128afdo

← 127afdo

128afdo

129afdo →

Prime factorization	27
Fifth	192/128 (701.955c)

128afdo (arithmetic frequency division of the octave), or 128odo (otonal division of the octave), divides the octave into 128 parts of 1/128 each. It is a superset of 127afdo and a subset of 129afdo. As a scale it may be known as mode 128 of the harmonic series or the Over-128 scale.

The 8^th Octave Overtone Tuning, sometimes known as 128 Tuning, is a tuning developed by Johnny Reinhard. It is equivalent to 128afdo, except that it has a fixed root and cannot be rotated. It consists of harmonics of the harmonic series, numbers 128 (2⁷, hence 8^th octave) through 255. It is an Over-1 scale, specifically mode 128 of the harmonic series. 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¢).

Due to having only one prime factor (2), yet also being a higher octave of a prime mode (mode 2), it is a very strong tuning for primodality, providing a large gamut of intervals without compromising their clear prime identity.

Music

Georg Friedrich Haas

• For Johnny Reinhard (2015)

La Monte Young

• The Well-Tuned Piano (1964) – actually up to the 11^th octave harmonics, but the same idea

Johnny Reinhard

• True (2014)

Glenn Branca

• Symphony #3 "Gloria" (1983) – actually only the 7^th octave harmonics, but the same idea

Philipp Gerschlauer

• 128 notes per octave on Alto Saxophone (2015)

Juhani Nuorvala

• Toivo 128 (2017) recording score

Composers John Eaton, Anton Rovner, Peter Alexander Thoegersen, Monroe Golden, and others have also worked with 8^th Octave Overtone Tuning.^{[citation needed]}

External links

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