<P> The rhythmic mode can generally be determined by the patterns of ligatures used . Once a rhythmic mode had been assigned to a melodic line, there was generally little deviation from that mode, although rhythmic adjustments could be indicated by changes in the expected pattern of ligatures, even to the extent of changing to another rhythmic mode . The next step forward concerning rhythm came from the German theorist Franco of Cologne . In his treatise Ars cantus mensurabilis ("The Art of Mensurable Music"), written around 1280, he describes a system of notation in which differently shaped notes have entirely different rhythmic values . This is a striking change from the earlier system of de Garlandia . Whereas before the length of the individual note could only be gathered from the mode itself, this new inverted relationship made the mode dependent upon--and determined by--the individual notes or figurae that have incontrovertible durational values, an innovation which had a massive impact on the subsequent history of European music . Most of the surviving notated music of the 13th century uses the rhythmic modes as defined by Garlandia . The step in the evolution of rhythm came after the turn of the 13th century with the development of the Ars Nova style . </P> <P> The theorist who is most well recognized in regard to this new style is Philippe de Vitry, famous for writing the Ars Nova ("New Art") treatise around 1320 . This treatise on music gave its name to the style of this entire era . In some ways the modern system of rhythmic notation began with Vitry, who completely broke free from the older idea of the rhythmic modes . The notational predecessors of modern time meters also originate in the Ars Nova . This new style was clearly built upon the work of Franco of Cologne . In Franco's system, the relationship between a breve and a semibreves (that is, half breves) was equivalent to that between a breve and a long: and, since for him modus was always perfect (grouped in threes), the tempus or beat was also inherently perfect and therefore contained three semibreves . Sometimes the context of the mode would require a group of only two semibreves, however, these two semibreves would always be one of normal length and one of double length, thereby taking the same space of time, and thus preserving the perfect subdivision of the tempus . This ternary division held for all note values . In contrast, the Ars Nova period introduced two important changes: the first was an even smaller subdivision of notes (semibreves, could now be divided into minim), and the second was the development of "mensuration ." </P> <P> Mensurations could be combined in various manners to produce metrical groupings . These groupings of mensurations are the precursors of simple and compound meter . By the time of Ars Nova, the perfect division of the tempus was not the only option as duple divisions became more accepted . For Vitry the breve could be divided, for an entire composition, or section of one, into groups of two or three smaller semibreves . This way, the tempus (the term that came to denote the division of the breve) could be either "perfect" (tempus perfectum), with ternary subdivision, or "imperfect" (tempus imperfectum), with binary subdivision . In a similar fashion, the semibreve's division (termed prolation) could be divided into three minima (prolatio perfectus or major prolation) or two minima (prolatio imperfectus or minor prolation) and, at the higher level, the longs division (called modus) could be three or two breves (modus perfectus or perfect mode, or modus imperfectus or imperfect mode respectively). Vitry took this a step further by indicating the proper division of a given piece at the beginning through the use of a "mensuration sign", equivalent to our modern "time signature". </P> <P> Tempus perfectum was indicated by a circle, while tempus imperfectum was denoted by a half - circle (the current symbol, used as an alternative for the time signature, is actually a holdover of this symbol, not a letter C as an abbreviation for "common time", as popularly believed). While many of these innovations are ascribed to Vitry, and somewhat present in the Ars Nova treatise, it was a contemporary--and personal acquaintance--of de Vitry, named Johannes de Muris (Jehan des Mars) who offered the most comprehensive and systematic treatment of the new mensural innovations of the Ars Nova (for a brief explanation of the mensural notation in general, see the article Renaissance music). Many scholars, citing a lack of positive attributory evidence, now consider "Vitry's" treatise to be anonymous, but this does not diminish its importance for the history of rhythmic notation . However, this makes the first definitely identifiable scholar to accept and explain the mensural system to be de Muris, who can be said to have done for it what Garlandia did for the rhythmic modes . </P>

What is the cultural background of medieval music