Algebra, Basses, and Me!

sylasvondrac · #1 01-31-2009, 03:37 PM

Help! I have an algebra project due on the ninth, and I have to answer the following questions:

What is the algebraic equation for the increase of the surface area of the varying sizes of upright bass?

What is the algebraic equation for the decrease of the surface area of the varying sizes of upright bass?

Thanks to Lunker, I know that there probably isn't an exact measurement for every type of upright, but I would be perfectly happy with an approximation.

< Sylas >

Eli_Upright12 · #2 01-31-2009, 04:48 PM

Quote:

Originally Posted by sylasvondrac

Help! I have an algebra project due on the ninth, and I have to answer the following questions:

What is the algebraic equation for the increase of the surface area of the varying sizes of upright bass?

What is the algebraic equation for the decrease of the surface area of the varying sizes of upright bass?

Thanks to Lunker, I know that there probably isn't an exact measurement for every type of upright, but I would be perfectly happy with an approximation.

< Sylas >

Your gonna need a lot of fancy calc to even consider that kind of equation, and it might even really be feasible to consider it using math. It will vary from bass to bass, depends on arching, bout shapes and what you define as sizes. Technically you could go from 4/4 to 7/8 to 3/4 to 1/2 to 1/4 with out changing the surface area, because our measurement of basses revolves around string length.

sylasvondrac · #3 01-31-2009, 04:59 PM

Scratch that... i'm looking for the string length equations

**Matthew Tucker** · #4 01-31-2009, 10:25 PM

google fretcalc

ozrider · #5 01-31-2009, 11:02 PM

what's your algebra project exactly? Just curious..

ctregan · #6 02-01-2009, 05:02 AM

If we answer this question, we will be footnoted in your project?

robobass · #7 02-01-2009, 05:15 AM

The sizes (4/4, 3/4, 5/8 etc.) don't correspond linearly to the actual size or string length. If we say 44" is average mensure for a 4/4 (it's probably less) Then a 3/4 would logically be 33". I don't think you'll find an exact algebraic equation, but there must be some kind of rough formula that could be written mathematically. I've always wondered about this sizing nomenclature, but unfortunately cannot say more.

sylasvondrac · #8 02-01-2009, 07:52 AM

To Ozrider: I'm doing an algebra project on the mathematics of the double bass.

To ctregan: Yes, you will get cited as a resource in my project if you answer.

To Everyone: Thanks for all the help!

fdeck · #9 02-01-2009, 09:28 AM

I suggest a bit of an alternative... since the size designators aren't really algebraic in nature, take a look into some other properties that are more mathematical, such as the relationship between the frequencies of the notes and factors such as string tension and mass, and finger placement on the fingerboard. Then you have to footnote Pythagoras.

Blake Bass · #10 02-01-2009, 09:40 AM

You could present the different string lenghts as relations and show it as some sort of function f(x) and g(x).. like 41" scale length is a function of 3/4 bass etc.

TroyK · #11 02-01-2009, 10:20 AM

F (squared) + U (squared) = A (squared)/T

sylasvondrac · #12 02-01-2009, 10:22 AM

Quote:

Originally Posted by TroyK

F (squared) + U (squared) = A (squared)/T

Care to elaborate?

TroyK · #13 02-01-2009, 11:01 AM

Sure, it's hard to work out without knowing something about the basses you're considering, but you'll need some values to start with.

A = Area
T = is the rate of change calculated through parabolic consideration of the shape of the table.

Once you have those, plug them into the equation, follow standard Order of Operations and you should be able to solve for
F and U.

Good luck with your project.

sylasvondrac · #14 02-01-2009, 11:02 AM

Thanks, TroyK. That's really helpful!

Eli_Upright12 · #15 02-01-2009, 11:30 AM

In a 12 tone even temperament and standard tuning you have this equation P=440*2^(n/12)

P is the frequency of the pitch you are finding
440 is your reference pitch
n is the number of pitches between the reference pitch and the note your are calculating.

TroyK · #16 02-01-2009, 12:02 PM

You're quite welcome, it's no problem at all. I'm always happy to help someone who registered with an assumed identity 10 minutes before posting such an interesting question that it no way related to my post to 200$Bass last week.

For some reason, I harken back to the ever quotable movie The Princess Bride. I may not have this quite right, but I think there was a bit of dialogue that went something like this:

Rule 1 is never get into a land war in Asia
Rule 2 is never go in with a Sicilian when death is involved
and
Rule 3 is never challenge someone from Seattle to a battle of passive aggressiveness. We're brilliant at it. We also tend to read, do math and know a lot about computers and IP addresses.

Don't know what made me think of that, but I love that movie.

Anyway, hope your project goes well, please keep us posted.

Jake deVilliers · #17 02-01-2009, 12:59 PM

"My name is Inigo Montoya, you killed my father, prepare to die!"

A truly remarkable movie.

jsbarber · #18 02-01-2009, 03:10 PM

The surface area of an object in three dimensions is proportional to the square of a linear dimension. (For a sphere it is SA=4*pi*R*R; for a cube it is SA=6*E*E where E is the edge length, for example) If you take the string length as you linear dimension, and assume a family of basses of the same shape, but just scaled/sized differently, then a 10% increase in string length should yield a 21% increase in surface area. If you reduce the string length by 10% then the surface are should drop by 19%.

Hope this helps,

Jim

Bass · #19 02-02-2009, 10:05 AM

More interesting would be to examine the location of the notes along the fingerboard in terms of length, and notice how their ratios can be represented as whole numbers (integers)!

Furthermore, these integers are represented by the Fibbonaci Series, which you could probably express as an algebraic function.

Even more interesting, the golden mean phi (upon which the Fibbonaci Series converges) is found throught the construction of the Double Bass. For example, the length from the top of the headstock to the top of the shoulder is related to the length of the body of the bass by the same ratio that the length of the body of the bass is related to the total length of the bass.

Quote:

Originally Posted by jsbarber

The surface area of an object in three dimensions is proportional to the square of a linear dimension...

Actually, that is calculus. Take the cirumference of a circle, 2*pi*r and integragte, it becomes pi*r^2 the area of a circle. Integrate again and it become the volume of a sphere (pi*r^3)/4.

And very interestingly, the F-hole of the DB very much resembles the symbol for integrate:

jsbarber · #20 02-02-2009, 06:30 PM

The formula for determing the position of a note on the fingerboard is:
Ln = Lo * (1/2)^(n/12)
where Ln is the distance from the bridge to the stopped postion, Lo is the open note string length, and ^ denotes exponentiation. This is exact. The fibonacci sequence you reference seems to provide an approximation to the frequency sequence, not the stopping positions.

The link you provided for the Fibonacci numbers doesn't mention that the nodes of the harmonics/overtone locations are located at the positions determined by dividing the string length by natural number divisions of the open note vibrating string length:

1/2
1/3 2/3
1/4 2/4 3/4
1/5 2/5 3/5 4/5
etc

corresponding to an integer number of half wavelenth vibrations between the nut and the bridge.

Jim

ps. To my eye, the f-hole more closely resembles the symbol for the function being integrated than the integration symbol...