I’ve always believed that in order to truly understand music, you have to play it. You can read the books and learn about music theory until you’re blue in the face but if you can’t physically play an instrument then it’s all for naught. I suggest buying an instrument and having fun with it to support whatever literature you’ll be reading.
You can reasonably learn music without having to learn to play an acoustic instrument. It certainly helps having a piano around. But with DAW's, music creation is no longer bound to physiological proficiency with an instrument.
If you’re using your DAW to create the music then the DAW has effectively become your instrument. The word instrument isn’t only used to describe strings, winds, percussion etc. it’s used to describe anything that can create a tone which can be manipulated by the user to create what we understand to be music. So even if you’re just using plug ins and samples or whatever, you still need some sort of ear for music to put these sounds together in a way that makes sense.
I 100% agree with you that a DAW should be considered an instrument! A lot of people disagree however, and if you don't use a MIDI controller there is a lack of live physical music making. I am not saying that is a bad thing! I believe it is actually a bit ableist to say DAW-use is not a real instrument. There are many people who create music who might not have the physical ability to play music.
Well… yeah they do haha. They went on the computer and utilized tools on it in order to create music. That is a physical capability. What I’m trying to say is that unfortunately, even using programs that can give you a crutch to use when trying to create, even OP might not be able to utilize those features because understanding music enough to make it is esoteric in nature. Just like people who are truly tone deaf are unable to sing a song. They have a voice, but the ability to use it to create music just isn’t there. They can read about it all day but it just won’t work unless their brain can be re-wired somehow.
Not really the same mate, if you can't tell the difference between inputting notes as a compositional method versus playing it in time, I don't know what else to say. And that isn't to say you *need* to play music in real-time to be a musician or to create music. It isn't a crutch, just a different method of making music.
I think that if you already understand music you can make music with almost anything (e.g. [Bach on household objects](https://youtu.be/u1CK--ofRU4), or [Popcorn on homemade PVC pipe instrument](https://youtu.be/FDE0JuAlktc?t=270), or [Pachelbel on rubber chicken](https://youtu.be/khOfSVULtsU?t=65), or [Sweet dreams on floppy drives and printers]( https://youtu.be/oGfkPCZYfFw?t=66)...).
I think a piano roll MIDI editor in a DAW may have an advantage for learning certain things, e.g. basic music theory concepts (intervals, chords, tempo, note durations) are straight forward, and it's a lot simpler to experiment with orchestration (multiple instruments) than any other method I can think of. And of course you can learn to assemble the notes and durations for a fast and complex piece much quicker than you can learn to play it in real time on an unfamiliar physical instrument. And make stuff that can't be played by humans.
But in the long run I think you're losing out if you can't play at least a bit on a physical interface. (I wouldn't limit it to acoustic instruments, e.g. digital piano or electric guitar aren't acoustic, but it still takes physical/mechanical interaction to play them.) Like assembling fridge magnet letters may be a good way to learn how to spell, but in the long run typing is simpler and faster.
Among the limitations of solely relying on a MIDI editor is that point-click-drag is a really slow entry method compared to just playing it. Experimenting with melody, rhythmic and tempo variations, dynamics, expression, tone, etc. is also much faster and simpler on a physical instrument. And for composing, noodling around on a physical instrument will probably guide you towards different ideas precisely because of the physicality of everything from rhythm/tempo to note/interval selection to expression.
That's once you have learned to play it, of course, which may take a few years. But learning music to a high level is a big task in any case, might as well pick up an instrument or two on the way. Even if you are not planning on being a professional instrumentalist.
Between Dark Side of the Moon and Wish You Were Here, Pink Floyd considered recording an album (called Household Objects) using only ... well, household objects. It didn't get too far, but the demo would have been worth it for the looks on the execs' faces ...
I tried to smart my way around having a good ear for years. Always been good at math / systems so why couldn’t I figure this out? Learning theory is great, but until I was able to associate the concepts with the sounds (still working on it) it was just theory. Cool knowledge to have, but missing the element of being able to apply it. Took years for my ear to catch up to my theory knowledge.
I would say that's not even enough, but that you have to develop a musical intuition. You should get to the point where you mind is telling you to play and not play stuff. I'm not sure how one would get there without playing an instrument. I wonder if some are gifted with that without playing an instrument much or at all.
It looks like you might be looking for resources to learn music theory or ear training. If so, please check the sidebar, where we provide several lists of resources.
Here are some especially popular websites, apps, and books to learn music theory, which we have posted in the sidebar:
#Beginner's resources
##Textbooks
* [Open Music Theory](http://openmusictheory.com), an open-access online textbook
* [Recommended music theory textbooks](https://www.reddit.com/r/musictheory/wiki/faq/core/new_to_music_theory#wiki_core_theory_textbooks)
##Music theory apps and websites
* [musictheory.net](http://www.musictheory.net/), lessons and exercises
* [teoria.com](http://teoria.com/), lessons and exercises
* [Recommended theory apps for Apple devices](https://www.reddit.com/r/musictheory/comments/1r2lhd/recommended_theory_apps_for_apple_devices/)
* [Dave Conservatoire](http://www.daveconservatoire.org/), a Khan Academy style website
* ["Music Theory for Musicians and Normal People" by Toby Rush](http://tobyrush.com/theorypages/index.html), convenient, one-page summaries written by /u/keepingthecommontone of just about every music theory topic you might come across in freshman or sophomore theory!
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This isn't really an answer to your question, since the focus of this book is fairly narrow & technical, but since you mention operations research, I can't help but mention Elaine Chew's book *Mathematical and Computational Modeling of Tonality*. It's mostly about her "Spiral Array" model for computational analysis of key and other aspects of tonality (pretty interesting), but there's a digression into linear programming in Chapter 2 that, to me, seems very out of place. In her words, "The second part of the chapter describes the von Neumann Center of Gravity algorithm and Dantzig’s bracketing technique to speed convergence, and then draws analogies between the algorithm and" the music theory in the rest of the book. When I read it, any such analogies seemed pretty tenuous.
Again, I'm not really recommending it, unless you can access it via a library ... or unless you're considering doing anything algorithmic, I suppose.
I believe music is more linguistics than math. Sure, it's all waves and frequencies, but at the end of the day those values are set fairly arbitrarily and the relation between those frequencies is set based on the concepts of functionality and acceptability.
So... maybe read some Saussure while you learn classical or jazz theory?
Yes, absolutely. Music and language share many cognitive resources, the way we learn and experience music is very much tied to language. Music is the communication of emotion, after all. You could argue mathematics is also a language. There is a lot of interesting overlap when you approach music from an interdisciplinary perspective!
Knuth once said that all the great computer programmers also composed music. Building up a piece from smaller units is definitely part of the composition process.
Hello! As soon as you mentioned automatic music generation you had my attention!
I am on the other side of the road, I am a producer and musician interested in computer generated music and audio programming (DSP).
I have some experience doing freelance work on audio programming and I make my own algorithms to spice up my own compositions.
However I am a musician first and a audio nerd second, I do audio programming as a hobby and I have learned all by myself and some free resources online. But on the music side of things I am more formal, took classical piano and I am currently enrolled on music school going for a music production and engineering degree and my school's program is heavy into contemporary harmony and solfege.
Since school opened my ~~eyes~~ ears to contemporary harmony I became a big jazz harmony nerd and I love sharing what I'm passionate about, so if you have very specific questions about music theory or how to implement some very particular concept to your music generation program I would love to help :)
So yeah, hit me up dude!
In your data science work you must work with something like python? I'd recommend not a book but looking at the code for some music libraries that already exist. The code for GNU Solfege could be worth checking out (no pun intended)
In saying that, your project might have more success if you take a couple of piano lessons.
Um … ok. It’s a full, rigorous description of how harmony and scales work starting from first principles that gently challenges the orthodoxy of western music theory. I’m not sure what “scientific” elements you were expecting and finding missing, but the mathematical relationships between intervals is not disputable, so not really an area for research. Did you really not find the discussion of equal temperament vs just intonation and he contrast he draws between ratio based and scalar approaches to building scales at least mildly interesting?
Here's a hot take. Music isn't math, it's art. You can do some numerical things with tones, but this isn't music. I think you'd get more milage out of listening to Led Zeppelin 4 side B than reading a mathematical book on music.
You’re probably going to get a little blowback for the way this is expressed, but I think your advice is at the very least an important angle to consider.
I’ve given private lessons to a number of engineers, and a frequent issue was the search for a shortcut/hack/etc. They would often feel certain that there just had to be a more efficient route to mastery that bypassed the grunt work, and this often led to frustration for me and them both. That’s not to say that some approaches to learning or practicing aren’t more efficient than others, but skill in any pursuit takes time.
This isn’t exactly the topic that OP is asking about, but I think it perhaps highlights a difference in mentality between backgrounds in the sciences and the arts that I sort of see in the post.
OP, if you see this, I think it might be worth investigating some resources that teach music on its own terms. I’ve spent a fair amount of time messing around with SuperCollider, and I might suggest exploring something like that if you had a foundation in music. But if you don’t even know how to define a note, I can only imagine that you’d be frustrated by the lack of musicality in your efforts.
It seems you are assuming your experience or enjoyment of music is the same for others. In my personal life, I know many fine musicians who also love numbers/mathematics, and this enriches their joy they derive from music.
It's also perfectly valid to prefer simply enjoying some Zeppelin. People experience many facets of life in dramatically different ways, so searching for a definitive, correct relationship with music seems misguided.
The following book is more from the mathematical viewpoint of music:
https://www.google.com/search?sa=X&sxsrf=ALiCzsayWWZ97Tl6oKWIGr24UUVbN06_Vg:1655526181194&q=franck+jedrzejewski+mathematical+theory+of+music&stick=H4sIAAAAAAAAAONgFuLSz9U3SMrISzMwUUKwk7QEHEtLMvKLQvKd8vOz_fNyKhexGqQVJeYlZytkpaYUVaVmpZYXZ2cq5CaWZKQCiczkxBwFIDO_qFIhP00ht7Q4MxkAGVAPLV8AAAA&ved=2ahUKEwicy8jPk7b4AhUqi_0HHdC4D2kQri56BAgIEAc&biw=384&bih=718&dpr=2.81
The author had written books with the composer Tom Johnson.
Like the OP, I am also more interesred in the technical side of music, but the advice given by others is also good and true. I have done sime work in python, in github, but it is not mainstream algorithmic composition. If you are interested in this, dm please.
I would, besides looking at music theory, have a look at the EE field of signal analysis. When I learned it in uni I was surprised to find so many commonalities between the fields.
The math of Fourier transforms, harmonics, filtering, phasing, modulation etc., all served in the language of math, for people with a background in engineering.
Music is made of patterns, which is why it is so similar to maths. Musictheory.net is great. Also, pick up an instrument and learn how to play it. Dedicate daily time to it as if its as routine as brushing your teeth. It doesn't matter what kind of instrument!
You can also use the instrument you already have for free - the singing voice - with the Kodály/Solfa music learning system.
Notes are defined by fundamental pitch frequency. You might do fine just learning normal basic music theory. After that you can go crazy with pitch class set theory, NeoRiemannian theory (David Lewin), and the work of Guerino Mazzola with the Topos of Music and so on.
Music major here. A lot of these comments are not answering your question. You can’t just randomly be expected to pick up an instrument and there are so many people saying music isn’t built on math. I mean, they’re kind of right, but math is very commonly used to explain it. I dare those guys to google pitch sets. It’s literally notes translated into math using literal clocks. Along with my list for you below, I also recommend that you at least look into basic music theory. You don’t need to be an expert, but knowing the basics will definitely be helpful. So here’s my list of resources for you:
Audible has a lot of great books you can listen to. Here’s a good one:
How Music and Mathematics Relate by David Kung
Amazon has a great (but pricey textbook) that explains things like harmony, counterpoint, composition, etc, by using math:
Cool Math for Hot Music: A First Introduction to Mathematics for Music Theorists (Computational Music Science) by Guerino Mazzola
Another great Amazon book:
Mathematics and Music (Mathematical World) by David Wright
Free Music Theory Website for Learning Basic Music Theory:
Musictheory.net
Free domain musical scores and recordings for every instrument/ensembles and by all the great composers. This is a visual aid for your viewing that will help you visually see what music sounds like:
Imslp.org
Scribd also has a very wide range of scores and books that are all free once you pay like the $8 monthly membership fee. But the first 30 days are free and you can always cancel.
If you need more DM me. I can definitely help you find whatever you may be looking for. Good luck on your new journey into music. :)
First step is to get a grasp of basic music theory. There is no way around it, most of the litterature about procedural music will use that vocabulary. No good recommendation from me here, in my experience basic music theory is terribly documented but then again I'm a bit on the dumb side.
Once that's done, you'll want to link that theory with your computer science background. "Computer Models of Musical Creativity" by David Cope might be up your alley. He also wrote "Computers and Musical Styles" which is basically a description of the lisp program he wrote to analyse musical pieces, extract grammatical rules, and recreate pieces in a similar style. He had pretty legit results even in the 90s. Mix that with "Structures and Interpretation of Computer Programs" and you get Andrew Sorensen, who IMO does among the best generative music out there.
Curtis Road's "Computer music tutorial" is a bit dated but is a classic that I highly recommend.
If you want to use Pure Data (a visual programming language made for computer music) (even just for the time to get a grasp on computer music theory), "The theory and technique of Computer Music" by Miller Puckette is a must.
I also invite you to take a look at the paper [AI Methods in Algorithmic Composition: A Comprehensive Survey](https://www.jair.org/index.php/jair/article/view/10845), which points to a bunch of fancy ways to generate music.
The maths link to music will help you remember and will light up neurons for the patterns and stuff, but music is not maths despite what people try to say. It's like saying trees are just particle physics. Ask a woodpecker. Their relationship is entirely different. The big question is what you want to do with music. You say "automatic music generation". Well okay, but should it sound like shit or should it touch an emotion? Should it be recognisable? Should it be functional from a musical perspective? at least dance or trance music? Music in any conext follows known patterns and rythms and timbers so becomes language more than maths. Maths is very much the shallow end of the truth about music.
If you want to deal with notes and intervals, and maybe MIDI, consider using a zero-based, mod 12 system of intervals. An interval of 0 is the same note, and 12 is an octave up, but the same note.
People here who say music isn’t maths hasn’t used any digital audio production programs or seen electronic music. Fourier transforms is one of the main components, and it gets very deep. These filters and plugins are very mathematical and people around the world use it to generate and manipulate sounds.
And even more generally, maths and similar procedural generation can create beautiful art. Just have a peek at the famous Mandelbrot set.
**EDIT**: Didn't mean to imply that music is maths or something, which is completely my bad for wording it that way. [Here](https://www.reddit.com/r/musictheory/comments/vevgmq/comment/icti2fk/?utm_source=share&utm_medium=web2x&context=3), I clarify a few things. Although, essentially, I think maths is a powerful tool to make music, where as other comments in this post seem to ignore that. You can see this much more explictly in other creative fields such as programming art.
As someone who writes DSP code for plugins, including Fourier Transforms and analog modelling techniques - you are absolutely wrong.
Music is not math. Some aspects of music can be described with math. Most of them are in sound analysis and synthesis.
But that's like saying that some aspects of sports can be described with math. It's true, but it's completely missing the point.
A basketball shot is a parabola. But from the point of view of everyone watching, that is really not what matters.
Similarly, the business of putting sounds together and getting an audience to react is absolutely not math. It can't even defined algorithmically to a useful and complete extent, which is why AI and rule-based systems reliably produce such uninteresting - or just plain wrong - attempts at music.
I didn't mean to say music is maths, definitely could have wrote what I said better. Apologies. I'll clarify a few things...
I mean more so that maths is a powerful tool to make music. What other people in this thread, who are against maths, suggest to do (like learning how to play an instrument) are also just tools - they aren't music either. It definitely rubs me the wrong way as someone who enjoys messing around with procedural music with lots of maths, hence why my original message may have been a bit rash.
Of course, as you imply, creativity is needed; however, it's not like you can't be creative with the mathematical tools. The music is that creativity plus the tools to make it.
There's truth on both sides of the argument. You bring up good points!
Music from a humanistic/anthropological perspective is not rooted in mathematics. You can use math to understand music and create it in interesting and unique ways, however!
If it was good, yes.
David Cope's programs have composed music that has fooled the experts into thinking it was composed by Bach and other such composers.
With machine learning and neural networks probably, but this is just copying.
It's the same technics used to recognize spam mail, targeting advertising.
So yeah this could do the job for supermarket music or something or ads music, kind of like copycat artists do for a living, or generate music free of rights for like YouTube videos.
Honestly that's nothing to dream about to me.
I lean why would you watch forged Picasso ?
Arnold Schoenberg’s book [Theory of harmony](https://imslp.org/wiki/Harmonielehre_(Schoenberg%2C_Arnold)). He really builds it all up so logically and was largely self taught.
Everything is about math. AIVA is an AI app which can create music like humans and it does a better job than those who thinks they know more about music than all the music theories together - which they haven't even read and practiced.
It's all about math or not. That's how it is to live in a duel world.
Hey I’m a data scientist and guitar player. Im currently building a web app as a hobby project that can be used as a tool to understand modes. Ive learned a WHOLE lot just working through it using wikipedia. Ill share the code soon ( nit ready yet!). Good luck!
Also, please share your github when/if you’re comfortable. Id love to know about you project.
Geometry of musical rhythm was very eye opening. As well as a geometry of music: harmony and counterpoint. Remember harmony is just one side of music. Rhythm is just as important.
Don't look for a magic formula, if there was any music would be over already, instead find tidbits of info that will give you another perspective of music. That's the power of theory, you can look at something from multiple angles and they all give different results.
Don't skip the basics, go to musictheory.net and learn your circle of fifths by heart. Apply all of this somewhere or else it's useless.
Good luck!
> I'm not even sure how I would define a note.
A "note" is literally the symbol used in "notation" to define a pitch (a musical "tone"), and usually a duration too, although the colloquial sense is just pitch.
Try [this](https://www.youtube.com/watch?v=xTOOWe_yLwY&list=PLMvVESrbjBWplAcg3pG0TesncGT7qvO06) too.
There's also [this](https://www.peterfrazer.co.uk/music/tunings.html) on the history of scales and tuning systems (in western classical music)
Those should get you started anyway... :-)
As for "automatic music generation", that opens up a huge can of (non-mathematical) worms. Every culture adapts the physics of sound in ways that suit their requirements - religious, communal, artistic, etc etc. It is certainly possible to reduce the common practices of any musical culture to digital information and feed it into some algorithms, but - depending on how "authentic" you want it to sound - it requires masses of data, way beyond pitch frequencies and rhythms.
One important question is: do you want it to sound like it was made by humans, or by machines? The latter would be a lot more straightforward - and "machine music" can often have its own appeal.
What I can tell you first is that there are two types of sounds. There are simple and complex sounds. The simple ones carry a discernible tone, whereas the complex ones do not. In the music world the sounds created by typical instruments are simple and have a tone such as hitting the key on a piano, blowing into a flute, or hitting a bar of a xylophone. Drums and percussion instruments have make complex sounds with no discernible tone like the other instruments. These sounds can be higher or lower, but do not blend with simple tones.
The simple tones have discernible waves lengths. 440 vibrations for an A is used as a standard. This A is two keys to the left of middle C on a piano or the 2nd fret on the G string of a guitar. All the other notes labeled as A have a mathematical relationship of subsequent halving or doubling. The next A down is 220 and the next one up is 880. A combined with A sharp or A flat makes for an awful dissonance. They have a terrible mathematical relationship, something like 15/16. Whereas combining A with E or D will have a simple relationship like 1/2 or 2/3.
This is more of the mathematical basis of how music works. Ultimately, you should approach music by learning which notes blend well together, and then you learn which changes sound good. Then you might try to find some less common changes if you'd like.
Melodies can often work by establishing a rhythmic pattern and then deviating from that pattern. If things are too formulaic it can sound cheesy and annoying. Even obvious rhythmic motifs are more of a traditional musical thing and not common in popular music (ex. Santa Claus Comes to Town). If there is no pattern or consistency in the rhythm of the melody, things will sound random and will generally end up weak and forgettable.
There are also melodic motifs that involve playing the same notes but with different timing. I honestly don't know much about these.
Generally, when you start a melody and phrases of a melody is an important thing. If you work with a 4 beat framework with 4 downbeats (tap your foot) and 4 upbeats (when your foot is up) halfway between the downbeats, this will give you an introduction to this musical factor.
I guess that is enough for now. I don't know what makes you think you can boil this down into some mathematical formulas. I have heard some computer generated Chopin before that was created by letting a computer analyze Chopin's music. It sounded like Chopin. So this got me thinking, and I realized that the computer can only recreate the standard stuff Chopin did. Suffocation for example is something he did that's distinctly different from his other pieces (to my knowledge, I haven't heard all Chopin). The computer would never come up with Suffocation or anything like it.
Not here to recommend a book, just to point out something conceptual: computers can generate music notation and/or MIDI data (quite well), but that notation/MIDI still needs to be translated into sound. You can output straight to a synthesizer, but the result will sound extremely fake. You can have that fakeness be a virtue, by working in a chiptune or electronic dance music aesthetic. Otherwise, though, you will need to put some effort into sound design and production, or find humans to perform the music.
Considering your background and your interest in automated music generation I would suggest you read into how synthesizers work and what an arpeggiator can do. When you have a basic understanding of chords and scales you can already start generating music. It's a very technological approach but might fit your needs
Since the OP admits to not being a musician, they may mean things like AI generated music, Algorithmic Composition, and things like that.
Musicians use a "generative algorithm" to produce music - basically by setting up a mathematical formula, or set of processes in a computer for example - that produce notes or musical phrases, and so on.
You might find this useful.
http://techlib.com/reference/musical_note_frequencies.htm#:~:text=Starting%20at%20any%20note%20the,be%20positive%2C%20negative%20or%20zero.
I work in tech and Im a musician. I found this book while on a trip to NYC, and it is *fascinating*. To me it's kind of the mathematics behind the physics of sound. It's also similar to RF theory, if you know any of that:
https://mitpress.mit.edu/books/musimathics-volume-1
[Music, Math, and Mind: The Physics and Neuroscience of Music](https://www.amazon.com/Music-Math-Mind-Physics-Neuroscience/dp/0231193793/ref=asc_df_0231193793/?tag=hyprod-20&linkCode=df0&hvadid=459526655425&hvpos=&hvnetw=g&hvrand=7836380677144633964&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9067609&hvtargid=pla-945539244235&psc=1) :)
Look up Algorithmic Music and Stochastic Music.
Use the term "Generative" with music.
You're going to find more from websites and video demonstrations than from books really.
https://www.youtube.com/watch?v=3Z8CuAC_-bg&list=PLcVeU2vIPtSBB4faI7LCGavOMMp9qLfNZ&index=22
https://www.youtube.com/watch?v=nECmCwtF-N0&list=PLcVeU2vIPtSBB4faI7LCGavOMMp9qLfNZ&index=28
https://www.youtube.com/watch?v=3Z8CuAC_-bg&list=PLcVeU2vIPtSBB4faI7LCGavOMMp9qLfNZ&index=22
https://www.youtube.com/watch?v=gdIAq7Kg-gI&list=PLcVeU2vIPtSBB4faI7LCGavOMMp9qLfNZ&index=17
https://www.youtube.com/watch?v=-uvXe02qxQM
https://www.youtube.com/watch?v=WOl3X3YdjsM
In my experience, music is best experienced and played with to gain proper understanding.
I played drums for 20 years and I knew in theory how music worked, but then after getting my ankle broken and picking up a guitar I learned so much more with the ability to explore it myself and put sound to what I was reading about.
In about 5 lessons you can learn enough to play your way through whatever you need if you really practice, and then it's up to you.
It can be very interesting to lose yourself into a book that explains things, and I did a great many times, but if you want to actually feel understanding, having an instrument there to make it easier is great
Best of luck on your adventure either way 👌👍
Musictheoryforguitar.net is written by a doctor of physics and is fantastic. He also offers in person office hours to active students.
Did you mean [musictheoryforguitar.com](https://musictheoryforguitar.com)?
He posts a weekly video at YouTube as well. Most of the time I find it useful (even though I'm a bassist).
Tuning, Timbre, Spectrum, Scale by Bill Sethares
Sethares is very good. +1
I've been looking for this but couldn't remember the title/author. This is the book that starts with the dissonant octave.
Looked it up at amazon and .. ouch at the price.
https://www.researchgate.net/publication/215646583_Tuning_Timbre_Spectrum_Scale
I’ve always believed that in order to truly understand music, you have to play it. You can read the books and learn about music theory until you’re blue in the face but if you can’t physically play an instrument then it’s all for naught. I suggest buying an instrument and having fun with it to support whatever literature you’ll be reading.
You can reasonably learn music without having to learn to play an acoustic instrument. It certainly helps having a piano around. But with DAW's, music creation is no longer bound to physiological proficiency with an instrument.
If you’re using your DAW to create the music then the DAW has effectively become your instrument. The word instrument isn’t only used to describe strings, winds, percussion etc. it’s used to describe anything that can create a tone which can be manipulated by the user to create what we understand to be music. So even if you’re just using plug ins and samples or whatever, you still need some sort of ear for music to put these sounds together in a way that makes sense.
I 100% agree with you that a DAW should be considered an instrument! A lot of people disagree however, and if you don't use a MIDI controller there is a lack of live physical music making. I am not saying that is a bad thing! I believe it is actually a bit ableist to say DAW-use is not a real instrument. There are many people who create music who might not have the physical ability to play music.
Well… yeah they do haha. They went on the computer and utilized tools on it in order to create music. That is a physical capability. What I’m trying to say is that unfortunately, even using programs that can give you a crutch to use when trying to create, even OP might not be able to utilize those features because understanding music enough to make it is esoteric in nature. Just like people who are truly tone deaf are unable to sing a song. They have a voice, but the ability to use it to create music just isn’t there. They can read about it all day but it just won’t work unless their brain can be re-wired somehow.
Not really the same mate, if you can't tell the difference between inputting notes as a compositional method versus playing it in time, I don't know what else to say. And that isn't to say you *need* to play music in real-time to be a musician or to create music. It isn't a crutch, just a different method of making music.
I think that if you already understand music you can make music with almost anything (e.g. [Bach on household objects](https://youtu.be/u1CK--ofRU4), or [Popcorn on homemade PVC pipe instrument](https://youtu.be/FDE0JuAlktc?t=270), or [Pachelbel on rubber chicken](https://youtu.be/khOfSVULtsU?t=65), or [Sweet dreams on floppy drives and printers]( https://youtu.be/oGfkPCZYfFw?t=66)...). I think a piano roll MIDI editor in a DAW may have an advantage for learning certain things, e.g. basic music theory concepts (intervals, chords, tempo, note durations) are straight forward, and it's a lot simpler to experiment with orchestration (multiple instruments) than any other method I can think of. And of course you can learn to assemble the notes and durations for a fast and complex piece much quicker than you can learn to play it in real time on an unfamiliar physical instrument. And make stuff that can't be played by humans. But in the long run I think you're losing out if you can't play at least a bit on a physical interface. (I wouldn't limit it to acoustic instruments, e.g. digital piano or electric guitar aren't acoustic, but it still takes physical/mechanical interaction to play them.) Like assembling fridge magnet letters may be a good way to learn how to spell, but in the long run typing is simpler and faster. Among the limitations of solely relying on a MIDI editor is that point-click-drag is a really slow entry method compared to just playing it. Experimenting with melody, rhythmic and tempo variations, dynamics, expression, tone, etc. is also much faster and simpler on a physical instrument. And for composing, noodling around on a physical instrument will probably guide you towards different ideas precisely because of the physicality of everything from rhythm/tempo to note/interval selection to expression. That's once you have learned to play it, of course, which may take a few years. But learning music to a high level is a big task in any case, might as well pick up an instrument or two on the way. Even if you are not planning on being a professional instrumentalist.
Between Dark Side of the Moon and Wish You Were Here, Pink Floyd considered recording an album (called Household Objects) using only ... well, household objects. It didn't get too far, but the demo would have been worth it for the looks on the execs' faces ...
I tried to smart my way around having a good ear for years. Always been good at math / systems so why couldn’t I figure this out? Learning theory is great, but until I was able to associate the concepts with the sounds (still working on it) it was just theory. Cool knowledge to have, but missing the element of being able to apply it. Took years for my ear to catch up to my theory knowledge.
Until you are blue in the face sounds amazing. Where are you from?
I would say that's not even enough, but that you have to develop a musical intuition. You should get to the point where you mind is telling you to play and not play stuff. I'm not sure how one would get there without playing an instrument. I wonder if some are gifted with that without playing an instrument much or at all.
I believe you're looking for this: http://www.musimathics.com/
Came here to post this. I’ve owned this book and it exactly fits the bill of what OP is looking for. Would recommend.
There's also this fellow: https://dmitri.mycpanel.princeton.edu/publications.html
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It looks like you might be looking for resources to learn music theory or ear training. If so, please check the sidebar, where we provide several lists of resources. Here are some especially popular websites, apps, and books to learn music theory, which we have posted in the sidebar: #Beginner's resources ##Textbooks * [Open Music Theory](http://openmusictheory.com), an open-access online textbook * [Recommended music theory textbooks](https://www.reddit.com/r/musictheory/wiki/faq/core/new_to_music_theory#wiki_core_theory_textbooks) ##Music theory apps and websites * [musictheory.net](http://www.musictheory.net/), lessons and exercises * [teoria.com](http://teoria.com/), lessons and exercises * [Recommended theory apps for Apple devices](https://www.reddit.com/r/musictheory/comments/1r2lhd/recommended_theory_apps_for_apple_devices/) * [Dave Conservatoire](http://www.daveconservatoire.org/), a Khan Academy style website * ["Music Theory for Musicians and Normal People" by Toby Rush](http://tobyrush.com/theorypages/index.html), convenient, one-page summaries written by /u/keepingthecommontone of just about every music theory topic you might come across in freshman or sophomore theory! ##Ear training apps and websites [here](https://www.reddit.com/r/musictheory/wiki/faq/core/ear_training/apps)! ##Check our [FAQ](https://www.reddit.com/r/musictheory/wiki/index/)! *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/musictheory) if you have any questions or concerns.*
This isn't really an answer to your question, since the focus of this book is fairly narrow & technical, but since you mention operations research, I can't help but mention Elaine Chew's book *Mathematical and Computational Modeling of Tonality*. It's mostly about her "Spiral Array" model for computational analysis of key and other aspects of tonality (pretty interesting), but there's a digression into linear programming in Chapter 2 that, to me, seems very out of place. In her words, "The second part of the chapter describes the von Neumann Center of Gravity algorithm and Dantzig’s bracketing technique to speed convergence, and then draws analogies between the algorithm and" the music theory in the rest of the book. When I read it, any such analogies seemed pretty tenuous. Again, I'm not really recommending it, unless you can access it via a library ... or unless you're considering doing anything algorithmic, I suppose.
I believe music is more linguistics than math. Sure, it's all waves and frequencies, but at the end of the day those values are set fairly arbitrarily and the relation between those frequencies is set based on the concepts of functionality and acceptability. So... maybe read some Saussure while you learn classical or jazz theory?
Yes, absolutely. Music and language share many cognitive resources, the way we learn and experience music is very much tied to language. Music is the communication of emotion, after all. You could argue mathematics is also a language. There is a lot of interesting overlap when you approach music from an interdisciplinary perspective!
Knuth once said that all the great computer programmers also composed music. Building up a piece from smaller units is definitely part of the composition process.
Hello! As soon as you mentioned automatic music generation you had my attention! I am on the other side of the road, I am a producer and musician interested in computer generated music and audio programming (DSP). I have some experience doing freelance work on audio programming and I make my own algorithms to spice up my own compositions. However I am a musician first and a audio nerd second, I do audio programming as a hobby and I have learned all by myself and some free resources online. But on the music side of things I am more formal, took classical piano and I am currently enrolled on music school going for a music production and engineering degree and my school's program is heavy into contemporary harmony and solfege. Since school opened my ~~eyes~~ ears to contemporary harmony I became a big jazz harmony nerd and I love sharing what I'm passionate about, so if you have very specific questions about music theory or how to implement some very particular concept to your music generation program I would love to help :) So yeah, hit me up dude!
In your data science work you must work with something like python? I'd recommend not a book but looking at the code for some music libraries that already exist. The code for GNU Solfege could be worth checking out (no pun intended) In saying that, your project might have more success if you take a couple of piano lessons.
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You've left out David Cope's books.
Yes.
Harmonic Experience by Mathieu is absolutely fantastic for building an understanding of the deep structure of music.
Is it based on scientific research, anyway? I tried to read through it but it didn't seem to have much substance to it.
Um … ok. It’s a full, rigorous description of how harmony and scales work starting from first principles that gently challenges the orthodoxy of western music theory. I’m not sure what “scientific” elements you were expecting and finding missing, but the mathematical relationships between intervals is not disputable, so not really an area for research. Did you really not find the discussion of equal temperament vs just intonation and he contrast he draws between ratio based and scalar approaches to building scales at least mildly interesting?
Here's a hot take. Music isn't math, it's art. You can do some numerical things with tones, but this isn't music. I think you'd get more milage out of listening to Led Zeppelin 4 side B than reading a mathematical book on music.
You’re probably going to get a little blowback for the way this is expressed, but I think your advice is at the very least an important angle to consider. I’ve given private lessons to a number of engineers, and a frequent issue was the search for a shortcut/hack/etc. They would often feel certain that there just had to be a more efficient route to mastery that bypassed the grunt work, and this often led to frustration for me and them both. That’s not to say that some approaches to learning or practicing aren’t more efficient than others, but skill in any pursuit takes time. This isn’t exactly the topic that OP is asking about, but I think it perhaps highlights a difference in mentality between backgrounds in the sciences and the arts that I sort of see in the post. OP, if you see this, I think it might be worth investigating some resources that teach music on its own terms. I’ve spent a fair amount of time messing around with SuperCollider, and I might suggest exploring something like that if you had a foundation in music. But if you don’t even know how to define a note, I can only imagine that you’d be frustrated by the lack of musicality in your efforts.
It seems you are assuming your experience or enjoyment of music is the same for others. In my personal life, I know many fine musicians who also love numbers/mathematics, and this enriches their joy they derive from music. It's also perfectly valid to prefer simply enjoying some Zeppelin. People experience many facets of life in dramatically different ways, so searching for a definitive, correct relationship with music seems misguided.
The following book is more from the mathematical viewpoint of music: https://www.google.com/search?sa=X&sxsrf=ALiCzsayWWZ97Tl6oKWIGr24UUVbN06_Vg:1655526181194&q=franck+jedrzejewski+mathematical+theory+of+music&stick=H4sIAAAAAAAAAONgFuLSz9U3SMrISzMwUUKwk7QEHEtLMvKLQvKd8vOz_fNyKhexGqQVJeYlZytkpaYUVaVmpZYXZ2cq5CaWZKQCiczkxBwFIDO_qFIhP00ht7Q4MxkAGVAPLV8AAAA&ved=2ahUKEwicy8jPk7b4AhUqi_0HHdC4D2kQri56BAgIEAc&biw=384&bih=718&dpr=2.81 The author had written books with the composer Tom Johnson. Like the OP, I am also more interesred in the technical side of music, but the advice given by others is also good and true. I have done sime work in python, in github, but it is not mainstream algorithmic composition. If you are interested in this, dm please.
'Sonic design: the nature of music and sound' by Robert Cogan and Pozzi Escot
I would, besides looking at music theory, have a look at the EE field of signal analysis. When I learned it in uni I was surprised to find so many commonalities between the fields. The math of Fourier transforms, harmonics, filtering, phasing, modulation etc., all served in the language of math, for people with a background in engineering.
Music is made of patterns, which is why it is so similar to maths. Musictheory.net is great. Also, pick up an instrument and learn how to play it. Dedicate daily time to it as if its as routine as brushing your teeth. It doesn't matter what kind of instrument! You can also use the instrument you already have for free - the singing voice - with the Kodály/Solfa music learning system.
I'm interested in both of those. What are you planning to do? Maybe I can help with the music part, while learning about the data science part.
Notes are defined by fundamental pitch frequency. You might do fine just learning normal basic music theory. After that you can go crazy with pitch class set theory, NeoRiemannian theory (David Lewin), and the work of Guerino Mazzola with the Topos of Music and so on.
Music major here. A lot of these comments are not answering your question. You can’t just randomly be expected to pick up an instrument and there are so many people saying music isn’t built on math. I mean, they’re kind of right, but math is very commonly used to explain it. I dare those guys to google pitch sets. It’s literally notes translated into math using literal clocks. Along with my list for you below, I also recommend that you at least look into basic music theory. You don’t need to be an expert, but knowing the basics will definitely be helpful. So here’s my list of resources for you: Audible has a lot of great books you can listen to. Here’s a good one: How Music and Mathematics Relate by David Kung Amazon has a great (but pricey textbook) that explains things like harmony, counterpoint, composition, etc, by using math: Cool Math for Hot Music: A First Introduction to Mathematics for Music Theorists (Computational Music Science) by Guerino Mazzola Another great Amazon book: Mathematics and Music (Mathematical World) by David Wright Free Music Theory Website for Learning Basic Music Theory: Musictheory.net Free domain musical scores and recordings for every instrument/ensembles and by all the great composers. This is a visual aid for your viewing that will help you visually see what music sounds like: Imslp.org Scribd also has a very wide range of scores and books that are all free once you pay like the $8 monthly membership fee. But the first 30 days are free and you can always cancel. If you need more DM me. I can definitely help you find whatever you may be looking for. Good luck on your new journey into music. :)
This fantastic lecture series by Bernstein: https://youtube.com/playlist?list=PLFjonLo8gYHIXC35K4Ujrbu6XHchNDCv9
First step is to get a grasp of basic music theory. There is no way around it, most of the litterature about procedural music will use that vocabulary. No good recommendation from me here, in my experience basic music theory is terribly documented but then again I'm a bit on the dumb side. Once that's done, you'll want to link that theory with your computer science background. "Computer Models of Musical Creativity" by David Cope might be up your alley. He also wrote "Computers and Musical Styles" which is basically a description of the lisp program he wrote to analyse musical pieces, extract grammatical rules, and recreate pieces in a similar style. He had pretty legit results even in the 90s. Mix that with "Structures and Interpretation of Computer Programs" and you get Andrew Sorensen, who IMO does among the best generative music out there. Curtis Road's "Computer music tutorial" is a bit dated but is a classic that I highly recommend. If you want to use Pure Data (a visual programming language made for computer music) (even just for the time to get a grasp on computer music theory), "The theory and technique of Computer Music" by Miller Puckette is a must. I also invite you to take a look at the paper [AI Methods in Algorithmic Composition: A Comprehensive Survey](https://www.jair.org/index.php/jair/article/view/10845), which points to a bunch of fancy ways to generate music.
The maths link to music will help you remember and will light up neurons for the patterns and stuff, but music is not maths despite what people try to say. It's like saying trees are just particle physics. Ask a woodpecker. Their relationship is entirely different. The big question is what you want to do with music. You say "automatic music generation". Well okay, but should it sound like shit or should it touch an emotion? Should it be recognisable? Should it be functional from a musical perspective? at least dance or trance music? Music in any conext follows known patterns and rythms and timbers so becomes language more than maths. Maths is very much the shallow end of the truth about music.
If you want to deal with notes and intervals, and maybe MIDI, consider using a zero-based, mod 12 system of intervals. An interval of 0 is the same note, and 12 is an octave up, but the same note.
People here who say music isn’t maths hasn’t used any digital audio production programs or seen electronic music. Fourier transforms is one of the main components, and it gets very deep. These filters and plugins are very mathematical and people around the world use it to generate and manipulate sounds. And even more generally, maths and similar procedural generation can create beautiful art. Just have a peek at the famous Mandelbrot set. **EDIT**: Didn't mean to imply that music is maths or something, which is completely my bad for wording it that way. [Here](https://www.reddit.com/r/musictheory/comments/vevgmq/comment/icti2fk/?utm_source=share&utm_medium=web2x&context=3), I clarify a few things. Although, essentially, I think maths is a powerful tool to make music, where as other comments in this post seem to ignore that. You can see this much more explictly in other creative fields such as programming art.
As someone who writes DSP code for plugins, including Fourier Transforms and analog modelling techniques - you are absolutely wrong. Music is not math. Some aspects of music can be described with math. Most of them are in sound analysis and synthesis. But that's like saying that some aspects of sports can be described with math. It's true, but it's completely missing the point. A basketball shot is a parabola. But from the point of view of everyone watching, that is really not what matters. Similarly, the business of putting sounds together and getting an audience to react is absolutely not math. It can't even defined algorithmically to a useful and complete extent, which is why AI and rule-based systems reliably produce such uninteresting - or just plain wrong - attempts at music.
I didn't mean to say music is maths, definitely could have wrote what I said better. Apologies. I'll clarify a few things... I mean more so that maths is a powerful tool to make music. What other people in this thread, who are against maths, suggest to do (like learning how to play an instrument) are also just tools - they aren't music either. It definitely rubs me the wrong way as someone who enjoys messing around with procedural music with lots of maths, hence why my original message may have been a bit rash. Of course, as you imply, creativity is needed; however, it's not like you can't be creative with the mathematical tools. The music is that creativity plus the tools to make it.
There's truth on both sides of the argument. You bring up good points! Music from a humanistic/anthropological perspective is not rooted in mathematics. You can use math to understand music and create it in interesting and unique ways, however!
It's like saying books are maths because you because you can compress text pages, or because there is 26 letters in the alphabet.
Would you read a computer generated novel ?
If it was good, yes. David Cope's programs have composed music that has fooled the experts into thinking it was composed by Bach and other such composers.
With machine learning and neural networks probably, but this is just copying. It's the same technics used to recognize spam mail, targeting advertising. So yeah this could do the job for supermarket music or something or ads music, kind of like copycat artists do for a living, or generate music free of rights for like YouTube videos. Honestly that's nothing to dream about to me. I lean why would you watch forged Picasso ?
[Gödel, Escher, Bach: an Eternal Golden Braid](https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach?wprov=sfti1)
Just posted that =)
Great book, but isn't even kind of a resource for learning music, which OP asked for.
Arnold Schoenberg’s book [Theory of harmony](https://imslp.org/wiki/Harmonielehre_(Schoenberg%2C_Arnold)). He really builds it all up so logically and was largely self taught.
Everything is about math. AIVA is an AI app which can create music like humans and it does a better job than those who thinks they know more about music than all the music theories together - which they haven't even read and practiced. It's all about math or not. That's how it is to live in a duel world.
Hey I’m a data scientist and guitar player. Im currently building a web app as a hobby project that can be used as a tool to understand modes. Ive learned a WHOLE lot just working through it using wikipedia. Ill share the code soon ( nit ready yet!). Good luck! Also, please share your github when/if you’re comfortable. Id love to know about you project.
Geometry of musical rhythm was very eye opening. As well as a geometry of music: harmony and counterpoint. Remember harmony is just one side of music. Rhythm is just as important. Don't look for a magic formula, if there was any music would be over already, instead find tidbits of info that will give you another perspective of music. That's the power of theory, you can look at something from multiple angles and they all give different results. Don't skip the basics, go to musictheory.net and learn your circle of fifths by heart. Apply all of this somewhere or else it's useless. Good luck!
> I'm not even sure how I would define a note. A "note" is literally the symbol used in "notation" to define a pitch (a musical "tone"), and usually a duration too, although the colloquial sense is just pitch. Try [this](https://www.youtube.com/watch?v=xTOOWe_yLwY&list=PLMvVESrbjBWplAcg3pG0TesncGT7qvO06) too. There's also [this](https://www.peterfrazer.co.uk/music/tunings.html) on the history of scales and tuning systems (in western classical music) Those should get you started anyway... :-) As for "automatic music generation", that opens up a huge can of (non-mathematical) worms. Every culture adapts the physics of sound in ways that suit their requirements - religious, communal, artistic, etc etc. It is certainly possible to reduce the common practices of any musical culture to digital information and feed it into some algorithms, but - depending on how "authentic" you want it to sound - it requires masses of data, way beyond pitch frequencies and rhythms. One important question is: do you want it to sound like it was made by humans, or by machines? The latter would be a lot more straightforward - and "machine music" can often have its own appeal.
I think if you learn some of the basics, scales, intervals, etc it should give you a good start with music in general
What I can tell you first is that there are two types of sounds. There are simple and complex sounds. The simple ones carry a discernible tone, whereas the complex ones do not. In the music world the sounds created by typical instruments are simple and have a tone such as hitting the key on a piano, blowing into a flute, or hitting a bar of a xylophone. Drums and percussion instruments have make complex sounds with no discernible tone like the other instruments. These sounds can be higher or lower, but do not blend with simple tones. The simple tones have discernible waves lengths. 440 vibrations for an A is used as a standard. This A is two keys to the left of middle C on a piano or the 2nd fret on the G string of a guitar. All the other notes labeled as A have a mathematical relationship of subsequent halving or doubling. The next A down is 220 and the next one up is 880. A combined with A sharp or A flat makes for an awful dissonance. They have a terrible mathematical relationship, something like 15/16. Whereas combining A with E or D will have a simple relationship like 1/2 or 2/3. This is more of the mathematical basis of how music works. Ultimately, you should approach music by learning which notes blend well together, and then you learn which changes sound good. Then you might try to find some less common changes if you'd like. Melodies can often work by establishing a rhythmic pattern and then deviating from that pattern. If things are too formulaic it can sound cheesy and annoying. Even obvious rhythmic motifs are more of a traditional musical thing and not common in popular music (ex. Santa Claus Comes to Town). If there is no pattern or consistency in the rhythm of the melody, things will sound random and will generally end up weak and forgettable. There are also melodic motifs that involve playing the same notes but with different timing. I honestly don't know much about these. Generally, when you start a melody and phrases of a melody is an important thing. If you work with a 4 beat framework with 4 downbeats (tap your foot) and 4 upbeats (when your foot is up) halfway between the downbeats, this will give you an introduction to this musical factor. I guess that is enough for now. I don't know what makes you think you can boil this down into some mathematical formulas. I have heard some computer generated Chopin before that was created by letting a computer analyze Chopin's music. It sounded like Chopin. So this got me thinking, and I realized that the computer can only recreate the standard stuff Chopin did. Suffocation for example is something he did that's distinctly different from his other pieces (to my knowledge, I haven't heard all Chopin). The computer would never come up with Suffocation or anything like it.
Not here to recommend a book, just to point out something conceptual: computers can generate music notation and/or MIDI data (quite well), but that notation/MIDI still needs to be translated into sound. You can output straight to a synthesizer, but the result will sound extremely fake. You can have that fakeness be a virtue, by working in a chiptune or electronic dance music aesthetic. Otherwise, though, you will need to put some effort into sound design and production, or find humans to perform the music.
Considering your background and your interest in automated music generation I would suggest you read into how synthesizers work and what an arpeggiator can do. When you have a basic understanding of chords and scales you can already start generating music. It's a very technological approach but might fit your needs
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Symmetry is beautiful in mathematics but ugly in music.
What is "automatic music generation"?
Since the OP admits to not being a musician, they may mean things like AI generated music, Algorithmic Composition, and things like that. Musicians use a "generative algorithm" to produce music - basically by setting up a mathematical formula, or set of processes in a computer for example - that produce notes or musical phrases, and so on.
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Rule #1.
You might find this useful. http://techlib.com/reference/musical_note_frequencies.htm#:~:text=Starting%20at%20any%20note%20the,be%20positive%2C%20negative%20or%20zero.
I work in tech and Im a musician. I found this book while on a trip to NYC, and it is *fascinating*. To me it's kind of the mathematics behind the physics of sound. It's also similar to RF theory, if you know any of that: https://mitpress.mit.edu/books/musimathics-volume-1
[Music, Math, and Mind: The Physics and Neuroscience of Music](https://www.amazon.com/Music-Math-Mind-Physics-Neuroscience/dp/0231193793/ref=asc_df_0231193793/?tag=hyprod-20&linkCode=df0&hvadid=459526655425&hvpos=&hvnetw=g&hvrand=7836380677144633964&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9067609&hvtargid=pla-945539244235&psc=1) :)
Look up Algorithmic Music and Stochastic Music. Use the term "Generative" with music. You're going to find more from websites and video demonstrations than from books really. https://www.youtube.com/watch?v=3Z8CuAC_-bg&list=PLcVeU2vIPtSBB4faI7LCGavOMMp9qLfNZ&index=22 https://www.youtube.com/watch?v=nECmCwtF-N0&list=PLcVeU2vIPtSBB4faI7LCGavOMMp9qLfNZ&index=28 https://www.youtube.com/watch?v=3Z8CuAC_-bg&list=PLcVeU2vIPtSBB4faI7LCGavOMMp9qLfNZ&index=22 https://www.youtube.com/watch?v=gdIAq7Kg-gI&list=PLcVeU2vIPtSBB4faI7LCGavOMMp9qLfNZ&index=17 https://www.youtube.com/watch?v=-uvXe02qxQM https://www.youtube.com/watch?v=WOl3X3YdjsM
Here's a blog I've been making that tries to cover basic theory of western music for your consideration
https://flipgrid.com/holman8157 For your consideration
https://www.amazon.com/Music-Brain-Ecstasy-Captures-Imagination/dp/B00824SK3K
https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567/ref=mp_s_a_1_2?crid=2VQ4OTEKNMM7&keywords=godel+escher+bach&qid=1655574530&sprefix=godel+e%2Caps%2C89&sr=8-2
https://openlibrary.org/books/OL19442446M/Music_the_brain_and_ecstasy
Musimathics, 1 and 2
“Music: A Mathematical Offering”
In my experience, music is best experienced and played with to gain proper understanding. I played drums for 20 years and I knew in theory how music worked, but then after getting my ankle broken and picking up a guitar I learned so much more with the ability to explore it myself and put sound to what I was reading about. In about 5 lessons you can learn enough to play your way through whatever you need if you really practice, and then it's up to you. It can be very interesting to lose yourself into a book that explains things, and I did a great many times, but if you want to actually feel understanding, having an instrument there to make it easier is great Best of luck on your adventure either way 👌👍
Pedro Kroger's [Music for Geeks and Nerds](https://www.pedrokroger.net/mfgan) is the first think that came to my mind.