Is there a term for metric equivalence analogous to "enharmonic" for pitch equivalence?
Key signatures, chords, scales, and phrases are said to be enharmonically equivalent if they contain the same pitches, but are notated differently.
Is there an analogous term to express that time signatures, meters, or rhythmic phrases are metrically equivalent when notated differently?
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For some pieces of music from medieval days (or English descriptions of some Indian ragas), the term is isorhythmic. This may be commonly used in a more narrow sense than is being asked about. It applies to a rhythm pattern that is applied to a given tone sequence and repeated throughout a piece. If the lengths of tone sequence (called the color) and the rhythmic pattern (called the tala) differ, the entire pattern repeats after the LCM of their lengths. (I think the tala or rhythmic pattern is also called the hand.
en.wikipedia.org/wiki/Isorhythm
I think that isorhythmic would be a good term and not introduce confusion.
If you have durations with different rhythmic meaning in parallel (either due to polyrhythmic notation or because of using duplets or quadruplets), I'd lean towards calling them commensurate.
I don't know of a term as universally used as "enharmonic" (I've never heard "enmetric," for instance), but with the use of algebraic group structures in music theory over the past few decades, the term "isomorphism" is becoming much more common.
Thus you may choose to say that the two key signatures, or two rhythmic profiles, etc. are "isomorphic."
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