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In Francisco Correa de Arauxo's Faculdad Organica, he titles his pieces like "Tiento de primero tono". A complete recording of the Faculdad Organica is here: https://open.spotify.com/album/7eizHDN8NcG4KsYrX2NezP?si=psRnMtX-RlS7yJ9u3Z4I5A

What is the "first/second/..." tone that he's referring to?

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As with the proposed duplicate question, these tones refer to the authentic and plagal modes, but note that the linked duplicate, which is answered with respect to the music of Manuel Rodriguez Coelho, refers to the medieval 8-mode system. The recording of Francisco Correa de Arauxo, however, has pieces in "decimo tono" and "dozeno tono." This shows that he is not using the eight traditional church tones but rather the twelve tones of the expanded system introduced by Heinrich Glarean, who invented the Aeolian and Ionian modes in his Dodecachordon of 1547 (along with hypoaeolian and hypoionian, bringing the number from 8 to 12).

The 12-mode system was not accepted universally, which explains Manuel Rodriguez Coelho's use of the 8-tone system in the 17th century.

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