Strangely the “Agogique” Wikipedia article is in French only, here:
Thus I asked Oxford about “agogic”, I copy/paste:
1 An adjective indicating a variety of accentuation demanded by the nature of a particular musical phrase, rather than by the regular metric pulse of the mus. The first note of a phrase, for instance, may be felt to suggest a slight lingering which confers the effect of an accent: similarly, a leap to note significantly higher or lower than the preceding notes, or a strong discord resolving to a concord, may convey an effect of accentuation (by means of lingering, pressure, etc.) and there are other examples. The complementary term to ‘agogic accent’ (accent of movement) is ‘dynamic accent’ (accent of force), which implies the normal and regular rhythmic accentuation of a piece of music.
2 In a wider sense, ‘agogic’ covers everything connected with ‘expression’, e.g. rallentando, accelerando, rubato, pause, accentuation as described above, etc.
Well of course it’s a tool, a state of mind.
I read about this in a Sol Gabetta (a cello player) interview. If we follow the score, it’s gives a computer mood. One needs groove, or rubato, expression. And it’s linked of course (because we follow the sheet music score, right?) to the idea of “freedom blossoming on constraint”. And it’s linked to the two-to-tango idea of “singing melody seems free but it’s conducted”, enchanted and tamed at the same time.
“The interpreter juggles with spells”. Ces sortilèges sont l’agogique.
Of course we have to dig the “-agogy” word. Pedagogy. Andragogy?
And also, seeing this as a pattern for life, action, methods, rules, creation, art. Follow some rules but add some life, some “expression”, freedom into frames, etc.
Have a nice Christmas!