Its full specification is (n-)AFSp: (n pitches of an) arithmetic frequency sequence adding by (irrtional) interval p. The n is optional. If not provided, the sequence is open-ended.
The formula for step [math]k[/math] of an AFSp is:
[math] f(k) = 1 + k⋅p [/math]
Relationship to other tunings
The only difference between an OS (overtone sequence) and AFS is that for OS the p is rational.
As shifted overtone series
An AFS could also be described as a shifted overtone series (± frequency). Both AFS and OS are equivalent to taking an overtone series and adding (or subtracting) a constant amount of frequency. By doing this, the step sizes remain equal in frequency, but their relationship in pitch changes. For a detailed explanation of this, see derivation of OS.
By specifying n, your sequence will be equivalent to some EFD (equal frequency division). Specifically, n-EFDp = n-AFS((p-1)/n).
The analogous utonal equivalent of an AFS is an ALS (arithmetic length sequence).
If we wanted to move by steps of φ, like this: [math]1, 1+φ, 1+2φ, 1+3φ...[/math] etc. we could have the AFSφ.
Here's another example:
|frequency (f)||(1 + 0/⁴√2)||1 + 1/⁴√2||1 + 2/⁴√2||1 + 3/⁴√2||1 + 4/⁴√2||1 + 5/⁴√2||1 + 6/⁴√2||1 + 7/⁴√2||1 + 8/⁴√2|