A few examples of definitions and characterizations of rhythm, both ancient and modern. (from the book "The geometry of musical rhythm: What makes a 'Good' Rhythm good?" by Godfried T. Toussaint (abstract)

Definitions ​

• Plato: “An order of movement.”
• Baccheios the Elder: “A measuring of time by means of some kind of movement.”††† Phaedrus: “Some measured thesis of syllables, placed together in certain ways.”‡‡‡ Aristoxenus: “Time, divided by any of those things that are capable of being rhythmed.”
• Nichomacus: “Well marked movement of ‘times’.”
• Leophantus: “Putting together of ‘times’ in due proportion, considered with regard to symmetry amongst them.”
• Didymus: “A schematic arrangement of sounds.”
• D. Wright: “Rhythm is the way in which time is organized within measures.”
• A. C. Lewis: “Rhythm is the language of time.”
• J. Martineau: “Rhythm is the component of music that punctuates time, carrying us from one beat to the next, and it subdivides into simple ratios.”
• A. C. Hall: “Rhythm is made by durations of sound and silence and by accent.”
• T. H. Garland and C. V. Kahn: “Rhythm is created whenever the time continuum is split up into pieces by some sound or movement.”
• J. Bamberger: “The many different ways in which time is organized in music.”
• J. Clough, J. Conley, and C. Boge: “Patterns of duration and accent of musical sounds moving through time.”
• G. Cooper and L. B. Meyer: “Rhythm may be defined as the way in which one or more unaccented beats are grouped in relation to an accented one.”
• D. J. Levitin: “Rhythm refers to the durations of a series of notes, and to the way that they group together into units.”
• A. D. Patel: “The systematic patterning of sound in terms of timing, accent, and grouping.”
• R. Parncutt: “A musical rhythm is an acoustic sequence evoking a sensation of pulse.”
• C. B. Monahan and E. C. Carterette: “Rhythm is the perception of both regular and irregular accent patterns and their interaction.”
• M. Clayton: “Rhythm, then, may be interpreted either as an alternation of stresses or as a succession of durations.”
• B. C. Wade: “A rhythm is a specific succession of durations.”
• S. Arom: “For there to be rhythm, sequences of audible events must be characterized by contrasting features.”‡‡‡‡ Arom goes on to specify that there are three types of con- trasting features that may operate in combination: duration, accent, and tone color (timbre). Contrast in each of these may be present or absent, and when accentuation or tone contrasts are present they may be regular or irregular. With these marking parameters, Arom generates a combinatorial classification of rhythms.
• C. Egerton Lowe writes: “There is, I think, no other term used in music over which more ambiguity is shown.” Then he provides a discussion of a dozen definitions found in the literature.

Timelines, Ostinatos and Meter ​

In much traditional, classical, and contemporary music around the world, one hears a distinctive and characteristic rhythm that appears to be an essential feature of the music, that stands out above the other rhythms, and that repeats throughout most if not the entire piece. Sometimes this essential feature will be merely an isochronous pulsation without any recognizable periodicity. At other times, the music will be characterized by unique periodic patterns. These special rhythms are generally called timelines.* Timelines should be distinguished from the more general term rhythmic ostinatos. A rhythmic ostinato (from the word obstinate) refers to a rhythm or phrase that is continually repeated during a musical piece. Timelines, on the other hand, are more particular ostinatos that are easily recognized and remembered, play a distinguished role in the music, and also serve the functions of conductor and regulator, by signaling to other musicians the fundamen- tal cyclic structure of the piece. Thus, timelines act as an orienting device that facilitates musicians to stay together and helps soloists navigate the rhythmic landscape offered by the other instruments.

In ethnomusicology, the use of the word timeline is generally limited to asymmetric durational patterns of sub-Saharan origin such as the tresillo. In this book, however, the term is expanded to cover similar notions used in other cultures such as compás in the flamenco music of Southern Spain, tala in India, loop in electronic dance music (EDM), and just plain rhythmic ostinatos in any type of music. A word is in order concerning the ubiquitous related concept referred to as meter in Western music. There is slightly less vagueness present in the many definitions of meter published, as there is of the definitions of rhythm listed above. There is also much discussion about the differences between meter and rhythm. Meter is usually defined in terms of a hierarchy of accent pat- terns, and considered to be more regular than rhythm. Some music, such as sub-Saharan African music is claimed to have only pulsation as a temporal reference, and no meter in the strict sense of the word. Christopher Hasty’s book titled Meter as Rhythm considers meter to be a special case of rhythm. In this book, the word “timeline” is expanded to include all those meters used in music around the world, that function as time-keepers, or ostinatos, and determine the predominant underlying rhythmic structure of a piece. Here, meter is viewed as just another rhythm that may be sounded or merely felt by the performer or listener, and it is also represented as a binary sequence. While consideration of a metric context is indispensable for a complete understanding of rhythm, the underlying assumption in this book is that it can also be profitable to focus on purely inter-onset durational issues.

https://en.wikipedia.org/wiki/Additive_rhythm_and_divisive_rhythm