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.

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