Acoustic phi

Phi taken as a musical ratio (ϕ*f where f=1/1) is about 833.1 cents. This is sometimes called acoustical phi, or the phi neutral sixth.

As the ratios of successive terms of the Fibonacci sequence converge on phi, the just intonation intervals 3/2, 5/3, 8/5, 13/8, 21/13, ... converge on ~833.1 cents.

Additional reading

• 833 Cent Golden Scale (Bohlen)
• The Noble Mediant: Complex ratios and metastable musical intervals, by Margo Schulter and David Keenan
• Phi as a Generator
• sqrtphi, a temperament based on the square root of phi (~416.5 cents) as a generator