User:BudjarnLambeth/1ed28.7c: Difference between revisions

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{{todo|merge articles|inline=1|text='''Do not merge until discussion is complete. See [[User talk:BudjarnLambeth/1ed28.7c]]'''. Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}

'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning|equal-step]] scale with steps of 720 [[30103edo|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].

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==Theory==

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

APS720jot divides [[2/1]] into ~41.8097 equal parts, making it close to [[42edo]], but with [[pseudo-octave|impure octaves]] and better approximations of harmonics [[3/1]] and [[5/1]].

~~APS720jot divides~~ [[~~2/1~~]] ~~into ~41.8097 equal parts~~, ~~making it close to~~ [[~~42edo~~]], but ~~with [[pseudo-octave|impure octaves]] and better approximations of~~ harmonics ~~[[3/1]] and [[5/1]]~~.

It is a kind of opposite twin to the scale [[1ed28.5c|APS715jot]], 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).

It is ~~a kind~~ of ~~opposite twin to the scale~~ [[~~191zpi~~]]~~. 191zpi makes~~ [[~~42edo~~]] ~~into a better 2.3.5.11.13 tuning, while APS720jot 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 [[42ed257/128]] and [[zpi|189zpi]].

~~APS720jot is very similar to~~ [[~~42ed257/128~~]]~~, 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===

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+{{todo|merge articles|inline=1|text='''Do not merge until discussion is complete. See [[User talk:BudjarnLambeth/1ed28.7c]]'''. Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}
+{{Editable user page}}
 {{Infobox ET|1ed31444/30927}}
 '''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning|equal-step]] scale with steps of 720 [[30103edo|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].
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 ==Theory==
-''See also: [[Table of stretched 42edo tunings]]''
+APS720jot divides [[2/1]] into ~41.8097 equal parts, making it close to [[42edo]], but with [[pseudo-octave|impure octaves]] and better approximations of harmonics [[3/1]] and [[5/1]].
-APS720jot divides [[2/1]] into ~41.8097 equal parts, making it close to [[42edo]], but with [[pseudo-octave|impure octaves]] and better approximations of harmonics [[3/1]] and [[5/1]].
+It is a kind of opposite twin to the scale [[1ed28.5c|APS715jot]], 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).
-It is a kind of opposite twin to the scale [[191zpi]]. 191zpi makes [[42edo]] into a better 2.3.5.11.13 tuning, while APS720jot 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 [[42ed257/128]] and [[zpi|189zpi]].
-APS720jot is very similar to [[42ed257/128]], 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===