128afdo

The 8^th 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 8^th 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 8^th 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¢).

Reading

Johnny Reinhard's original paper.

128 NOTES PER OCTAVE ON THE SAXOPHONE: HOW I DID IT AND WHY!: Saxophonist Philipp Gerschlauer on how he went about devising a 128-note per octave fingering chart

Johnny Reinhard - 8th Octave Overtone Tuning and Bassoon Fingerings in 128

See also

The tuning for Nursery Tunes for Demented Children by Kyle Gann is a subset of 8th Octave Overtone Tuning.

Scores

Juhani Nuorvala - Toivo 128

Listening

Georg Friedrich Haas - FOR JOHNNY REINHARD for bassoon in 128

Juhani Nuorvala - Toivo 128 for bassoon and pre-recording

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)

Johnny Reinhard - True

128 notes per octave on Alto Saxophone - Philipp Gerschlauer

Composers John Eaton, Rovner, Thoegersen, Golden, and others have also worked with 8^th Octave Overtone Tuning.