Subgroup temperaments: Difference between revisions

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=== Barbados ===

Barbados ~~is the restriction of~~ [[~~#Bridgetown|bridgetown~~]] to the 2.3.13/5 subgroup, and ~~tempers out~~ [[~~676~~/~~675~~]] ~~alone~~. The [[minimax tuning]] ~~for this makes the generator the cube root of 20~~/13, ~~or 248.5953 cents~~. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo~~]] and [[111edo~~]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. If tuned near-optimally, it is just barely a [[microtemperament]], with errors of under one cent for 3 and 13/5, and given its ultra-low complexity, this makes ~~Barbados~~ an extremely low-[[badness]] temperament within its subgroup.

Barbados tempers out [[676/675]] alone in the 2.3.13/5 subgroup. It melodically resembles [[semaphoresmic clan #Semaphore|semaphore]], but targets specifically the interseptimal intervals like [[13/10]] and [[15/13]]. [[#Bridgetown|Bridgetown]], which adds 11/5, is a notable extension of it.

The {1, 3, 13/5} and {1, 3, 9, 13/5} [[minimax tuning]]s have 13/5 and 3 tuned pure, respectively. Edos which may be used for it include but are not limited to [[24edo]], [[29edo]], and [[53edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. If tuned near-optimally, it is just barely a [[microtemperament]], with errors of under one cent for 3 and 13/5, and given its ultra-low complexity, this makes barbados an extremely [[badness|low-badness]] temperament within its subgroup.

Several related temperaments, all tempering out 676/675, can be found in [[The Archipelago]].

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[[Optimal tuning]]s:

* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.9502{{c}}, ~26/15 = 951.0713{{c}}

: [[error map]]: {{val| -0.050 +0.188 -0.950 }}

* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.0933{{c}}

: error map: {{val| 0.000 +0.232 -0.934 }}

{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 29, 53, 82, 135 }}

[[Badness]] (~~Smith~~): 0.~~002335~~

[[Badness]] (Sintel): 0.022

; Music

@@ Line 378: / Line 378: @@
 === Barbados ===
-Barbados is the restriction of [[#Bridgetown|bridgetown]] to the 2.3.13/5 subgroup, and tempers out [[676/675]] alone. The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. If tuned near-optimally, it is just barely a [[microtemperament]], with errors of under one cent for 3 and 13/5, and given its ultra-low complexity, this makes Barbados an extremely low-[[badness]] temperament within its subgroup.
+Barbados tempers out [[676/675]] alone in the 2.3.13/5 subgroup. It melodically resembles [[semaphoresmic clan #Semaphore|semaphore]], but targets specifically the interseptimal intervals like [[13/10]] and [[15/13]]. [[#Bridgetown|Bridgetown]], which adds 11/5, is a notable extension of it.
+The {1, 3, 13/5} and {1, 3, 9, 13/5} [[minimax tuning]]s have 13/5 and 3 tuned pure, respectively. Edos which may be used for it include but are not limited to [[24edo]], [[29edo]], and [[53edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. If tuned near-optimally, it is just barely a [[microtemperament]], with errors of under one cent for 3 and 13/5, and given its ultra-low complexity, this makes barbados an extremely [[badness|low-badness]] temperament within its subgroup.
 Several related temperaments, all tempering out 676/675, can be found in [[The Archipelago]].
@@ Line 391: / Line 393: @@
 [[Optimal tuning]]s:
 * [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.9502{{c}}, ~26/15 = 951.0713{{c}}
+: [[error map]]: {{val| -0.050 +0.188 -0.950 }}
 * [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.0933{{c}}
+: error map: {{val| 0.000 +0.232 -0.934 }}
 {{Optimal ET sequence|legend=1| 5, 14, 19, 24, 29, 53, 82, 135 }}
-[[Badness]] (Smith): 0.002335
+[[Badness]] (Sintel): 0.022
 ; Music

Subgroup temperaments: Difference between revisions

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