Master Tuning

The master tuning of the Tonal Plexus was determined by way of thorough research in music theory, music notation, and pitch perception. The result is a system which allows the free exploration of all possible pitch combinations in a coherent way, according to reasonable limits of human perception.

NOTE: The videos on this page are quite old now, and the keyboard shown in them is a prototype. Videos of the currently shipping keyboard can be seen here and also on the blog. Close-up images of shipping keyboards can be seen here.

Octaves, Fifths & Diatonic Scales

Octaves and fifths define the basis of Western music theory and notation. Hence, these intervals form the basis of the master tuning. Octaves are tuned purely, and fifths are tuned virtually purely, with a deviation of less than half of one cent. These two intervals provide a reference for pitch ordering and naming relative to which all other intervals are defined.

Diatonic scales tuned in fifths serve as the basis for melody and harmony in Western music. These scales are easily played using the master tuning.

Commas & JNDs

The master tuning is designed around the comma as a basic interval. The comma used is just under 30 cents in size, forming the basis of a key layout in which one octave contains 41 commas.

To maximize pitch control and expressivity, each comma is broken into 5 JNDs, so that the smallest steps on the keyboard are just under 6 cents in size.

Each octave contains 205 JNDs. Using JND fine tuning, any interval can be played with a maximum tuning deviation of less than 3 cents. Though under certain conditions we are able to hear such small mistunings, in practice the errors are so small that they are not noticable; other natural variables such as timbre and duration introduce similar small margins of error. The master tuning is thus able to produce all pitches and intervals in a managable way.

Scale of 205 JNDs played on the Tonal Plexus:

Just Intonation

Just intonation of any interval is easily achieved on the Tonal Plexus through the use of comma shifting and JND fine tuning; for example, a harmonic series.

Extended harmonies such as 13th chords can easily be played in Just intonation.

J.S. Bach's Aria from the Goldberg Variations opening played in Just Intonation.

Pachelbel's Canon in D opening played in fifths tuning and Just Intonation.

Passage in C Major Just Intonation:

Equal Temperaments

The master tuning is itself an equal temperament: 205ET. ETs with smaller numbers of pitches can be found within the master tuning. For example, virtually exact 12ET is found in a line straight across the middle of the keyboard.

Other ETs are possible, such as 5ET, 7ET, 19ET, etc.