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 ===

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 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 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~~.

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

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

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* Qeema/Skateboard[15]: '''2 5 2 2 2 5 2 2 2 5 2 2 2 5 2'''

* Qeema/Skateboard[19]: '''2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2'''

* ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and ~~APS720jot~~ is designed to improve 42edo’s flat fifth instead''

* ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and 42ed257/128 is designed to improve 42edo’s flat fifth instead''

; Subsets of MOS scales

''(Names used are [[Template:Idiosyncratic|idiosyncratic]].)''

* Eugene/Tritikleismic[9]

** Groovy aeolian pentatonic: '''11 6 8 3 14'''

** [[Otonal]] mixolydian pentatonic: '''14 3 8 11 6'''

** Pseudo-[[equipentatonic]]: '''11 6 8 6 11'''

** Septimal melodic minor pentatonic: '''8 3 14 14 3'''

** Septimal Picardy pentatonic: '''8 6 11 3 14'''

** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6'''

** Yokai pentatonic: '''3 14 8 3 14'''

; [[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 ===
-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 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 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.
+ed257/128’s step size is very close to that of [[1ed28.7c|APS720jot]] and [[zpi|189zpi]].
+See [[Table of stretched 42edo tunings]] for more.
 {{Harmonics in equal|42|257|128|intervals=prime}}
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 * Qeema/Skateboard[15]: '''2 5 2 2 2 5 2 2 2 5 2 2 2 5 2'''
 * Qeema/Skateboard[19]: '''2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2'''
-* ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and APS720jot is designed to improve 42edo’s flat fifth instead''
+* ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and 42ed257/128 is designed to improve 42edo’s flat fifth instead''
+; Subsets of MOS scales
+''(Names used are [[Template:Idiosyncratic|idiosyncratic]].)''
+* Eugene/Tritikleismic[9]
+** Groovy aeolian pentatonic: '''11 6 8 3 14'''
+** [[Otonal]] mixolydian pentatonic: '''14 3 8 11 6'''
+** Pseudo-[[equipentatonic]]: '''11 6 8 6 11'''
+** Septimal melodic minor pentatonic: '''8 3 14 14 3'''
+** Septimal Picardy pentatonic: '''8 6 11 3 14'''
+** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6'''
+** Yokai pentatonic: '''3 14 8 3 14'''
 ; [[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'''