8th Octave Overtone Tuning
The 8th Octave Overtone Tuning, sometimes known as 128 Tuning, is a tuning developed by Johnny Reinhard.
It consists of harmonics of the harmonic series, numbers 128 (28, hence 8th octave) through 255.
Scales can be selected as subsets of these 128 pitches, or the entire set can be used.
A key benefit of using pitches exclusively from the same harmonic series is that they share a fundamental. By using the 8th octave of a harmonic series, said fundamental will almost certainly be infrasonic, but it will still have a psychoacoustic presence.
An illustratively surprising result of this higher harmonic tuning is that, since a just 4/3 does not have a power of 2 in the denominator and thus does not exist in the (octave-reduced) harmonic series, it will not be used in this tuning. Instead, when the inverse of the 3/2 ratio is needed, one may use 43/32 (511.517706¢) or 171/128 (501.423018¢).
Well Tuned Piano (actually up to the 11th octave harmonics, but same idea)
Symphony #3 “Gloria” (actually only the 7th octave harmonics, but the same idea)
Composers John Eaton, Rovner, Thoegersen, Golden, and others have also worked with 8th Octave Overtone Tuning.