The letters originally came from Greek. In Greek music theory, there were originally four modes, roughly corresponding with our modern Dorian (starts on D), Phrygian (starts on E), Lydian (F), and Mixolydian (G). There were no sharps or flats. There were also four “hypo” modes (Hypodorian, etc.) that used the same tonic (“home note”) as their corresponding non-hypo modes, but ran from a fourth down to a fifth up. So hypodorian was A to A, all white keys, but with the tonic on D. In this system, A (“alpha”) was the lowest note available.
As others have pointed out, this system stopped being used for a long time after the fall of classical Greek civilization. In the middle of the middle ages, around 900-1100 AD, various Europeans began to redevelop systems of notation and note naming. Initially they used the syllables of the first lines of the chant “Ut queant laxis”, giving us “Ut re mi fa sol la”. Eventually (like way later, I believe in the 19th century) ut was changed to do and the modern solfege system was developed. It wasn’t until a bit later, when more modes started to be added, that theorists in certain regions began reviving the Greek letter name system.
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