"I've been listening to Christoph Gallio and the various incarnations of DAY & TAXI for over three decades - almost since its inception. On this album, however, the Swiss saxophonist makes a debut with a different trio, featuring British improvisers Dominic Lash and Mark Sanders. The result is pungent, powerful music on the cusp of free jazz and free improv - a dichoto- my that helps define Gallio's work, though he also composes. Listening to this wonderful album invites re-consideration of the rhythmic complexities and subtleties of free jazz, which may now be in a "common practice" era after nearly sixty years of development.

New Grove [Dictionary of Music] defines free jazz in terms of its rejection of tonality and predetermined chord sequences, its vocalised timbres rather than cool sounds, and its free rubato as opposed to swing groove. However, "free jazz" is a continuum, I'd argue. We can distinguish the following styles:

(1) Modal jazz, pioneered by Miles Davis in Kind of Blue, reacted against to the rapid chord-changes of bebop, which culminated in John Coltrane's Giant Steps from the same year. Modal players were meant to improvised on scales or modes rather than chords - this was avantgarde, but not yet "free jazz".

(2) Time no changes describes the groove-based playing of Ornette Coleman's quartets, and Miles Davis's second quintet at its freest. Coleman's work is often modal, but freer than modal jazz, avoiding 32-bar structures.

(3) Pulse no metre is the canonical free jazz style - often ecstatic, its advocates were Cecil Taylor, Albert Ayler, late Coltrane (1965-7), and sometimes Ornette Coleman. Rather than four-in-the-bar swing or groove, there's a feeling of tumbling momentum that's a kind of residual swing - sometimes, as on the present album, more groove-like than others. There's also a cooler, more lyrical free jazz pioneered by Tristano, Konitz and Marsh, and exemplified by Bley and Giuffre.

(4) Free improv is a later, initially European development that excludes the residues of jazz and swing found in free jazz.

Gallio's new album is closest to (3), but draws on (4). Like the work of the best free players, its rhythmic spectrum ranges from swing groove to tumbling momentum, moving between these different feels.

The nature of swing has been debated in every era of jazz, from "sweet versus hot" in the 1930s onwards. "Does Brubeck swing?" was a favourite question that failed to recognise swing's many varieties; Sun Ra could produce an inept swing that was a put-on or provocation. New Grove defines swing as "a feeling of forward motion or momentum, often accompanied by a propensity to embody the music in some form of rhythmic movement." It usually results from a combination of characteristics of musical pulse: "how [it] is divided, phrasing, and articulation... there are different degrees and kinds...depending on the interplay of these characteristics." For instance, musicians accent offbeats by placing them at salient points in the melodic phrase, such as the last note.

A useful concept is that rhythm is felt in a circle. As Brian Priestley explains in his biography, this is what Charles Mingus wanted his bands to create.

Some musicians play on the front of the beat, pushing it to create an edgy effect: Jackie McLean, Art Taylor. There are those who play on the back of the beat, giving a laid-back feel (Elvin Jones, Art Ensemble of Chicago, Dexter Gordon, Billie Holiday); and finally those who play in the centre, "deep in the pocket" (Mingus himself, with Tal Farlow and Red Norvo; Dave Holland, Art Blakey). But it would be crude to generalise, for these micro-rhythmic variations can occur within a single album or performance.

Theorists have characterised symmetrical eighth notes (swing eighth notes) as a tied triplet feel, with first and third notes played. More broadly, though, "jazzing" simply means "messing with something", as in "jazzing the classics". Tied triplets are perhaps a development of Baroque notes inégales - a thesis that might be approved by musicologist Peter van der Merwe, whose groundbreaking Origins of the Popular Style interprets the blues as an international phenomenon. International or not, the geographical element reflects a music-language connection. Historically, jazz musicians of Chicago, New Orleans and the East and West Coasts each had a different feel to their swing; indeed one could argue that American and Irish speech, for instance, have an intrinsic swing or lilt. There is a classical comparison here. Different countries have different cultures of classical music, and their approach to rhythm will vary. In Italy, for example, the timing is distinctively different.

In fact the "tied triplet" ratio varies according to tempo, instrument, individual style, phrasing and group chemistry. As Newcastle-based guitarist and teacher Mick Wright comments, "What we call 'tied triplet' or 'jazz swing feel' is a tempo-related sliding scale, from equal pairs of quavers played 50:50 at the highest tempos, to unequal pairs when tempos are less breakneck." Tied triplets are in a ratio 2/3:1/3, dotted quavers are 75:25. Of course, he adds, "only machines play as mechanically as that."

Hiphop producer J Dilla, on his influential album Donuts, uses drum machines with a slightly weird beat to "jazz" RnB samples. Dan Charnas describes how Dilla "turned what one generation deemed musical error into what the next knew to be musical innovation". That's what I call an aesthetics of imperfection - a joyful embracing of artistic contingencies. It's exemplified here by the work of Gallio, Lash and Sanders - but that issue must remain material for another occasion."-Andy Hamilton, Durham UK