AFS: Difference between revisions
Cmloegcmluin (talk | contribs) →Relationship to other tunings: fix section capitalization |
Cmloegcmluin (talk | contribs) →Examples: update row headers per agreement at https://en.xen.wiki/w/Talk:APS |
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== Specification == | == Specification == | ||
Its full specification is (n-)AFSp: (n pitches of an) arithmetic frequency sequence adding by ( | Its full specification is (n-)AFSp: (n pitches of an) arithmetic frequency sequence adding by (irrational) interval p. The n is optional. If not provided, the sequence is open-ended. | ||
== Formula == | == Formula == | ||
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=== Vs. OS === | === Vs. OS === | ||
The only difference between an [[OS|OS (overtone sequence)]] and AFS is that for OS the p | The only difference between an [[OS|OS (overtone sequence)]] and AFS is that for OS the p must be rational. | ||
=== As shifted overtone series === | === As shifted overtone series === | ||
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=== Vs. EFD === | === Vs. EFD === | ||
By specifying n, your sequence will be equivalent to some [[EFD|EFD (equal frequency division)]]. Specifically, n-EFDp = n-AFS((p-1)/n). | By specifying n, your sequence will be equivalent to one period of some [[EFD|EFD (equal frequency division)]]. Specifically, n-EFDp = n-AFS((p-1)/n). | ||
=== Vs. ALS === | === Vs. ALS === | ||
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!8 | !8 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(1 + 0/⁴√2) | |(1 + 0/⁴√2) | ||
|1 + 1/⁴√2 | |1 + 1/⁴√2 | ||
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|1 + 8/⁴√2 | |1 + 8/⁴√2 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
| (0) || 0.88 | | (0) || 0.88 | ||
|1.42 | |1.42 | ||
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|2.95 | |2.95 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
| (1) || 0.54 | | (1) || 0.54 | ||
|0.37 | |0.37 | ||
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[[Category:Harmonic]] | [[Category:Harmonic]] | ||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||
[[Category:Xenharmonic series]] | |||