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Topic: Beginner music theory for people OK with some maths?  (Read 4715 times)

Offline motivation

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Hi all and thanks for all your efforts - I've already learned some useful things from this forum.

Quick version: any entry-level music theory books / websites / apps / etc. that don't try to hide mathematical concepts where they come up, and assume only a bare minimum of musical literacy?

Not looking for "the maths of music" - just basic music theory but presented by somebody who "gets" how to explain things to people who know nothing yet about music but enough about maths.



Long version:

My background: I'm in my mid forties, didn't learn any instrument as a child, and I'm now learning from Faber "Adult Piano Adventures" without a teacher, wanting to play classical music.  Slow progress at the moment due to only 2 practice sessons of 40 mins per week - I need to increase that.  I started 15 months ago, slipped into just learning / playing only Messiaen's "Regards du Pere" instead of actual practice (I know, that's weird and I've ruined my learning process, you're probably right - but it was and is very motivating!).  5 months ago started on the Fabers' book, I'm only 1/3 through still.

I think I would benefit from starting to learn about music theory, but right now I'm doing nothing on that.

I'm a hard science/maths sort of person and I think music theory connects with that well, but my very strong impression from my limited past experience is that many (most?) authors/teachers/learning materials don't do well communicating music theory to people like me: no music background but not scared of maths.  From my point of view, musicians write in a very quirky foreign language, which obscures, for musical illiterates like me, what are sometimes relatively simple concepts behind a wall of "the curse of knowledge" https://en.wikipedia.org/wiki/Curse_of_knowledge.

To be clear, I'm happy to eventually learn that foreign language over time, I don't expect music theory to be 100% maths about music, and nor do I want to learn about the maths of music for its own sake.  But I do think at my level the "language issue" and perhaps a presumption that "obviously nobody wants to see ANY maths" are potentially major hindrances for me in making some rapid initial and motivating progress, given that I've seen from occasional glimpses that some of the musical content is far easier for me to start to grasp with the help of somebody who has some mathematical background and knows how to talk to other people with that sort of background.  In fact I have a strong memory of being put off music as a child by exactly this kind of problem (not the only problem, but certainly one).

Any advice for somebody like me?  Books, general advice/tips, suggestions how to stay motivated, online tools, ... whatever you think is relevant.

One note: I'm keen to hear about online things, but to avoid annoyance let me be open up front about one of my peculiarities: I'm also a free (as in freedom) software geek who's keen on decentralisation, and often steer away from many online services (music or otherwise).  So I'm actually very keen to hear about such things, but I'm interested much more in what they do, and not so much in simple links to websites or apps that are rather opaque until you sign up - I *might* not sign up, but I think I might well still learn something very useful from hearing about what it is they're doing!

Thanks again

Offline mad_max2024

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Re: Beginner music theory for people OK with some maths?
Reply #1 on: March 26, 2022, 03:56:19 PM
to be honest I find watching youtube videos on theory concepts to be both fun and educational (Though you always need to be critical about them)
Some channels I follow are Musictheoryforguitar, Jazzpianoschool, Rick Beato, Charles Cornell, Adam Neely, Noah Kellman, Jen Larsen. There are probably many others.

When it comes to books I found Mark Levine's books on Jazz Harmony to be helpful (but maybe not very accessible for beginners)

Some things to keep in mind for music theory:
The point of theory (imo) is to explain the sounds you hear and to build a system that allows you to understand, replicate and change those sounds to express what you want. Different people will often have their own systems and their own ways of thinking using their own labels which can make things confusing if you don't understand the concepts and focus on the labels they use.

Also don't think of theory as a set of rules that you can't break. It is more like a map of what people before you found that works and that you can use to guide yourself to get the sound you want. If you ever find something that sounds good to you but doesn't "fit" the rules you learned just go with it. You can try to find a way to explain it or analize it later (There usually will be one). The sound is always more important than the theory. Theory is not there to restrict you.

Also, music is subjective and relative and you should always keep in mind that there is usually not one way to interpret something. Very often you can ask the same question to two different people and get two different answers that can both be right. It is a bit unlike maths in that regard. Chords are not the notes you play or the physics of the sounds you make, they are the sounds you hear in your brain. And your brain will fill in gaps and interpret things as it wants, and different brains might fill in the gaps in different ways.
So... while it's good to analyze and build a system try to keep in mind that things are often not black and white and there might be none or more than one correct answer. ie You may be taught that C, E, G, B make a Cmaj7 chord (which is true) but it can also be a rootless Am9 depending on context. Bb, Db, E(Fb), Ab is a Bbm7b5 chord but it's also a voicing I use all the time for C7alt or C7b9b13. I remember transcribing a Bill Evans solo where he phrased an Fm with just an Ab and a G.
Sometimes even in the same context I can disagree with my teacher on what a chord is and we can both just understand each other's point of view and agree that we are just hearing it differently or thinking about it in a different way and that we are both "right".
So try to understand the concepts and make your own judgements. Trust your ears (and brain) and stay away from internet arguments.
Musicians love to argue.
Good Luck
I am perfectly normal, it is everyone else who is strange.

Offline motivation

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Re: Beginner music theory for people OK with some maths?
Reply #2 on: March 26, 2022, 04:11:12 PM
to be honest I find watching youtube videos on theory concepts to be both fun and educational (Though you always need to be critical about them)
Some channels I follow are Musictheoryforguitar, Jazzpianoschool, Rick Beato, Charles Cornell, Adam Neely, Noah Kellman. There are probably many others.
Thanks!

Quote from: mad_max2024
Different people will often have their own systems and their own ways of thinking using their own labels which can make things confusing if you don't understand the concepts and focus on the labels they use.

So... while it's good to analyze and build a system try to keep in mind that things are often not black and white and there might be none or more than one correct answer.
This seems good advice, but though I sneaked in a very broad request for random good advice and am grateful for it, it's true the main focus of my question is on those parts of music theory whose explanations are fundamentally mathematical.  It's not that I want to focus on those parts of music theory, rather that I don't want to suffer through needlessly non-mathematical attempts to explain them.

Quote from: mad_max2024
So try to understand the concepts and make your own judgements and stay away from internet arguments.
Musicians love to argue.
Wait surely people on web forums never get into arguments??

Offline mad_max2024

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Re: Beginner music theory for people OK with some maths?
Reply #3 on: March 26, 2022, 04:17:46 PM
yes, I know I ranted a bit. That happens.

I am perfectly normal, it is everyone else who is strange.

Offline motivation

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Re: Beginner music theory for people OK with some maths?
Reply #4 on: March 26, 2022, 04:34:27 PM
yes, I know I ranted a bit. That happens.
It didn't come across as one.

In fact perhaps I need to be clearer just how basic where I'm starting from is: maybe the phase "music theory" is too grand?  I don't even have the knowledge to explain what I don't know, because I don't know any of it.  Basically whatever your expectations are of my knowledge level, lower them and you won't be far off :)

Here's an example of what I had in mind when I said I'd had glimpses of understanding as an adult of some things I suspect I was frustrated about as a child because of technical musical language obscuring simple concepts (and you can see "mathematical" is also perhaps too grand a phrase in this case) - scroll down to "Diatonic Chords" "Chords that fit in a particular Key.":

https://www.lightnote.co/

But I looked at that website before I got my piano and have since forgotten even what little I learned from this!

Offline bwl_13

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Re: Beginner music theory for people OK with some maths?
Reply #5 on: March 26, 2022, 06:45:29 PM
I agree with the statements about theory and pretty much everything mad_max2024 said.

I might be missing something but mathematical background isn't really something that is needed for music theory, especially introductory stuff. Perhaps tuning theory or the physics of sound but that stuff isn't really the sort of stuff that musicians use on a day to day basis. If mathematics is required to teach a concept, most resources and teachers will explain it as such. However, most music theory does not require it and if it were to use it, then it would be needlessly mathematical. If you insist that these concepts are fundamentally mathematical, I would appreciate you giving me the name of an introductory concept like that.

If you're frustrated about technical language in theory, it's kind of like being frustrated with doctors using medical terminology or any other system that professionals use. This stuff is really necessary when you're trying to be specific and communicate your ideas to another musician, and again, most of this language is best expressed in musical terms and not mathematical. If you prefer to call perfect fifths "3:2s" then you're be missing the point of the terminology. Music is just not as universal as maths, so explaining that "A simple ratio between the notes means they sound nice together" is a statement assumed to be true in Western tonal music, it's not the case across the globe. The tuning systems and intervals across the world do tend to follow some universals (harmonic series for instance) and I'm also pretty sure fifths are quite universal as intervals, but regardless this stuff isn't really introductory and won't help expand your knowledge of the piano.

Feel free to let me know if I missed something in your post or misunderstood it. I'm still confused as to why this thread focuses on mathematical explanations of theory.
Second Year Undergrad:
Bach BWV 914
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Reger Op. 24 No. 5
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Offline lelle

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Re: Beginner music theory for people OK with some maths?
Reply #6 on: March 26, 2022, 06:56:17 PM
Hi all and thanks for all your efforts - I've already learned some useful things from this forum.

Quick version: any entry-level music theory books / websites / apps / etc. that don't try to hide mathematical concepts where they come up, and assume only a bare minimum of musical literacy?

Not looking for "the maths of music" - just basic music theory but presented by somebody who "gets" how to explain things to people who know nothing yet about music but enough about maths.



Long version:

My background: I'm in my mid forties, didn't learn any instrument as a child, and I'm now learning from Faber "Adult Piano Adventures" without a teacher, wanting to play classical music.  Slow progress at the moment due to only 2 practice sessons of 40 mins per week - I need to increase that.  I started 15 months ago, slipped into just learning / playing only Messiaen's "Regards du Pere" instead of actual practice (I know, that's weird and I've ruined my learning process, you're probably right - but it was and is very motivating!).  5 months ago started on the Fabers' book, I'm only 1/3 through still.

I think I would benefit from starting to learn about music theory, but right now I'm doing nothing on that.

I'm a hard science/maths sort of person and I think music theory connects with that well, but my very strong impression from my limited past experience is that many (most?) authors/teachers/learning materials don't do well communicating music theory to people like me: no music background but not scared of maths.  From my point of view, musicians write in a very quirky foreign language, which obscures, for musical illiterates like me, what are sometimes relatively simple concepts behind a wall of "the curse of knowledge" https://en.wikipedia.org/wiki/Curse_of_knowledge.

To be clear, I'm happy to eventually learn that foreign language over time, I don't expect music theory to be 100% maths about music, and nor do I want to learn about the maths of music for its own sake.  But I do think at my level the "language issue" and perhaps a presumption that "obviously nobody wants to see ANY maths" are potentially major hindrances for me in making some rapid initial and motivating progress, given that I've seen from occasional glimpses that some of the musical content is far easier for me to start to grasp with the help of somebody who has some mathematical background and knows how to talk to other people with that sort of background.  In fact I have a strong memory of being put off music as a child by exactly this kind of problem (not the only problem, but certainly one).

Any advice for somebody like me?  Books, general advice/tips, suggestions how to stay motivated, online tools, ... whatever you think is relevant.

One note: I'm keen to hear about online things, but to avoid annoyance let me be open up front about one of my peculiarities: I'm also a free (as in freedom) software geek who's keen on decentralisation, and often steer away from many online services (music or otherwise).  So I'm actually very keen to hear about such things, but I'm interested much more in what they do, and not so much in simple links to websites or apps that are rather opaque until you sign up - I *might* not sign up, but I think I might well still learn something very useful from hearing about what it is they're doing!

Thanks again

I'm quite the music theory nerd, but I wouldn't necessarily say that there is a lot of math involved. It's just kind of a logical system where things fit neatly together in a very satisfying way once you get it - which can take a while.

I'm curious if you could write an example or two of this:

Quote
I'm a hard science/maths sort of person and I think music theory connects with that well, but my very strong impression from my limited past experience is that many (most?) authors/teachers/learning materials don't do well communicating music theory to people like me: no music background but not scared of maths. From my point of view, musicians write in a very quirky foreign language, which obscures, for musical illiterates like me, what are sometimes relatively simple concepts behind a wall of "the curse of knowledge"

I could try to offer some explanations of the things that were unclear to get you going!

Offline mad_max2024

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Re: Beginner music theory for people OK with some maths?
Reply #7 on: March 26, 2022, 07:12:53 PM
Yes, if there are any specific things you don't understand you can ask in this forum and you're likely to get a few replies.


I am perfectly normal, it is everyone else who is strange.

Offline mad_max2024

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Re: Beginner music theory for people OK with some maths?
Reply #8 on: March 26, 2022, 07:20:23 PM
I don't think I can help you with a mathematical language or application for music theory.  Like I said music is highly subjective and I don't really see how you can apply mathematics to explain it (and I also like maths).

That being said, if the physics behind the sounds interest you you can try to do some research on the harmonic series. Or acoustics in general. That is a very interesting read.
I am perfectly normal, it is everyone else who is strange.

Offline frodo1

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Re: Beginner music theory for people OK with some maths?
Reply #9 on: March 26, 2022, 07:20:55 PM
I'm sorry, but I just can't resist asking:

Why "maths"?  We say "math" in English?

Actually I just googled "maths vs math" and it took google 6 seconds to come up with this.  It usually takes google a millisecond.  Must be a tough question  ;)

Math is preferred in the U.S. and Canada, and maths is preferred in the U.K., Australia, and most other English-speaking areas of the world.

Offline ranjit

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Re: Beginner music theory for people OK with some maths?
Reply #10 on: March 26, 2022, 08:00:54 PM
There is actually not that much mathematics involved in music, people who say there is usually have a pretty poor and superficial understanding of math. It's unfortunate, because I had hoped there would be more math involved as it would allow me a shortcut to learn the subject (just as math students often breeze through physics courses for example).

It's a logical system for the most part, that's all there is to it. Perhaps you need to use some fractions to line up pitches and rhythms, but that's hardly enough to claim that math is present in music, unless you're in elementary school yourself! (As a side note, it might reflect on our education system that it's a common sentiment that music involves quite a bit of math...)

I would say it actually involves more ear training. You need to be able to hear the chords and process voice leading and such in your head. It requires a bit of visualization to be able to see the keyboard with shifting chords in your mind's eye.

The closest I have seen to math is by our very own Ted, using the Polya theorem to enumerate all possible distinct chords, if I remember correctly. But that in of itself probably won't be useful to most in order to create music.

I do think there is some overlap among people who are good at math and those who are good at music/music theory. However in my experience this is mostly due to a preference for logical thinking which speeds up the learning of certain systems and general smarts. I do think mathematics students are better than average at learning and processing music in most cases, but I don't see a direct link from math to music. It's probably somewhat better pattern recognition ability when it comes to musical structures.

Offline motivation

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Re: Beginner music theory for people OK with some maths?
Reply #11 on: March 26, 2022, 08:13:11 PM
If you insist that these concepts are fundamentally mathematical, I would appreciate you giving me the name of an introductory concept like that.
Hi, thanks for replying!

Not sure how to make this not sound prickly, but: did you look at the post of mine immediately before yours?  I'm talking about the part that starts with "Here's an example"

If you prefer to call perfect fifths "3:2s" then you're be missing the point of the terminology. Music is just not as universal as maths, so explaining that "A simple ratio between the notes means they sound nice together" is a statement assumed to be true in Western tonal music, it's not the case across the globe. The tuning systems and intervals across the world do tend to follow some universals (harmonic series for instance) and I'm also pretty sure fifths are quite universal as intervals, but regardless this stuff isn't really introductory and won't help expand your knowledge of the piano.
I think you might be hearing more in my request than I actually intended, or likely I was unclear  :)

I don't want somebody to write a book in which everything is renamed - really I'm looking for material from people who understand where somebody like me is coming from, so that I don't struggle needlessly with concepts described in terms of a lot of musical background knowledge involving quirky conventions and language.  I'm sure often concepts don't really depend on those things, and may be actually obscured by it.  I don't insist that then a standard English musical language term must not be introduced, having explained the concept - more the opposite.  I think there's nothing special to music here, it's common to communication of all knowledge.  My guess is that somebody with the same mindset will do better at that job.  That is going on my actual, if limited, experience - even my limited experience about music theory! - as I've explained.

And as I say, I know basically nothing about music theory, so I'm sure you wouldn't expect me to dump a long series of music theory examples to back up my hunch here.  That's not how this works  ;)

Quote
Feel free to let me know if I missed something in your post or misunderstood it. I'm still confused as to why this thread focuses on mathematical explanations of theory.
Just one other example: the one you gave above about perfect fifths being related to ratios (being vague here since I don't know what a perfect fifth is!).

One more: I very vaguely recall doing a tiny bit of scribbling to see how the 12-note thing works out sort of neatly mathematically.  I honestly don't remember enough right now to tell you exactly what I did.

Offline frodo1

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Re: Beginner music theory for people OK with some maths?
Reply #12 on: March 26, 2022, 08:18:08 PM
Pythagoras was a brilliant mathematician but unfortunately did not believe irrational numbers existed.  I think he drowned a person that believed otherwise.  And so he was not able to come up with the formula:

2^(1/12) is the ratio of 2 frequencies that are a semitone apart.

Offline motivation

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Re: Beginner music theory for people OK with some maths?
Reply #13 on: March 26, 2022, 08:27:28 PM
I'm quite the music theory nerd, but I wouldn't necessarily say that there is a lot of math involved. It's just kind of a logical system where things fit neatly together in a very satisfying way once you get it - which can take a while.
Ha, I think some people are latching on to the word maths as if I'm talking about knot theory or something.  But I hoped I'd already corrected that misconception with the first example I posted (search for "and you can see "mathematical" is also perhaps too grand a phrase in this case") and again, I'm talking much more about people's backgrounds making it easier or harder for them to explain concepts to people of other backgrounds than I am about anything fancy.

Quote
kind of a logical system where things fit neatly together in a very satisfying way once you get it

Yep, sounds like maths to me  ;)

Quote
I could try to offer some explanations of the things that were unclear to get you going!

Thanks, I might take you up on that later!  As I say, I've not studied anything like this for years, so naturally I'm not coming at this with a list of specific questions.  However, my experience is that often musical people suffer badly from the curse of knowledge when writing notionally introductory explanations - as everybody does - and that on the occasion when I've come across people with some other background in addition to music (or just having thought about or tested their explanations carefully perhaps) explaining similar concepts, I've understood them and thought: that's night and day from other experiences I've had where more musical people tried to explain similar concepts to me.  I'm sure you'll agree that those experiences over 40 years are not really something that can easily be dumped out onto a web page.
Quote
I'm curious if you could write an example or two of this:
As I say, I've done really nothing on this for years, so my position here is based on past experience of being perplexed, then enlightened on a few little things over past years (some of this from childhood!).

But some things from this thread:

https://www.pianostreet.com/smf/index.php?topic=68835.msg718024#msg718024
https://www.pianostreet.com/smf/index.php?topic=68835.msg718037#msg718037

Offline frodo1

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Re: Beginner music theory for people OK with some maths?
Reply #14 on: March 26, 2022, 08:39:50 PM
There is actually not that much mathematics involved in music, people who say there is usually have a pretty poor and superficial understanding of math. It's unfortunate, because I had hoped there would be more math involved as it would allow me a shortcut to learn the subject (just as math students often breeze through physics courses for example).

It's a logical system for the most part, that's all there is to it. Perhaps you need to use some fractions to line up pitches and rhythms, but that's hardly enough to claim that math is present in music, unless you're in elementary school yourself! (As a side note, it might reflect on our education system that it's a common sentiment that music involves quite a bit of math...)

I would say it actually involves more ear training. You need to be able to hear the chords and process voice leading and such in your head. It requires a bit of visualization to be able to see the keyboard with shifting chords in your mind's eye.

The closest I have seen to math is by our very own Ted, using the Polya theorem to enumerate all possible distinct chords, if I remember correctly. But that in of itself probably won't be useful to most in order to create music.

I do think there is some overlap among people who are good at math and those who are good at music/music theory. However in my experience this is mostly due to a preference for logical thinking which speeds up the learning of certain systems and general smarts. I do think mathematics students are better than average at learning and processing music in most cases, but I don't see a direct link from math to music. It's probably somewhat better pattern recognition ability when it comes to musical structures.

I agree with all here.  Polya theorem - that's impressive!  Is Ted a mathematician?

Edit:  Polya theorem?  Can you explain how combinatorics can be used in a meaningful way for chord construction??  ???

Offline motivation

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Re: Beginner music theory for people OK with some maths?
Reply #15 on: March 26, 2022, 08:53:28 PM
There is actually not that much mathematics involved in music, people who say there is usually have a pretty poor and superficial understanding of math. It's unfortunate, because I had hoped there would be more math involved as it would allow me a shortcut to learn the subject (just as math students often breeze through physics courses for example).
I'm happy that you know some fancy maths.  Well done.  ;)

Quote
It's a logical system for the most part, that's all there is to it. Perhaps you need to use some fractions to line up pitches and rhythms, but that's hardly enough to claim that math is present in music, unless you're in elementary school yourself!
Think "curse of knowledge" and "mindset", not "abstract algebra".

It does seem a little bit ironic that I've showed up proclaiming my total ignorance of music theory, only to find the response is that I'm... wrong about music theory!

I guess I over-used the word maths in my first post - put that down to my not having studied any music theory.  But I hope I've clarified the thought and experiences behind it?  I think those are unchanged.  And heck, I even stick by the word "mathematical", ha.

Quote
I would say it actually involves more ear training. You need to be able to hear the chords and process voice leading and such in your head. It requires a bit of visualization to be able to see the keyboard with shifting chords in your mind's eye.
Can you explain what "process voice leading" means?

Quote
The closest I have seen to math is by our very own Ted, using the Polya theorem to enumerate all possible distinct chords, if I remember correctly. But that in of itself probably won't be useful to most in order to create music.
Thanks, but definitely not what I have in mind!  Again, think "mindset" not "Polya theorem"!

Quote
I do think there is some overlap among people who are good at math and those who are good at music/music theory.
I think this question is quite distinct from the one I raise in this thread.

Offline frodo1

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Re: Beginner music theory for people OK with some maths?
Reply #16 on: March 26, 2022, 09:00:10 PM
OP - If you are able to read and understand any standard pre-calculus book - you will have no problem reading and understanding ANY standard beginner level music theory book. 

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