User:BudjarnLambeth/1ed28.5c - Revision history

BudjarnLambeth at 00:17, 2 August 2025

2025-08-02T00:17:03Z

← Older revision		Revision as of 00:17, 2 August 2025
Line 1:		Line 1:
	{{todo\|merge articles\|inline=1\|text=Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}		{{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}}		{{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]].		'''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]].

Fredg999: Propose merge (similar tunings)

2025-08-01T04:19:56Z

Propose merge (similar tunings)

← Older revision		Revision as of 04:19, 1 August 2025
Line 1:		Line 1:
			{{todo\|merge articles\|inline=1\|text=Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}
	{{Infobox ET\|1ed13167/12952}}		{{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]].		'''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]].

BudjarnLambeth: BudjarnLambeth moved page 1ed28.5c to User:BudjarnLambeth/1ed28.5c

2025-05-18T13:19:05Z

BudjarnLambeth moved page 1ed28.5c to User:BudjarnLambeth/1ed28.5c

← Older revision	Revision as of 13:19, 18 May 2025
(No difference)

BudjarnLambeth: /* Instruments */

2024-12-13T01:54:00Z

Instruments

← Older revision		Revision as of 01:54, 13 December 2024
Line 106:		Line 106:
	== Instruments ==		== Instruments ==
	* [[Lumatone]]		* [[Lumatone]]
	** ~~APS720jot~~ can use most types of [[Lumatone mapping for 42edo]]		** APS715jot can use most types of [[Lumatone mapping for 42edo]]

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

BudjarnLambeth: /* Scales */

2024-12-13T01:53:51Z

Scales

← Older revision		Revision as of 01:53, 13 December 2024
Line 81:		Line 81:

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


	; [[MOS scale]]s		; [[MOS scale]]s

BudjarnLambeth: /* Notation */

2024-12-13T01:53:37Z

Notation

← Older revision		Revision as of 01:53, 13 December 2024
Line 23:		Line 23:

	== Notation ==		== 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==		==Scala file==

BudjarnLambeth: /* Theory */

2024-12-12T22:51:16Z

Theory

← Older revision		Revision as of 22:51, 12 December 2024
Line 9:		Line 9:
	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]].		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).

	APS715jot’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===		===Harmonics===

BudjarnLambeth: /* Theory */

2024-12-12T22:50:34Z

Theory

← Older revision		Revision as of 22:50, 12 December 2024
Line 11:		Line 11:
	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 [[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 [[42ed255/128]] and [[191zpi]].

	===Harmonics===		===Harmonics===

BudjarnLambeth: Created page with "{{Infobox ET|1ed13167/12952}} '''Arithmetic pitch sequence of 715jot''' ('''APS715jot'''), also known as '''1 equal division of 715jot''' ('''1ed715jot''') or '''715-jot equal..."

2024-12-12T22:39:09Z

Created page with "{{Infobox ET|1ed13167/12952}} '''Arithmetic pitch sequence of 715jot''' ('''APS715jot'''), also known as '''1 equal division of 715jot''' ('''1ed715jot''') or '''715-jot equal..."

New 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]].

Although it is not exactly 28.5 cents, it is close enough that it can reasonably be referred to as '''1 equal division of 28.5 cents''' ('''1ed28.5c'''). This title is used for ease of navigation and comparison with other [[arithmetic pitch sequence]]s on the wiki.

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

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).

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

===Harmonics===
APS720jot has less than 40% relative error on every single prime harmonic from 2 up to 19, making it a suitable full [[19-limit]] tuning.

No other stretched or compressed version of 42edo has that property.
{{harmonics in cet|28.5021426|intervals=prime|columns=10|title=Harmonics in APS715jot}}

42edo for comparison:
{{harmonics in equal|42|intervals=prime|columns=10|title=Harmonics in 42edo}}

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

==Scala file==
Tuning file for anything that supports [[Scala]]. Made with [[Scale Workshop]].
<pre>
! aps715jot.scl
! Created using Scale Workshop 3.0.1
!
! https://scaleworkshop.plainsound.org/scale/ecmf6OFjI
!
Arithmetic pitch sequence of 715jot
42
!
28.502143
57.004285
85.506428
114.008570
142.510713
171.012856
199.514998
228.017141
256.519283
285.021426
313.523569
342.025711
370.527854
399.029996
427.532139
456.034282
484.536424
513.038567
541.540709
570.042852
598.544995
627.047137
655.549280
684.051422
712.553565
741.055708
769.557850
798.059993
826.562135
855.064278
883.566421
912.068563
940.570706
969.072848
997.574991
1026.077134
1054.579276
1083.081419
1111.583561
1140.085704
1168.587847
1197.089989
</pre>

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

; [[MOS scale]]s
* Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3'''
* Eugene/Tritikleismic[15]: '''3 3 2 3 3 3 3 2 3 3 3 3 2 3 3'''
* Lemba[16]: '''3 2 3 2 3 3 2 3 3 2 3 2 3 3 2 3'''
* 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[14] 1st mode: '''1 5 1 5 1 5 1 5 1 5 1 5 1 5'''
* Seville/Sevond[14] 2nd mode: '''5 1 5 1 5 1 5 1 5 1 5 1 5 1'''
* Seville/Sevond[21]: '''1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4'''

; 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'''

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

== See also ==
* [[Gallery of arithmetic pitch sequences]]

[[Category:42-tone scales]]
[[Category:Tempered scales]]
[[Category:42edo]]
[[Category:Pages with Scala files]]