Tonality, Centricity, and Atonality

New Kinds of Music in the Early Twentieth Century

In the early 20th-century some western art music opened up new paths and departed from those of tonal music, the kind of music we have been studying up to this point. Music could be tonal, but it could also be centric or atonal.

 

             Tonal music             Centric music          Atonal Music

         Tonic pc                     pc center                    focal pc

 

Tonal Music: A Clear and Multi-Layered Hierarchy

In tonal music there is one tonic pitch class (pc) to which all the other pcs are subordinate.   The tonic pc and the triad of which it is the root serve as a starting point and an end point, a “home” from which the music departs and to which it returns. At points of ultimate closure and resolution, as in a perfect authentic cadence, the music arrives on the tonic pc as the bass note, the melody note, and the root of the chord.

Hierarchy manifests in two main ways: Notes either (a) belong to another note or (b) resolve to another note. Let’s see how notes can “belong” to and “resolve” to other notes.

 

Kinds of Hierarchy: Belonging and Resolution

Belonging

Chord members belong to a root and are subordinate to it. This is one kind of hierarchy.

Beethoven’s song, Ich Liebe dich, has G as tonic, and notes within the G major triad belong to it. The opening phrase of the song, shown below, begins with a G major triad in measure 1 and ends with a G major triad on beat 2 of measure 8. The opening two notes of the vocal melody (D and B) “belong” to the fourth note in this melody, G, which is the root of the G major chord that these three notes arpeggiate (with a passing tone, A, added in).  At the cadence, the pc G appears simultaneously in the vocal melody, the pianist’s topmost line, and the bass. The one other pc, B, that occurs together with G on beat 2 “belongs” to the G. It joins with pc G to form a chord in which G is the root and B is the third.

 

Resolution

A second kind of hierarchy is present when resolution occurs. A melody note that is a dissonant interval from the pc in the bass, from the root, or from the tonic pc, creates instability. The note resolves by moving by step to a note that is more consonant with its surroundings and thus more stable.

In the song, Ich Liebe dich, measure 8, the vocal melody moves from A to G. The pc A is dissonant with the bass note, and root of G, and it resolves as a 9-8 suspension to G. The unstable note, A, is subordinate to the more stable note G.

 

Hierarchy in Tonal Music

Hierarchy in tonal music is clearly defined and multilayered. Resolutions are fairly predictable: suspensions and chordal sevenths generally resolve down by step and scale degree seven tends to go to the tonic. It is not that every note either belongs to the tonic pc or resolves directly to a note of the tonic triad, thus making them directly subordinate to the notes of the tonic triad. The hierarchy is multilayered. For instance, a suspension, dissonant with the current bass note and chord, might resolve into a dominant seventh chord, bringing resolution at one level, but then the chord needs resolution.

In Ich Liebe dich, the G in measure 7 is a suspension. Previously, in measure 6, beat 2, the note G was the seventh in an A7 (V65/V) chord. As the seventh from a root (and a tritone from the bass note), we expect it to resolve down by step, which it eventually does. The delay in its resolution to F-sharp creates a 4-3 suspension in measure 7.  Once G resolves to F-sharp, another source of instability arises. As the leading tone in the key of G major, F-sharp needs to resolve, but this resolution, too, is delayed. In the last measure of the excerpt, F-sharp is retained as a 7-8 retardation and only resolves to G on beat 2.

The melodic path from the note G in measure 6 toward ultimate resolution, in the perfect authentic cadence in measure 8, illustrates some of the complexity of the multilayered hierarchy in tonal music. A long series of resolutions occurs before the music comes home to its most stable and conclusive point. The tonic pc, then, is the pc to which the other notes in the passage belong and the root of the chord in which they ultimately find resolution.

 

Centric Music: A Less Defined, Less Conventional Hierarchy

In centric music there is a pc, a pc center, to which other pcs are subordinate, but the expectation of resolution is not as strong as in tonal music.

In the Russian Dance from Stravinsky’s Petrushka (1911), the melody presented in measures 1-2 and restated in measures 3-4 starts and ends on B. It is the “home base” for the melody—the place from which it departs and to which it returns. The melody approaches this pc center from the pc A, which is the lower version of ^7 of pc B. There is a sense of resolution, but it is not as predictable as the behavior of the leading tone to B (A#) would have been.

The harmonic context, however, makes the pc B subordinate to G. The B’s that start and end the 2-bar melodic units are each part of a G9 chord. Not only is G the root of this chord, but it is also constantly present in the bass. Thus we see two kinds of hierarchy here: the note A resolves to B and the note B, in turn, belongs to G.

The music does not consistently adhere to tonal common practices, however, which makes the hierarchy seem less clearly determined. In tonal music, G9 should resolve to C, but here the chord remains unresolved for the whole 8-bar unit.   When the G9 chord finally ends, it unexpectedly gives way to a passage with E as its pc center (although that is a matter for debate). Listen to this passage and to at least a minute more of the music, and notice that the music is often built out of fairly static block or “moments”, not phrases. These moments do not come to a cadence, as a phrase would. Instead, they simply end and another moment begins, often without any warning.

 

Atonal Music: Absence of Hierarchy

In atonal music there is no one pc to which the other pcs are subordinate. There is no clear hierarchy among the pcs. The pcs coexist but do not “belong” to any particular pc, and resolution is lacking.

Neither belonging nor resolution is operative in the opening of movement 3 of Webern’s Five Movements for String Quartet, Op. 5 (1909). There is a pedal tone, C-sharp, that continues throughout the first six measures, but the notes above it do not belong to it nor even join with it. Notes are juxtaposed, not united. On the downbeats of measures 2 and 3, for instance, pcs G, B-flat, and B occur above the pedal tone. There is dissonance between the B-flat and B and between all three of these notes and the cello’s C-sharp. Furthermore, there is no sense of resolution even with all the stepwise motion in measures 5-7.

In the absence of a hierarchy among pcs, a note can be prominent, but it cannot be a center, much less a tonic. If a note is prominent due to register, dynamic level, repetition, or some other reason, its pc is called a focal pitch class. In the opening of Webern’s Op. 5, No. 3, C-sharp qualifies as a focal pitch class because it is low in register and frequently repeated.