While reading about Vavilov's "Ave Maria" previously attributed to Caccini, I met an interesting argument, that probably nobody in the USSR and maybe later in the western countries noticed that the usage of circle of fifths here (if Caccini is the author) predates the widespread usage if it at least by several decades. So is there really no known examples of circle of fifths at the age when Caccini lived and created?
There's an early example in a treatise on rasguedo for Spanish guitars; this treatise was written by Joan Carles Amat about 1595 or so. It does show how to move guitar accompaniments around the cycle of fifths. Some things are not so clear; the harmonic organization is in terms of 8 modes rather than major and minor scales. Joan does use both root position and first inversion chords as chords. Not everything in music theory happens at once. (Hexachordal theory was important at least up to 1800.
It looks like the rasguedos may have often followed a cycle of fifths but whether this is counted as a composition is unclear.
I think the question is: Why didn‘t musicians or editors doubt that Caccini was the Composer of this Ave Maria.
I thought one premise must be the well tempered tuning, but:
The Circle of Fifths was invented by Nikolai Diletskii in his late 1670's treatise on composition called the Grammatika. In 1728, Johann David Heinichen improved upon the design to bring us the modern version we use today. https://en.wikipedia.org/wiki/Circle_of_fifths
And it‘s said that Schütz and Monteverdi used this sequence:
Descending fifths sequences, also known as "circle of fifths" sequences, are the most commonly used types of sequences, singular extended in some works of Claudio Monteverdi and Heinrich Schütz. It usually consists of a series of chords whose bass or "root" notes follow a pattern of descending fifths (or ascending fourths)
So Giulio Romano Caccini lived from 1551-1618, Monteverdi 1567-1643, Schütz 1585-1672.
Obviously we can assume that descending 5ths like Vavilovs uses in this Ave Maria could have been practiced too by Caccini.