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:
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
Related tuning systems
Hybrid systems which attempt to combine tempered and just tuning, often tend to employ similar techniques to adaptive JI. Examples of such systems include:
- Barbershop music
- Neely-intonalism [idiosyncratic term ]
- Described in Intonalism