Music and Maths

[Leon Sumbitches]

This might be a bit of a weird one so bear with me.

 

I've finally got round to learning a lot of music theory lately

(I've been working through this, it comes recommended if anyone else is so inclined: http://www.amazon.co.uk/Theory-Computer-Musicians-Michael-Hewitt/dp/1598635034)

and what's striking is that pretty much every aspect of music boils down to mathematics of one sort or another- melody and scales, harmony, rhythm, synthesis and all sorts of sound design/effects shenanigans are rooted in numbers. For whatever reason, music seems far more maths-based than other creative arts like writing or painting.

 

Are there any aspects of maths that you've found useful to you musical development in some way? Any particular principles, etc? Anything worth learning or looking into?

 

It just seems interesing that most aspects of music can be broken down into numbers, and yet it can still move us in such awesome ways.

 

In all likelihood I'll probably lose interest and not bother following this up but I thought it worth posting while the thought's on my mind, seems like quite a watmm-ish topic.

 

[Squee]

Counting to 4 has helped me quite a bit :)

[plastic]

2^(1/12) for life, fool.

[Ragnar]

I'm over it now but I liked how the pythagorean tuning all worked out to whole numbers... somehow. Considering a second (the time unit) is kinda arbitrary as fuck?

[xox]

on number that's hunting me for yrs now in music production is the 7th root of -1 ...damned those chords!

[joseph]

1+2+3+4+...=-1/12

[Diabrotikos]

Music theory made me understand i was using the same harmonic progression in most of my songs. Besides that, i already knew i was writing all my stuff in 4/4, but i never really got good results with other time signatures, so music theory allow me to understand better what is "working" in the music of other artists. Nowadays, i can make more varied and playful music, and that is very satisfying.

 

I think ignorance is bliss when you start making music, cause you're focused on your sensations and not your logic. But at a certain point, you should move to music theory, or your art will stagnate.

[Guest brendyman]

I think ignorance is bliss when you start making music, cause you're focused on your sensations and not your logic. But at a certain point, you should move to music theory, or your art will stagnate.

 

I wholeheartedly disagree.

 

So, for the longest time (as early in life as I can remember) I've wanted to be a professional musician. I've wanted to go to school for music and stuff since I even knew there was school for music. And, since I'm going into college now I figured I should finally take some music classes, this will be fun, right?

 

Ha, no.

 

The introduction to music theory class is a piece of cake (I took 10 years of piano lessons, starting from a young age so most of it was review). But when we got into the actual music theory class, Music Theory I, it was (and still is, I'm still enduring this class) hell. I've spent the past 7 years (I started when I was 12, I'm 19 now) honing my own composition techniques. My own rules, my own things that work for me, things I've found out that work for certain things and don't work for others, I feel like I've got a pretty good understanding at this point. So when I got into this class (and it's at this point I'd like to point out, I'm pretty sure the majority of my hate is stemming from my contempt for my instructor, she's extremely biased against anything that isn't classical), I was hit with a bunch of awful "rules" for writing music.

 

--------------

 

"You can't have two consecutive perfect fifths."

"Why?"

"It sounds...empty, just trust me, you don't want to do it."

"But what if that's what I'm going for?"

"You're not."

"I can think of a couple instances where it might be fitting."

"No, you can't. It sounds bad, and you'll learn why later."

 

--------------

 

"You can't have more than an octave between two voices."

"Why?"

"Same thing as with the perfect fifths, it just sounds empty."

 

---------------

 

"The Dominant (V) chord must always resolve to the Tonic (I), but the Subdominant (IV) can either resolve to the Dominant (V), or the Tonic (I)."

 

"P.S Beethoven broke these rules and was revolutionary BUT YOU CAN'T"

 

---------------

 

"Anyone who writes music in strophic form is mentally retarded."

 

---------------

 

"You can take your 20th-century experimental John Cage and shove it."

 

---------------

 

"Rap isn't music."

 

---------------

 

And she conveniently skips over any segment of our textbook that says "Despite all of these rules, a melody or compositional choice may supersede these rules" or anything along those lines.

 

Like, she's supposed to be teaching the next generation of musicians, composers, etc. and how can she even do that if she discourages experimentation?

 

Okay, I ranted. Sorry about that. But my point is, I don't think learning music theory is going to help my music one bit. I feel like if I start to learn all these rules and regulations (and exceptions to the rules [then exceptions to those exceptions, I'm not joking]) I'm just going to start subconsciously following them and then my art will stagnate.

[LimpyLoo]

Well there's the problem: can't and shouldn't have no place in music theory.

 

 

 

Music theory isn't a bunch of rules to be followed. You simply have a shitty teacher. That's not music theory's fault.

[YEK]

my piano teacher once told me that the pink panther theme song breaks all of the theory rules... i know nothing of theory but yeah

[LimpyLoo]

 

But my point is, I don't think learning music theory is going to help my music one bit. I feel like if I start to learn all these rules and regulations (and exceptions to the rules [then exceptions to those exceptions, I'm not joking]) I'm just going to start subconsciously following them and then my art will stagnate.

 

 

Get a better theory teacher, and don't dissuade people from learning. That's just idiotic.

[jmbf44]

The first three semesters of music theory are really just a summation of the "common practice" period of western art music (read: old white Europeans males writing classical music between 1600 and 1900). If you actually write music like that you'll be taken seriously in a very small number of circles (if you plan on sticking with it, during the fourth semester you basically study how composers in the 20th/21st centuries completely disregard and actively rebel against that kind of stuff). Theory classes are useful for understanding why things sound a certain way, like your example of parallel 5ths, but I don't think they're particularly applicable to pop music. Theory isn't necessarily going to make you a better musician, it's just going to give you more tools. Also, your teacher sounds like a dick.

 

On topic: I remember reading a book by Charles Wuorinen called Simple Composition and early in the book, he talks about the sort of raw materials of music. He had pitch and rhythm lumped into the same category, because it turns out both pitch and rhythm are the same thing (oscillations), rhythm being around 0-5 hz and (audible) pitch being between 20 and 20,000 hz. That was sort of a mind blowing concept when I first read it.

[Guest brendyman]

On topic: I remember reading a book by Charles Wuorinen called Simple Composition and early in the book, he talks about the sort of raw materials of music. He had pitch and rhythm lumped into the same category, because it turns out both pitch and rhythm are the same thing (oscillations), rhythm being around 0-5 hz and (audible) pitch being between 20 and 20,000 hz. That was sort of a mind blowing concept when I first read it.

 

Wow, I've never thought about it like that, that's definitely really interesting.

 

And yeah, I know it's more of my teacher that's the problem and not the theory itself, but it's one of those things that sort of gave me an awful first impression of what it would be like.

 

That being said, I'm probably doing to switch my degree to sound design instead. It's a much more experimental field and it's more up my alley than theory (although I might still try to learn more on my own).

 

Back on topic, I've always wanted to learn more about the mathematics of music. Acoustics fascinate me (one time I tried tuning two octaves on my piano to "just intonation" and that was cool as hell). I picked up Oliver Sacks' Musicophilia at Goodwill not too long ago but I haven't gotten around to reading it yet.

[LimpyLoo]

<p>But back to the math issue...I have found geometry to be more instructive than math per se.</p>
<p> </p>
<p>As pretentious as it may sound, I have a fascination with applying the ideas of cubism to the cliches and conventions of harmony, rhythm, melody and form. The appeal for me is taking very simple stuff--the elements of a kindergarten music class, really--and toying with it like a cubist would. </p>
<p> </p>
<p>Everything can be stretched like silly puddy: '8th-note', '8th-note', 'quarter-note' can be elongated to make 'dotted-8th', 'dotted-8th', 'dotted-quarter,' for instance. (Obviously this is kiddie stuff on the surface, but when actually applied in the context of music it makes for interesting results).</p>
<p> </p>
<p>Harmony offers some pretty cool opportunities. A basic triad can be treated like a normal human face, or anything familiar, and distorted with dissonant color tones or bass notes, or large intervals. You could, say, take the top note of a chord and add above it a minor-9th, and then do that to an entire chord sequence, you would get a very cubist effect, like a face with an ear on top of the head.</p>
<p> </p>
<p> </p>
<p>And I think melody is the most overtly geometric, and so can be manipulated just like geometric shapes.</p>
<p> </p>
<p>                                                                     G</p>
<p> </p>
<p>      E</p>
<p>   D   D                                                      D     D</p>
<p>C        C        can be warped to make    C           C     or inverted to make  C         C</p>
<p>                                                                                                                     Bb  Bb</p>
<p>                                  </p>
<p>                                                                                                                         F</p>
<p> </p>
<p> </p>
<p>And then there's form, which is pretty thoroughly explored in <em>Godel, Escher, Bach</em>.</p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p>Anyway, taken as fragments none of this stuff is very groundbreaking, of course. But I think it's potent stuff and whenever I actually hear it being applied or explored in someone's music I get a half-chub.</p>

 

 

edit: uh, I worked so hard on this post *cries*

[peace 7]

I'm much more into the *heartfelt* side of ze arts. Everything can be broken down into maths in this world, but numbers cannot translate directly from the heart. So numbers and all can help one with scales and harmonic progression and general composition-- one can even use ze maths to recreate known emotional effects from patterns. BUT, the best and deepest and most important aspect of art- for me- is to express the self. We do not feel directly in numbers. We feel directly in emotion; emotion in pure form that cannot be expressed with words or numbers. Mathematical analysis is steps away from the emotion. Words are steps away from the emotion. Visual art and music are much closer to emotion, because they translate to emotion directly without the need for analysis.

 

Soooooo, I have learnt a lot from music theory, but it was mostly stuffs I was coming across from experimentation anyway. Feel how you feel, then express that in sound. If you cannot find the right sound? Then you do not have the sound vocabulary in your brain to connect to your heart, so listen to more music and feel what it all means to you. As with creation in all arts, one needs a massive vocabulary to make emotional associations and regurgitate (and one's art-emotion vocabulary is personal, so only experience is needed to build it (i.e. no analysis)).

 

That being said, the whole piano roll DAW thing has made my composition different than playing with something without a screen, because you know, visual patterns (maths), etc.

 

So whatevz yo. IT'S ALL GOOD, YO~

 

Emotion>Music>Patterns>Visual interpretation by writing maths down --so yah, mathematics is far away, and is pointless for awesome creation. Even Ae and Richard Devine have to use their hearts to analyse their math driven glitch. In that sense, working with maths is good for experimentation and coming up with sounds that one would generally not easily come to.

[Entorwellian]

This might be a bit of a weird one so bear with me.

 

I've finally got round to learning a lot of music theory lately

(I've been working through this, it comes recommended if anyone else is so inclined: http://www.amazon.co.uk/Theory-Computer-Musicians-Michael-Hewitt/dp/1598635034)

and what's striking is that pretty much every aspect of music boils down to mathematics of one sort or another- melody and scales, harmony, rhythm, synthesis and all sorts of sound design/effects shenanigans are rooted in numbers. For whatever reason, music seems far more maths-based than other creative arts like writing or painting.

 

Are there any aspects of maths that you've found useful to you musical development in some way? Any particular principles, etc? Anything worth learning or looking into?

 

It just seems interesing that most aspects of music can be broken down into numbers, and yet it can still move us in such awesome ways.

 

In all likelihood I'll probably lose interest and not bother following this up but I thought it worth posting while the thought's on my mind, seems like quite a watmm-ish topic.

 

 

 

I've read that book front to back twice and is my second favourite computer book on music and math. Aside from some formatting and spelling errors, the authors work is really worth a read for anyone doing music on their computers. Even if you decide to disregard everything in it afterwards and go avant-gard, it does an amazing job teaching you everything progressively and you can read it straight through like a mystery novel.

[peace 7]

peace 7 - everything can be broken down into mathematics, including emotions. it's incredibly complex and i certainly don't claim to have any knowledge about how it works but the idea is still sound, i think.

 

If you cannot use those numbers to re-create what they are representing, then such analysis is useless for emotive purposes (math can work with music creation, because formulas can be used to abstractly create emotive sounds). Good for statistical analysis or something like that-- but even if all emotions can be broken down into brain chemicals and neuron-firings, they say nothing about the subjective experience of actually perceiving.

[LimpyLoo]

 

peace 7 - everything can be broken down into mathematics, including emotions. it's incredibly complex and i certainly don't claim to have any knowledge about how it works but the idea is still sound, i think.

 

If you cannot use those numbers to re-create what they are representing, then such analysis is useless for emotive purposes (math can work with music creation, because formulas can be used to abstractly create emotive sounds). Good for statistical analysis or something like that-- but even if all emotions can be broken down into brain chemicals and neuron-firings, they say nothing about the subjective experience of actually perceiving.

 

 

I think you underestimate the expressiveness of patterns, mathematical elegance, concepts, etc. And I think you overemphasize the role of consciously expressing emotions in music (or art, or anything creative).

 

Listen to Eno's generative music and tell me its emotionally sterile.

 

This comes back to the whole 'death of the artist' thing. For a piece of art to have meaning, it doesn't require the artist to put that meaning there.

 

This is most evident in modern art. Simple shapes and colors can be expressive. Paul Klee and Piet Mondrian makes me feel something. You don't have to paint someone looking bummed out to evoke melancholia.

[LimpyLoo]

Here is Stravinsky's take on this shit:

 

"For I consider that music is, by its very nature, essentially powerless to express anything at all, whether a feeling, an attitude of mind, a psychological mood, a phenomenon of nature, etc. Expression has never been an inherent property of music. That is by no means the purpose of its existence. If, as is nearly always the case, music appears to express something, this is only an illusion and not a reality. It is simply an additional attribute which, by tacit and inveterate agreement, we have lent it, thrust upon it, as a label, a convention – in short, an aspect which, unconsciously or by force of habit, we have come to confuse with its essential being."

 

and then

 

"The over-publicized bit about expression (or non-expression) was simply a way of saying that music is supra-personal and super-real and as such beyond verbal meanings and verbal descriptions. It was aimed against the notion that a piece of music is in reality a transcendental idea "expressed in terms of" music, with the reductio ad absurdum implication that exact sets of correlatives must exist between a composer's feelings and his notation. It was offhand and annoyingly incomplete, but even the stupider critics could have seen that it did not deny musical expressivity, but only the validity of a type of verbal statement about musical expressivity. I stand by the remark, incidentally, though today I would put it the other way around: music expresses itself."

[Guest brendyman]

As with creation in all arts, one needs a massive vocabulary to make emotional associations and regurgitate (and one's art-emotion vocabulary is personal, so only experience is needed to build it (i.e. no analysis)).

 

This is exactly what I was trying to say earlier

[LimpyLoo]

 

As with creation in all arts, one needs a massive vocabulary to make emotional associations and regurgitate (and one's art-emotion vocabulary is personal, so only experience is needed to build it (i.e. no analysis)).

 

This is exactly what I was trying to say earlier

 

 

From thought to expression, technique is required. This is where music theory comes in.

[Guest brendyman]

 

 

As with creation in all arts, one needs a massive vocabulary to make emotional associations and regurgitate (and one's art-emotion vocabulary is personal, so only experience is needed to build it (i.e. no analysis)).

 

This is exactly what I was trying to say earlier

 

 

From thought to expression, technique is required. This is where music theory comes in.

 

 

I suppose no matter how you're making music you're still using theory, it's just up to you how you learn it (teaching yourself through experience and trial + error / taking courses / trekking up a mountain in Germany for 40 days and 40 nights to read the sacred scrolls of Beethoven)

[LimpyLoo]

 

 

 

As with creation in all arts, one needs a massive vocabulary to make emotional associations and regurgitate (and one's art-emotion vocabulary is personal, so only experience is needed to build it (i.e. no analysis)).

 

This is exactly what I was trying to say earlier

 

 

From thought to expression, technique is required. This is where music theory comes in.

 

 

I suppose no matter how you're making music you're still using theory, it's just up to you how you learn it (teaching yourself through experience and trial + error / taking courses / trekking up a mountain in Germany for 40 days and 40 nights to read the sacred scrolls of Beethoven)

 

 

I just don't see the advantage in ignoring a vast history of musical knowledge. While music is nebulous and mystical and personal and all these things, when you lift the hood it's still just nuts and bolts.

 

If you use chords and rhythm and melody like the rest of us slobs, then there's hundreds of years worth of examples of people using chords and rhythm and melody to express...whatever it is they're trying to express. I can't see a possible upside to ignoring all of it.

 

I think there's a common fallacy where someone wants creative freedom, and think that working in a vacuum is the best way to do that. It just usually doesn't work like that. Studying music will make you more aware of what you're actually doing. It's the old unconscious incompetence thing. When you study something like syncopation or harmonic rhythm or strong beat/weak beat, you will start to become aware of the rhythmic phrasing of your melodies, or your drums. You will become aware of your tendencies, like if you always start your melodies on beat one, or always end them on a down-beat.

 

I tell everyone who will listen to study bebop, regardless of what kinda music you make. Almost all the best musicians I've ever known have strong fundamentals. Bibio could sit down and play a Woodie Guthrie tune, or a Jobim tune, or make a classic-era house tune. Tom Jenkinson could sit down and play a couple choruses of "Giant Steps." It's not a coincidence that they make good music. They have a huge repertoire of these musical nuts and bolts.

 

Now of course strong fundamentals aren't necessary, but that doesn't therefor mean that the best way forward is without them.

[LimpyLoo]

Music theory has become a dirty word because of its association with snooty academia and stale mechanical exercises and rules and reductionism.

 

 

It really doesn't have to be that way.

[luke viia]

music is math, but trying to write it through the lens of numerical relationships will not lead to emotionally satisfying music most of the time (see many of ragnar's poly-rhythmic ylc threads). imo it'd be like trying to cook through the lens of math: "i'll make this pie with only prime numbers of tablespoons of all ingredients!" -- you will get an intellectually curious pie, but it will likely taste horrible, because it puts the underlying mathematics before the purpose of the thing (which is to eat, or to enjoy listening to it).

 

good music can be extremely mathematically simple (squee's comment "counting to four helps") or it can be made very complex, as in some types of classical or jazz -- but if you're going to add that sort of complexity, it may behoove you to take along a set of rules which shows the most effective paths, which is where music theory comes in. otherwise feel free to just enjoy intuiting your way to fun results bit by bit, as a good, inspired amateur cook would do.)

 

i see no reason why anyone needs to think of their music in terms of mathematics, or even in terms of music theory, but they are helpful conceptual frameworks if you are aiming to do certain things, so let's please not shit on them, or put them on any unnecessary pedestals.