In addition to Nietzsche:
Rousseau wrote both the music and libretto for an opera - Le Devin du Village.
Rousseau - Le Devin du Village on YouTube
Adorno was a classically trained pianist, studied composition with Berg in Vienna, and wrote piano music and a number of string quartets.
A selection of Adorno string quartets on YouTube
Why restrict yourself to philosophers and mathematicians?
Lots of people are interested in music, many more than are actually interested in either of the disciplines mentioned above. And most are moved more by music than by poetry and the literary arts; and likewise, the visual or dramatic arts. Music has been of perennial interest in mankind.
Aristotle discusses celestial music in On the Heavens (De Caelo) book II part 9. He does not dispute (but also does not show much interest in) the claim that the distances between celestial bodies form harmonious ratios. What he does dispute is the Pythagorean theory that the movements of the stars subsequently produce actual music. He regards the ...
Gabriel Marcel according to Brendan Sweetman composed music:
He also developed a keen interest in classical music and composed a number of pieces.
However, I could not find a list of these compositions.
Thanks to @sand1 from comments: "La Biblitheque Nationale Francaise list has a section for him as Compositeur(54) data.bnf.fr/fr/11914394/gabriel_marcel"...
In medieval & renaissance religious music, ie what got recorded, use of certain intervals was banned, like the flattened fifth nicknamed 'the devil's tritone'. It was considered discordant, sinister. But, it's widely used now, & we don't have the same association.
We think of notes in relation to vibration of plucked strings, but it's interesting to ...
Charles Darwin is seldom regarded as a philosopher, but his ideas certainly have profound philosophical implications. His view, in summary, was:
"As neither the enjoyment nor the capacity for producing musical notes are faculties of the least use to Man in reference to his daily habits of life, they must be ranked among the most mysterious with which he ...
Adorno might be interesting to you, but consider looking at certain composers who also “write” — Cage and Xenakis come to mind.
Attali’s Noise: The Political Economy of Music is also highly recommended in this vein.
I think this is a rather deep topic, worthy of more than just an answer. However, I think the musings of Alan Watts provide an excellent answer: music is intrinsically close in nature to the act of life. He also suggests another art which is in a similar class: dance.
The existence, the physical universe is basically playful. There is no necessity for it ...
One of music's fundamentals is the way in music, like an octopus, people convincingly imitate other things... then quickly doff the masquerade and swim off.
In the example below, Duane Shinn uses a piano to imitate bells and chimes (i.e. physical bells and chimes, like in a bell tower).
This is more than just a ...
The link may be astronomy.
The planets in our solar system are said to be organized in a similar manner to a musical chord. There are also claims that rotating planets produce sounds. In fact, when I was in the Navy, we were told that a certain ultra-low frequency sound we monitored was thought to be Earth's "heartbeat."
I couldn't find a single article ...
I came up with a list of things that good music communicates. I'll repeat it here:
Emotion (or drama)
Imitation (of nature)
Bigness (or awe)
Virtuosity (of the performer)
Practical social functions (like dance or work songs)
Unifying social functions (like anthems)
Memory (or recognition)