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 [[ | 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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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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; | ; APS11/12méride | ||
*Step size: | *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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; | ; APS7/8méride | ||
*Step size: | *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 better 11/1, 23/1 | **Slightly better 11/1, 23/1 | ||
**Slightly worse 2/1 | **Slightly worse 2/1 | ||
; 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== | ==APS of tinas== | ||
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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 | [[Category:Equal-step tuning]] [[Category:Lists of scales]] | ||