In music the axis system, proposed by Ernő Lendvai (1971, p.1-16) in his analysis of the use of tonality in the music of Béla Bartók, is an assignment of harmonic function to all twelve pitch classes in relation to an assigned tonic, determined by that pitch classes interval from the tonic. The three functions used are tonic, subdominant, and dominant, and each contains four notes (forming three diminished seventh chords). Each group is then divided into principal and secondary groups a tritone apart. Thus there are six pairs of notes in three categories. If the tonic is C, then the functions are as follows:
| Tonic | Subdominant | Dominant | |||
|---|---|---|---|---|---|
| Primary | Secondary | Primary | Secondary | Primary | Secondary |
| C, A | F♯, D♯ | F, D | B, G♯ | G, E | C♯, A♯ |
Functions are assigned based on position within the circle of fifths, starting with F as subdominant: F (s), C (t), G (d), D (s), etc. The system is critiqued by Paul Wilson (1992, p.203-208).
Possible Analyses and Use of the Axis System
It may be noted that each of the above notes forms a descending diminished chord. In the case of I or C, C A F♯ D♯, or an E♭ fully diminished chord. This connects the axis system not only with diminished chords, which often form the basis for the movement in a piece based on the axis system, but also links the axis system with the diminished scales formed on bIII of each of the principal tones: root, subdominant, and dominant. The axis system is probably used more in analysis, and less in composition. Uses of the system have a characteristic sound, but that sound can also be found in uses of tritone Dominant Substitutions, and Deceptive Cadences using the ♭VII dominant chord. It is possible that people have used this system to compose, but the older systems of harmonic theory segue very easily into it, and it might be noted that while Bartók is an extremely mathematical composer, many composers are not. However, the connection between math and western art music is large.
The Axis System and Jazz
Brazilian music, especially the music of Antonio Carlos Jobim, uses harmonies that are easily analyzed by the axis system and not easily analyzed in other ways. A great example is the bridge of The Girl from Ipanema, which uses a series of ♭III dominant and ♭VII dominant chords that looks like a real mess according to normal jazz analysis. It's a great study for budding jazz musicians, because the melodies for the chorus and the bridge are simple, but the harmonies are quite complex.
Source
- Wilson, Paul (1992). The Music of Béla Bartók. ISBN 0-300-05111-5.
- Lendvai, Ernő (1971). Béla Bartók: An Analysis of His Music. London: Kahn and Averill.
