Acoustic phi: Difference between revisions
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| Name = acoustic phi | | Name = acoustic phi | ||
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[[ | ϕ taken as a [[frequency ratio]] (ϕ*''f'' where ''f'' = 1/1) is about 833.1 [[cent]]s. This [[metastable]] interval is sometimes called '''acoustic phi''', or the ''phi neutral sixth''. It is wider than a [[12edo]] minor sixth (800 cents) by about a sixth-tone (33.3... cents). | ||
ϕ is the most difficult interval to approximate by rational numbers, as {{w|Golden ratio #Continued fraction and square root|its continued fraction}} consists entirely of 1's. The [[wikipedia:Convergent (continued fraction)|convergents]] (rational number approximations, obtained from the continued fractions) are the ratios of successive terms of the Fibonacci sequence converge on ϕ, the just intonation intervals 3/2, [[5/3]] (~884.4¢), [[8/5]] (~814.7¢), [[13/8]] (~840.5¢), [[21/13]] (~830.3¢), … converge on ~833.1 cents. | |||
[[Erv Wilson]] accordingly described | [[Erv Wilson]] accordingly described ϕ as "the worstest of the worst — and yet somehow with divinity imbued, Lord have mercy!", inspiring the term [[merciful intonation]]. | ||
Acoustic phi is not to be confused with [[logarithmic phi]], which is 1941.6¢ (741.6¢ octave-reduced). | Acoustic phi is not to be confused with [[logarithmic phi]], which is 1941.6¢ (741.6¢ octave-reduced). | ||
== | == See also == | ||
* [[833 Cent Golden Scale (Bohlen)]] | * [[833 Cent Golden Scale (Bohlen)]] | ||
* [[Phi as a | * [[Phi as a generator]] | ||
* [[sqrtphi]], a temperament based on the square root of phi (~416.5 cents) as a generator. | * [[sqrtphi]], a temperament based on the square root of phi (~416.5 cents) as a generator. | ||
* [[Edφ]], tunings created by dividing acoustic phi into equally sized smaller steps | * [[Edφ]], tunings created by dividing acoustic phi into equally sized smaller steps | ||