Hewuermera comma: Difference between revisions

(One intermediate revision by the same user not shown)

Line 6:

}}

'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount by which a stack of six [[8/7]]s exceed [[20/9]]. It can also be expressed as the difference between three intervals of {{S|7}} = [[49/48]] and S4 = [[16/15]].

'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount by which a stack of six [[8/7]]s exceed [[20/9]]. It can also be expressed as the difference between three intervals of {{S|7}} = [[49/48]] and S4 = [[16/15]], or as (S6/S7 = [[1728/1715]])/(S7/S8 = [[1029/1024]]).

== Factorizations ==

Line 14:

== Temperaments ==

Tempering it out alone in the 7-limit leads to the '''hewuermera''' [[rank-3 temperament]], and in combination with another comma, to the [[hewuermera temperaments]], the most notable of which are [[hemiwürschmidt]] and [[mothra]]. For highest accuracy, this comma demands that 8/7 be tuned slightly flat, as it is in [[EDO]]s such as {{EDOs|26, 99, and ~~161~~}}.

Tempering it out alone in the 7-limit leads to the '''hewuermera''' [[rank-3 temperament]], and in combination with another comma, to the [[hewuermera temperaments]], the most notable of which are [[hemiwürschmidt]] and [[mothra]]. For highest accuracy, this comma demands that 8/7 be tuned slightly flat, as it is in [[EDO]]s such as {{EDOs|26, 68, and 99}}.

== Etymology ==

@@ Line 6: / Line 6: @@
 }}
-'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount by which a stack of six [[8/7]]s exceed [[20/9]]. It can also be expressed as the difference between three intervals of {{S|7}} = [[49/48]] and S4 = [[16/15]].
+'''589824/588245''', the '''hewuermera comma''', is a [[7-limit]] [[small comma]] measuring about 4.6 cents. It is the amount by which a stack of six [[8/7]]s exceed [[20/9]]. It can also be expressed as the difference between three intervals of {{S|7}} = [[49/48]] and S4 = [[16/15]], or as (S6/S7 = [[1728/1715]])/(S7/S8 = [[1029/1024]]).
 == Factorizations ==
@@ Line 14: / Line 14: @@
 == Temperaments ==
-Tempering it out alone in the 7-limit leads to the '''hewuermera''' [[rank-3 temperament]], and in combination with another comma, to the [[hewuermera temperaments]], the most notable of which are [[hemiwürschmidt]] and [[mothra]]. For highest accuracy, this comma demands that 8/7 be tuned slightly flat, as it is in [[EDO]]s such as {{EDOs|26, 99, and 161}}.
+Tempering it out alone in the 7-limit leads to the '''hewuermera''' [[rank-3 temperament]], and in combination with another comma, to the [[hewuermera temperaments]], the most notable of which are [[hemiwürschmidt]] and [[mothra]]. For highest accuracy, this comma demands that 8/7 be tuned slightly flat, as it is in [[EDO]]s such as {{EDOs|26, 68, and 99}}.
 == Etymology ==