User:BudjarnLambeth/42ed257/128: Difference between revisions

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'''42ed257/128''' is the [[Ed257/128|equal division of the interval 257/128]] into forty-two parts of 28.73 [[cents]] each, corresponding to ~41.77[[edo]].

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=== Harmonics ===

~~''See also:~~ [[~~Table of stretched 42edo tunings~~]]''

42ed257/128 is a kind of opposite twin to the scale [[ed255/128#42ed255/128|42ed255/128]], as they improve 42edo’s [[JI]] approximation by about the same amount, but in opposite directions (those harmonics which are slightly sharp in one are slightly flat in the other).

42ed257/~~128~~ is ~~a kind~~ of ~~opposite twin to the scale~~ [[~~191zpi~~]]~~. 191zpi makes~~ [[~~42edo~~]] ~~into a better 2.3.5.11.13 tuning, while 42ed257/128 makes 42edo into a better 2.3.5.7.17 tuning. They both improve 42edo but in opposite directions~~.

42ed257/128’s step size is very close to that of [[1ed28.7c|APS720jot]] and [[zpi|189zpi]].

~~42ed257/128 is very similar to~~ [[~~1ed28.7c|APS720jot~~]]~~, which achieves many of the same aims. The difference is that 42ed257/128 has better harmonics 3, 5 and 7, while APS720jot has better harmonics 2, 11 and 13~~.

See [[Table of stretched 42edo tunings]] for more.

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; [[Tonality diamond]]s

These take advantage of 42ed257/128’s improved approximations of the full 47-limit compared to 42edo, especially its improved 3/1 and 5/1.

These take advantage of 42ed257/128’s improved approximations of the full 7-limit compared to 42edo, especially its improved 3/1 and 5/1.

* [[Diamond7]]: '''8 1 2 2 4 3 2 2 4 3 2 2 8'''

* [[Diamond9]]: '''6 1 1 1 2 2 2 2 3 2 2 3 1 3 1 2 1 1 6'''

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-{{Infobox ET}}
+{{Infobox ET|42ed257/128}}
 '''42ed257/128''' is the [[Ed257/128|equal division of the interval 257/128]] into forty-two parts of 28.73 [[cents]] each, corresponding to ~41.77[[edo]].
@@ Line 5: / Line 5: @@
 === Harmonics ===
-''See also: [[Table of stretched 42edo tunings]]''
+ed257/128 is a kind of opposite twin to the scale [[ed255/128#42ed255/128|42ed255/128]], as they improve 42edo’s [[JI]] approximation by about the same amount, but in opposite directions (those harmonics which are slightly sharp in one are slightly flat in the other).
-ed257/128 is a kind of opposite twin to the scale [[191zpi]]. 191zpi makes [[42edo]] into a better 2.3.5.11.13 tuning, while 42ed257/128 makes 42edo into a better 2.3.5.7.17 tuning. They both improve 42edo but in opposite directions.
+ed257/128’s step size is very close to that of [[1ed28.7c|APS720jot]] and [[zpi|189zpi]].
-ed257/128 is very similar to [[1ed28.7c|APS720jot]], which achieves many of the same aims. The difference is that 42ed257/128 has better harmonics 3, 5 and 7, while APS720jot has better harmonics 2, 11 and 13.
+See [[Table of stretched 42edo tunings]] for more.
 {{Harmonics in equal|42|257|128|intervals=prime}}
@@ Line 98: / Line 98: @@
 ; [[Tonality diamond]]s
-These take advantage of 42ed257/128’s improved approximations of the full 47-limit compared to 42edo, especially its improved 3/1 and 5/1.
+These take advantage of 42ed257/128’s improved approximations of the full 7-limit compared to 42edo, especially its improved 3/1 and 5/1.
 * [[Diamond7]]: '''8 1 2 2 4 3 2 2 4 3 2 2 8'''
 * [[Diamond9]]: '''6 1 1 1 2 2 2 2 3 2 2 3 1 3 1 2 1 1 6'''