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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]]




Line 81: Line 98:
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 genes==
''See also: [[311edo|gene]].''


; APS13farab
*Step size: 13 farabs (~108.33 cents)
*Close to: [[11edo]]
*Special properties: no-3s
*Compared to 11edo:
**7/1 is about the same
**Much better 5/1, 13/1, 19/1, 23/1, 29/1, 31/1
**Slightly worse 2/1
**Much worse 11/1, 17/1
==APS of [[311edo|gene]]s==


;APS1gene
;APS1gene
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*Compared to 197edt:
*Compared to 197edt:
**197edt is not dual-2, so APS2.5gene completely restructures the tuning
**197edt is not dual-2, so APS2.5gene completely restructures the tuning
;APS6gene
*Step size: 6 genes (~23.15 cents)
*Close to: [[52edo]]
*Compared to 52edo:
**Much better 3/1, 17/1
**Slightly better 13/1
**Slightly worse 2/1, 5/1, 11/1
**Much worse 7/1
;APS8gene
*Step size: 8 genes (~30.87 cents)
*Close to: [[39edo]]
*Compared to 39edo:
**Much better 5/1, 7/1, 17/1, 19/1, 23/1, 29/1
**Slightly better 13/1
**Slightly worse 2/1
**Much worse 3/1, 11/1




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**Slightly worse 3/1, 17/1
**Slightly worse 3/1, 17/1
**Much worse 11/1, 23/1
**Much worse 11/1, 23/1
;APS11gene
*Step size: 11 genes (~42.44 cents)
*Close to: [[28edo]]
*Compared to 28edo:
**7/1, 13/1, 17/1 are about the same
**Much better 3/1, 23/1, 31/1
**Slightly worse 11/1, 19/1
**Much worse 2/1, 5/1, 29/1




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


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


;APS16gene
*Step size: 16 genes (~61.74 cents)
*Close to: [[31edt]]
*Special properties: no-2s
*Compared to 31edt:
**Much better 5/1, 13/1
**Slightly better 11/1
**Much worse 3/1, 7/1
;APS19gene
*Step size: 19 genes (~73.31 cents)
*Close to: [[26edt]]
*Special properties: no-2s
*Compared to 26edt:
**Much better 23/1, 31/1
**Slightly better 5/1, 7/1
**Slightly worse 3/1, 11/1, 13/1, 17/1, 19/1, 29/1
==APS of [[hekt]]s==


; APS1hekt
; APS1hekt
*Step size: 1 hekt (~1.46304 cents)
*Step size: 1 hekt (~1.46304 cents)
*Trivial case. This is exactly [[1300edt]].
*Trivial case. This is exactly [[1300edt]].
; APS(pi)hekt
*Step size: ~3.14159 hekts (~4.59628 cents)
*Close to: [[261edo]]
*Compared to 261edo:
**2/1, 17/1 are about the same
**Slightly better 3/1, 7/1, 13/1, 19/1, 23/1
**Slightly worse 5/1, 11/1, 29/1, 31/1




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**Slightly worse 2/1, 11/1, 19/1
**Slightly worse 2/1, 11/1, 19/1
**Much worse 13/1
**Much worse 13/1
; APS11hekt
*Step size: 11 hekts (~16.09 cents)
*Close to: [[118edt]]
*Special properties: dual-2s
*Compared to 118edt:
**5/1, 19/1 are about the same
**Much better 11/1, 13/1, 17/1
**Slightly worse 3/1
**Much worse 7/1




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**Slightly better 7/1, 19/1
**Slightly better 7/1, 19/1
**Slightly worse 2/1, 3/1, 13/1
**Slightly worse 2/1, 3/1, 13/1
; APS17hekt
*Step size: 17 hekts (~24.87 cents)
*Close to: [[48edo]]
*Special properties: dual-3
*Compared to 48edo:
**11/1, 13/1, 17/1, 19/1 are about the same
**Much better 5/1
**Much worse 3/1, 7/1




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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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; APS720jot
; APS715jot
 
Main page: [[1ed28.5c|APS715jot]]


Main page: [[1ed28.7c|APS700jot]]


; APS720jot


;APS777jot
Main page: [[1ed28.7c|APS720jot]]
*Step size: 777 jot (~30.97 cents)
*Close to: [[39edo]]
*Compared to 39edo:
**Much better 5/1, 7/1
**Slightly better 11/1
**Slightly worse 2/1, 13/1
**Much worse 3/1




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*Close to: [[38edo]]
*Close to: [[38edo]]
*Compared to 38edo: Mostly slightly worse than 38edo, but a much better 11/1 than 38edo
*Compared to 38edo: Mostly slightly worse than 38edo, but a much better 11/1 than 38edo
;APS999jot
*Step size: 999 jot (~39.82 cents)
*Close to: [[30edo]]
*Compared to 30edo:
**Much better 3/1, 5/1, 17/1
**Slightly worse 2/1
**Much worse 7/1, 13/1




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**Much worse 7/1
**Much worse 7/1


 
==APS of mérides==
; APS2500jot
''See also: [[méride]].''
*Step size: 2500 jots (~99.66 cents)
*Close to: [[12edo]]
*Compared to 12edo:
**Much better 5/1, 7/1, 11/1
**Much worse 3/1, 17/1, 19/1
 
==APS of [[méride]]s==
 
; APS4méride
*Step size: 4 méride (~111.63 cents)
*Close to: [[17edt]]
*Special properties: no-2s
*Compared to 17edt:
**3/1 is about the same
**Much better 5/1, 13/1, 17/1
**Much worse 7/1, 11/1
 
 
; APS2méride
*Step size: 2 méride (~55.81 cents)
*Close to: [[34edt]]
*Compared to 34edt:
**3/1, 13/1 are about the same
**Much better 5/1, 17/1
**Much worse 7/1, 11/1




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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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; APS0.75méride
; APS8/11méride
*Step size: 0.75 mérides (~20.93 cents)
*Step size: 8/11 of a méride (~20.30 cents)
*Close to: [[57edo]]
*Close to: [[59edo]]
*Compared to 57edo:
*Compared to 59edo:
**7/1 is about the same
**Much better 3/1, 7/1, 19/1
**Much better 3/1, 5/1
**Slightly better 13/1
**Slightly worse 11/1, 13/1
**Slightly worse 2/1, 5/1, 17/1
**Much worse 2/1, 17/1, 19/1
**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


; APS0.3méride
==APS of tinas==
*Step size: 0.3 mérides (~8.37 cents)
''See also: [[tina]].''
*Close to: [[143edo]]
*Compared to 143edo:
**7/1 is about the same
**Much better 17/1, 19/1
**Slightly better 3/1, 11/1
**Slightly worse 2/1, 5/1, 13/1


==APS of [[tina]]s==


;APS1tina
;APS1tina
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**Slightly better 3/1, 5/1, 7/1, 11/1, 13/1, 17/1, 29/1
**Slightly better 3/1, 5/1, 7/1, 11/1, 13/1, 17/1, 29/1
**Slightly worse 2/1, 19/1, 23/1, 31/1
**Slightly worse 2/1, 19/1, 23/1, 31/1
;APS123tina
*Step size: 123 tina (~17.29 cents)
*Close to: [[110edt]]
*Special properties: dual-2s
*Compared to 110edt:
**Slightly better 7/1, 13/1, 17/1, 19/1, 23/1, 31/1
**Slightly worse 3/1, 5/1, 11/1, 29/1
;APS250tina
*Step size: 250 tina (~35.13 cents)
*Close to: [[34edo]]
*Compared to 34edo:
**3/1 is about the same
**Much better 7/1, 11/1, 19/1, 29/1, 31/1
**Slightly worse 2/1
**Much worse 5/1, 13/1, 17/1, 23/1
;APS300tina
*Step size: 300 tina (~42.16 cents)
*Close to: [[45edt]]
*Special properties: no-2s
*Compared to 45edt:
**5/1 is about the same
**Much better 7/1, 19/1, 23/1, 31/1
**Slightly worse 3/1
**Much worse 11/1, 13/1, 17/1
;APS400tina
*Step size: 400 tina (~56.21 cents)
*Close to: [[34edt]]
*Special properties: no-2s
*Compared to 34edt:
**Much better 7/1, 11/1, 13/1
**Slightly better 17/1, 31/1
**Slightly worse 29/1
**Much worse 3/1, 5/1, 19/1, 23/1




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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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