13edt: Difference between revisions

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~~13edt~~ divides the tritave (3/1) into 13 equal parts of 146.304 cents each, corresponding to 8.202[[~~edo~~]]. It is the equal-tempered version of the well-known '''[[Bohlen-Pierce]]''' scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as [[Sensamagic_clan#Bohpier|bohpier temperament]]. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 ([[26edt]], [[39edt]] and [[52edt]]) come to the fore.

13EDT divides the [[tritave]] (3/1) into 13 equal parts of 146.304 cents each, corresponding to 8.202[[EDO]]. It is the equal-tempered version of the well-known '''[[Bohlen-Pierce]]''' scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as [[Sensamagic_clan#Bohpier|bohpier temperament]]. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 ([[26edt|26EDT]], [[39edt|39EDT]] and [[52edt|52EDT]]) come to the fore.

Below is 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~~.

Below is 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|alt=13edt.png|13edt.png]]

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* [[Relationship between Bohlen-Pierce and octave-ful temperaments]]

==Intervals==

== Intervals ==

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[[Category:Edt]]

[[Category:Tritave]]

[[~~category~~:Macrotonal]]

[[Category:Macrotonal]]

[[~~category~~:Nonoctave]]

[[Category:Nonoctave]]

[[Category:Bohlen-Pierce]]

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-edt divides the tritave (3/1) into 13 equal parts of 146.304 cents each, corresponding to 8.202[[edo]]. It is the equal-tempered version of the well-known '''[[Bohlen-Pierce]]''' scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as [[Sensamagic_clan#Bohpier|bohpier temperament]]. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 ([[26edt]], [[39edt]] and [[52edt]]) come to the fore.
+EDT divides the [[tritave]] (3/1) into 13 equal parts of 146.304 cents each, corresponding to 8.202[[EDO]]. It is the equal-tempered version of the well-known '''[[Bohlen-Pierce]]''' scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as [[Sensamagic_clan#Bohpier|bohpier temperament]]. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 ([[26edt|26EDT]], [[39edt|39EDT]] and [[52edt|52EDT]]) come to the fore.
-Below is 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.
+Below is 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|alt=13edt.png|13edt.png]]
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 * [[Relationship between Bohlen-Pierce and octave-ful temperaments]]
-==Intervals==
+== Intervals ==
 {{See also|Bohlen-p_et}}
@@ Line 193: / Line 193: @@
 [[Category:Edt]]
 [[Category:Tritave]]
-[[category:Macrotonal]]
+[[Category:Macrotonal]]
-[[category:Nonoctave]]
+[[Category:Nonoctave]]
+[[Category:Bohlen-Pierce]]