13edt: Difference between revisions

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~~The 13 equal division of 3,~~ the tritave~~, divides it~~ into 13 equal parts of 146.304 cents each, corresponding to 8.202 edo. ~~An alternative name for it~~ is the [[~~Bohlen-Pierce|~~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.

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.

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.

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| | 25/21

| |

| | [[~~Sirius|~~Sirius]]

| | [[Sirius]]

|-

| | 3

Line 42:

| | 7/5

| |

| | [[~~Canopus|~~Canopus]]

| | [[Canopus]]

|-

| | 5

Line 56:

| | 5/3

| |

| | [[~~Arcturus|~~Arcturus]]

| | [[Arcturus]]

|-

| | 7

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==See also==

~~<ul><li>~~[[~~Catalog_of_3.5.7_subgroup_rank_two_temperaments|~~Catalog of 3.5.7 subgroup rank two temperaments]]~~</li></ul>~~ [[Category:~~3th_harmonic~~]]

*[[Catalog of 3.5.7 subgroup rank two temperaments]]

[[Category:3/1]]

[[Category:edt]]

[[Category:tritave]]

[[category:macrotonal]]

[[category:nonoctave]]

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-The 13 equal division of 3, the tritave, divides it into 13 equal parts of 146.304 cents each, corresponding to 8.202 edo. An alternative name for it is the [[Bohlen-Pierce|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.
+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.
 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.
@@ Line 28: / Line 28: @@
 | | 25/21
 | |
-| | [[Sirius|Sirius]]
+| | [[Sirius]]
 |-
 | | 3
@@ Line 42: / Line 42: @@
 | | 7/5
 | |
-| | [[Canopus|Canopus]]
+| | [[Canopus]]
 |-
 | | 5
@@ Line 56: / Line 56: @@
 | | 5/3
 | |
-| | [[Arcturus|Arcturus]]
+| | [[Arcturus]]
 |-
 | | 7
@@ Line 109: / Line 109: @@
 ==See also==
-<ul><li>[[Catalog_of_3.5.7_subgroup_rank_two_temperaments|Catalog of 3.5.7 subgroup rank two temperaments]]</li></ul>      [[Category:3th_harmonic]]
+*[[Catalog of 3.5.7 subgroup rank two temperaments]]
+[[Category:3/1]]
 [[Category:edt]]
 [[Category:tritave]]
 [[category:macrotonal]]
+[[category:nonoctave]]