13edt: Difference between revisions

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[[File:13edt.png|thumb|alt=13edt.png|A plot of the [[~~The_Riemann_Zeta_Function_and_Tuning~~#Removing primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak [[EDT]].]]

[[File:13edt.png|thumb|alt=13edt.png|A plot of the [[the Riemann zeta function and tuning#Removing primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak [[EDT]].]]

'''13 equal divisions of the tritave''' ('''13edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 13 equal steps of 146.3 [[cent]]s each, or the thirteenth root of 3. It is best known as the equal-tempered version of the [[Bohlen–Pierce]] scale, and therefore has received by far the most attention among equal divisions of the tritave.

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13edt can be described as approximately 8.202[[edo]]. This implies that each step of 13edt can be approximated by 5 steps of [[41edo]].

In the [[no-2]] [[3/1-equave-7-limit]], [[13edt]] maintains the smallest relative error of any EDT until [[258edt]] and [[271edt]], and the smallest absolute error until [[56edt]].

In the [[no-2]] [[3/1]]-[[equave]]-[[7-limit]], [[13edt]] maintains the smallest relative error of any EDT until [[258edt]] and [[271edt]], and the smallest absolute error until [[56edt]].

== Theory ==

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! [[4L 5s (3/1-equivalent)|Enneatonic]] degree

! Corresponding 3.5.7 subgroup intervals

! [[Lambda ups and downs notation|Lambda]] ~~(sLsLsLsLs,~~ E = 1/1)

! [[Lambda ups and downs notation|Lambda]] (sLsLsLsLs, {{nowrap|E {{=}} 1/1}})

|-

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* [[23ed7|23ED7]]: relative ED7

~~[[Category:Edt]]~~

[[Category:Tritave]]

[[Category:Macrotonal]]

[[Category:Nonoctave]]

[[Category:~~Bohlen-Pierce~~]]

[[Category:Bohlen–Pierce]]

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 {{Infobox ET}}
-[[File:13edt.png|thumb|alt=13edt.png|A plot of the [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak [[EDT]].]]
+[[File:13edt.png|thumb|alt=13edt.png|A plot of the [[the Riemann zeta function and tuning#Removing primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak [[EDT]].]]
 '''13 equal divisions of the tritave''' ('''13edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 13 equal steps of 146.3 [[cent]]s each, or the thirteenth root of 3. It is best known as the equal-tempered version of the [[Bohlen–Pierce]] scale, and therefore has received by far the most attention among equal divisions of the tritave.
@@ Line 8: / Line 8: @@
 edt can be described as approximately 8.202[[edo]]. This implies that each step of 13edt can be approximated by 5 steps of [[41edo]].
-In the [[no-2]] [[3/1-equave-7-limit]], [[13edt]] maintains the smallest relative error of any EDT until [[258edt]] and [[271edt]], and the smallest absolute error until [[56edt]].
+In the [[no-2]] [[3/1]]-[[equave]]-[[7-limit]], [[13edt]] maintains the smallest relative error of any EDT until [[258edt]] and [[271edt]], and the smallest absolute error until [[56edt]].
 == Theory ==
@@ Line 26: / Line 26: @@
 ! [[4L 5s (3/1-equivalent)|Enneatonic]]<br />degree
 ! Corresponding<br />3.5.7 subgroup<br />intervals
-! [[Lambda ups and downs notation|Lambda]] (sLsLsLsLs,<br />E = 1/1)
+! [[Lambda ups and downs notation|Lambda]]<br />(sLsLsLsLs, {{nowrap|E {{=}} 1/1}})
 |-
 | 0
@@ Line 203: / Line 203: @@
 * [[23ed7|23ED7]]: relative ED7
-[[Category:Edt]]
 [[Category:Tritave]]
 [[Category:Macrotonal]]
 [[Category:Nonoctave]]
-[[Category:Bohlen-Pierce]]
+[[Category:Bohlen–Pierce]]