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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}}
{{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]].
'''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==
==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===
===Harmonics===
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; Subsets of MOS scales  
; Subsets of MOS scales  
''(Names used are [[Template:Idiosyncratic|idiosyncratic]]. Cent values rounded to 1 dec pl.)''
''(Names used are [[Template:Idiosyncratic|idiosyncratic]].)''
* Eugene/Tritikleismic[9]
* Eugene/Tritikleismic[9]
** Groovy aeolian pentatonic: 315.7, 487.9, 717.5, 803.6, 1205.5
** Groovy aeolian pentatonic: '''11 6 8 3 14'''
** Major pseudo-[[pelog]]: 401.8, 487.9, 717.5, 1119.4, 1205.5
** [[Otonal]] mixolydian pentatonic: '''14 3 8 11 6'''
** Pseudo-[[equipentatonic]]: 315.7, 487.9, 717.5, 889.7, 1205.5
** Pseudo-[[equipentatonic]]: '''11 6 8 6 11'''
** Septimal melodic minor pentatonic: 229.6, 315.7, 717.5, 1119.4, 1205.5
** Septimal melodic minor pentatonic: '''8 3 14 14 3'''
** Septimal Picardy pentatonic: 229.6, 401.8, 717.5, 803.6, 1205.5
** Septimal Picardy pentatonic: '''8 6 11 3 14'''
** Undecimal lydian-aeolian pentatonic: 229.6, 631.4, 1033.3, 1205.5
** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6'''
** Yokai pentatonic: 86.1, 487.9, 717.5, 803.6, 1205.5
** Yokai pentatonic: '''3 14 8 3 14'''




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* [[Lumatone]]
* [[Lumatone]]
** APS720jot can use most types of [[Lumatone mapping for 42edo]]
** APS720jot can use most types of [[Lumatone mapping for 42edo]]
== Music ==
* ''[https://www.youtube.com/watch?v=vdjhC9i5KF4 Four Short Experiments in Octave Stretched 42edo (Dec 2024)]'' - [[Budjarn Lambeth]]


== See also ==
== See also ==
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