What is a musical thought? Are melodies and chords logical reasonings?
The syllogistics Aristoteles invented is the first formal and complete logical system ever developed. Still it is no formal logic system most often used today, a system solely working with symbols. Contrary, syllogistics also contains words and meaning. The syllogistic method combines two sentences containing two notions each, where one notion is common in both sentences. Therefore one can make a conclusion about the connection of the two other notions, if and how they are connected. The most famous syllogism is:
A) Sokrates is a human being.
B) All human beings must die.
=> Therefore Sokrates must die.
The syllogistic music theory tries to match musical notes into such a logic system leading to a musical thought intrinsic to a melody or harmony.
Bader, R., Diezt, M.-K., Elvers, P, Elias, M., & Tolkien, L.: Foundation of a Syllogistic Music Theory. In: Bader, R. (ed. / Hrsg.).: Musical Acoustics, Neurocognition and Psychology of Music / Musikalische Akustik, Neurokognition und Musikpsychologie. Hamburger Jahrbuch für Musikwissenschaft 25, 177-196, 2009.