Adaptive just intonation: Difference between revisions

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== Definition ==

Adaptive Just Intonation is an approach to tuning that employs predefined musical intervals as frequency ratios over a floating tonal center that is defined by the most recent context.

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

== 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==

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+== Definition ==
+Adaptive Just Intonation is an approach to tuning that employs predefined musical intervals as frequency ratios over a floating tonal center that is defined by the most recent context.
 [http://www.tonalsoft.com/enc/a/adaptive-ji.aspx Definition of Adaptive JI (Tonalsoft encyclopedia)]
+== 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==