Physics Behind Music: Unsuccesful Research, Help Explain Octave?

[Andy]

Have been doing some research on the Physics behind Music and it has been unsuccesful, i need to know how the octave is structured and why it is structured in that way. Can someone please help explain this to me or provide me with some helpful links, if i find any good websites on my own then i will let you know.

 

[Artman]

The octave bands are created when the frequency of the wave doubles. For instance, if you play a violin string open and then play the same string at half way from bridge to the top of the neck, it should raise the tone by one octave.

 

[selfAdjoint]

The pysthagoreans are said to have discovered the relationship between frequency and pitch. Two frequncies have pitches an octave apart if one frequency is double the other. The intervals of a "third" and a "fifth" also have frequencies in those small ratios of whole numbers.

Pythagoreans understood that as you went up the scale of pitches, an arithmetic series, the corresponding frequencies were multiples of a factor, a geometric series. This is part of the prehistory of logarithms.

Back around 1800, keyboardists devised the "equal temperament scale." Starting from some note (say middle C) you define twelve steps to go up the octave. Each corresponding frequency is multiplied by the twelfth root of two, so that by the end of the octave you will have multiplied by the twelfth root of two twelve times - for a factor of two, which is correct for the two ends of an octave.

The keyboardist's twelfth roots do not exactly represent true thirds fifths and sevenths as played on a stringed instrument. This is a problem that has to be worked around by composers and arrangers.

 

[Izzle]

Originally posted by Artman
The octave bands are created when the frequency of the wave doubles. For instance, if you play a violin string open and then play the same string at half way from bridge to the top of the neck, it should raise the tone by one octave.

Exactly what he said.

The frequency is exactly doubled.

To tell you the truth, there isn't much physics involved behind music. You might be hard praised to fill 5 pages on the real physics, with no BS.

 

[Andy]

Yea thanks for that, don't spose you know of any good sites that show all of the notes in a scale with there frequencies?

 

[arcnets]

Originally posted by Izzle
there isn't much physics involved behind music.

Disagree. There is a LOT of physics behind music.

There's also some interesting math behind the problem of octave division. As selfAdjoint said, the division into 12 equal steps is just an approximation to what would be perfect, but an astonishingly good one. 11 or 13 steps would be much worse.

Here's a link:

http://www.wikipedia.org/wiki/Just_intonation

There are lots like this. Search for: "pythagorean comma", and "just intonation"

 

[Andy]

Thanks a lot arcnets, that is really apreciated.

 

[Hurkyl]

The standard tuning system nowadays is equal temperament; the ratio between every semitone is equal.

Since 12 semitones is an octave (a 2:1 ratio), to go up a semitone you multiply your frequency by the 12-th root of 2.


For more interesting systems, do a search for "equal temperament", or try "well" and "just" in place of "equal".

 

[sheldon]

In case you didn't see this link here it is. It may help you.
http://hyperphysics.phy-astr.gsu.ed...usic/otone.html

 

[sheldon]

is that link working I can't seem to get it to work, if not go to how stuff works under vocal chord relations topic.

 

[Izzle]

Originally posted by arcnets
Disagree. There is a LOT of physics behind music.

Nah - there really isn't. There's a lot of physics dealing with waves, but that's not music. I meant unique to music. There is almost none.

 

[quartodeciman]

So, what is music?

(1) the meaningless acoustical racket that is made

or

(2) the conceptual idea that is trying to get out using acoustical means for some strange reason?

 

[arcnets]

Originally posted by Izzle
I meant unique to music. There is almost none.

Here's some examples why I think there's a lot:
1) Musical instruments. Take e.g. the guitar. OK, it works with oscillating strings. Seems simple. But if you want it to sound right, you have to obey some rules. Different string materials give different sounds. Gut sounds different from nylon, or steel. And there's even different types of steel strings. Bronze-wound sounds different from Phosphor-bronze. A set of .008's will sound very different from .013's, and will show another sensitivity to fingering, bending, hammering, tremolo, etc. Maybe you must redjust the neck & bridge if you use different strings. Next, it's important what kind of frets you use, and how the fretboard is curved. Also, the sound depends heavily on where and how you pick - the theory of the oscillating guitar string is quite complicated in fact. OK, maybe the guitarist doesn't have to 'know' any physics, but it's behind all this.
2) The human ear. It has interesting properties concerning pitch perception, pitch resolution, time resolution, loudness perception, etc. OK, it's 'just' a Fourier analyzer, but a very flexible one. For engineers who are concerned with the mixing and mastering of records, it's surely good to know some rules, since the effect can be dramatic if you turn the wrong knob.
3) Electroacoustics. Anybody who works with microphones, pickups, amplifiers, speakers, FX processors etc. must have some knowledge about how these work and what equipment to choose for a given task. This is even more true for the engineer who designs them.

 

[arcnets]

Originally posted by quartodeciman
So, what is music?

To me, music is one of the basic communication channels of mankind.
It's like language, math, art or sports: From very early age, a child will take interest in words, numbers, pictures, body movements - and also in rhythmic, harmonic sound. It will develop likes and dislikes, it will associate feelings. Music is another way to express yourself.