In order to work out a new, individual method of composition and free himself from tonal associations, Baird studied works composed by representatives of the so-called Second Viennese School – Arnold Schönberg and Anton Webern. For three successive years, between 1954 and 1956, he devoted himself to testing the possibilities and limitations of dodecaphony, writing numerous compositional exercises, which have not survived, however. As he recalled:

[...] I tried to come up with music that would be different from the one I had been able to imagine until then. [...] I did dodecaphonic exercises and it seemed to me that this could be something for me, provided that I didn’t bow to the system as a matter of doctrine, but that the system bowed to my musical needs [...].

A breakthrough in this quest came when he heard two works by Alban Berg – Wozzeck and Lyric Sutite. It was in these works that Baird found what was close to him – lyrical expression combined with liberation from formal relationships. When he decided to apply the dodecaphonic technique to his main works, he already had a recipe for how to treat it. The basic feature of Baird’s dodecaphony is thus his thematic treatment of the series and preservation of the relation of identity between serial structures and syntactical units of music. What was also important to him was the expressive value of the series and its components (the various intervals), but he was quite free in his approach to the technical side of “the method of composition by means of twelve tones”:

I have never really used the so-called strict serialism in my works [...]. In a number of my works written after 1956-57 you can find elements of the serial technique, but faithfulness to this technique was not the most important thing.

The group of works with dodecaphonic features, written in 1956-1967, encompasses 10 items:

• 4 orchestral works (Cassazione, Four Essays, Expressions, Four Dialogues),
• 4 vocal-instrumental works for bigger ensembles (Exhortation, Erotic Poems, Four Songs, Five Songs),
• 2 chamber works (Divertimento, String Quartet).

As time went by, Baird’s dodecaphony softened. Initially, it was associated with the neo-classical style (Divertimento, Cassazione), then went through a period of becoming independent (String Quartet), reached full maturity (Four Essays, Expressions) and technical mastery with a touch of sonorism (Exhortation, Erotic Poems), to finally remain only in a residual form in his works (Four Dialogues,  Four Songs,  Five Songs). As a result of his experiments with dodecaphony, Baird came to the conclusion that it had two basic shortcomings: first – not having a fixed point of reference (e.g. a note, a chord), it did not take into account the physiological properties of hearing, second – by giving up attempting to make even a general distinction of intervals between dissonances and consonances, it made music sterile, depriving it of any tension. This conviction made Baird gradually free himself from serial thinking; he focused his attention on sound as a factor shaping the energy of musical progression.