copyright © 2003 by Larry J Solomon
"One can take the view that even with us there is still a tonic present -- I certainly think so . . ." [Anton Webern, 1933] 
Webern was already writing 12-tone serial "atonal" music when he said this. Yet today his music is usually described as atonal. Exactly what is atonal music if it has a tonic? Paradoxically, "atonal" means lacking a tonic or lacking tonality. So, how can atonal music have a tonic? To understand atonality, a negative term, we must first examine what it means for music to be tonal.
Many definitions, some conflicting, have been given for the term "tonality". (Tonality is the noun, and tonal is the adjective for the same concept.) One definition is from Mark DeVoto in the New Harvard Dictionary of Music: "In Western music, the organized relationship of tones with reference to a definite center, the tonic, and generally to a community of pitch classes, called a scale, of which the tonic is the principle tone; sometimes also synonymous with key."  He goes on to limit tonality to music beginning at the end of the seventeenth century and embodied by the use of major and minor scales, their triads and functions. This confines tonality to the Western tradition after the mid-seventeenth century, and seems to deny tonality to music outside the Western tradition; i.e., non-Western music evidently has no tonality. DeVoto's tonality is limited then to a harmonic context where triads, major and minor scales, and their traditional functions must be present. A little later he states "Tonality in a very limited sense can be said to exist in the tone-centering properties of monophonic Christian chant; the same kind of centricity can be traced, in varying degrees, in surviving instances of much older Semitic and Asian monophony, even in nondiatonic music." This broadens the field somewhat, but only "in a very limited sense", whatever that means. DeVoto's definition seems too confined today, and is ethnocentric.
H.K. Andrews' definition in Groves Dictionary (1970)  is just as confined as DeVoto's concept, and precludes tonality from non-Western and non-tertian music. Brian Hyer's brilliant expose in Grove's Online (2003) states: "Perhaps the most common use of the term, then, in either its noun or adjective forms, is to designate the arrangement of musical phenomena around a referential tonic in European music from about 1600 to about 1910."  Even this definition includes location and date restrictions that are problematic. Tonal music is at least as common today around the world as it was between 1600 and 1910, and examples of tonality certainly exist prior to 1600.
A mode is a series of intervals used to construct a scale. Therefore, TTSTTTS is called the major mode. Modes have no specific tones, notes, or pcs; they are simply a series of intervals or distances. Scales, on the other hand, contain specific notes or pcs. A scale is a group of pcs or notes arranged in ascending or descending order. ABCDEFGA is a simple scale. Its mode is TSTTSTT. Modes and scales may or may not have a tonic. The chromatic scale has no tonic. However, a C major scale has the tonic C. Modes can only have relative tonics; e.g., the major mode has no specific tonic, but some tonic is implied at the beginning of the mode. Major and minor modes are regarded today as the most important modes, since most music around the world now conforms to these two modes. Minimally, key consists of tonic plus the mode, e.g., "C major" or "E Mixolydian".
Music which conforms to modes other than major and minor is called modal, hence modality. Arguably, music in major and minor keys is also modal, but due to the need to separate these categories, it is best to reserve the term "modality" for music that uses other modes. Modal music is "keyed", because it has a tonic and a mode, hence A-Lydian is a key.
Stripping the date and location restrictions we arrive at a valuable concept that is necessary for tonality. Tonicity is a hierarchy of pitch class (pc), where at minimum, one pc predominates, the tonic. Music having this property may be called pitchcentric. Now that we have some working definitions, consider some ways in which one pc can predominate over others.
The simplest possible example would consist of music composed with just two notes. (A two-note scale is called ditonic.) If one of these notes is repeated more than another, it is made more important, hence it becomes tonic. If one is accented over the other it will also predominate. There are two different types of accents: one is a stress accent, where a note is played louder. The other is an agogic accent, where one note is longer in time than another. Long notes by virtue of their length are more important than short notes. Endings, or cadences, are very important contributors to creating a tonic. The last tone or chord tends to linger in memory.
There is a need for a term that separates major and minor from the other modes, and that term is tonality. Tonal music, hence tonality, is that which conforms to major and minor keys and has, at least a minimal pc hierarchy (a tonic and probably also a dominant). Tonic is the most important, or emphasized pc. Dominant is second in importance and is normally located a perfect fifth above the tonic.
Atonicity or atonic music would have no tonic, no pc dominance, and no pitch hierarchy. Atonicity is built upon a premise of negation. But is this really possible? To create completely atonic music would involve a negation of the five attributes listed above: no repetitions, no accents, no durational differences, no endings (cadences), no strategic placements.
Arnold Schoenberg (1874-1951), who believed that music was evolving necessarily and inevitably toward pantonality, where all tones are equalized in importance, tried to rush to what he believed to be its inexorable outcome and claim priority of the new "discovery" before Josef Hauer (1883-1959). Schoenberg tried to write music without repeating notes. His twelve-tone row technique was invented to alter traditional tonality by equalizing the importance of tones. By stating all twelve notes without repetition none would sound more prominent than others -- they would all be equal in importance. Although this seems logical at first glance, Schoenberg probably discovered that this logic is flawed in practice. First of all, notes have durational differences, whereby long notes become more important than short ones. Furthermore, our ubiquitous metrical music has a built in accent on the first beat, which helps to establish tonicity. Additionally, regular, repeating rhythms contribute to tonicity. High notes, especially climaxes (strategically placed), are also more prominant than low notes. There can be no music without cadence, since it must stop sometime. So, cadences do occur in serial twelve-tone music, and these contribute to a sense of tonic. Schoenberg also repeats notes, even in his twelve-tone music, belying a lack of pc priority. Schoenberg and others tried to combat note repetitions by using combinatoriality. Durational and rhythmic priorities were combatted with irregular rhythms and changing meters. Even these techniques fail to prevent pitch priorities. Such techniques may serve to delay a sense of tonicity, but they cannot eliminate it. It is clear that Schoenberg tried to "democratize" tones, believing this to be the logical conclusion of musical evolution, but the very nature of time in music inhibits atonicity. We can only imagine atonicity, but inevitably some notes will have priority over others. Webern was right. Tonicity can be established in atonal music. For an example of how atonal music can have tonicity, see an analysis of Webern's Op 27, Variations for Piano.
Atonality is an apparent lack of key. This excludes modality and tonality. However, atonality, meaning a lack of intelligible key, is actually a calculated confusion of tonicity; i.e., most listeners will not be able to discern a tonic. Objectively, there can be no atonality, as Schoenberg himself maintained. Composers of atonal music try to avoid all reminders of tonal music, evading major and minor chords (tertian chords in general), scales, keys, dominant functions, regular rhythms, repetition, etc. This means that atonality is psychoacoustical; i.e., it depends, at least partly, upon individual sensibilities and subjectivity.
1. Webern, 39
2. M. Devoto in Randel, 862
3. Andrews, H.K. in Groves Dictionary, 499
4. Hyer, Brian : 'Tonality', Grove Music Online
5. Schoenberg, My War Years
Groves Dictionary of Music and Musicians, Fifth Edition, 1954, 1970
Grove Music Online ed. L. Macy (Accessed 23 Dec 2003), <http://www.grovemusic.com>
Schoenberg, Arnold. My War Years, Bullfrog Films, 1992
Webern, Anton. The Path to the New Music, 1933. translation: Leo Black, Theodore Presser, 1963
Randel, Don. The New Harvard Dictionary of Music, 1986