music and maths....again!!!!

[lea]

hello everyone, i know that i have this in another topic but i actually put it in there by accident so i am putting it in here!

i am really fascinated by music and its connection with maths...........such as time signatures and fractions and counting beats, as you have to do alot when you play the piano.............and also if you listen to piano  music then u can do better in maths...........but mainly the time signatures-fractions part etc

does any one have info on this or websites so i could look at this fascinating subject better.........if only i was good at maths when i was at school!!!!

i have looked up alot of websites but all they go on about is the mozart effect, but its quite complex language....does anyone have any good websites/books that they know of??

[88keys]

The connection between music and math is much deeper than you think...

Take note intervals, for example. If you multiply the frequency of sound wave by two, you raise the pitch of the note by an octave. If you multiply the frequency by 3/2, the pitch is raised by a perfect fifth. A ratio of 4/3 will give you a perfect fourth.

Strike any major chord (such as C, E, G, C). The frequency ratios between the notes will be 4 : 5 : 6 : 8.

Strike any minor chord (such as C Eb G C). The frequency ratios between the notes will be 10 : 12 : 15 : 20.

Cool, heh?

[chopinetta]

cool!!! but i don't understand it. can you explain again? please?

[88keys]

Think of a four-stringed instrument, like a violin.

The pitch coming out of a string depends only on one thing: the speed at which the string vibrates. For example, if a string vibrates 262 times per second, you get middle C.  The higher the vibration rate, the higher the pitch of the resulting note.

If you pluck two strings together, and one of them vibrates exactly twice as fast as the other, you will hear a perfect octave.

If the first string vibrates 3 times for every 2 vibrations of the second one, you will hear a perfect fifth (e.g. C-G). If ithe first string vibrates 4 times for every 3 vibrations of the second on, the result will be a perfect fourth (e.g. C-F). Or in convinient shorthand: A ratio of 3:2 gives you a perfect fifth, and a ratio of 4:3 gives you a perfect fourth.

In a major chord, the ratio between the vibration rates of all 4 strings is 4:5:6:8. Thus, if the first string vibrates 400 times per second, the second vibrates 500 times, the third 600 times, and the fourth 800 times, you will hear a major chord (G major, in this case).

Hope I explained it well, this time.

[lea]

v. cool, i think i get it but if i dont ill post another thingy in this subject

cheers

lea

[Rach3]

You mean you haven't heard? Its flawed, they discovered an error! Seven octaves up would be 128 times the frequency (2 ^ 7) but twelve fifths (12 fifths = 7 octaves) is (3/2)^12 = 1.5 ^ 12 = 129.746!! So twelve fifths are not really seven octaves! Its even worse for higher harmonics. So when pianos are tuned, either they are not exactly equal, or not exactly harmonic, or both!

[BuyBuy]

There is actually an excellent book that just came out on the subject of tuning and history of musical concepts regarding to tone production. It's called "Temperament".

[bachopoven]

I don't believe that math skills help in playing music though. I am very good at math but that hasn't helped me so far. Math may help in understanding music, but not in executing it. And i don't think that much math is given in music schools.

But not to take away all the great advantages of music, in the opposite direction. Music can help math skills as it does other skills too, since most skills require the focus, concentration, analysis, quick thinking and memory that are extensively exploited in music. The mozart effect is the effect of music on math and other skills, not the other way around.

[kevink]

Lately I've been thinking that music and math are two diametrically opposed ways of approaching the same thing: human experience.  I'm reading "The Art of Piano Playing", by Heinrich Neuhaus (out of print, check the library... it is a very, very helpful read), "Science and Music" by James Jeans, and "Temperament" by Stuart Isacoff.  Learning about music from a mathematical reference point (as well as artistically, of course) has suggested to me that math should be thought of less as the supreme laws governing reality than as an attempt to express human experience in objective terms.  Music, however, expresses human experience in subjective terms.  Math says,"This IS."  Music says, "This is how this appears to me."  Subsequently, we do not need to create a syntax for understanding music; it is natural to an ear that has grown up hearing music to interpret its meaning.  Math, on the other hand, requires that a broad syntax be learned, a kind of proxy for understanding objective expressions.  Human beings are totally incapable of achieving a truly objective perspective about anything, so it is no coincidence that our knowledge of physics is still very contradictory and theoretical, whereas the meaning we find in music (due to the subjective nature of music's purpose) is so self-evident.

[88_keys]

You mean you haven't heard? Its flawed, they discovered an error! Seven octaves up would be 128 times the frequency (2 ^ 7) but twelve fifths (12 fifths = 7 octaves) is (3/2)^12 = 1.5 ^ 12 = 129.746!! So twelve fifths are not really seven octaves! Its even worse for higher harmonics. So when pianos are tuned, either they are not exactly equal, or not exactly harmonic, or both!

I've heard... But this is only a problem with the well-tempered piano.

On a violin, a fifth does correspond to a ratio of exactly 2 : 3, and an octave does correspond to a ratio of exactly 1 : 2.

Indeed, on a violin, seven octaves and 12 fifths are two different intervals:

12 fifths are equal to six octaves plus an augmented seventh, rather than seven octaves. Starting from C, 12 fifths will get you to a high B# (rather then a high C).

On the piano, of-course, B# and C are one and the same. But musically speaking, they are different notes, and on a violin they would indeed have slightly different pitches.

By the way, can you guess the what the frequency span  of seven octaves is, on a standard grand piano? (hint: it isn't 1 : 128 ).

[rEdundant]

Maths comes from the mind.

Music comes from the soul.


Thats the only difference that matters.

[cziffra]

in cziffra's autobiography he talks about meeting some mathemitician who talked about the connection between music and maths- i remember it was quite funny, because he dismissed it as utter rubbish.  he thought it was ridiculous.  

i wish i could remember the quote

[liszmaninopin]

While there is a connection between math and music, I don't think one should adhere to it very literally.  There are books by Xenakis on this matter.  In fact, he used monstrous mathematical work to create monstrous pieces.  You be the judge of the result.

[chopiabin]

I utterly despise math, yet music comes pretty easily to me. I notice that a lot of the mathematician/musician kids in my school can play things that may be tyechnically difficult, but there is little emotion, which to me is the most important part of music.

[trunks]

Mathematics is not pure reason. I see beauty in maths. I consider mathematics more as a branch of art than of science. Look at those many beautiful, flowery figures. All of them correspond to the graphical representation of some mathematical equations.

Which perhaps explains why my favourite subject to teach was maths. I could anytime give a 'recital' on my secondary school (high school) mathematics lessons before a whole class (40 students per class in Hong Kong, ugh . . . they treat us like superhumans, which was why I quit!)

On the other hand while music is more on the beauty side, it has underlying mathematical basis. The scales we use every day (even those foreign scales like dorian, Hungarian, pentatonic . . .) are entirely based on base-2 logarithms, for example.

[faulty_damper]

88 Keys, you have confirmed my suspicion about the well-tempered clavier and strings.  This is the reason I don't like piano concertos, because the strings are out of tune! (But really, the piano is. )  But it's so much easier to blame the violinists, eh?  

But yeah, I don't like ANY piano concertoes for just that reason.  Is it wrong?  I mean, the clavier is out of tune... all the time. :-/  And it can't help itself!  (Unless the techy is really fast at tuning and he doesn't have to tune all the strings, just the ones the pianist will use.)

And yeah, I tune my own piano.  And yeah, I've tuned it to perfect.  And yeah, the octaves are so off that way.  And yeah, I tuned it back to tempered.  And yeah, why did they bother with such... er, crappy, scalings?

I'll be checking out the book, Temperament.  I need answers. ( And a better tuner.)

[faulty_damper]

By the way, can you guess the what the frequency span  of seven octaves is, on a standard grand piano? (hint: it isn't 1 : 128 ).

Ummm... 7:1?