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Topic: Mathematics in music, Logical/creative< Next Oldest | Next Newest >
Silver Negus Offline




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Posted: Dec. 21 2007, 14:47

I have two freinds who are artists, and yet suprisingly both these people had a doctor as a parent.- And doctors are seen more as logical thinkers.
I think we see it quite a lot where this is the case, where people can grow up having a mixture of logical thought and creative thought, and in many ways the two combine.
Any performance art industry needs to have a structure, and maybe this is why some artists actors musicians become successful.  Because although they are creative, they are also very precise and structured, in the way they approach their art form.
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jonnyw Offline




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Posted: Dec. 22 2007, 22:18

I had an art teacher who would disagree. He always said, that in all His years of teaching he felt students were really one or the other, 90% of the time. You'll find that they wont be successful because they can "structure" themselves better at all, because the ones who are REALLY good, and are able to make it a living or be famous, are lucky enough to have someone behind them who is a "structured" thinker.

I wouldn't like to use the word logical though, as artists think as logically as mathematicians. The thing is that mathematician's logic isn't always creative, and artists logic isn't always set by rules.

My art teacher found it hard to get some of the best artists to pass through the school to analyse their work for the exams, they were fantastic artists, and thier medium of communication was by creating, and not analysis and following rules, and i see it every day at college, when I see my freinds in less creative subjects, who follow rules a bit easier and have set ways about doing  things, that works well in thier subject.

I think that there are bound to be people who are both, but generally speaking, I think that I agree more with my old art teacher.

j


ps. about the "maths in music" title.. I'd like to say that there is none, and whatever Mathematics that are involved in the theory I feel were placed by logical thinkers who need some kind of rule! controversial as that may sound ;)


--------------
Grand piano.
Reed and pipe organ.
Glockenspeil.
Bass guitar.
Vocal chords.
Two slightly sampled electric guitars.
The venitian effect.
Digital sound processor.
And Tubular bells.

Solo music - http://-terrapin-.bebo.com

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Sentinel101 Offline




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Posted: Dec. 23 2007, 05:52

I'm currently reading a fascinating book called "The Music of the Primes" which explains the on-going quest to prove the so called Riemann Hypothesis (RH). The RH describes a method to unlock the pattern in which prime numbers occur. There are many connections made to music and even the "music of the spheres" is mentioned in this context. Worthy read.

http://www.amazon.com/Music-P....&sr=8-1
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Sir Mustapha Offline




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Posted: Dec. 23 2007, 06:42

Quote (jonnyw @ Dec. 22 2007, 22:18)
ps. about the "maths in music" title.. I'd like to say that there is none, and whatever Mathematics that are involved in the theory I feel were placed by logical thinkers who need some kind of rule! controversial as that may sound ;)

There are mathematics in everything! Whether you see it or not, is another point. You can express music entirely in mathematical terms, be it as a score, a function of time, a huge string of bits; and if it weren't for those logical thinkers who need rules, CDs, MP3 and all that nazz was out of question. :) Sorry, every day I love science more, so I can't help but defend it. In the words of George Starostin, "The continuous struggle between science and art is even more stupid - and harmful - than the struggle between science and religion".

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Moz Offline




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Posted: Dec. 23 2007, 07:25

I agree with Sir Mustapha. :)
You only have to look at a time signature to see mathematics in music. 4/4, 3/4, 2/4, 7/8, 6/8, 12/8...


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Ray Offline




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Posted: Dec. 23 2007, 09:20

Quote (Moz @ Dec. 23 2007, 12:25)
I agree with Sir Mustapha. :)
You only have to look at a time signature to see mathematics in music. 4/4, 3/4, 2/4, 7/8, 6/8, 12/8...

Aha!  Yes, music is very mathematical, it's all about resonant frequencies, combinations of sine waves at various frequencies to give new tones......but the ability to string together a series of notes in to a striking tune is far from mathmatical - it comes from having a ear for such things.  I'm pretty good at maths but crap at making up a string of notes into a tune that you would like such as the start of Ommadawn or anything else....  :D   Although I would consider myself to be very creative, in lots of other ways.  I guess I missed out on the musical Gene?

Ray


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Ray Offline




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Posted: Dec. 23 2007, 09:21

In terms of music I am a repeater rather than a transmitter!!!   ;)
Ray


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jonnyw Offline




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Posted: Dec. 23 2007, 09:48

you are all missing the point!!


Do you honestly think that a composer sits down and mathematically and systematically works out the prime numbers that make up a tune?!



oh my god!


Its laughable and futile do do such things, because you take away any sort of beauty in it, I cant honetly believe that you can sit there and say that you can work out exactly why music is there, by numbers, and ergo know what SHOULD come next, and still believe it it truly being naturally beautiful. Its unnatrual and a very cold view of music if you ask me.

Seriously people, the "struggle" between science and art is only brought on by people who NEED rules on things. I love science too, I studied Physics for years and still study physics of sound. But I think there are lines that shouldn't be crossed.

But of course.. I grow frustrated again at this.. and disappointed by some of these replies. So Ill leave you all to believe what you want to.


--------------
Grand piano.
Reed and pipe organ.
Glockenspeil.
Bass guitar.
Vocal chords.
Two slightly sampled electric guitars.
The venitian effect.
Digital sound processor.
And Tubular bells.

Solo music - http://-terrapin-.bebo.com

Band music - http://www.rsimusic.com
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jonnyw Offline




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Posted: Dec. 23 2007, 10:00

Quote (Moz @ Dec. 23 2007, 12:25)
I agree with Sir Mustapha. :)
You only have to look at a time signature to see mathematics in music. 4/4, 3/4, 2/4, 7/8, 6/8, 12/8...

And if you had read what I said.. I mean that those mathematical rules in "theory" were placed pureley to take note of a composition, by people who necessarily were adapted to incorporating some kind of rule in it...

Rules were placed in it for certain people, because its much easier to play by the rules than to break them. which is why most great music is a complete break from all rules previous.

Its fine if you want to analyse things this way.. But art is art and science is science. there is no struggle, its when people like George Starostin need to be by the book and follow the rules, make sure its neatly organized and thats that, nice and explained. Its doesn't need to be explained, (this is partly out of why modern art became so popular and controversial at the same time) you think about how many people got frustrated at people who were able to think up some damn theory as to why the mona lisa is what it is, and so decided to scatter random paint on a canvas and have others buy it for millions! it would piss people who need rules right off!


I digress. My point is that you can put maths into anything, but you don't have to to understand it THAT way.


--------------
Grand piano.
Reed and pipe organ.
Glockenspeil.
Bass guitar.
Vocal chords.
Two slightly sampled electric guitars.
The venitian effect.
Digital sound processor.
And Tubular bells.

Solo music - http://-terrapin-.bebo.com

Band music - http://www.rsimusic.com
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Sir Mustapha Offline




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Posted: Dec. 23 2007, 10:31

You don't put maths into things; you extract it out of things.

Anyway, yes, I think it's primarily a question of belief. If the human mind is, in essence, a Turing machine - and I'm getting convinced it is - then there's no magic in music making, and yes, people do systematically combine mathematical elements - subconsciously. The mind is able to abstract those things, and that's why music exists. We can see the product as something else entirely, both when we listen and when we compose; so the inner workings of the brain aren't relevant to the conscious side of the brain. That's what always happens - we don't know how our brain works, we're only barely scraping the bottom of the barrel of its secrets. But if it is a fact that the brain is a deterministic machine, then there's no way out: in the end, music is mathematics. But so far, you're right when you say it doesn't need to be.

And the concept of beauty? Beauty exists in the brain, and as such, there definitely has to be a systematic manner of defining beauty in a piece of music, according to one brain's criteria. Thoughts and feelings don't snap out of the aether - and that's what I believe in, so like I said, all a matter of belief. As of now, we have no way of developing an equation of beauty in music, so the formation of our feelings and opinions is a mystery to us - and that's why people like music, because that's FUN.

In a less philosophical view, what's with all those people who reduce music and sound to maths? Well, thanks to them, we have all that music equipment, recording, synthesizers, machines and all. Just that. :)


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jonnyw Offline




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Posted: Dec. 23 2007, 11:29

No, maths did not give us the recording ability, physics did, the mathematics in the physics behind the recording is nothing to do with the mathematics of composing......



Sad really that you need to do things so exactly by the book. I am getting really aggravated here, because this is my life that you are trying to simplify down to a few numbers. its not just "FUN" its an expression, a way for someone who cannot communicate any other way properly to communicate. a release of issues. Not just some silly subconscious maths equation.

Ugh.


--------------
Grand piano.
Reed and pipe organ.
Glockenspeil.
Bass guitar.
Vocal chords.
Two slightly sampled electric guitars.
The venitian effect.
Digital sound processor.
And Tubular bells.

Solo music - http://-terrapin-.bebo.com

Band music - http://www.rsimusic.com
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Sir Mustapha Offline




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Posted: Dec. 23 2007, 12:29

No need to be aggravated. If I'm simplifying your life down to numbers, I'm simplifying my own, as well. But you skipped over the parts when I said we have the power to abstract, and we all do that, all the time. I have to say it again, it's a matter of belief.

I didn't say that the science of music was the same for every area there is. But the fact is, there's nothing soulless about the science that goes behind all of that, especially when you see how much music has benefited with the advancements it made possible.


--------------
Check out http://ferniecanto.com.br for all my music, including my latest albums: Don't Stay in the City, Making Amends and Builders of Worlds.
Also check my Bandcamp page: http://ferniecanto.bandcamp.com
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jonnyw Offline




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Posted: Dec. 23 2007, 16:14

I can appreciate that science has improved musical recording, hell I study it at college, and am fascinated by physics of sound. I love being part of how to put what I compose and what others compose down to recording, and love to see advancements in that area.

However one thing I cant stand is the attempted simplification of art by scientists who believe that it can be explained. Recording audio is not art, and I agree mathematics involved in audio recording is intregal to todays music industry. Composition however, IS art, and it may have rules put in place, and it may be possible for someone to write a book to be able to say "1+1=2 as much as E min7 + C maj = nice" But for me.. people like Mike Oldfield are great because they didn't need to know the maths that you believe is necessary to include.


Ill take my leave now. See you all later.


--------------
Grand piano.
Reed and pipe organ.
Glockenspeil.
Bass guitar.
Vocal chords.
Two slightly sampled electric guitars.
The venitian effect.
Digital sound processor.
And Tubular bells.

Solo music - http://-terrapin-.bebo.com

Band music - http://www.rsimusic.com
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Sir Mustapha Offline




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Posted: Dec. 23 2007, 17:47

Right. Well, there's more to it than just recording equipment. Synthesizers, electric pianos, sound processors; basically the entire electronic music is built on it. I also think recording audio - recording music, in particular - is an art form. Much of today's music depends a lot on the producing and recoding and engineering, you got to agree. With that, even the most technical things can be art. There's architecture, for one: completely dependant on mathematics, yet artistic. And if we're going extreme on this, there's the Golden Ratio - a constant that has much to do with what humans perceive as pleasant, natural and harmonic. It goes on and on. But the main point? Hm, er...

Oh, yes... I'm not defending the use of science to explain the mystery of art completely, but it's inevitable: you can't completely separate science from art. One is inserted into the other. Yes, I think science can be art in a way, and I think science opens a lot of possibilities for art. There is no opposition, there.


--------------
Check out http://ferniecanto.com.br for all my music, including my latest albums: Don't Stay in the City, Making Amends and Builders of Worlds.
Also check my Bandcamp page: http://ferniecanto.bandcamp.com
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jonnyw Offline




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Posted: Dec. 23 2007, 19:42

I think I know a little bit about it, don't patronize me.. you tend to do that quite a lot.


You can have your last word, I am sick of this place anyway.


Bye!


--------------
Grand piano.
Reed and pipe organ.
Glockenspeil.
Bass guitar.
Vocal chords.
Two slightly sampled electric guitars.
The venitian effect.
Digital sound processor.
And Tubular bells.

Solo music - http://-terrapin-.bebo.com

Band music - http://www.rsimusic.com
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Sir Mustapha Offline




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Posted: Dec. 23 2007, 20:37

Wow. I was in a flame war and I didn't even know it. I mean, if I intended to rile someone up, I'd be on the IMDb forums, not here...

I swear to goodness, I thought this was going to be a cool discussion. Now, if someone else hates me, private messaging works better for that, I believe. But now that I'm some sort of evil overlord, everybody will just glare at me, instead... I'm honest here, did it really look like I wanted to kick him out of here?

And are there any hopes that this thread will go back into topic?


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Check out http://ferniecanto.com.br for all my music, including my latest albums: Don't Stay in the City, Making Amends and Builders of Worlds.
Also check my Bandcamp page: http://ferniecanto.bandcamp.com
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Moz Offline




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Posted: Dec. 23 2007, 22:05

Jonny, I did read what you said.  I found this to be of particular interest:

Quote
ps. about the "maths in music" title.. I'd like to say that there is none, and whatever Mathematics that are involved in the theory I feel were placed by logical thinkers who need some kind of rule! controversial as that may sound


Do you mean you would like there to be no maths in music?  Or do you claim that there really is no maths in music?

I don't believe maths in music forces unnecessary rules on people... actually, if we stick to the subject of time signatures, it can create some really odd music.  Look at how much pop and rock music is in 4/4.  Now compare that to some of the time signatures used in Mike Oldfield's music.  I can't list all of them, but I know that Tubular Bells starts in 7/8, to give one example, and Incantations Part 1 seems to alternate between 5/8 and 6/8 (though I'm sure someone will correct me if I'm wrong).

Now, I don't know if Mike sat down and said to himself, "right, I'm going to use these time signatures for this length of time, then I'll move onto this time signature and this key".  But whatever he did, writing a music score requires you to indicate what key it's in, where the notes appear in each bar, and so on.  I know Mike has played most if not all of the instruments on many of his albums, but if he wants anyone to play a part for him (a good example has to be Music of the Spheres) then a musician needs to know HOW to play the music.  That's what a score is for.

Depending on the genre of music, the musician, the instrument and the composer's wishes, there may be some deviation from the score.  My dad owns a large Beatles book that contains literally every note in every track the group recorded - even bizarre tracks such as Revolution 9! - but a lot of the sheet music I've seen is not 100% accurate when compared with the actual recording.

Musicians can and do add their own little idiosyncrasies when they play, and this may be the part that you do not think is mathematical.  I won't argue that, but the original score that a musician plays from needs to be organised in such a way that it can be played.  It doesn't mean that composers can't break the rules, but we need to be able to express our musical ideas in a format that other musicians can understand.  That format is the score, and I personally think that the score is mathematical. :)


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Sweetpea Offline




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Posted: Dec. 24 2007, 05:26

I am fascinated by this subject though I have very little knowledge of it, but I expect mathematics exist in nearly all things. Surely, there is room for math in art and vice versa?

Sir Mustapha, you mentioned artistry in architecture, which - having an interest in the subject - is an idea I can easily grasp. I appreciate both symmetry and asymmetry in architecture, but I am more likely to choose the former over the latter. I wonder if symmetry has much to do with the "Golden Ratio" you've mentioned? I feel I should be familiar with this concept, but I'm afraid it's a bit vague for me. You described it as "a constant that has much to do with what humans perceive as pleasant, natural and harmonic". Perhaps this may explain, as Moz has also mentioned, the prevalence of 4/4 in popular music? And is there more to it than that?


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"I'm no physicist, but technically couldn't Mike both be with the horse and be flying through space at the same time? (On account of the earth's orbit around the Sun and all that). So it seems he never had to make the choice after all. I bet he's kicking himself now." - clotty
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Sir Mustapha Offline




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Posted: Dec. 24 2007, 07:00

The golden ratio is very often connected to the proportion of things, as in the shape of the spirals in molluscs' shells, the sizes of leaves in a tree branch, and if we go into architecture, the proportion between the length and the height of structures and so on. Symmetry is a common concept in architecture, and it doesn't necessarily have to be connected to the golden ratio.

I haven't researched much into this, so I don't know how often the ratio is found in music. I think the binary rhythms - be it 4/4, 2/4, 4/8, etc. - are used so often because the mind adapts easily to it, and it's easy to dance, and such, and the harmonies used have their explanation on the natural harmonies between frequencies. But that would be merely scraping the bottom of the barrel, I think. :)


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moonchildhippy Offline




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Posted: Dec. 24 2007, 10:23

Quote (Ray @ Dec. 23 2007, 13:20)
Quote (Moz @ Dec. 23 2007, 12:25)
I agree with Sir Mustapha. :)
You only have to look at a time signature to see mathematics in music. 4/4, 3/4, 2/4, 7/8, 6/8, 12/8...

Aha!  Yes, music is very mathematical, it's all about resonant frequencies, combinations of sine waves at various frequencies to give new tones......but the ability to string together a series of notes in to a striking tune is far from mathmatical - it comes from having a ear for such things.  I'm pretty good at maths but crap at making up a string of notes into a tune that you would like such as the start of Ommadawn or anything else....  :D   Although I would consider myself to be very creative, in lots of other ways.  I guess I missed out on the musical Gene?

Ray

I agree that there's maths in music up to a point, but the only maths I can see is the timing/rythym of a piece. Then again is rythym matematical, well yes and no.  Poetry has a rythym, but I would say that there's no maths in poetry.  To illustrate my point here's "The Night Mail" by WH Auden

This is the Night Mail crossing the border,
Bringing the cheque and the postal order,
Letters for the rich, letters for the poor,
The shop at the corner and the girl next door.
Pulling up Beattock, a steady climb:
The gradient's against her, but she's on time.
Past cotton-grass and moorland boulder
Shovelling white steam over her shoulder,
Snorting noisily as she passes
Silent miles of wind-bent grasses.

Birds turn their heads as she approaches,
Stare from the bushes at her blank-faced coaches.
Sheep-dogs cannot turn her course;
They slumber on with paws across.
In the farm she passes no one wakes,
But a jug in the bedroom gently shakes.

Dawn freshens, the climb is done.
Down towards Glasgow she descends
Towards the steam tugs yelping down the glade of cranes,
Towards the fields of apparatus, the furnaces
Set on the dark plain like gigantic chessmen.
All Scotland waits for her:
In the dark glens, beside the pale-green sea lochs
Men long for news.

Letters of thanks, letters from banks,
Letters of joy from the girl and the boy,
Receipted bills and invitations
To inspect new stock or visit relations,
And applications for situations
And timid lovers' declarations
And gossip, gossip from all the nations,
News circumstantial, news financial,
Letters with holiday snaps to enlarge in,
Letters with faces scrawled in the margin,
Letters from uncles, cousins, and aunts,
Letters to Scotland from the South of France,
Letters of condolence to Highlands and Lowlands
Notes from overseas to Hebrides
Written on paper of every hue,
The pink, the violet, the white and the blue,
The chatty, the catty, the boring, adoring,
The cold and official and the heart's outpouring,
Clever, stupid, short and long,
The typed and the printed and the spelt all wrong.

Thousands are still asleep
Dreaming of terrifying monsters,
Or of friendly tea beside the band at Cranston's or Crawford's:
Asleep in working Glasgow, asleep in well-set Edinburgh,
Asleep in granite Aberdeen,
They continue their dreams,
And shall wake soon and long for letters,
And none will hear the postman's knock
Without a quickening of the heart,
For who can bear to feel himself forgotten?

To me this poem has the rythym of a train at speed on the tracks.

Back to music, I agree that having the ability to put a series of chords/notes together into a striking tune is far from matematical.  Speaking as a would be guitarist, well I try to play my guitar, I don't really consider the maths involved in a piece of music, other than trying to keep the rythym.  When I listen to a piece of music I don't really think of the maths behind it other than the timing of the piece, for me I just wish to engage in the pleasure the combination of notes/chords brings to my ears   :)  :D, which to me ia more of an art form than a mathematical equation.

I just wonder how many musicians were good at maths at school, the only one I can think of that springs to mind is Brian May, as I know he has maths/science degrees, but I wonder what was going through Brian's mind when he compsed some of his masterpieces with Queen, I doubt very much he was thinking about maths.  
I consider the ability to compose music as an art form, reliant more on harmonics rather than maths, harmonics is more of a physics than maths, as in say guitar strings vibrate at so many hertz.  Maybe music is one art form where maths, physics and art successfully combine.
I know a few musicians, and many of them would admit to not being good at maths.   In conclusion I would say that music has an element of maths within it, but in maths 2+2 always equals 4, there is only one correct answer but music is an art form, where the possibilities are  limitless           ;) .


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