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Most music notation give very binary accents for beats (either there or not), but there are many "degrees" of accenting a beat.

One bar of 4 4 time, "one two three four", is equivalent to two bars of 2 4 time, "one two one two."

What makes the difference is the subtle emphasis:

"ONE two three four" is distinguished from "ONE two ONE two."

I would like to know how I could potentially alter this pattern. For example, if I wanted to change my 4 4 rhythm, "ONE two three four", to "one two THREE four," or "ONE two three four."

Is there any musical notation for this?

Post Script: Just for anyone's curiosity, if no such notation exists and I'm forced to create it for my own use, my system would involve superscripting any notes with numbers (1 being most accented, 2 being less so, etc.).

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    The levels of accenting you describe are referred to in A generative theory of tonal music, though I don't recall them using conventional notation. – topo Reinstate Monica May 13 '17 at 9:24
  • Beware--at least for piano, tiny numbers next to notes (i.e. at least resembles superscript) are for fingering. – Dekkadeci May 13 '17 at 13:50
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Not sure if you'll like this answer, but the examples you're giving for the problem are actually the answers to your question.

There are a couple ways the composer can impact stress with the meter:

  • Orchestration: give players accent, staccato, legato, marcato, etc; to impact the stress a listener will feel on any given beat.
  • Instrumentation: choose which instruments play which parts to change the stress; a trumpet or a snare drum will have a stronger attack than a legato violin, so make stronger attacks on beats you want to feel heavier
  • Subdivision: often next to or above the time signature, a composer will notate the subdivision that the player is intended to feel. For example: 10 8 (3+3+2+2) versus 10 8 (2+3+3+2)

I think the real answer is that as a composer/arranger, your role is to make the feel apparent through the music. The feel is a compilation of each individual part coming together, not something that is independent of the music for you to notate at a later time.

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If the accent pattern changes often, then just use conventional accents. Chopin's Etudes op. 10 and op. 25 are full of this.

For varying amounts of accent, also use the "marcato" accents favored by Liszt in e.g. his Transcendental Etudes.

For many finely distinguished degrees of accent (like klangfarbenmelodie or integral serialism), alter the note itself (replace a quarter note with an eighth note and an eighth rest), specify the dynamics (p, mf) for every single note head, etc. Because now the interpretation of accent is done by the composer rather than the performer. So make it official. Remove the performer's interpretive freedom in this regard.

If the accent pattern remains constant for many bars at a time, then notate it explicitly (however you like) for the first three bars, and then write simile.

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