AFS

An AFS, or arithmetic frequency sequence, is a kind of arithmetic and harmonotonic tuning.

Its full specification is (n-)AFSp: (n pitches of an) arithmetic frequency sequence adding by (irrtional) interval p. The only difference between an OS (overtone sequence) and AFS is that for OS the p is rational.

The n is optional. If not provided, the sequence is open-ended. By specifying n, your sequence will be equivalent to some EFD (equal frequency division).

The analogous utonal equivalent of an AFS is an ALS (arithmetic length sequence).

An AFS could also be described as a shifted overtone series (± frequency).

OS and AFS 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 the later section on the derivation of OS.

Examples

If we wanted to move by steps of φ, like this: [math]\displaystyle{ 1, 1+φ, 1+2φ, 1+3φ... }[/math] etc. we could have the AFSφ.

Here's another example:

example: (1/⁴√2)-shifted overtone series segment = 8-AFS(1/⁴√2)

quantity	(0)	1	2	3	4	5	6	7	8
frequency (f)	(1)	1.84	2.68	3.52	4.36	5.20	6.05	6.89	7.73
pitch (log₂f)	(0)	0.88	1.42	1.82	2.13	2.38	2.60	2.78	2.95
length (1/f)	(1)	0.54	0.37	0.28	0.23	0.19	0.17	0.15	0.13