[[Category:Marvel temperaments]]~~

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

~~{{IoT}}~~

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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 40: / Line 40: @@
 * 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]
-[[Optimal GPV sequence]]s:
+[[Optimal ET sequence]]s:
-* 7-limit: {{Vals| 10, 30b, 40, 50, 60, 110d, 170cdd }}
+* 7-limit: {{Optimal ET sequence| 10, 30b, 40, 50, 60, 110d, 170cdd }}
-* 11 and 13-limit: {{Vals| 10, 30be, 40, 50 }}
+* 11 and 13-limit: {{Optimal ET sequence| 10, 30be, 40, 50 }}
-* 17-limit: {{Vals| 10, 30beg, 40, 50 }}
+* 17-limit: {{Optimal ET sequence| 10, 30beg, 40, 50 }}
 [[Badness]]:
@@ Line 51: / Line 51: @@
 * 17-limit: 0.025064
 </div></div>
 <div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
@@ Line 81: / Line 82: @@
 * 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]
-[[Optimal GPV sequence]]s:
+[[Optimal ET sequence]]s:
-* 11 and 13-limit: {{Vals| 10e, 30bee, 40e, 50, 60e, 110de }}
+* 11 and 13-limit: {{Optimal ET sequence| 10e, 30bee, 40e, 50, 60e, 110de }}
-* 17-limit: {{Vals| 10e, 30beeg, 40e, 50, 60e, 110deg }}
+* 17-limit: {{Optimal ET sequence| 10e, 30beeg, 40e, 50, 60e, 110deg }}
 [[Badness]]:
@@ Line 90: / Line 91: @@
 * 17-limit: 0.026050
 </div></div>
 <div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
@@ Line 119: / Line 121: @@
 * 11, 13, 15, and 17-odd-limit: ~3/2 = [700.00000, 702.85714]
-[[Optimal GPV sequence]]s:
+[[Optimal ET sequence]]s:
-* 11, 13, and 17-limit: {{Vals| 10, 40ee, 50e, 60e }}
+* 11, 13, and 17-limit: {{Optimal ET sequence| 10, 40ee, 50e, 60e }}
 [[Badness]]:
@@ Line 259: / Line 261: @@
 <nowiki>*</nowiki> in 17-limit POTE tuning
 </div></div>
 <div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
@@ Line 390: / Line 393: @@
 <nowiki>*</nowiki> in 17-limit POTE tuning
 </div></div>
 <div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
@@ Line 525: / Line 529: @@
 * [[Decic50]] - [[10L 40s]] scale
+[[Category:Decic| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Marvel temperaments]]
 [[Category:Cloudy clan]]
-[[Category:Marvel temperaments]]
-[[Category:Decic| ]]<!-- main article -->
-{{IoT}}