User:BudjarnLambeth/1ed28.5c: 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 715jot''' ('''APS715jot'''), also known as '''1 equal division of 715jot''' ('''1ed715jot''') or '''715-jot equal temperament''' ('''715jot-et'''), is an [[Equal-step tuning|equal-step]] scale with steps of 715 [[30103edo|jots]] (~28.50215 [[cents]]), or each 715th step of [[30103edo]].

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APS715jot divides [[2/1]] into ~42.1021 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 [[APS720jot]], 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 [[1ed28.7c|APS720jot]], 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).

~~APS720jot’s~~ step size is very close to that of [[42ed255/128]] and [[191zpi]].

APS715jot’s step size is very close to that of [[ed255/128#42ed255/128|42ed255/128]] and [[191zpi]].

===Harmonics===

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== Notation ==

~~APS720jot~~ can use most notation systems designed for 42edo. See [[42edo#Notation]].

APS715jot can use most notation systems designed for 42edo. See [[42edo#Notation]].

==Scala file==

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== Scales ==

~~To generate these in [[Scale Workshop]], you can first generate them in 42edo, then apply a stretch of 1.00455012.~~

; [[MOS scale]]s

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== Instruments ==

* [[Lumatone]]

** ~~APS720jot~~ can use most types of [[Lumatone mapping for 42edo]]

** APS715jot can use most types of [[Lumatone mapping for 42edo]]

== See also ==

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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|1ed13167/12952}}
 '''Arithmetic pitch sequence of 715jot''' ('''APS715jot'''), also known as '''1 equal division of 715jot''' ('''1ed715jot''') or '''715-jot equal temperament''' ('''715jot-et'''), is an [[Equal-step tuning|equal-step]] scale with steps of 715 [[30103edo|jots]] (~28.50215 [[cents]]), or each 715th step of [[30103edo]].
@@ Line 9: / Line 11: @@
 APS715jot divides [[2/1]] into ~42.1021 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 [[APS720jot]], 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 [[1ed28.7c|APS720jot]], 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).
-APS720jot’s step size is very close to that of [[42ed255/128]] and [[191zpi]].
+APS715jot’s step size is very close to that of [[ed255/128#42ed255/128|42ed255/128]] and [[191zpi]].
 ===Harmonics===
@@ Line 23: / Line 25: @@
 == Notation ==
-APS720jot can use most notation systems designed for 42edo. See [[42edo#Notation]].
+APS715jot can use most notation systems designed for 42edo. See [[42edo#Notation]].
 ==Scala file==
@@ Line 81: / Line 83: @@
 == Scales ==
-To generate these in [[Scale Workshop]], you can first generate them in 42edo, then apply a stretch of 1.00455012.
 ; [[MOS scale]]s
@@ Line 108: / Line 108: @@
 == Instruments ==
 * [[Lumatone]]
-** APS720jot can use most types of [[Lumatone mapping for 42edo]]
+** APS715jot can use most types of [[Lumatone mapping for 42edo]]
 == See also ==