Little music tuition
Basics
The natural scale untempered
Nature is not only manifested, so there is "somewhere" an "indefinable" reality. Mathematics, and therefore music, make it possible to better understand this reality.
Every civilization has its musical system, always drawn from the contemplation [1] of numbers and their relationships.
The basics of Western music are found in Plato, mainly Timaeus.
It explains how the World Soul is constituted, between the world that is not yet manifested (the "same", i.e. 1), the matter (the "other" i.e. 2) and what's in between.
A traditional civilization recognizes three worlds: spiritual, psychic and physical.[2]
As everyone can see, the music acts directly on the listener. It will promote a certain spiritual, psychic or physical state, if he allows it.
The ancients rightly considered the importance of harmony for the proper balance of the world and of a society.
From the most remote antiquity in the Middle Ages, it was perfectly natural to conceive music, which was of course nothing but sacred, as "in harmony" with the very constitution of the Universe.
The Timaeus teaches us that making music is acting on the World Soul - just that! - and how we get the notes that make up the scales, or more exactly the modes, starting with the mode he calls Dorian, but today corresponds to Phrygian.
As it would be much too long to translate the whole article in French of my friend Xavier Mignon, if you want more explanations on Plato and music, please read Ernest McClain´s wonderful book
“The Pythagorean Plato: Prelude to the song itself” here as free download (the author´s stated wish):
[1] Originally, the word theory, in Greek, means "contemplation". “The role of the Wise Man who studies mathematics, like any artist, is to contemplate the divinity, and to transmit to us the signs or symbols, expressed in such a way that we can, from these signs, find the object of the initial contemplation. This is the subject of all sacred art and all traditional knowledge”. (A.K. Coomaraswamy)
[2] Why I speak of "music between the (3) worlds", even if sometimes one can recognize Indian, African or Asian influences, it is because I focus on the spiritual world that includes everything.