When was the Imperfect Authentic Cadence invented?
Inverted IAC (1st example) : Either one, or both chords, are not in the root position.
Root position IAC (2nd example) : Both chords are in root position, but the highest voice of the final chord is not the tonic.
Leading-tone IAC (3rd example) : The V chord is replaced by the VII chord.
When were the three types of IAC invented?
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I think the TERM 'Imperfect Authentic Cadence' may be quite new. I've only started hearing it quite recently, and always, I think, from the direction of America. (Where that sort of cadence, if not the name, certainly WASN'T invented :-)
You've been asking a series of questions about when various musical devices were 'invented.'
I think you should try to get out of this mind set. These things were not 'invented.' "How did they evolve' or perhaps 'how has their use changed over time' would be a more informative way to look at them.
You probably need to go back to musica ficta to get the origins of the classical cadences.
My cursory understanding of that topic is that treatises from that time reflect unwritten performance practices that had already evolved!
That's the problem you will run into with this and similar questions. Theory texts listing and defining cadences or other musical devices will describe long established practices.
This question is analogous to asking when were thee and thou invented in English, when did their usage end?
These things are about how cultures evolve. At best you may find an era and region about origins, and for some things first know recorded usage.
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