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Example in the context of music theory:

Tuplets can be nested. Is there any nesting level of tuplets above which any nested tuplet of that level or higher could be rewritten with lower-level nested tuplets?

I wrote nesting because I sometimes hear that term in computer science. Is it correct to use nesting in the example above, or is there better or more generic term to express the quality of being nested?

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    Maybe "nesting level" == "depth"? That's what I usually name the function parameter that keeps track of how many recursive calls have directly preceded the current one. Apr 14 at 4:59
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    I don't think this is an English question, as it is music terminology (which in turn is mainly derived from Italian and Latin). But to answer the question, "levels of nesting" is commonly used by musicians and teachers.
    – Astralbee
    Apr 14 at 16:23
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    It brings to mind the mathematically based (as is music) poem by De Morgan, "Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so ad infinitum." (Yes, nesting seems applicable.) Apr 14 at 23:29

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Everything you have assumed seems correct.

The verb to nest means to fit an object or objects inside a larger one. So the subject carrying out the action nests the objects, and the process is nesting. Then, the adjective nested describes the embedded objects.

As to the 'levels', this resource uses the term 'divisions' to refer to each set of tuplets, but also 'levels', as you suggest. The first tuplet within a musical measure is referred to as the top-level or first-level tuplet, and then each nested tuplet as 'second-level tuplet divisions':

the composer creates a top-level or first-level tuplet and each of the individual divisions of the tuplet can then be further divided into second-level tuplet divisions, and those into even further tuplet divisions (this can get out of hand very quickly…) to create a multi-level nested tuplet unit

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