Adaptive just intonation: Difference between revisions

'''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 ==

 

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.  

 

 

* Major Second: [[9/8|9:8]]

* Major Third: [[5/4|5:4]]

* Perfect Fourth: [[4/3|4:3]]

* Perfect Fifth: [[3/2|3:2]]

* Dominant Seventh: [[9/5|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 ==

* [http://www.math.tu-dresden.de/%7Emutabor/ Mutabor] Windows, Linux and Mac OS X. Uses its own programming language to describe pitches, (re)tunings and reactions to events.

* [http://www.TallKite.com/alt-tuner.html alt-tuner] PCs, macs and Linux/Wine. DAW plug-in (requires [http://reaper.fm/ REAPER]) that retunes almost every midi keyboard or softsynth.

* [http://www.nonoctave.com/tuning/LilMissScaleOven/features.html L'il Miss' Scale Oven] OS X application. Has a proprietary dynamic retuning system called ''Nuscale.''

* [http://tonesintune.com/ TonesInTune] Add-in to Microsoft Excel (x32 & composition only). Re-introduces dynamic intonation, a key feature of most acoustic music instruments.

* [http://www.hermode.com/index_en.html Hermode tuning] Algorithm/feature embedded in 3rd party applications. Tunes only the fifths and thirds of electronic instruments dynamically in real time.

* [https://www.dmitrivolkov.com/projects/pivotuner/ Pivotuner] VST3/AU plugin for macOS/Windows. Uses fixed just intervals to a dynamically-changing root.

 

== Music ==

* [http://www.seraph.it/XenoTunes2.html ''Piano11''] by [[Carlo Serafini]]

* [http://www.seraph.it/dep/det/CarlosGlass1.mp3 ''Carlos Glass 1''] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/6188507c0c6f464ef6c23330eb9153e9-16.html blog entry])

* [http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/localanomaly.html ''Local Anomaly''] by [[William Sethares]]

* [http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/three_ears.html ''Three Ears''] by William Sethares

* ''Microtonal Composition in "Fluid Just Intonation"'' by [[Rosie Sheldon]] (2021)

** [https://www.youtube.com/watch?v=IKjNIBEGtVc listen on YouTube]

** [https://rosiesheldon.bandcamp.com/track/microtonal-composition-in-fluid-just-intonation listen on Bandcamp]

* [https://youtu.be/idUG-x8kT3o ''Gesualdo's Dolcissima mia vita in three comparative tunings after translation to english''] (0:00 to 5:05) — rendered by [[Chris Vaisvil]], 2025

* [https://youtu.be/Vl-hpAL9Ouc ''Xenexhibition (for solo keyboard)''] by [[Dmitri Volkov]]

 

This is a list of specific subtypes of adaptive just intonation.

 

This list is by nature always incomplete as there are so many possible approaches. Feel free to add to it:

 

 

 

 

* [http://www.tonalsoft.com/enc/a/adaptive-ji.aspx Definition of Adaptive JI (Tonalsoft encyclopedia)]