Does anyone else see the close relationship between math
& music ? I've always thought that they are the only two
disciplines that take place only in the mind. There is no physical
representation of either. A CD can reproduce a series of sounds
& equations can be written but there is no tangible by product.
Different then say a painting, sculpture, dance, etc. Pitch is a wave
length, loudness is an addition/subtraction of db's - equations too
follow a cadence. Any reflections on this ?
Full Version: Music & Math
Give me my music......and keep the math out of it. 
QUOTE(Rick McDaniel @ Jan 15 2010, 12:04 PM) 
Give me my music......and keep the math out of it.
look up Pythagoras on google
probably best known for a squared + b squared = c squared
but he did major work on analysis of music, pitch, overtones and physical sizes of instruments
http://en.wikipedia.org/wiki/Pythagorean_tuning
http://en.wikipedia.org/wiki/Pythagoras
pie are square....no, pie are round :-)
probably best known for a squared + b squared = c squared
but he did major work on analysis of music, pitch, overtones and physical sizes of instruments
http://en.wikipedia.org/wiki/Pythagorean_tuning
http://en.wikipedia.org/wiki/Pythagoras
pie are square....no, pie are round :-)
QUOTE(Mark Reinheimer @ Jan 15 2010, 12:57 PM)
look up Pythagoras on google
probably best known for a squared + b squared = c squared
but he did major work on analysis of music, pitch, overtones and physical sizes of instruments
http://en.wikipedia.org/wiki/Pythagorean_tuning
http://en.wikipedia.org/wiki/Pythagoras
pie are square....no, pie are round :-)
probably best known for a squared + b squared = c squared
but he did major work on analysis of music, pitch, overtones and physical sizes of instruments
http://en.wikipedia.org/wiki/Pythagorean_tuning
http://en.wikipedia.org/wiki/Pythagoras
pie are square....no, pie are round :-)
Pythagoras splitting up the octave in a orderly & pleasing way was a major
achievement. I was more just thinking about how interesting it is that sound
behaves in such an ordered way- overtone series, travels at a constant rate and all that stuff. "pie are square....no, pie are round"
Who originally said that ?Was it Piethagoras ? :-)
Thanks for taking up this fascinating thing! Math and music are related in several ways. Of course music is based on sound and sound can be described in a mathematical way as any physical phenomenon. Sound is waves, which behave in a very orderly matter.
But I think there is more to it. A sense for music and a sense for math are related. The brain seems to deal with both in similar ways. Many mathematicians can intuitively say that a certain mathematical solution is not "beautiful" and feel intuitively something is wrong. And some say that seeing a nice symmetrical and beautiful mathematical expression gives the same kind of experience as hearing a beautiful symphony. I can feel like that myself. Mathematical beauty and musical beauty have many similarities.
A friend of mine talked about research showing that playing music stimulates mathematical competence more than giving children computers etc.
I do think that a talent for music and a talent for math are if not the same highly correlated. I am not talking about having mastered the methodology of maths - even if you haven't learned them you can still have that intuitive feeling for math. The same way as one can be musically gifted, but never have learned to play an instrument
Looking forward to more opinions on this!
But I think there is more to it. A sense for music and a sense for math are related. The brain seems to deal with both in similar ways. Many mathematicians can intuitively say that a certain mathematical solution is not "beautiful" and feel intuitively something is wrong. And some say that seeing a nice symmetrical and beautiful mathematical expression gives the same kind of experience as hearing a beautiful symphony. I can feel like that myself. Mathematical beauty and musical beauty have many similarities.
A friend of mine talked about research showing that playing music stimulates mathematical competence more than giving children computers etc.
I do think that a talent for music and a talent for math are if not the same highly correlated. I am not talking about having mastered the methodology of maths - even if you haven't learned them you can still have that intuitive feeling for math. The same way as one can be musically gifted, but never have learned to play an instrument
Looking forward to more opinions on this!
I'm with Gerard, I've been a math geek most of my life... so thank you for bringing this up!!!
I see tons of numerical relationships when I'm trying to read music... lol
But aside from "how many quarter notes + how many 16th notes"... kinda thing, I found something much more basic, but still very mathmatical, that really made a huge difference how I play.
I really like what you said:
"And some say that seeing a nice symmetrical and beautiful mathematical expression gives the same kind of experience as hearing a beautiful symphony. I can feel like that myself. Mathematical beauty and musical beauty have many similarities."
When I started playing, really playing, and still had the $$$...
I bought up almost all the "Idiot's Guides" pertaining to music I could find: Theory, Composition, Soloing and Improv... etc, etc
I have all of them except one...I saw the Idiot's Guide to Music History" last time I was at the music store and I must have it someday...hehehe
Anyway, when I was reading on how a song is actually structured into beats, measures and lines, it all started to click into place. And the weird thing is I don't think I would have been able to do this back in High School... my real bad geek days.
Until this point when I played something, although I tried to make it sound good, it was still just a sort of rambling series of notes... there was no structure to it, no pattern. Just pretty flute notes.
But like I said, when I sat and thought about it... and I'm talking days of just letting it roll around in my head... it all began to really make sense. And when I was playing, almost without trying I found when I played there was a form to it now.. I was almost instinctivly counding off notes in my head, paying attention to how many measures I had played and knowing now when to repeat the beginning line...
It made a huge difference to how I approach playing something. Almost overnight suff I was making up had form and symetry and sounded amazing compaired to before. Now granted I still have a ton to learn, but talk about a defining monent... this was it!
This was when I began to wonder if I could actually get good at playing these wonderful things.
I see tons of numerical relationships when I'm trying to read music... lol
But aside from "how many quarter notes + how many 16th notes"... kinda thing, I found something much more basic, but still very mathmatical, that really made a huge difference how I play.
I really like what you said:
"And some say that seeing a nice symmetrical and beautiful mathematical expression gives the same kind of experience as hearing a beautiful symphony. I can feel like that myself. Mathematical beauty and musical beauty have many similarities."
When I started playing, really playing, and still had the $$$...
I bought up almost all the "Idiot's Guides" pertaining to music I could find: Theory, Composition, Soloing and Improv... etc, etcI have all of them except one...I saw the Idiot's Guide to Music History" last time I was at the music store and I must have it someday...hehehe
Anyway, when I was reading on how a song is actually structured into beats, measures and lines, it all started to click into place. And the weird thing is I don't think I would have been able to do this back in High School... my real bad geek days.
Until this point when I played something, although I tried to make it sound good, it was still just a sort of rambling series of notes... there was no structure to it, no pattern. Just pretty flute notes.
But like I said, when I sat and thought about it... and I'm talking days of just letting it roll around in my head... it all began to really make sense. And when I was playing, almost without trying I found when I played there was a form to it now.. I was almost instinctivly counding off notes in my head, paying attention to how many measures I had played and knowing now when to repeat the beginning line...
It made a huge difference to how I approach playing something. Almost overnight suff I was making up had form and symetry and sounded amazing compaired to before. Now granted I still have a ton to learn, but talk about a defining monent... this was it!
This was when I began to wonder if I could actually get good at playing these wonderful things.
I guess it would follow the rules applied to sine waves. Since sound travels in a sine wave as does water, light, etc... Just look at the waves in the ocean. I would imagine a lot of things in nature follow these rules. We just don't realize it. Even a square wave in a computer has the basic sine wave shape except it is square.
QUOTE(gregshaku @ Jan 16 2010, 05:29 AM)
I guess it would follow the rules applied to sine waves. Since sound travels in a sine wave as does water, light, etc... Just look at the waves in the ocean. I would imagine a lot of things in nature follow these rules. We just don't realize it. Even a square wave in a computer has the basic sine wave shape except it is square.
That was the point that I was getting at. You know that it also seems that
we are 'hard wired' to prefer certain intervals of notes. No matter if you're
dealing with 5 tone, 7 tone, 12 tone or 24 tone scales. The same holds for
what ever the standard pitch - we know that varies over time, but the relative
pitches hang around. Every one seems to have always wanted a series of
notes (song) to resolve to it's home key. I'd guess that's how its been since
the beginning. Go and try google search on 'NEANDERTHAL FLUTE'
QUOTE(great blue heron @ Jan 16 2010, 01:22 PM)
That was the point that I was getting at. You know that it also seems that
we are 'hard wired' to prefer certain intervals of notes. No matter if you're
dealing with 5 tone, 7 tone, 12 tone or 24 tone scales. The same holds for
what ever the standard pitch - we know that varies over time, but the relative
pitches hang around. Every one seems to have always wanted a series of
notes (song) to resolve to it's home key. I'd guess that's how its been since
the beginning. Go and try google search on 'NEANDERTHAL FLUTE'
we are 'hard wired' to prefer certain intervals of notes. No matter if you're
dealing with 5 tone, 7 tone, 12 tone or 24 tone scales. The same holds for
what ever the standard pitch - we know that varies over time, but the relative
pitches hang around. Every one seems to have always wanted a series of
notes (song) to resolve to it's home key. I'd guess that's how its been since
the beginning. Go and try google search on 'NEANDERTHAL FLUTE'
here is a link to above mentioned flute
http://www.greenwych.ca/fl-compl.htm
It is some interesting speculation any way.
QUOTE(Mark Reinheimer @ Jan 15 2010, 12:57 PM)
look up Pythagoras on google
probably best known for a squared + b squared = c squared
but he did major work on analysis of music, pitch, overtones and physical sizes of instruments
probably best known for a squared + b squared = c squared
but he did major work on analysis of music, pitch, overtones and physical sizes of instruments
I'd say that's acoustics, not music. (Of course Helmholtz actually used the theory of sound as a basis for the theory of music, but he was miles beyond pythagoras.)
Really, I have a ph.d. in math, and, well, judge my music for yourself, I'm here in the portal, but I don't see many direct connections between math and music. Maybe some in spirit; the love of form and all that, but that might just as well relate to poetry, and I don't think anyone ever makes that parallel.
Maybe it's just that math and music are creative activities, so there is a higher chance that someone with a feel for the one can have a feel for the other.
But stuff like string ratios like pythagoras did is hardly serious math or serious music. It's arithmetic and acoustics. It's much harder to make any firm connection between math and music. Except in metaphorical ways.
Victor.
QUOTE(Victor @ Jan 17 2010, 10:46 PM)
I'd say that's acoustics, not music. (Of course Helmholtz actually used the theory of sound as a basis for the theory of music, but he was miles beyond pythagoras.)
Really, I have a ph.d. in math, and, well, judge my music for yourself, I'm here in the portal, but I don't see many direct connections between math and music. Maybe some in spirit; the love of form and all that, but that might just as well relate to poetry, and I don't think anyone ever makes that parallel.
Maybe it's just that math and music are creative activities, so there is a higher chance that someone with a feel for the one can have a feel for the other.
But stuff like string ratios like pythagoras did is hardly serious math or serious music. It's arithmetic and acoustics. It's much harder to make any firm connection between math and music. Except in metaphorical ways.
Victor.
Really, I have a ph.d. in math, and, well, judge my music for yourself, I'm here in the portal, but I don't see many direct connections between math and music. Maybe some in spirit; the love of form and all that, but that might just as well relate to poetry, and I don't think anyone ever makes that parallel.
Maybe it's just that math and music are creative activities, so there is a higher chance that someone with a feel for the one can have a feel for the other.
But stuff like string ratios like pythagoras did is hardly serious math or serious music. It's arithmetic and acoustics. It's much harder to make any firm connection between math and music. Except in metaphorical ways.
Victor.
"Music is the pleasure of the human soul experiences from counting without being aware that it is counting". - Gottfried Leibniz
Mathematics and music have a strange connection. Music is the only art form, where the form and the medium are the same. Mathematics is the only science where the methods and the subject are the same. Mathematics is the study of mathematics using mathematics. Music is only created and experienced as music. Thus, there is a natural connection between mathematics and music: Both are experienced as pure objects of the brain, and both have meaning outside of the brain only by artificial connections.
QUOTE(Jeff G @ Jan 17 2010, 08:21 PM)
Music is the only art form, where the form and the medium are the same.
The medium is vibrations of the air, or maybe vibrations in the little hairs in your ears. Is that really the form of music? I'd say that the distance between moving air and moving my heart with a song, is about the same as between the electric currents in my nerves and the feeling of love I have for my girlfriend. The medium and the message are miles apart.
QUOTE
Mathematics is the only science where the methods and the subject are the same.
That may actually be true. In some parts of math: logic analyses logic. I doubt that you do algebra with algebra. You do algebra with logic.
QUOTE
Music is only created and experienced as music.
Sculpting is only created and experienced as sculpting?
Victor.
QUOTE(Victor @ Jan 17 2010, 10:46 PM)
It's arithmetic and acoustics. It's much harder to make any firm connection between math and music. Except in metaphorical ways.
Victor.
Victor.
OK, Dr. Victor. I'm gonna ask a dumb question. What the difference between arithmetic and mathematics?
Seriously. I don't know.
QUOTE(tootieflutie58 @ Jan 18 2010, 03:06 PM)
What the difference between arithmetic and mathematics?
That's a perfectly natural question for a lot of people, since you likely won't have seen much that qualifies as true math in school.
Arithmetic is a branch of math that's about performing calculations. Mathematics in general is much more abstract, making general statements. Arithmetic is specific, math is about theory. Arithmetic is to math as spelling is to literature.
If I give you a formula x3+5x2-3x-2, and I ask you to evaluate that with x=3, that's arithmetic. If I ask you to prove that there is a value for which the result is zero (note: you only have to show that it exists, you don't actually have to compute it), that's math.
Victor.
QUOTE(Victor @ Jan 18 2010, 09:54 PM)
That's a perfectly natural question for a lot of people, since you likely won't have seen much that qualifies as true math in school.
Arithmetic is a branch of math that's about performing calculations. Mathematics in general is much more abstract, making general statements. Arithmetic is specific, math is about theory. Arithmetic is to math as spelling is to literature.
If I give you a formula x3+5x2-3x-2, and I ask you to evaluate that with x=3, that's arithmetic. If I ask you to prove that there is a value for which the result is zero (note: you only have to show that it exists, you don't actually have to compute it), that's math.
Victor.
Arithmetic is a branch of math that's about performing calculations. Mathematics in general is much more abstract, making general statements. Arithmetic is specific, math is about theory. Arithmetic is to math as spelling is to literature.
If I give you a formula x3+5x2-3x-2, and I ask you to evaluate that with x=3, that's arithmetic. If I ask you to prove that there is a value for which the result is zero (note: you only have to show that it exists, you don't actually have to compute it), that's math.
Victor.
Well, thank you very much! I learned something new!
QUOTE(Victor @ Jan 18 2010, 06:54 PM)
That's a perfectly natural question for a lot of people, since you likely won't have seen much that qualifies as true math in school.
Arithmetic is a branch of math that's about performing calculations. Mathematics in general is much more abstract, making general statements. Arithmetic is specific, math is about theory. Arithmetic is to math as spelling is to literature.
If I give you a formula x3+5x2-3x-2, and I ask you to evaluate that with x=3, that's arithmetic. If I ask you to prove that there is a value for which the result is zero (note: you only have to show that it exists, you don't actually have to compute it), that's math.
Victor.
Arithmetic is a branch of math that's about performing calculations. Mathematics in general is much more abstract, making general statements. Arithmetic is specific, math is about theory. Arithmetic is to math as spelling is to literature.
If I give you a formula x3+5x2-3x-2, and I ask you to evaluate that with x=3, that's arithmetic. If I ask you to prove that there is a value for which the result is zero (note: you only have to show that it exists, you don't actually have to compute it), that's math.
Victor.
victor, you might want to check out Marko Rodin's work on youtube.. you'll either love it or hate it.
I'd say Jeff is thinking in the right direction. It does strike me really how the beauty in math (which several mathematicians speak about) seems to be experienced in a similar way as musical beauty. I am not sure that sculpture, as mentioned above, is really comparable...
I have a scientific article published recently saying that the essence of mathematics really exists independent of the material universe. It is discovered rather than created. I have another article saying similar things about music. Somewhere there on a plane difficult to grasp is the connection. I agree, this is not about Pythagoras and sinus equations. It is about something abstract. I do feel a connection, but have difficulty to describe it.
I have a scientific article published recently saying that the essence of mathematics really exists independent of the material universe. It is discovered rather than created. I have another article saying similar things about music. Somewhere there on a plane difficult to grasp is the connection. I agree, this is not about Pythagoras and sinus equations. It is about something abstract. I do feel a connection, but have difficulty to describe it.
QUOTE(Victor @ Jan 18 2010, 01:24 AM)
The medium is vibrations of the air, or maybe vibrations in the little hairs in your ears. Is that really the form of music? I'd say that the distance between moving air and moving my heart with a song, is about the same as between the electric currents in my nerves and the feeling of love I have for my girlfriend. The medium and the message are miles apart.
That may actually be true. In some parts of math: logic analyses logic. I doubt that you do algebra with algebra. You do algebra with logic.
Sculpting is only created and experienced as sculpting?
Victor.
That may actually be true. In some parts of math: logic analyses logic. I doubt that you do algebra with algebra. You do algebra with logic.
Sculpting is only created and experienced as sculpting?
Victor.
Music is the art form and the medium.. Sculpting.. can be clay, wood, salt.. almost any media.
Oh.. this is just some culmination of things read, but I think it is cool.. Music is the art, it is practiced...by playing or listening to music...
QUOTE(jim cook @ Jan 19 2010, 10:33 AM)
victor, you might want to check out Marko Rodin's work on youtube.. you'll either love it or hate it.
Hm. How shall I put this.....
I would tell you what I thought of it if he actually said anything that means anything. Lots of big words that may describe something but he never explains what. His math is on the level of party tricks.
He seems to have invented a coil that is 20 percent more efficient than guys from HP thought it should be. Big woop-tee-doo.
But I only sat through 2 of his 45 youtube videos. If you can tell me anything specific that he has shown or developed, I'll let you know what I think of it.
Personally I think it is what people in science call "not even wrong": so ludicrously off the chart that you can't even point at something and say "that is wrong".
Victor.
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