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Gallery of arithmetic pitch sequences: Difference between revisions

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This gallery can never realistically be complete as there are so many possible such scales, so feel free to add to it.
This gallery can never realistically be complete as there are so many possible such scales, so feel free to add to it.


For a shorter, more strictly curated list of only the most widely used or most mathematically important APS scales, see [[APS#List of APSs]].
For a shorter, more strictly curated list of only the most widely used or most mathematically important APS scales, see [[Equal-step tuning#List of notable APS]].


==Terms==
==Terms==
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** [[Edo]], [[Edt]], [[Ed4]], [[Ed13]]
** [[Edo]], [[Edt]], [[Ed4]], [[Ed13]]


==APS of [[cent]]s==
==APS of cents==
''See also: [[cent]].''
 


; 1ed1c
; 1ed1c


Trivial case. This is exactly [[1200edo]].
Trivial case. This is exactly [[1200edo]].
; 1ed13.94—13.97c
Main page: [[8ed16/15|Delta scale]]




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Main page: [[1ed44c]]
Main page: [[1ed44c]]
; 1ed63.59—63.82c
Main page: [[Phoenix]]




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Main page: [[1ed125c]]
Main page: [[1ed125c]]
; 1ed148.5c
Main page: [[1ed148.5c]]




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Main page: [[1ed237.8c]]
Main page: [[1ed237.8c]]


==APS of [[farab]]s==
==APS of farabs==
''See also: [[farab]].''
 


; APS1farab
; APS1farab
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**Slightly worse 2/1
**Slightly worse 2/1


==APS of [[311edo|gene]]s==
==APS of genes==
''See also: [[311edo|gene]].''
 


;APS1gene
;APS1gene
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**Much worse 11/1, 13/1, 17/1
**Much worse 11/1, 13/1, 17/1


==APS of [[hekt]]s==
==APS of hekts==
''See also: [[hekt]].''
 


; APS1hekt
; APS1hekt
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**Much worse 19/1
**Much worse 19/1


==APS of [[jot]]s==
==APS of jots==
''See also: [[jot]].''
 


; APS1jot
; APS1jot
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**Much worse 7/1
**Much worse 7/1


==APS of [[méride]]s==
==APS of mérides==
''See also: [[méride]].''




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; APS0.9méride
; APS11/12méride
*Step size: 0.9 mérides (~25.12 cents)
*Step size: 11/12 of a méride (~25.58 cents)
*Close to: [[47edo]]
*Compared to 47edo:
**Much better: 3/1, 11/1, 23/1
**Slightly better 5/1, 19/1
**Slightly worse 2/1, 7/1, 13/1, 17/1
**Much worse 13/1
 
 
; APS9/10méride
*Step size: 9/10 of a méride (~25.12 cents)
*Close to: [[48edo]]
*Close to: [[48edo]]
*Compared to 48edo:
*Compared to 48edo:
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; APS0.8méride
; APS7/8méride
*Step size: 0.8 mérides (~22.33 cents)
*Step size: 7/8 of a méride (~24.42 cents)
*Close to: [[49edo]]
*Compared to 49edo:
**Much better 3/1, 7/1, 11/1, 13/1, 11/1
**Slightly better 5/1, 23/1
**Slightly worse 2/1, 19/1
 
 
; APS5/6méride
*Step size: 5/6 of a méride (~23.26 cents)
*Close to: [[52edo]]
*Compared to 52edo:
**Better 3/1, 13/1, 17/1
**Slightly better 5/1
**Slightly worse 7/1, 19/1, 23/1
**Worse 2/1, 11/1
 
 
; APS4/5méride
*Step size: 4/5 of a méride (~22.33 cents)
*Close to: [[54edo]]
*Close to: [[54edo]]
*Compared to 54edo:
*Compared to 54edo:
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**Slightly worse 2/1
**Slightly worse 2/1


==APS of [[tina]]s==
 
; APS8/11méride
*Step size: 8/11 of a méride (~20.30 cents)
*Close to: [[59edo]]
*Compared to 59edo:
**Much better 3/1, 7/1, 19/1
**Slightly better 13/1
**Slightly worse 2/1, 5/1, 17/1
**Much worse 11/1, 23/1
 
 
; APS2/3méride
*Step size: 2/3 of a méride (~18.60 cents)
*Close to: [[103edt]], [[130ed4]], [[181ed7]]
*Special properties: pretty much exactly 50% relative error (but less than 10c absolute) on 2/1, and low relative error on everything else, making it a great [[dual-n|dual-2]] tuning.
*Comparison:
**Step size (biggest to smallest): 181ed7, APS2/3méride, 130ed4, 103edt
**Dual harmonics
***APS2/3méride & 130ed4 have slightly better ''dual''-2 than the others
**Non-dual harmonics
***181ed7 is slightly better than the others at 7/1, 11/1
***APS2/3méride is slightly better than the others at 7/1, 13/1, 17/1, 19/1
***130ed4 is slightly better than the others at 3/1, 5/1, 17/1, 23/1
***103edt is slightly better than the others at 3/1, 5/1, 23/1
 
 
; APS7/11méride
*Step size: 7/11 of a méride (~17.76 cents)
*Close to: [[107edt]], [[135ed4]], [[157ed5]]
*Special properties: almost 50% relative error (but less than 10c absolute) on 2/1, and low relative error on everything else, making it a great [[dual-n|dual-2]] tuning.
*Comparison:
**Step size (biggest to smallest): 135ed4, 107edt, APS7/11méride, 175ed5
**Dual-2
***Excellent: 135ed4, 107edt
***Good: APS7/11méride
***Weak: 175ed5
**Non-dual harmonics
***135ed4 is slightly better than the others at 3/1, 17/1
***107edt is slightly better than the others at 3/1, 17/1
***APS7/11méride is slightly better than the others at 3/1, 5/1, 7/1, 11/1, 13/1, 19/1
***175ed5 is slightly better than the others at 5/1, 7/1, 11/1, 23/1
 
 
; APS5/8méride
*Step size: 5/8 of a méride (~17.44 cents)
*Close to: [[69edo]]
*Compared to 69edo:
**5/1 is about the same
**Slightly better 3/1, 7/1, 11/1
**Slightly worse 2/1, 13/1, 17/1, 19/1, 23/1
 
 
; APS7/12méride
*Step size: 7/12 of a méride (~16.28 cents)
*Close to: [[74edo]]
*Compared to 74edo:
**11/1 is about the same
**Better 3/1, 5/1, 7/1, 17/1, 19/1
**Worse 2/1, 13/1, 23/1
 
 
; APS6/11méride
*Step size: 6/11 of a méride (~15.22 cents)
*Close to: [[79edo]]
*Compared to 79edo:
**Better 3/1, 5/1, 11/1, 13/1, 19/1
**Worse 2/1, 7/1, 17/1, 23/1
 
==APS of tinas==
''See also: [[tina]].''
 


;APS1tina
;APS1tina
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==Non-integer equal divisions==
==Non-integer equal divisions==
''See also: [[EDO#Non-integer EDO]].''


;Pi-edo
;Pi-edo
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{{navbox scale gallery}}
{{navbox scale gallery}}


[[Category:Equal-step tunings]] [[Category:Lists of scales]]
[[Category:Equal-step tuning]] [[Category:Lists of scales]]
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