Music: A Mathematical Offering (2006)

http://freecomputerbooks.com/Music-A-Mathematical-Offering.html

by ghosthamlet • 7 years ago

80 38 7 years ago

freecomputerbooks.com

ghosthamlet• 7 years ago

Pdf is here: https://eclass.uoa.gr/modules/document/file.php/MATH379/1.%2...

mikorym• 7 years ago

Has it not been updated since 2008? The intro suggests it has been; web searches suggest it has not.

codegladiator• 7 years ago

Correct, its not been updated though the book says it would probably have been updated.

I found the link to the new home page of the author:

https://homepages.abdn.ac.uk/d.j.benson/pages/

which links to the same version of the book.

foobar_2• 7 years ago

Music has little to do with math. The math is useful in measuring things and developing the tools but basically, music is about emotional expressivity.

TheOtherHobbes• 7 years ago

True. Math nerds get excited by the ratios, roots, and groups, but all of that is a rabbit hole - useful for DSP code, but it will do nothing to help you write memorable music.

jimhefferon• 7 years ago

The book does not assert that to write memorable music you only need mathematics.

johnr24• 7 years ago

Knowing how to count beats and bars can be helpful when writing music, as can knowing how string lengths are related to notes when playing a stringed instrument.

johnr24• 7 years ago

Music has little to do with math.

As a musician (and audio engineer) I disagree. You don't need to think about math while writing or playing music, just like you don't need to think about physics when riding a bike, but that doesn't mean it has little to do with it.

coldtea3• 7 years ago

The kind of math musicians talk about are elementary ratios that concern the relationships between tones and between frequencies, nothing to write home about. And even the latter have little application to composition.

You can be a great musician and even original songwriter and not know any math (or even the names of chords for that matter) at all. And that's even in folk -- it's even less so in electronic music and other genres.

boomlinde4• 7 years ago

When I am riding a bike, I am very much thinking about physics, in order not to fall over and hurt myself. I can say that I have to think about physics regardless of whether I am thinking of it in the terms Newton did, because the physical world exists without the theoretical framework to describe it.

Mathematics on the other hand is purely theoretical. Unless I am engaging in mathematical reasoning, I'm not doing maths.

That said, when I am musicking, I am doing mathematics all the time, at least for things like basic counting, arithmetic and logic. But that's true for so much of the basic activities we do every day that saying that music has a lot to do with maths becomes a pointless truism. Similarly, I may be doing maths when I'm cooking, but no one is going to try to tell me that "cooking is maths". Cooking has little to do with maths, but maths has a lot to do with everything.

dcassett• 7 years ago

The author says as much in the introduction:

"I should close with a disclaimer. Music is not mathematics."

ebj73• 7 years ago

It's not math, per se. But music is certainly about patterns. And some of the ratios in musical patterns certainly have a foundation in math. I think you cannot arrive at beautiful music starting from math. But you probably can arrive at some interesting mathematical patterns starting from music.

jedimastert• 7 years ago

As a jazz musician, you have no idea what you're talking about. Music theory is a subset of set and group theory, and there's no way to analyse music without math.

foobar_2• 7 years ago

Music is not meant to be analysed. It is felt. The opera singer is the model for all music. TBH I have often felt jazz and classical music to be cold and mechanical, except for a few songs.

manifestsilence• 7 years ago

You don't need math to enjoy or even perform music, or to understand it in a certain way. But there is another way to understand it that is purely mathematical, and it is quite enriching.

The start of the rabbit hole is the pythagorean comma and it has a very real effect on the real-world messy compromises that are involved in tuning instruments to play with each other in multiple keys.

The terrible beauty and ugliness that are one and the same stems from the simple fact that if you go up a fifth, say, C to G, it sounds the purest if the pitch is exactly 1.5 times as high, or 3/2. If you keep going up five notes at a time, eventually you get back to a C, having gone through all the other notes in the process.

But the pure, good sounding way to get from a C to a higher C is to double its frequency. And you never can get to exactly a power of two by repeatedly multiplying by 1.5. So the C you get by going up by octaves and the C you get by going up by fifths come out different.

A consequence of that is it is impossible to play all the different chords in a key as pure, perfectly-in-tune chords without at least one "floater" note (my term) that changes pitch depending on which chord it's part of at the time. See Just Intonation for more information. It's geeky stuff, but has an effect on the way real musicians play certain instruments, such as harpsichord and pedal steel guitar, and it has bothered and fascinated certain musicians ever since the ancient Greeks if not before.

8bitsrule• 7 years ago

Agreed on what music is intended to do. But being expressive can mean understanding different scales, different rhythms, different harmonic progressions, the capabilities of different instruments, etc.

One thing I did not learn in my childhood music lessons is basic stuff like musical intervals, chord structure, circle of fifths. These are very practical math relationships ... essential to knowing about your options, for both expressive performance and for on-paper composition and arranging.

In later years, I regretted that none of my teachers knew enough about them to help me understand them. They're an indispensable tool in the pro musician's arsenal.

tokai• 7 years ago

What a great website.

jwiesenborn• 7 years ago

Music has everything to do with mathematics. It’s all waves just like y = sin(x). Digital music in particular has much in common with calculus in the piecewise manner that discrete samples approximate analog waves. I wrote a program in vanilla JS to demonstrate this idea. It converts XML-formatted music into mathematical terms, and then encodes it into pulse code modulation for playback. Feel free to peek at dietpumpkinmachine.com if you don't mind the sloppy code.

schemathings• 7 years ago

"David J. Benson is a 6th Century Professor in the Department of Mathematical Sciences at the University of Aberdeen." ? Piqued my curiosity!

Music: A Mathematical Offering (2006)

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