Voice leading tool

Based on and inspired by Dmitri Tymozcko's "A Geometry of Music"

See below for the description of the tool the instructions.

IMPORTANT: Make sure that the target chord has the same amount of tones.If the target chord is of the same type as the initial chord this can be left empty.

Instructions

To function this tool requires three parameters. A scale size (often the size of an EDO), the initial chord (in degrees) and the target chord (in degrees). The chords should be both have the same amount of notes, otherwise the results will not be correct.

Note that the target chord's root degree is actually unimportant, as the algorithm will return the closest progression for that chord type sorted by the voice leading balance.

To build a chord progression simply choose a chord from the results and feed it back as the initial chord in the calculator.

To try out your chord progressions you can use Xenpaper, which uses the same chord syntax as the target chords produced by this calculator.

Purpose and theory

The followig algorithm will provide the 15 closest target chords to any chord. The closeness of one chord to another is judged by the sum of the movements of each individual voice (positive if the voice moves to a higher pitch, and negative if it moves to a lower pitch). According to Tymozcko balanced chord progressions, where the voice movement is near 0 leads to smooth voice leading, which is often a desired characteristic in common practice music styles (obviously this is a matter of taste).

For Tymozcko, a particular type of chord progression that is of interest is one where a chord leads to another chord of the same type. To facilitate finding such progressions one can leave the "target chord" field empty. Another chord progression of interest according to Tymozcko would be one where the intervals of a target chord are a permutation of the initial chord (i.e. in 12EDO a major chord (4 3 5) leading to a minor chord (3 4 5)). So the user of this tool may find it interesting to try out such chords.

Lastly for Tymozcko the best progressions for a given EDO usually revolve around chords whose intervals are almost an equal division of such EDO. So for example, in 12EDO (4 4 4) divides the scale in three equal parts, thus chords like (4 3 5) and (3 4 5) which are near the symmetrical division will work very well at producing balanced voice leading. This of course poses a problem of what to do with prime EDOs, and as Tymozcko only deals with 12EDO, then the question remains open. Regardless of this, the tool will provide the most balanced options for any give chord pair.