13edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
[[File:13edt.png|thumb|alt=13edt.png|A plot of the [[ | [[File:13edt.png|thumb|alt=13edt.png|A plot of the [[Riemann zeta function#Removing primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak [[EDT]].]] | ||
[[File:pts-3-5-7-e3-twtop.jpg|thumb|Projective tuning space of the [[3.5.7 subgroup]], showing 13edt near the center.]] | |||
'''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. | '''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]]. | 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 == | == Theory == | ||
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* [[23ed7|23ED7]]: relative ED7 | * [[23ed7|23ED7]]: relative ED7 | ||
[[Category:Tritave]] | [[Category:Tritave]] | ||
[[Category:Macrotonal]] | [[Category:Macrotonal]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:Bohlen–Pierce]] | [[Category:Bohlen–Pierce]] | ||