Can the rhythm of any music with a consistent pulse be represented through a time signature?
I tried this with a lot of world music (I myself am an Indian) and majority of it, that followed a consistent pulse or a well timed rhythm, could be expressed neatly using time signatures.
Can this be applied to all music? If yes, does it mean that any systematic rhythm does follow an underlining pulse?
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I think it depends what you mean by 'consistent pulse' and 'represented'!
A single time signature by itself tells you that there are a certain number of a particular note value per bar. The rhythm of the music is then notated with notes and rests within each bar that add up to the length of the bar. Note and rest values in standard notation are fractional, such that any mathematically rational note length can be represented. However, if you had a repeating (and perfectly systematic) rhythm of notes of relative length 1:?2:1:?2:1:?2... , that isn't possible to represent using standard note values within the context of a single time signature. Of course you might consider that this isn't a regular pulse; you could still use some other notational device to represent this; and you could also argue that it's more a limitation of the note value system than the way time signatures work.
However. a time signature also often implies something about the relative strengths of each beat - the meter of the music. The first beat of the bar is usually inferred to be strong; the beats within the bar are then also assumed to follow a certain pattern - for example 6/8 is something like strong-weak-weak-medium-weak-weak. However, it is possible to think of a regular stress pattern that doesn't have a time signature commonly understood to imply it. In these cases, it might be useful to consider the music as a number of different time signatures alternating in a pattern, forming a mixed meter that is still a regularly repeating pattern. This is still expressing the meter through time signatures, but not a single time signature.
Merely having consistent time intervals establishes a pulse, but not a meter. You can very well have an irregular succession of groupings of events that defies any single time signature.
Imagine a work song that accompanies rhythmic chopping of something (perhaps logs swimming by, or stones to hew...). The items of work might require one, two, three, etc. chops depending on how big each one happens to be, but the worker would still try to space the chops (and the notes) regularly. This would represent a consistent pulse with an irregular meter that can be described only through changing the time signature for every bar, which becomes pointless.
If you're interested in the point at which a time signature no longer makes sense, or at least where the composer decided not to use one in an otherwise (more or less) conventional score, consider this excerpt from the first page of Tristan Murail's "Les Travaux et les Jours" for piano. (Information and score preview here; listen to part I here.)
The sense of pulse and meter in this composition is so elastic that the composer has resorted to non-standard methods to notate the rhythm: there is no time signature, there are no bars (though there is an indication of equal time segments at the top), the note beams indicate a gradual shift from 1/8 to 1/16 to 1/32 note lengths and back, and the horizontal distance between the notes is used as an indication of the pulse.
Also, at some points in the score, the length of pauses is indicated in seconds, and there is a pedal point indicated as "very long". This is mixed with more standard indications of tempo, such as "meno presto", "accel. poco a poco", "rall." and even "?=66-70".
Yes, as long as the music's pulse is consistent, it can be expressed with a time signature. Given polymeter music, you might need a separate time signature for each instrument/part, but you can still go for one time signature per instrument!
The time signature can look vaguely ridiculous such as 13/8 or 22/16, but hey, it's only one time signature!
(You'd be surprised how common music with an inconsistent pulse is, though!)
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