User:Cmloegcmluin/APS: Difference between revisions
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An '''APS''', or '''arithmetic pitch sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning. | An '''APS''', or '''arithmetic pitch sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning. | ||
(n-)APSp: (n pitches of an) arithmetic pitch sequence adding by p | Its full specification is (n-)APSp: (n pitches of an) arithmetic pitch sequence adding by irrational interval p. It is equivalent to a [[Tour_of_Regular_Temperaments#Equal_temperaments_.28Rank-1_temperaments.29|rank-1 temperament]] with generator p. It is also equivalent to an [[Equal-step_tuning#Equal_multiplications|equal multiplication]] of p. | ||
The only difference between an APS and an [[AS|AS (ambitonal sequence)]] is that the p for an APS is irrational. | |||
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Revision as of 22:51, 22 March 2021
An APS, or arithmetic pitch sequence, is a kind of arithmetic and monotonic tuning.
Its full specification is (n-)APSp: (n pitches of an) arithmetic pitch sequence adding by irrational interval p. It is equivalent to a rank-1 temperament with generator p. It is also equivalent to an equal multiplication of p.
The only difference between an APS and an AS (ambitonal sequence) is that the p for an APS is irrational.
| quantity | (0) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| frequency (f) | (1) | 1.19 | 1.41 | 1.68 | 2 |
| pitch (log₂f) | (2⁰⸍⁴) | 2¹⸍⁴ | 2²⸍⁴ | 2³⸍⁴ | 2⁴⸍⁴ |
| length (1/f) | (1) | 0.84 | 0.71 | 0.59 | 0.5 |