Adaptive just intonation

Adaptive just intonation (adaptive JI) is an approach to just intonation that employs predefined musical intervals as frequency ratios over a floating tonal center that is defined by the most recent context.

Description

In an adaptive JI context, any given moment during a piece of music has a reference pitch to which the rest of the music is compared.

For example, take a song in the key of A major with a basic cadence of I - IV - V7 - I. Traditionally, the chords would be A - D - E7 - A, spelled A C# E, D F# A, E G# B D, and then again A C# E. Although the key of the cadence is always A, the reference pitch for each chord in the cadence is different.

If we further define JI intervals in this example as:

• Major Second: 9:8
• Major Third: 5:4
• Perfect Fourth: 4:3
• Perfect Fifth: 3:2
• Dominant Seventh: 9:5

Then the D in the IV chord is 4:3 with respect to A, which was the tonic of the chord immediately proceeding it. The E in the E7 chord is the same whether defined relative to the proceeding D chord (9:8 relative to D) or referencing back to the original tonal center of A (because 3:2 is the same as 9:8 of 4:3), but the D in the E7 chord is 9:5 relative to the E (9:5 of 3:2 is 27:20 compared to the original A), which is different than the D in the proceeding D major chord (which was 4:3 compared to the original A).

Software

• Mutabor Windows, Linux and Mac OS X. Uses its own programming language to describe pitches, (re)tunings and reactions to events.
• alt-tuner PCs, macs and Linux/Wine. DAW plug-in (requires REAPER) that retunes almost every midi keyboard or softsynth.
• L'il Miss' Scale Oven OS X application. Has a proprietary dynamic retuning system called Nuscale.
• TonesInTune Add-in to Microsoft Excel (x32 & composition only). Re-introduces dynamic intonation, a key feature of most acoustic music instruments.
• Hermode tuning Algorithm/feature embedded in 3rd party applications. Tunes only the fifths and thirds of electronic instruments dynamically in real time.
• Pivotuner VST3/AU plugin for macOS/Windows. Uses fixed just intervals to a dynamically-changing root.

Music

• Local Anomaly by William Sethares
• Three Ears by William Sethares
• Piano11 by Carlo Serafini
• Carlos Glass 1 by Carlo Serafini (blog entry)
• Xenexhibition (for solo keyboard) by Dmitri Volkov

External links

• Definition of Adaptive JI (Tonalsoft encyclopedia)