Music & Golden Mean and more.

[NavajoEverclear]

I'm back to beg satiety of the knowledge i hunger for. Please help where you can.

 

Why is the musical octave divided into twelve intervals? is there a universal mathmatical reason, or is it just cultural (as in, this is the way European music evolved, which is the basis of everything we listen to)

 

What would music sound like if we divided it in intervals with relationships to the golden mean? I don't necissarily need an answer to this one if someone can tell me where i can find a program where you can type in a specific number of hertz and listen to the results. It seems like it would be an exteremly simple feat, but i haven't found one, and i dont know how you would program such a thing.

 

Lastly, the simplest question, what is the inverted golden mean? ((one plus or minus the squaroot of five)/two) The little knowledge i had of mathmatics has sunk beneath my grasp anymore. If i remembered the name of the process i'd google it, but if i just typed in inversion, it would get me a million unrelated links, and i'm sure someone here knows.

[coquina]

This link might help you understand the math behind the music:

http://hyperphysics.phy-astr.gsu.edu/hbase/music/mussca.html#c4

 

More about scales here:

http://library.thinkquest.org/15413/theory/intervals.htm

 

. A pentatonic Scale is a five-tone scale, which has its beginning in antiquity. There are traces of this scale in Oriental and American Indian music. This scale does not have a leading tone, which gives the scale it's unique sound

 

Sorry - I can't help you with the golden mean - maybe someone else can.

[NavajoEverclear]

thanks sandi. The first link is particularly helpful, though i little technical. I'll keep trying to understand it.

 

so i guess i'll just change this thread with a main focus of that program. Shouldn't there be a program where you can type in a number hertz, and hear the note? That way of coarse i can do crap with my calculator and see what different relationships are like. It seem so simple, shouldn't there probably be a way i can just directly input into my soundcard?

[Martin]

Lastly, the simplest question, what is the inverted golden mean?

 

if the golden mean is the number 0.6180339

then its reciprocal is the same as itself plus one.

 

itself plus one = 1.6180339

 

reciprocal = 1/0.6180339 = 1.6180339

 

[math]\frac{\sqrt{5}-1}{2} + 1 = \frac{2}{\sqrt{5}-1} [/math]

 

======================

if the golden mean is the number 1.6180339

then its reciprocal is the same as itself minus one

 

itself minus one = 0.6180339

 

reciprocal = 1/1.6180339 = 0.6180339

 

[math]\frac{\sqrt{5}+1}{2} - 1 = \frac{2}{\sqrt{5}+1} [/math]

 

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numbers are just numbers, I am not sure what people call the golden mean but whatever it is it is largely just convention.

probably what they call the golden mean is one or the other of those two

[Martin]

If you want to get an idea of how the golden mean will sound as a musical interval, you do not need a computer program to control your sound card. You merely need access to a piano or a cheap electronic keyboard

 

the golden mean interval----going from some note up to another whose frequency is 1.6180339 higher---is indistinguishable from going up 8 and 1/3 halfsteps.

most people cant really hear a 1/3 of a halfstep, so the goldenmean interval is going to sound like jumping from C to G#

 

 

If you dont know how to count steps, it is a whole step (two halfsteps) from C to D and also from D to E

 

C to E is 4 halfsteps

C to F is 5 halfsteps

C to G is 7 halfsteps

C to G# is 8 halfsteps.

 

I guess with a violin one could measure the open string and then measure out 0.618 of the open string. then alternately pluck the open string and the 0.618 segment. then one would hear this interval too.

 

but if you have a piano and can find notes like C and G# on it then your work is already done for you.

 

what sounds good harmony to me is small whole-number ratios and simple whole-number fractions, like 3/2 and 4/3

I gather from coquina source that these intervals are common to peoples music all over the world in many cultures and historical periods and it is not hard to see why with an oscilloscope

simple interger ratios make the two waves overtones fit

so two voices in harmony share a lot of overtones even if they sing two different pitches IF the pitches are related by simple whole number ratio

 

the simplest case is the ratio of 2 to one, which make the octave.

 

every voice is a mix of fundamental with overtone vibrations and if two voices sing an octave apart they have very much overlap in the overtones (even if the fundamental note is differnt)

 

harmonies correspond to some physical reality, together with some learned response. it is not all learned, there is a physical basis to the musical scale.