Introduction to Computer Music [pdf]
90 points by luu 4 hours ago | 24 comments

arn3n 3 hours ago
I often see people frame music as mathematical manipulation or try to approach music making from a “first principles” approach, where those principles are mathematics and physics. But watching musicians talk about making music, I seldom see any discussion of the underlying math, and instead see discussions of timbres, instruments, and stylistic/historical influences; musicians who make good music seems to believe “first principles” involves historical knowledge and a well-listened ear, and nothing involving math. My question is: Is thinking about music as applied mathematics a good way to create good music? Or is it just the most easily digestible model of music for the crowd on this site?
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benrutter 57 seconds ago
[delayed]
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tossandthrow 20 minutes ago
Likely historically true, but not anymore.

As a software developer I see that LLMs are better at the "craft" of making software.

Software developers training are overwhelmingly analytical.

Musicians will experience the same. That the quality of Ai generated music is superior. But it will come more as a chock for the reasons you explain.

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Slow_Hand 60 minutes ago
In short: Not really.

As another commenter below has said, "mathematics might be a useful way to understand music", but it's not how compelling music is made.

Mathematics are fundamental to scales and the harmonic series, and knowing about them will help you refine certain choices, but it's not going to help you write a dramatic melody or an emotionally resonant chord progression, or play an energizing rhythm, even if there are mathematical explanations sometimes.

Good music comes from being a good listener, having a strong sense of what's possible, where it could go, and then delivering something surprising. Telling a story with your melody and supporting the arc of that gesture with harmony that accentuates or contrasts it.

Again, there's a mathematical explanation for harmony and dissonance, but players aren't thinking that granular. They're operating at a higher level of abstraction one, two, or three levels above that: They're thinking about telling a story, evoking an emotion, and exciting an audience in the moment.

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nxor3 13 minutes ago
I don't agree. I grew up with piano and had music friends all through my life. Classical music requires a certain level of math ability. Modern musicians scorn this and frankly it shows.
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nuclearnicer 3 hours ago
Wonderful question. I suspect it's partially the culture issue you point to, but also a practical issue of composition. If we decompose sound into the basic waveforms, similar to the subject pdf on page 18, we then have parts that we can reassemble. We can take the defense-funded DSP math of the likes of a John Cooley or a John Tukey and build an engine for assembling the parts of sound.

All this being said, I think that's a process of convenience and a historical path not a absolute constraint. We have some more flexible means of communicating with the machines today. And I strongly encourage someone to work on a new UI for computer music. "Jazz trio piano, upright bass, and drums. start drummer laid-back, piano blowing over the changes, then piano on top."

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xgulfie 3 hours ago
Thinking about music mathematically is at least a good way to understand music
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tclancy 3 hours ago
I am the least musical person I know, but I can help you out here. Math? John Coltrane has you covered. https://www.americanjazzmusicsociety.com/blog/john-coltrane-...
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jmyeet 16 minutes ago
It doesn't take that long to learn to read sheet music (or tabs especially) and you could treat it like just playing a sequence of notes but you're never going to get far that way. You need to understand why certain notes go together. Some people have done that without theory but you're going to get much further with even some basic theory.

Think of it this way: if you first saw the word "HELLO". You could deconstruct that and remember that there are 11 lines and 1 circle but that's not how you learn to read or write. You learn letters, which are collections of lines. So you learn the concept of "H" and it having a sound and that it is 3 lines. You then learn to put them together and how you can sound out something thats's written and with varying degree (depending on language) take something said and write it down.

Music theory is like that. Sheet music may be a bunch of circles and lines on a sheet but really it's describing keys and usually a chord-progression. Some sheet music will explicitly just list the chords at the top like A, Em, Asus4, etc.

The 12 notes are constructed from harmonics, specifically 2:1 and 3:2. This part is maths. But the frequencies are adjusted slightly in a system called "equal temperament" where the ratio of 2 adjacent notes is the 12th root of 2.

From there you generally play a subset of those notes (often 7). That's called a scale (eg major or minor scale). The chords in that scale can then be identified by a Roman numeral within a key. So the I chord in the C major scale is a C. The IV chord is the F. Depending on the starting note of the scale you'll get sharps (#) and flats (♭) to denote that they are a different pitch. An easy way to remember this is that the white keys represent those whole and half steps with just the white keys (starting from C). As an aside, so does the A minor scale.

Why do I say all this? Because a huge amount of modern music is simply a I-IV-V chord progression within whatever scale you're using. So if you know a little theory, you can choose a key and a chord progression that will inherently sound nice together. There's more to it of course but understanding what a key is, what chords are and what a chord progression is is a pretty good start.

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SanjayMehta 2 hours ago
> nothing involving math.

It's like Escher; he didn't have any clue that his intricate work would excite mathematicians and crystallographers.

Mandatory reference to GEB

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bikitan 2 hours ago
Understanding the soul of music and creativity at a mathematical is something that not that many people are trying to do. But there is an entire world of technology that underpins modern music and sound that is built soundly on math, like digital recording digital signal processing, synthesis, physical modeling, and plenty of other stuff, and this seems to be what the book's focus is.

Sure, there have been plenty of attempts to distill music to a mathematical essence. Certainly the ancient Greeks tried this, and traditional counterpoint resembles math in a number of ways. But at the end of the day, mathematical descriptions of math and music theory more generally are more useful as descriptive tools to help give language to what people are doing musically and to understand why we perceive some things as sounding better than others.

Starting with numbers can be good in some respects, like understanding the circle of fifths or how scales are built out of intervals, how chord progressions and harmony work and how to reharmonize, all of which can be augmented with a solid conceptual understanding. But at the end of the day, your ear and creative spirit are your primary asset when it comes to creating good music. This is why computer-generated music has been so bad up until AI took over. Great for building arpeggiators or backing tracks, but good luck creating a beautiful melody in a purely numerical rule-based system.

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colkassad 3 hours ago
I love the world of music production. I started with Ableton Live six years or so ago and it's been a wonderful hobby. It has such a vibrant cottage industry of plugins (sampled instruments, synthesizers, effects, etc) thanks to the VST standard.
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Dusseldorf 3 hours ago
Amusing to see how attitudes toward AI change over time. On page 6, part of the original text has a footnote apologizing to readers far in the future for outdated speculations, then mentions that future readers "may even be an artificial intelligence rather than a human, how wonderful!"

But just a bit before that in the foreword written in the present day, bars AI scrapers from reading or referencing the materials under any circumstances!

Anyway, this seems fantastic and I'll definitely be spending some time diving in.

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pwython 2 hours ago
> then mentions that future readers "may even be an artificial intelligence rather than a human, how wonderful!"

My first thought seeing this post was, I need to find more literature like this, fine-tune a model with that + Logic Pro documentation, then give it an MCP to control Logic Pro and see if it can be my music production assistant.

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DougMerritt 3 hours ago
This appears to be mercifully shorter and less intimidating than the must-have bible, "Curtis Roads. The Computer Music Tutorial. MIT Press, Cambs, MA, 1996".

It says it was originally published by Wiley in 2009, and the rights reverted to the author in 2025, whereupon the author released it on the net for free.

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Slow_Hand 49 minutes ago
If someone wanted to start making computer music I'm not sure I'd recommend this or Curtis Roads' book as a starting point.

These aren't resources for getting started. They're more like encyclopedias for learning about DSP and tech once you've established the fundamentals of music and sequencing.

If a beginner wants practical knowledge for making records with electronic instruments I'd give them a DAW, teach them to record and sequence, teach them basic music theory, and then point them to something like Ableton's synthesis tutorials that will teach them about oscillators, envelopes, filters, LFOs, and basic sample manipulation.

That's 80% of the necessary skills right there.

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ablanton 3 hours ago
I'm so happy to see Nick Collins taking this on. If you haven't seen his book, Handmade Music, it's an excellent book for music projects. This contribution looks exceptional as well.
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calny 3 hours ago
I was reading up on the author and saw this interesting bit[0]:

> An algorave (from an algorithm and rave) is an event where people dance to music generated from algorithms, often using live coding techniques. Alex McLean of Slub and Nick Collins coined the word "algorave" in 2011, and the first event under such a name was organised in London, England. It has since become a movement, with algoraves taking place around the world.

[0] https://en.wikipedia.org/wiki/Algorave

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florilegiumson 2 hours ago
Nicolas Collins is actually a different person: https://www.nicolascollins.com/handmade.htm
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ChrisArchitect 3 hours ago
The info page, perhaps a better url for submission instead of the large/hugged PDF

https://composerprogrammer.com/introcompmusic.html

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adultSwim 2 hours ago
I enjoyed Miller Puckette's Theory and Techniques of Electronic Music, using Pd. https://msp.ucsd.edu/techniques.htm
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ChrisArchitect 3 hours ago
A similar endeavour,

Introduction to Computer Music, by Prof. Jeffrey Hass

https://news.ycombinator.com/item?id=44744578

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ValveFan6969 2 hours ago
[dead]
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p1esk 3 hours ago
Wow, this book has been published in 2025, and it has zero mention of AI generated music. Not saying it's a bad thing - from the table of content it covers a lot of important fundamentals, but ignoring the elephant in the room is... weird.
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mb7733 3 hours ago
It wasn't published in 2025. It was published in 2009 and the rights reverted to the author in 2025, who released it for free.
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p1esk 3 hours ago
Oh ok, makes sense then
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